LMFDB - Embedded newform 735.2.g.c.734.7

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			734.7
Character	$\chi$	$=$	735.734
Dual form			735.2.g.c.734.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.04548 q^{2} +(0.965325 - 1.43811i) q^{3} +2.18398 q^{4} +(-2.23143 - 0.144014i) q^{5} +(-1.97455 + 2.94161i) q^{6} -0.376326 q^{8} +(-1.13630 - 2.77648i) q^{9} +(4.56433 + 0.294577i) q^{10} +5.15975i q^{11} +(2.10825 - 3.14079i) q^{12} +2.98151 q^{13} +(-2.36116 + 3.07001i) q^{15} -3.59819 q^{16} -1.35756i q^{17} +(2.32427 + 5.67922i) q^{18} +3.09389i q^{19} +(-4.87339 - 0.314523i) q^{20} -10.5542i q^{22} +7.22952 q^{23} +(-0.363276 + 0.541196i) q^{24} +(4.95852 + 0.642711i) q^{25} -6.09862 q^{26} +(-5.08976 - 1.04609i) q^{27} +2.69332i q^{29} +(4.82969 - 6.27963i) q^{30} -4.35249i q^{31} +8.11267 q^{32} +(7.42026 + 4.98083i) q^{33} +2.77686i q^{34} +(-2.48165 - 6.06377i) q^{36} +7.59884i q^{37} -6.32848i q^{38} +(2.87813 - 4.28773i) q^{39} +(0.839743 + 0.0541960i) q^{40} +7.68540 q^{41} -7.79107i q^{43} +11.2688i q^{44} +(2.13571 + 6.35915i) q^{45} -14.7878 q^{46} -6.07361i q^{47} +(-3.47342 + 5.17458i) q^{48} +(-10.1425 - 1.31465i) q^{50} +(-1.95232 - 1.31049i) q^{51} +6.51157 q^{52} -6.29231 q^{53} +(10.4110 + 2.13975i) q^{54} +(0.743074 - 11.5136i) q^{55} +(4.44934 + 2.98661i) q^{57} -5.50912i q^{58} +4.25005 q^{59} +(-5.15672 + 6.70483i) q^{60} -5.21377i q^{61} +8.90293i q^{62} -9.39791 q^{64} +(-6.65303 - 0.429379i) q^{65} +(-15.1780 - 10.1882i) q^{66} -5.65710i q^{67} -2.96489i q^{68} +(6.97884 - 10.3968i) q^{69} +11.2688i q^{71} +(0.427617 + 1.04486i) q^{72} +4.91216 q^{73} -15.5433i q^{74} +(5.71087 - 6.51045i) q^{75} +6.75699i q^{76} +(-5.88715 + 8.77046i) q^{78} +11.9294 q^{79} +(8.02910 + 0.518189i) q^{80} +(-6.41766 + 6.30980i) q^{81} -15.7203 q^{82} -12.1558i q^{83} +(-0.195507 + 3.02930i) q^{85} +15.9365i q^{86} +(3.87328 + 2.59993i) q^{87} -1.94175i q^{88} +9.32117 q^{89} +(-4.36855 - 13.0075i) q^{90} +15.7891 q^{92} +(-6.25935 - 4.20157i) q^{93} +12.4234i q^{94} +(0.445562 - 6.90378i) q^{95} +(7.83137 - 11.6669i) q^{96} +19.2504 q^{97} +(14.3259 - 5.86300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.04548			−1.44637			−0.723186	−	0.690654i	$-0.757323\pi$
$2$	−2.04548			−1.44637			−0.723186	+	0.690654i	$0.757323\pi$
$3$	0.965325	−	1.43811i	0.557331	−	0.830291i
$3$	0.965325	−	1.43811i	0.557331	−	0.830291i
$4$	2.18398			1.09199
$5$	−2.23143	−	0.144014i	−0.997924	−	0.0644048i
$5$	−2.23143	−	0.144014i	−0.997924	−	0.0644048i
$6$	−1.97455	+	2.94161i	−0.806107	+	1.20091i
$7$		0			0
$7$		0			0
$8$	−0.376326			−0.133051
$9$	−1.13630	−	2.77648i	−0.378765	−	0.925493i
$10$	4.56433	+	0.294577i	1.44337	+	0.0931533i
$11$			5.15975i			1.55572i	0.628436	+	0.777861i	$0.283695\pi$
$11$			5.15975i			1.55572i	−0.628436	+	0.777861i	$0.716305\pi$
$12$	2.10825	−	3.14079i	0.608599	−	0.906669i
$13$	2.98151			0.826923			0.413462	−	0.910522i	$-0.364320\pi$
$13$	2.98151			0.826923			0.413462	+	0.910522i	$0.364320\pi$
$14$		0			0
$15$	−2.36116	+	3.07001i	−0.609648	+	0.792672i
$16$	−3.59819			−0.899548
$17$		−	1.35756i		−	0.329257i	−0.986356	−	0.164629i	$-0.947357\pi$
$17$		−	1.35756i		−	0.329257i	0.986356	−	0.164629i	$-0.0526425\pi$
$18$	2.32427	+	5.67922i	0.547835	+	1.33861i
$19$			3.09389i			0.709786i	0.934907	+	0.354893i	$0.115483\pi$
$19$			3.09389i			0.709786i	−0.934907	+	0.354893i	$0.884517\pi$
$20$	−4.87339	−	0.314523i	−1.08972	−	0.0703294i
$21$		0			0
$22$		−	10.5542i		−	2.25015i
$23$	7.22952			1.50746			0.753730	−	0.657185i	$-0.228253\pi$
$23$	7.22952			1.50746			0.753730	+	0.657185i	$0.228253\pi$
$24$	−0.363276	+	0.541196i	−0.0741535	+	0.110471i
$25$	4.95852	+	0.642711i	0.991704	+	0.128542i
$26$	−6.09862			−1.19604
$27$	−5.08976	−	1.04609i	−0.979526	−	0.201320i
$28$		0			0
$29$			2.69332i			0.500136i	0.968228	+	0.250068i	$0.0804531\pi$
$29$			2.69332i			0.500136i	−0.968228	+	0.250068i	$0.919547\pi$
$30$	4.82969	−	6.27963i	0.881778	−	1.14650i
$31$		−	4.35249i		−	0.781731i	−0.920448	−	0.390865i	$-0.872176\pi$
$31$		−	4.35249i		−	0.781731i	0.920448	−	0.390865i	$-0.127824\pi$
$32$	8.11267			1.43413
$33$	7.42026	+	4.98083i	1.29170	+	0.867052i
$34$			2.77686i			0.476228i
$35$		0			0
$36$	−2.48165	−	6.06377i	−0.413608	−	1.01063i
$37$			7.59884i			1.24924i	0.780928	+	0.624621i	$0.214746\pi$
$37$			7.59884i			1.24924i	−0.780928	+	0.624621i	$0.785254\pi$
$38$		−	6.32848i		−	1.02661i
$39$	2.87813	−	4.28773i	0.460870	−	0.686587i
$40$	0.839743	+	0.0541960i	0.132775	+	0.00856914i
$41$	7.68540			1.20026			0.600129	−	0.799903i	$-0.295116\pi$
$41$	7.68540			1.20026			0.600129	+	0.799903i	$0.295116\pi$
$42$		0			0
$43$		−	7.79107i		−	1.18813i	−0.804418	−	0.594064i	$-0.797523\pi$
$43$		−	7.79107i		−	1.18813i	0.804418	−	0.594064i	$-0.202477\pi$
$44$			11.2688i			1.69883i
$45$	2.13571	+	6.35915i	0.318373	+	0.947966i
$46$	−14.7878			−2.18035
$47$		−	6.07361i		−	0.885927i	−0.896540	−	0.442963i	$-0.853927\pi$
$47$		−	6.07361i		−	0.885927i	0.896540	−	0.442963i	$-0.146073\pi$
$48$	−3.47342	+	5.17458i	−0.501346	+	0.746887i
$49$		0			0
$50$	−10.1425	−	1.31465i	−1.43437	−	0.185920i
$51$	−1.95232	−	1.31049i	−0.273379	−	0.183505i
$52$	6.51157			0.902992
$53$	−6.29231			−0.864316			−0.432158	−	0.901798i	$-0.642248\pi$
$53$	−6.29231			−0.864316			−0.432158	+	0.901798i	$0.642248\pi$
$54$	10.4110	+	2.13975i	1.41676	+	0.291183i
$55$	0.743074	−	11.5136i	0.100196	−	1.55249i
$56$		0			0
$57$	4.44934	+	2.98661i	0.589329	+	0.395586i
$58$		−	5.50912i		−	0.723383i
$59$	4.25005			0.553309			0.276655	−	0.960969i	$-0.410774\pi$
$59$	4.25005			0.553309			0.276655	+	0.960969i	$0.410774\pi$
$60$	−5.15672	+	6.70483i	−0.665729	+	0.865590i
$61$		−	5.21377i		−	0.667555i	−0.942652	−	0.333778i	$-0.891677\pi$
$61$		−	5.21377i		−	0.667555i	0.942652	−	0.333778i	$-0.108323\pi$
$62$			8.90293i			1.13067i
$63$		0			0
$64$	−9.39791			−1.17474
$65$	−6.65303	−	0.429379i	−0.825207	−	0.0532579i
$66$	−15.1780	−	10.1882i	−1.86828	−	1.25408i
$67$		−	5.65710i		−	0.691124i	−0.938396	−	0.345562i	$-0.887688\pi$
$67$		−	5.65710i		−	0.691124i	0.938396	−	0.345562i	$-0.112312\pi$
$68$		−	2.96489i		−	0.359545i
$69$	6.97884	−	10.3968i	0.840153	−	1.25163i
$70$		0			0
$71$			11.2688i			1.33736i	0.743551	+	0.668679i	$0.233140\pi$
$71$			11.2688i			1.33736i	−0.743551	+	0.668679i	$0.766860\pi$
$72$	0.427617	+	1.04486i	0.0503952	+	0.123138i
$73$	4.91216			0.574925			0.287463	−	0.957792i	$-0.407188\pi$
$73$	4.91216			0.574925			0.287463	+	0.957792i	$0.407188\pi$
$74$		−	15.5433i		−	1.80687i
$75$	5.71087	−	6.51045i	0.659434	−	0.751762i
$76$			6.75699i			0.775079i
$77$		0			0
$78$	−5.88715	+	8.77046i	−0.666589	+	0.993059i
$79$	11.9294			1.34217			0.671084	−	0.741381i	$-0.265829\pi$
$79$	11.9294			1.34217			0.671084	+	0.741381i	$0.265829\pi$
$80$	8.02910	+	0.518189i	0.897681	+	0.0579353i
$81$	−6.41766	+	6.30980i	−0.713074	+	0.701089i
$82$	−15.7203			−1.73602
$83$		−	12.1558i		−	1.33428i	−0.744934	−	0.667138i	$-0.767519\pi$
$83$		−	12.1558i		−	1.33428i	0.744934	−	0.667138i	$-0.232481\pi$
$84$		0			0
$85$	−0.195507	+	3.02930i	−0.0212057	+	0.328573i
$86$			15.9365i			1.71847i
$87$	3.87328	+	2.59993i	0.415259	+	0.278741i
$88$		−	1.94175i		−	0.206991i
$89$	9.32117			0.988042			0.494021	−	0.869450i	$-0.335527\pi$
$89$	9.32117			0.988042			0.494021	+	0.869450i	$0.335527\pi$
$90$	−4.36855	−	13.0075i	−0.460485	−	1.37111i
$91$		0			0
$92$	15.7891			1.64613
$93$	−6.25935	−	4.20157i	−0.649064	−	0.435682i
$94$			12.4234i			1.28138i
$95$	0.445562	−	6.90378i	0.0457137	−	0.708313i
$96$	7.83137	−	11.6669i	0.799285	−	1.19075i
$97$	19.2504			1.95458			0.977289	−	0.211910i	$-0.0679684\pi$
$97$	19.2504			1.95458			0.977289	+	0.211910i	$0.0679684\pi$
$98$		0			0
$99$	14.3259	−	5.86300i	1.43981	−	0.589254i
$100$	10.8293	+	1.40367i	1.08293	+	0.140367i
$101$	5.18940			0.516365			0.258183	−	0.966096i	$-0.416876\pi$
$101$	5.18940			0.516365			0.258183	+	0.966096i	$0.416876\pi$
$102$	3.99342	+	2.68057i	0.395408	+	0.265416i
$103$	4.66100			0.459262			0.229631	−	0.973278i	$-0.426248\pi$
$103$	4.66100			0.459262			0.229631	+	0.973278i	$0.426248\pi$
$104$	−1.12202			−0.110023
$105$		0			0
$106$	12.8708			1.25012
$107$	0.879852			0.0850585			0.0425293	−	0.999095i	$-0.486458\pi$
$107$	0.879852			0.0850585			0.0425293	+	0.999095i	$0.486458\pi$
$108$	−11.1159	−	2.28464i	−1.06963	−	0.219839i
$109$	5.87754			0.562966			0.281483	−	0.959566i	$-0.409174\pi$
$109$	5.87754			0.562966			0.281483	+	0.959566i	$0.409174\pi$
$110$	−1.51994	+	23.5508i	−0.144921	+	2.24548i
$111$	10.9279	+	7.33535i	1.03723	+	0.696241i
$112$		0			0
$113$	3.00476			0.282664			0.141332	−	0.989962i	$-0.454861\pi$
$113$	3.00476			0.282664			0.141332	+	0.989962i	$0.454861\pi$
$114$	−9.10102	−	6.10904i	−0.852389	−	0.572164i
$115$	−16.1321	−	1.04115i	−1.50433	−	0.0970877i
$116$			5.88215i			0.546144i
$117$	−3.38788	−	8.27811i	−0.313210	−	0.765312i
$118$	−8.69338			−0.800291
$119$		0			0
$120$	0.888564	−	1.15532i	0.0811144	−	0.105466i
$121$	−15.6230			−1.42027
$122$			10.6647i			0.965533i
$123$	7.41891	−	11.0524i	0.668940	−	0.996563i
$124$		−	9.50575i		−	0.853642i
$125$	−10.9720	−	2.14826i	−0.981366	−	0.192146i
$126$		0			0
$127$			4.49556i			0.398916i	0.979906	+	0.199458i	$0.0639182\pi$
$127$			4.49556i			0.398916i	−0.979906	+	0.199458i	$0.936082\pi$
$128$	2.99787			0.264977
$129$	−11.2044	−	7.52092i	−0.986491	−	0.662180i
$130$	13.6086	+	0.878285i	1.19356	+	0.0770306i
$131$	−7.64625			−0.668056			−0.334028	−	0.942563i	$-0.608408\pi$
$131$	−7.64625			−0.668056			−0.334028	+	0.942563i	$0.608408\pi$
$132$	16.2057	+	10.8780i	1.41053	+	0.946812i
$133$		0			0
$134$			11.5715i			0.999622i
$135$	11.2068	+	3.06726i	0.964526	+	0.263988i
$136$			0.510885i			0.0438080i
$137$	3.21110			0.274343			0.137172	−	0.990547i	$-0.456199\pi$
$137$	3.21110			0.274343			0.137172	+	0.990547i	$0.456199\pi$
$138$	−14.2751	+	21.2665i	−1.21517	+	1.81032i
$139$			10.1096i			0.857483i	0.903427	+	0.428741i	$0.141043\pi$
$139$			10.1096i			0.857483i	−0.903427	+	0.428741i	$0.858957\pi$
$140$		0			0
$141$	−8.73449	−	5.86300i	−0.735577	−	0.493754i
$142$		−	23.0500i		−	1.93432i
$143$			15.3839i			1.28646i
$144$	4.08861	+	9.99030i	0.340718	+	0.832525i
$145$	0.387874	−	6.00994i	0.0322112	−	0.499098i
$146$	−10.0477			−0.831555
$147$		0			0
$148$			16.5957i			1.36416i
$149$		−	6.51057i		−	0.533367i	−0.963784	−	0.266683i	$-0.914072\pi$
$149$		−	6.51057i		−	0.533367i	0.963784	−	0.266683i	$-0.0859278\pi$
$150$	−11.6815	+	13.3170i	−0.953787	+	1.08733i
$151$	−11.7522			−0.956382			−0.478191	−	0.878256i	$-0.658707\pi$
$151$	−11.7522			−0.956382			−0.478191	+	0.878256i	$0.658707\pi$
$152$		−	1.16431i		−	0.0944379i
$153$	−3.76924	+	1.54259i	−0.304725	+	0.124711i
$154$		0			0
$155$	−0.626818	+	9.71226i	−0.0503472	+	0.780108i
$156$	6.28578	−	9.36432i	0.503265	−	0.749746i
$157$	−12.0061			−0.958194			−0.479097	−	0.877762i	$-0.659036\pi$
$157$	−12.0061			−0.958194			−0.479097	+	0.877762i	$0.659036\pi$
$158$	−24.4014			−1.94127
$159$	−6.07412	+	9.04901i	−0.481709	+	0.717633i
$160$	−18.1028	−	1.16834i	−1.43115	−	0.0923650i
$161$		0			0
$162$	13.1272	−	12.9066i	1.03137	−	1.01404i
$163$			18.1973i			1.42532i	0.701510	+	0.712659i	$0.252509\pi$
$163$			18.1973i			1.42532i	−0.701510	+	0.712659i	$0.747491\pi$
$164$	16.7848			1.31067
$165$	−15.8405	−	12.1830i	−1.23318	−	0.948443i
$166$			24.8645i			1.92986i
$167$			20.6432i			1.59742i	0.601716	+	0.798710i	$0.294484\pi$
$167$			20.6432i			1.59742i	−0.601716	+	0.798710i	$0.705516\pi$
$168$		0			0
$169$	−4.11057			−0.316198
$170$	0.399906	−	6.19636i	0.0306714	−	0.475239i
$171$	8.59011	−	3.51557i	0.656902	−	0.268843i
$172$		−	17.0155i		−	1.29742i
$173$		−	18.4353i		−	1.40161i	−0.713352	−	0.700805i	$-0.752824\pi$
$173$		−	18.4353i		−	1.40161i	0.713352	−	0.700805i	$-0.247176\pi$
$174$	−7.92270	−	5.31809i	−0.600618	−	0.403163i
$175$		0			0
$176$		−	18.5658i		−	1.39945i
$177$	4.10268	−	6.11202i	0.308376	−	0.459408i
$178$	−19.0662			−1.42908
$179$			16.3297i			1.22054i	0.792195	+	0.610269i	$0.208938\pi$
$179$			16.3297i			1.22054i	−0.792195	+	0.610269i	$0.791062\pi$
$180$	4.66435	+	13.8882i	0.347660	+	1.03517i
$181$			3.55998i			0.264612i	0.991209	+	0.132306i	$0.0422381\pi$
$181$			3.55998i			0.264612i	−0.991209	+	0.132306i	$0.957762\pi$
$182$		0			0
$183$	−7.49796	−	5.03299i	−0.554265	−	0.372049i
$184$	−2.72065			−0.200569
$185$	1.09434	−	16.9562i	0.0804572	−	1.24665i
$186$	12.8034	+	8.59422i	0.938787	+	0.630159i
$187$	7.00468			0.512233
$188$		−	13.2646i		−	0.967423i
$189$		0			0
$190$	−0.911387	+	14.1215i	−0.0661189	+	1.02448i
$191$			0.329193i			0.0238196i	0.999929	+	0.0119098i	$0.00379110\pi$
$191$			0.329193i			0.0238196i	−0.999929	+	0.0119098i	$0.996209\pi$
$192$	−9.07204	+	13.5152i	−0.654718	+	0.975375i
$193$			8.06293i			0.580383i	0.956969	+	0.290191i	$0.0937189\pi$
$193$			8.06293i			0.580383i	−0.956969	+	0.290191i	$0.906281\pi$
$194$	−39.3762			−2.82705
$195$	−7.03982	+	9.15327i	−0.504132	+	0.655479i
$196$		0			0
$197$	9.61468			0.685017			0.342509	−	0.939515i	$-0.388723\pi$
$197$	9.61468			0.685017			0.342509	+	0.939515i	$0.388723\pi$
$198$	−29.3034	+	11.9926i	−2.08250	+	0.852280i
$199$		−	11.1595i		−	0.791079i	−0.918449	−	0.395540i	$-0.870558\pi$
$199$		−	11.1595i		−	0.791079i	0.918449	−	0.395540i	$-0.129442\pi$
$200$	−1.86602	−	0.241869i	−0.131947	−	0.0171027i
$201$	−8.13550	−	5.46093i	−0.573834	−	0.385185i
$202$	−10.6148			−0.746855
$203$		0			0
$204$	−4.26382	−	2.86208i	−0.298527	−	0.200386i
$205$	−17.1494	−	1.10680i	−1.19777	−	0.0773024i
$206$	−9.53397			−0.664263
$207$	−8.21488	−	20.0726i	−0.570974	−	1.39514i
$208$	−10.7281			−0.743857
$209$	−15.9637			−1.10423
$210$		0			0
$211$	1.20704			0.0830957			0.0415479	−	0.999137i	$-0.486771\pi$
$211$	1.20704			0.0830957			0.0415479	+	0.999137i	$0.486771\pi$
$212$	−13.7423			−0.943824
$213$	16.2057	+	10.8780i	1.11040	+	0.745351i
$214$	−1.79972			−0.123026
$215$	−1.12202	+	17.3852i	−0.0765212	+	1.18566i
$216$	1.91541	+	0.393670i	0.130327	+	0.0267859i
$217$		0			0
$218$	−12.0224			−0.814258
$219$	4.74183	−	7.06421i	0.320423	−	0.477355i
$220$	1.62286	−	25.1455i	0.109413	−	1.69531i
$221$		−	4.04759i		−	0.272270i
$222$	−22.3529	−	15.0043i	−1.50023	−	1.00702i
$223$	−4.30580			−0.288338			−0.144169	−	0.989553i	$-0.546051\pi$
$223$	−4.30580			−0.288338			−0.144169	+	0.989553i	$0.546051\pi$
$224$		0			0
$225$	−3.84987	−	14.4975i	−0.256658	−	0.966502i
$226$	−6.14618			−0.408837
$227$			4.04774i			0.268658i	0.990937	+	0.134329i	$0.0428879\pi$
$227$			4.04774i			0.268658i	−0.990937	+	0.134329i	$0.957112\pi$
$228$	9.71726	+	6.52269i	0.643541	+	0.431975i
$229$			8.57232i			0.566475i	0.959050	+	0.283238i	$0.0914085\pi$
$229$			8.57232i			0.566475i	−0.959050	+	0.283238i	$0.908592\pi$
$230$	32.9979	+	2.12965i	2.17582	+	0.140425i
$231$		0			0
$232$		−	1.01356i		−	0.0665438i
$233$	9.11912			0.597413			0.298707	−	0.954345i	$-0.403445\pi$
$233$	9.11912			0.597413			0.298707	+	0.954345i	$0.403445\pi$
$234$	6.92984	+	16.9327i	0.453018	+	1.10692i
$235$	−0.874682	+	13.5528i	−0.0570580	+	0.884087i
$236$	9.28202			0.604208
$237$	11.5158	−	17.1558i	0.748031	−	1.11439i
$238$		0			0
$239$		−	17.7528i		−	1.14834i	−0.818738	−	0.574168i	$-0.805326\pi$
$239$		−	17.7528i		−	1.14834i	0.818738	−	0.574168i	$-0.194674\pi$
$240$	8.49590	−	11.0465i	0.548408	−	0.713047i
$241$			24.0167i			1.54705i	0.633767	+	0.773524i	$0.281508\pi$
$241$			24.0167i			1.54705i	−0.633767	+	0.773524i	$0.718492\pi$
$242$	31.9565			2.05424
$243$	2.87904	+	15.3203i	0.184690	+	0.982797i
$244$		−	11.3868i		−	0.728964i
$245$		0			0
$246$	−15.1752	+	22.6075i	−0.967536	+	1.44140i
$247$			9.22447i			0.586939i
$248$			1.63795i			0.104010i
$249$	−17.4814	−	11.7343i	−1.10784	−	0.743633i
$250$	22.4430	+	4.39421i	1.41942	+	0.277914i
$251$	−8.80742			−0.555919			−0.277960	−	0.960593i	$-0.589658\pi$
$251$	−8.80742			−0.555919			−0.277960	+	0.960593i	$0.589658\pi$
$252$		0			0
$253$			37.3025i			2.34519i
$254$		−	9.19556i		−	0.576981i
$255$	4.16772	+	3.20542i	0.260993	+	0.200731i
$256$	12.6638			0.791484
$257$			11.6328i			0.725633i	0.931861	+	0.362816i	$0.118185\pi$
$257$			11.6328i			0.725633i	−0.931861	+	0.362816i	$0.881815\pi$
$258$	22.9183	+	15.3839i	1.42683	+	0.957758i
$259$		0			0
$260$	−14.5301	−	0.937754i	−0.901117	−	0.0581570i
$261$	7.47794	−	3.06041i	0.462873	−	0.189434i
$262$	15.6402			0.966257
$263$	−0.979701			−0.0604109			−0.0302055	−	0.999544i	$-0.509616\pi$
$263$	−0.979701			−0.0604109			−0.0302055	+	0.999544i	$0.509616\pi$
$264$	−2.79244	−	1.87442i	−0.171863	−	0.115362i
$265$	14.0408	+	0.906179i	0.862521	+	0.0556661i
$266$		0			0
$267$	8.99796	−	13.4048i	0.550666	−	0.820362i
$268$		−	12.3550i		−	0.754700i
$269$	−20.6092			−1.25656			−0.628282	−	0.777985i	$-0.716242\pi$
$269$	−20.6092			−1.25656			−0.628282	+	0.777985i	$0.716242\pi$
$270$	−22.9232	−	6.27402i	−1.39506	−	0.381825i
$271$			2.59970i			0.157920i	0.996878	+	0.0789602i	$0.0251600\pi$
$271$			2.59970i			0.157920i	−0.996878	+	0.0789602i	$0.974840\pi$
$272$			4.88477i			0.296183i
$273$		0			0
$274$	−6.56824			−0.396802
$275$	−3.31623	+	25.5847i	−0.199976	+	1.54282i
$276$	15.2416	−	22.7064i	0.917439	−	1.36677i
$277$			19.1495i			1.15058i	0.817948	+	0.575292i	$0.195111\pi$
$277$			19.1495i			1.15058i	−0.817948	+	0.575292i	$0.804889\pi$
$278$		−	20.6789i		−	1.24024i
$279$	−12.0846	+	4.94572i	−0.723486	+	0.296093i
$280$		0			0
$281$			14.8209i			0.884138i	0.896981	+	0.442069i	$0.145755\pi$
$281$			14.8209i			0.884138i	−0.896981	+	0.442069i	$0.854245\pi$
$282$	17.8662	+	11.9926i	1.06392	+	0.714151i
$283$	−2.28585			−0.135880			−0.0679398	−	0.997689i	$-0.521643\pi$
$283$	−2.28585			−0.135880			−0.0679398	+	0.997689i	$0.521643\pi$
$284$			24.6108i			1.46038i
$285$	−9.49825	−	7.30515i	−0.562628	−	0.432720i
$286$		−	31.4674i		−	1.86070i
$287$		0			0
$288$	−9.21840	−	22.5247i	−0.543200	−	1.32728i
$289$	15.1570			0.891590
$290$	−0.793388	+	12.2932i	−0.0465894	+	0.721881i
$291$	18.5829	−	27.6841i	1.08935	−	1.62287i
$292$	10.7281			0.627813
$293$		−	29.4268i		−	1.71913i	−0.511023	−	0.859567i	$-0.670733\pi$
$293$		−	29.4268i		−	1.71913i	0.511023	−	0.859567i	$-0.329267\pi$
$294$		0			0
$295$	−9.48367	−	0.612065i	−0.552160	−	0.0356358i
$296$		−	2.85964i		−	0.166213i
$297$	5.39756	−	26.2619i	0.313198	−	1.52387i
$298$			13.3172i			0.771446i
$299$	21.5549			1.24655
$300$	12.4724	−	14.2187i	0.720095	−	0.820917i
$301$		0			0
$302$	24.0389			1.38328
$303$	5.00946	−	7.46291i	0.287786	−	0.428733i
$304$		−	11.1324i		−	0.638487i
$305$	−0.750854	+	11.6341i	−0.0429938	+	0.666169i
$306$	7.70990	−	3.15534i	0.440745	−	0.180379i
$307$	−19.6726			−1.12278			−0.561388	−	0.827553i	$-0.689732\pi$
$307$	−19.6726			−1.12278			−0.561388	+	0.827553i	$0.689732\pi$
$308$		0			0
$309$	4.49938	−	6.70301i	0.255961	−	0.381321i
$310$	1.28214	−	19.8662i	0.0728208	−	1.12833i
$311$	−7.76453			−0.440286			−0.220143	−	0.975468i	$-0.570652\pi$
$311$	−7.76453			−0.440286			−0.220143	+	0.975468i	$0.570652\pi$
$312$	−1.08311	+	1.61358i	−0.0613193	+	0.0913512i
$313$	15.3891			0.869841			0.434921	−	0.900469i	$-0.356776\pi$
$313$	15.3891			0.869841			0.434921	+	0.900469i	$0.356776\pi$
$314$	24.5583			1.38590
$315$		0			0
$316$	26.0537			1.46563
$317$	1.61449			0.0906787			0.0453394	−	0.998972i	$-0.485563\pi$
$317$	1.61449			0.0906787			0.0453394	+	0.998972i	$0.485563\pi$
$318$	12.4245	−	18.5096i	0.696731	−	1.03796i
$319$	−13.8968			−0.778074
$320$	20.9707	+	1.35343i	1.17230	+	0.0756589i
$321$	0.849343	−	1.26532i	0.0474057	−	0.0706233i
$322$		0			0
$323$	4.20014			0.233702
$324$	−14.0160	+	13.7805i	−0.778669	+	0.765582i
$325$	14.7839	+	1.91625i	0.820063	+	0.106295i
$326$		−	37.2221i		−	2.06154i
$327$	5.67373	−	8.45252i	0.313758	−	0.467426i
$328$	−2.89221			−0.159696
$329$		0			0
$330$	32.4013	+	24.9200i	1.78363	+	1.37180i
$331$	30.4567			1.67405			0.837026	−	0.547163i	$-0.184292\pi$
$331$	30.4567			1.67405			0.837026	+	0.547163i	$0.184292\pi$
$332$		−	26.5481i		−	1.45702i
$333$	21.0980	−	8.63453i	1.15616	−	0.473170i
$334$		−	42.2253i		−	2.31046i
$335$	−0.814699	+	12.6234i	−0.0445117	+	0.689689i
$336$		0			0
$337$		−	22.5247i		−	1.22700i	−0.789696	−	0.613498i	$-0.789762\pi$
$337$		−	22.5247i		−	1.22700i	0.789696	−	0.613498i	$-0.210238\pi$
$338$	8.40808			0.457339
$339$	2.90057	−	4.32117i	0.157537	−	0.234694i
$340$	−0.426984	+	6.61592i	−0.0231565	+	0.358799i
$341$	22.4578			1.21616
$342$	−17.5709	+	7.19103i	−0.950124	+	0.388846i
$343$		0			0
$344$			2.93198i			0.158082i
$345$	−17.0700	+	22.1947i	−0.919020	+	1.19492i
$346$			37.7090i			2.02725i
$347$	−12.4516			−0.668436			−0.334218	−	0.942496i	$-0.608472\pi$
$347$	−12.4516			−0.668436			−0.334218	+	0.942496i	$0.608472\pi$
$348$	8.45915	+	5.67818i	0.453458	+	0.304383i
$349$			17.9519i			0.960945i	0.877010	+	0.480472i	$0.159535\pi$
$349$			17.9519i			0.960945i	−0.877010	+	0.480472i	$0.840465\pi$
$350$		0			0
$351$	−15.1752	−	3.11893i	−0.809993	−	0.166476i
$352$			41.8594i			2.23111i
$353$		−	12.6815i		−	0.674967i	−0.941331	−	0.337484i	$-0.890424\pi$
$353$		−	12.6815i		−	0.674967i	0.941331	−	0.337484i	$-0.109576\pi$
$354$	−8.39194	+	12.5020i	−0.446026	+	0.664474i
$355$	1.62286	−	25.1455i	0.0861324	−	1.33458i
$356$	20.3572			1.07893
$357$		0			0
$358$		−	33.4020i		−	1.76535i
$359$			0.0723421i			0.00381807i	0.999998	+	0.00190903i	$0.000607665\pi$
$359$			0.0723421i			0.00381807i	−0.999998	+	0.00190903i	$0.999392\pi$
$360$	−0.803722	−	2.39311i	−0.0423599	−	0.126128i
$361$	9.42786			0.496203
$362$		−	7.28187i		−	0.382727i
$363$	−15.0813	+	22.4675i	−0.791562	+	1.17924i
$364$		0			0
$365$	−10.9611	−	0.707418i	−0.573732	−	0.0370280i
$366$	15.3369	+	10.2949i	0.801673	+	0.538121i
$367$	−10.7188			−0.559519			−0.279760	−	0.960070i	$-0.590255\pi$
$367$	−10.7188			−0.559519			−0.279760	+	0.960070i	$0.590255\pi$
$368$	−26.0132			−1.35603
$369$	−8.73289	−	21.3383i	−0.454616	−	1.11083i
$370$	−2.23844	+	34.6836i	−0.116371	+	1.80312i
$371$		0			0
$372$	−13.6703	−	9.17614i	−0.708771	−	0.475761i
$373$		−	21.3802i		−	1.10702i	−0.832842	−	0.553511i	$-0.813288\pi$
$373$		−	21.3802i		−	1.10702i	0.832842	−	0.553511i	$-0.186712\pi$
$374$	−14.3279			−0.740879
$375$	−13.6810	+	13.7051i	−0.706482	+	0.707731i
$376$			2.28565i			0.117874i
$377$			8.03017i			0.413575i
$378$		0			0
$379$	24.3043			1.24843			0.624214	−	0.781253i	$-0.285419\pi$
$379$	24.3043			1.24843			0.624214	+	0.781253i	$0.285419\pi$
$380$	0.973098	−	15.0777i	0.0499189	−	0.773470i
$381$	6.46509	+	4.33967i	0.331216	+	0.222328i
$382$		−	0.673358i		−	0.0344520i
$383$		−	7.38680i		−	0.377448i	−0.982030	−	0.188724i	$-0.939565\pi$
$383$		−	7.38680i		−	0.377448i	0.982030	−	0.188724i	$-0.0604352\pi$
$384$	2.89392	−	4.31125i	0.147680	−	0.220008i
$385$		0			0
$386$		−	16.4925i		−	0.839449i
$387$	−21.6317	+	8.85297i	−1.09960	+	0.450022i
$388$	42.0424			2.13438
$389$		−	12.8681i		−	0.652440i	−0.945294	−	0.326220i	$-0.894225\pi$
$389$		−	12.8681i		−	0.652440i	0.945294	−	0.326220i	$-0.105775\pi$
$390$	14.3998	−	18.7228i	0.729162	−	0.948066i
$391$		−	9.81452i		−	0.496342i
$392$		0			0
$393$	−7.38111	+	10.9961i	−0.372328	+	0.554681i
$394$	−19.6666			−0.990789
$395$	−26.6197	−	1.71800i	−1.33938	−	0.0864421i
$396$	31.2875	−	12.8047i	1.57226	−	0.643459i
$397$	−16.2466			−0.815393			−0.407697	−	0.913117i	$-0.633668\pi$
$397$	−16.2466			−0.815393			−0.407697	+	0.913117i	$0.633668\pi$
$398$			22.8266i			1.14419i
$399$		0			0
$400$	−17.8417	−	2.31260i	−0.892086	−	0.115630i
$401$		−	10.2206i		−	0.510394i	−0.966889	−	0.255197i	$-0.917860\pi$
$401$		−	10.2206i		−	0.510394i	0.966889	−	0.255197i	$-0.0821404\pi$
$402$	16.6410	+	11.1702i	0.829977	+	0.557120i
$403$		−	12.9770i		−	0.646432i
$404$	11.3336			0.563865
$405$	15.2292	−	13.1556i	0.756747	−	0.653708i
$406$		0			0
$407$	−39.2081			−1.94347
$408$	0.734707	+	0.493170i	0.0363734	+	0.0244156i
$409$		−	18.1658i		−	0.898243i	−0.893471	−	0.449122i	$-0.851737\pi$
$409$		−	18.1658i		−	0.898243i	0.893471	−	0.449122i	$-0.148263\pi$
$410$	35.0787	+	2.26394i	1.73241	+	0.111808i
$411$	3.09976	−	4.61791i	0.152900	−	0.227785i
$412$	10.1795			0.501509
$413$		0			0
$414$	16.8034	+	41.0581i	0.825840	+	2.01789i
$415$	−1.75061	+	27.1249i	−0.0859339	+	1.33151i
$416$	24.1881			1.18592
$417$	14.5386	+	9.75902i	0.711960	+	0.477901i
$418$	32.6534			1.59713
$419$	3.38983			0.165604			0.0828019	−	0.996566i	$-0.473613\pi$
$419$	3.38983			0.165604			0.0828019	+	0.996566i	$0.473613\pi$
$420$		0			0
$421$	−5.12428			−0.249742			−0.124871	−	0.992173i	$-0.539852\pi$
$421$	−5.12428			−0.249742			−0.124871	+	0.992173i	$0.539852\pi$
$422$	−2.46896			−0.120187
$423$	−16.8632	+	6.90142i	−0.819919	+	0.335558i
$424$	2.36796			0.114998
$425$	0.872520	−	6.73150i	0.0423234	−	0.326526i
$426$	−33.1484	−	22.2508i	−1.60605	−	1.07805i
$427$		0			0
$428$	1.92158			0.0928830
$429$	22.1236	+	14.8504i	1.06814	+	0.716985i
$430$	2.29507	−	35.5610i	0.110678	−	1.71491i
$431$			13.1408i			0.632972i	0.948597	+	0.316486i	$0.102503\pi$
$431$			13.1408i			0.632972i	−0.948597	+	0.316486i	$0.897497\pi$
$432$	18.3140	+	3.76403i	0.881130	+	0.181097i
$433$	−4.76504			−0.228993			−0.114497	−	0.993424i	$-0.536525\pi$
$433$	−4.76504			−0.228993			−0.114497	+	0.993424i	$0.536525\pi$
$434$		0			0
$435$	−8.26850	−	6.35935i	−0.396444	−	0.304907i
$436$	12.8364			0.614753
$437$			22.3673i			1.06997i
$438$	−9.69932	+	14.4497i	−0.463451	+	0.690433i
$439$			28.6288i			1.36638i	0.730242	+	0.683189i	$0.239407\pi$
$439$			28.6288i			1.36638i	−0.730242	+	0.683189i	$0.760593\pi$
$440$	−0.279638	+	4.33286i	−0.0133312	+	0.206561i
$441$		0			0
$442$			8.27925i			0.393804i
$443$	28.4736			1.35282			0.676411	−	0.736525i	$-0.263534\pi$
$443$	28.4736			1.35282			0.676411	+	0.736525i	$0.263534\pi$
$444$	23.8664	+	16.0203i	1.13265	+	0.760287i
$445$	−20.7995	−	1.34238i	−0.985991	−	0.0636347i
$446$	8.80742			0.417043
$447$	−9.36289	−	6.28482i	−0.442849	−	0.297262i
$448$		0			0
$449$		−	3.55207i		−	0.167633i	−0.996481	−	0.0838164i	$-0.973289\pi$
$449$		−	3.55207i		−	0.167633i	0.996481	−	0.0838164i	$-0.0267109\pi$
$450$	7.87483	+	29.6544i	0.371223	+	1.39792i
$451$			39.6547i			1.86727i
$452$	6.56234			0.308666
$453$	−11.3447	+	16.9009i	−0.533021	+	0.794075i
$454$		−	8.27957i		−	0.388579i
$455$		0			0
$456$	−1.67440	−	1.12394i	−0.0784109	−	0.0526331i
$457$		−	29.2396i		−	1.36777i	−0.729590	−	0.683885i	$-0.760289\pi$
$457$		−	29.2396i		−	1.36777i	0.729590	−	0.683885i	$-0.239711\pi$
$458$		−	17.5345i		−	0.819333i
$459$	−1.42013	+	6.90967i	−0.0662860	+	0.322516i
$460$	−35.2323	−	2.27385i	−1.64271	−	0.106019i
$461$	−28.3247			−1.31921			−0.659607	−	0.751611i	$-0.729277\pi$
$461$	−28.3247			−1.31921			−0.659607	+	0.751611i	$0.729277\pi$
$462$		0			0
$463$		−	39.6458i		−	1.84249i	−0.388977	−	0.921247i	$-0.627172\pi$
$463$		−	39.6458i		−	1.84249i	0.388977	−	0.921247i	$-0.372828\pi$
$464$		−	9.69108i		−	0.449897i
$465$	13.3622	+	10.2769i	0.619656	+	0.476581i
$466$	−18.6530			−0.864082
$467$		−	20.5184i		−	0.949478i	−0.880127	−	0.474739i	$-0.842542\pi$
$467$		−	20.5184i		−	0.949478i	0.880127	−	0.474739i	$-0.157458\pi$
$468$	−7.39907	−	18.0792i	−0.342022	−	0.835712i
$469$		0			0
$470$	1.78914	−	27.7220i	0.0825270	−	1.27872i
$471$	−11.5898	+	17.2661i	−0.534031	+	0.795580i
$472$	−1.59940			−0.0736185
$473$	40.2000			1.84840
$474$	−23.5553	+	35.0918i	−1.08193	+	1.61182i
$475$	−1.98848	+	15.3411i	−0.0912375	+	0.703898i
$476$		0			0
$477$	7.14993	+	17.4705i	0.327373	+	0.799918i
$478$			36.3130i			1.66092i
$479$	−6.61875			−0.302418			−0.151209	−	0.988502i	$-0.548317\pi$
$479$	−6.61875			−0.302418			−0.151209	+	0.988502i	$0.548317\pi$
$480$	−19.1553	+	24.9060i	−0.874316	+	1.13680i
$481$			22.6561i			1.03303i
$482$		−	49.1255i		−	2.23761i
$483$		0			0
$484$	−34.1203			−1.55092
$485$	−42.9558	−	2.77231i	−1.95052	−	0.125884i
$486$	−5.88901	−	31.3373i	−0.267131	−	1.42149i
$487$			19.8399i			0.899032i	0.893272	+	0.449516i	$0.148404\pi$
$487$			19.8399i			0.899032i	−0.893272	+	0.449516i	$0.851596\pi$
$488$			1.96208i			0.0888191i
$489$	26.1696	+	17.5663i	1.18343	+	0.794374i
$490$		0			0
$491$			11.6654i			0.526454i	0.964734	+	0.263227i	$0.0847868\pi$
$491$			11.6654i			0.526454i	−0.964734	+	0.263227i	$0.915213\pi$
$492$	16.2027	−	24.1382i	0.730476	−	1.08824i
$493$	3.65634			0.164673
$494$		−	18.8684i		−	0.848932i
$495$	−32.8116	+	11.0197i	−1.47477	+	0.495300i
$496$			15.6611i			0.703205i
$497$		0			0
$498$	35.7578	+	24.0023i	1.60234	+	1.07557i
$499$	−14.9511			−0.669303			−0.334651	−	0.942342i	$-0.608619\pi$
$499$	−14.9511			−0.669303			−0.334651	+	0.942342i	$0.608619\pi$
$500$	−23.9626	−	4.69175i	−1.07164	−	0.209821i
$501$	29.6871	+	19.9274i	1.32632	+	0.890291i
$502$	18.0154			0.804066
$503$		−	2.45361i		−	0.109401i	−0.998503	−	0.0547006i	$-0.982580\pi$
$503$		−	2.45361i		−	0.109401i	0.998503	−	0.0547006i	$-0.0174204\pi$
$504$		0			0
$505$	−11.5798	−	0.747345i	−0.515293	−	0.0332564i
$506$		−	76.3015i		−	3.39201i
$507$	−3.96803	+	5.91143i	−0.176227	+	0.262536i
$508$			9.81820i			0.435612i
$509$	−9.02660			−0.400097			−0.200048	−	0.979786i	$-0.564110\pi$
$509$	−9.02660			−0.400097			−0.200048	+	0.979786i	$0.564110\pi$
$510$	−8.52498	−	6.55661i	−0.377493	−	0.290331i
$511$		0			0
$512$	−31.8992			−1.40976
$513$	3.23648	−	15.7472i	0.142894	−	0.695254i
$514$		−	23.7946i		−	1.04953i
$515$	−10.4007	−	0.671247i	−0.458308	−	0.0295787i
$516$	−24.4702	−	16.4255i	−1.07724	−	0.723093i
$517$	31.3383			1.37826
$518$		0			0
$519$	−26.5119	−	17.7961i	−1.16374	−	0.781160i
$520$	2.50371	+	0.161586i	0.109795	+	0.00708602i
$521$	21.4758			0.940872			0.470436	−	0.882434i	$-0.344097\pi$
$521$	21.4758			0.940872			0.470436	+	0.882434i	$0.344097\pi$
$522$	−15.2960	+	6.25999i	−0.669486	+	0.273992i
$523$	−33.4291			−1.46175			−0.730876	−	0.682510i	$-0.760888\pi$
$523$	−33.4291			−1.46175			−0.730876	+	0.682510i	$0.760888\pi$
$524$	−16.6992			−0.729510
$525$		0			0
$526$	2.00396			0.0873766
$527$	−5.90878			−0.257390
$528$	−26.6995	−	17.9220i	−1.16195	−	0.779955i
$529$	29.2660			1.27243
$530$	−28.7202	−	1.85357i	−1.24753	−	0.0805139i
$531$	−4.82931	−	11.8002i	−0.209574	−	0.512084i
$532$		0			0
$533$	22.9141			0.992521
$534$	−18.4051	+	27.4193i	−0.796467	+	1.18655i
$535$	−1.96332	−	0.126711i	−0.0848819	−	0.00547818i
$536$			2.12891i			0.0919549i
$537$	23.4838	+	15.7634i	1.01340	+	0.680243i
$538$	42.1557			1.81746
$539$		0			0
$540$	24.4754	+	6.69884i	1.05325	+	0.288272i
$541$	−4.71552			−0.202736			−0.101368	−	0.994849i	$-0.532322\pi$
$541$	−4.71552			−0.202736			−0.101368	+	0.994849i	$0.532322\pi$
$542$		−	5.31762i		−	0.228411i
$543$	5.11963	+	3.43654i	0.219705	+	0.147476i
$544$		−	11.0135i		−	0.472198i
$545$	−13.1153	−	0.846445i	−0.561797	−	0.0362577i
$546$		0			0
$547$		−	1.20004i		−	0.0513100i	−0.999671	−	0.0256550i	$-0.991833\pi$
$547$		−	1.20004i		−	0.0513100i	0.999671	−	0.0256550i	$-0.00816713\pi$
$548$	7.01298			0.299580
$549$	−14.4759	+	5.92439i	−0.617818	+	0.252847i
$550$	6.78327	−	52.3330i	0.289240	−	2.23149i
$551$	−8.33282			−0.354990
$552$	−2.62632	+	3.91259i	−0.111783	+	0.166531i
$553$		0			0
$554$		−	39.1699i		−	1.66417i
$555$	−23.3285	−	17.9421i	−0.990239	−	0.761598i
$556$			22.0791i			0.936362i
$557$	−11.0766			−0.469330			−0.234665	−	0.972076i	$-0.575399\pi$
$557$	−11.0766			−0.469330			−0.234665	+	0.972076i	$0.575399\pi$
$558$	24.7188	−	10.1164i	1.04643	−	0.428260i
$559$		−	23.2292i		−	0.982491i
$560$		0			0
$561$	6.76179	−	10.0735i	0.285483	−	0.425302i
$562$		−	30.3157i		−	1.27879i
$563$		−	4.49574i		−	0.189473i	−0.995502	−	0.0947364i	$-0.969799\pi$
$563$		−	4.49574i		−	0.189473i	0.995502	−	0.0947364i	$-0.0302008\pi$
$564$	−19.0759	−	12.8047i	−0.803242	−	0.539174i
$565$	−6.70490	−	0.432727i	−0.282077	−	0.0182049i
$566$	4.67565			0.196532
$567$		0			0
$568$		−	4.24073i		−	0.177937i
$569$		−	25.7605i		−	1.07993i	−0.841686	−	0.539967i	$-0.818437\pi$
$569$		−	25.7605i		−	1.07993i	0.841686	−	0.539967i	$-0.181563\pi$
$570$	19.4285	+	14.9425i	0.813769	+	0.625874i
$571$	12.3178			0.515484			0.257742	−	0.966214i	$-0.417022\pi$
$571$	12.3178			0.515484			0.257742	+	0.966214i	$0.417022\pi$
$572$			33.5980i			1.40480i
$573$	0.473415	+	0.317778i	0.0197772	+	0.0132754i
$574$		0			0
$575$	35.8477	+	4.64649i	1.49495	+	0.193772i
$576$	10.6788	+	26.0931i	0.444950	+	1.08721i
$577$	38.6072			1.60724			0.803619	−	0.595145i	$-0.202905\pi$
$577$	38.6072			1.60724			0.803619	+	0.595145i	$0.202905\pi$
$578$	−31.0034			−1.28957
$579$	11.5953	+	7.78335i	0.481886	+	0.323465i
$580$	0.847110	−	13.1256i	0.0351743	−	0.545010i
$581$		0			0
$582$	−38.0108	+	56.6271i	−1.57560	+	2.34727i
$583$		−	32.4668i		−	1.34464i
$584$	−1.84857			−0.0764945
$585$	6.36765	+	18.9599i	0.263270	+	0.783895i
$586$			60.1920i			2.48651i
$587$			36.4813i			1.50574i	0.658166	+	0.752872i	$0.271332\pi$
$587$			36.4813i			1.50574i	−0.658166	+	0.752872i	$0.728668\pi$
$588$		0			0
$589$	13.4661			0.554862
$590$	19.3986	+	1.25196i	0.798629	+	0.0515426i
$591$	9.28128	−	13.8269i	0.381781	−	0.568764i
$592$		−	27.3421i		−	1.12375i
$593$			29.4982i			1.21135i	0.795714	+	0.605673i	$0.207096\pi$
$593$			29.4982i			1.21135i	−0.795714	+	0.605673i	$0.792904\pi$
$594$	−11.0406	+	53.7181i	−0.453000	+	2.20408i
$595$		0			0
$596$		−	14.2190i		−	0.582431i
$597$	−16.0486	−	10.7726i	−0.656826	−	0.440893i
$598$	−44.0901			−1.80298
$599$			34.1007i			1.39332i	0.717403	+	0.696658i	$0.245331\pi$
$599$			34.1007i			1.39332i	−0.717403	+	0.696658i	$0.754669\pi$
$600$	−2.14915	+	2.45005i	−0.0877385	+	0.100023i
$601$		−	26.3724i		−	1.07575i	−0.843023	−	0.537877i	$-0.819227\pi$
$601$		−	26.3724i		−	1.07575i	0.843023	−	0.537877i	$-0.180773\pi$
$602$		0			0
$603$	−15.7068	+	6.42814i	−0.639630	+	0.261774i
$604$	−25.6666			−1.04436
$605$	34.8616	+	2.24993i	1.41732	+	0.0914725i
$606$	−10.2467	+	15.2652i	−0.416245	+	0.620107i
$607$	−26.0039			−1.05546			−0.527732	−	0.849411i	$-0.676958\pi$
$607$	−26.0039			−1.05546			−0.527732	+	0.849411i	$0.676958\pi$
$608$			25.0997i			1.01793i
$609$		0			0
$610$	1.53586	−	23.7974i	0.0621850	−	0.963528i
$611$		−	18.1085i		−	0.732593i
$612$	−8.23194	+	3.36899i	−0.332757	+	0.136183i
$613$		−	38.0000i		−	1.53480i	−0.641166	−	0.767402i	$-0.721549\pi$
$613$		−	38.0000i		−	1.53480i	0.641166	−	0.767402i	$-0.278451\pi$
$614$	40.2399			1.62395
$615$	−18.1464	+	23.5942i	−0.731735	+	0.951411i
$616$		0			0
$617$	11.9931			0.482824			0.241412	−	0.970423i	$-0.422390\pi$
$617$	11.9931			0.482824			0.241412	+	0.970423i	$0.422390\pi$
$618$	−9.20338	+	13.7109i	−0.370214	+	0.551532i
$619$		−	5.42320i		−	0.217977i	−0.994043	−	0.108988i	$-0.965239\pi$
$619$		−	5.42320i		−	0.217977i	0.994043	−	0.108988i	$-0.0347612\pi$
$620$	−1.36896	+	21.2114i	−0.0549787	+	0.851870i
$621$	−36.7966	−	7.56272i	−1.47660	−	0.303482i
$622$	15.8822			0.636817
$623$		0			0
$624$	−10.3561	+	15.4281i	−0.414574	+	0.617618i
$625$	24.1738	+	6.37379i	0.966954	+	0.254952i
$626$	−31.4780			−1.25811
$627$	−15.4101	+	22.9575i	−0.615422	+	0.916833i
$628$	−26.2212			−1.04634
$629$	10.3159			0.411322
$630$		0			0
$631$	−8.33250			−0.331711			−0.165856	−	0.986150i	$-0.553039\pi$
$631$	−8.33250			−0.331711			−0.165856	+	0.986150i	$0.553039\pi$
$632$	−4.48936			−0.178577
$633$	1.16518	−	1.73584i	0.0463118	−	0.0689936i
$634$	−3.30240			−0.131155
$635$	0.647421	−	10.0315i	0.0256921	−	0.398088i
$636$	−13.2658	+	19.7629i	−0.526022	+	0.783648i
$637$		0			0
$638$	28.4257			1.12538
$639$	31.2875	−	12.8047i	1.23772	−	0.506545i
$640$	−6.68952	−	0.431734i	−0.264426	−	0.0170658i
$641$		−	20.2291i		−	0.799003i	−0.916733	−	0.399501i	$-0.869183\pi$
$641$		−	20.2291i		−	0.799003i	0.916733	−	0.399501i	$-0.130817\pi$
$642$	−1.73731	+	2.58818i	−0.0685662	+	0.102147i
$643$	−15.2611			−0.601838			−0.300919	−	0.953650i	$-0.597293\pi$
$643$	−15.2611			−0.601838			−0.300919	+	0.953650i	$0.597293\pi$
$644$		0			0
$645$	23.9186	+	18.3959i	0.941796	+	0.724340i
$646$	−8.59130			−0.338020
$647$		−	1.33809i		−	0.0526056i	−0.999654	−	0.0263028i	$-0.991627\pi$
$647$		−	1.33809i		−	0.0526056i	0.999654	−	0.0263028i	$-0.00837340\pi$
$648$	2.41513	−	2.37454i	0.0948753	−	0.0932808i
$649$			21.9292i			0.860796i
$650$	−30.2401	−	3.91965i	−1.18612	−	0.153741i
$651$		0			0
$652$			39.7424i			1.55643i
$653$	−24.6933			−0.966325			−0.483162	−	0.875531i	$-0.660512\pi$
$653$	−24.6933			−0.966325			−0.483162	+	0.875531i	$0.660512\pi$
$654$	−11.6055	+	17.2894i	−0.453811	+	0.676071i
$655$	17.0620	+	1.10116i	0.666669	+	0.0430260i
$656$	−27.6535			−1.07969
$657$	−5.58167	−	13.6385i	−0.217762	−	0.532089i
$658$		0			0
$659$			26.9484i			1.04976i	0.851176	+	0.524880i	$0.175890\pi$
$659$			26.9484i			1.04976i	−0.851176	+	0.524880i	$0.824110\pi$
$660$	−34.5952	−	26.6074i	−1.34662	−	1.03569i
$661$		−	23.8228i		−	0.926599i	−0.886202	−	0.463300i	$-0.846665\pi$
$661$		−	23.8228i		−	0.926599i	0.886202	−	0.463300i	$-0.153335\pi$
$662$	−62.2985			−2.42130
$663$	−5.82086	−	3.90724i	−0.226064	−	0.151745i
$664$			4.57455i			0.177527i
$665$		0			0
$666$	−43.1555	+	17.6617i	−1.67224	+	0.684379i
$667$			19.4714i			0.753935i
$668$			45.0844i			1.74437i
$669$	−4.15650	+	6.19220i	−0.160699	+	0.239404i
$670$	1.66645	−	25.8209i	0.0643805	−	0.997547i
$671$	26.9018			1.03853
$672$		0			0
$673$		−	6.03450i		−	0.232613i	−0.993213	−	0.116307i	$-0.962895\pi$
$673$		−	6.03450i		−	0.232613i	0.993213	−	0.116307i	$-0.0371055\pi$
$674$			46.0737i			1.77469i
$675$	−24.5654	−	8.45830i	−0.945521	−	0.325560i
$676$	−8.97740			−0.345285
$677$			36.7316i			1.41171i	0.708357	+	0.705854i	$0.249437\pi$
$677$			36.7316i			1.41171i	−0.708357	+	0.705854i	$0.750563\pi$
$678$	−5.93305	+	8.83885i	−0.227858	+	0.339454i
$679$		0			0
$680$	0.0735744	−	1.14000i	0.00282145	−	0.0437171i
$681$	5.82108	+	3.90739i	0.223064	+	0.149731i
$682$	−45.9369			−1.75901
$683$	21.7755			0.833217			0.416609	−	0.909086i	$-0.363219\pi$
$683$	21.7755			0.833217			0.416609	+	0.909086i	$0.363219\pi$
$684$	18.7606	−	7.67794i	0.717330	−	0.293573i
$685$	−7.16534	−	0.462443i	−0.273774	−	0.0176690i
$686$		0			0
$687$	12.3279	+	8.27508i	0.470339	+	0.315714i
$688$			28.0338i			1.06878i
$689$	−18.7606			−0.714723
$690$	34.9164	−	45.3987i	1.32924	−	1.72830i
$691$		−	43.4413i		−	1.65258i	−0.563243	−	0.826292i	$-0.690446\pi$
$691$		−	43.4413i		−	1.65258i	0.563243	−	0.826292i	$-0.309554\pi$
$692$		−	40.2623i		−	1.53054i
$693$		0			0
$694$	25.4694			0.966806
$695$	1.45592	−	22.5588i	0.0552260	−	0.855702i
$696$	−1.45761	−	0.978419i	−0.0552507	−	0.0370869i
$697$		−	10.4334i		−	0.395193i
$698$		−	36.7203i		−	1.38988i
$699$	8.80291	−	13.1143i	0.332957	−	0.496027i
$700$		0			0
$701$		−	8.07995i		−	0.305176i	−0.988290	−	0.152588i	$-0.951239\pi$
$701$		−	8.07995i		−	0.305176i	0.988290	−	0.152588i	$-0.0487607\pi$
$702$	31.0405	+	6.37970i	1.17155	+	0.240786i
$703$	−23.5100			−0.886695
$704$		−	48.4909i		−	1.82757i
$705$	18.6460	+	14.3407i	0.702249	+	0.540104i
$706$			25.9397i			0.976253i
$707$		0			0
$708$	8.96016	−	13.3485i	0.336744	−	0.501668i
$709$	−20.2743			−0.761419			−0.380710	−	0.924695i	$-0.624320\pi$
$709$	−20.2743			−0.761419			−0.380710	+	0.924695i	$0.624320\pi$
$710$	−3.31952	+	51.4345i	−0.124579	+	1.93030i
$711$	−13.5554	−	33.1218i	−0.508367	−	1.24217i
$712$	−3.50780			−0.131460
$713$		−	31.4664i		−	1.17843i
$714$		0			0
$715$	2.21549	−	34.3280i	0.0828545	−	1.28379i
$716$			35.6637i			1.33281i
$717$	−25.5305	−	17.1373i	−0.953453	−	0.640003i
$718$		−	0.147974i		−	0.00552235i
$719$	30.4253			1.13467			0.567335	−	0.823487i	$-0.307974\pi$
$719$	30.4253			1.13467			0.567335	+	0.823487i	$0.307974\pi$
$720$	−7.68470	−	22.8814i	−0.286392	−	0.852741i
$721$		0			0
$722$	−19.2845			−0.717694
$723$	34.5385	+	23.1839i	1.28450	+	0.862217i
$724$			7.77493i			0.288953i
$725$	−1.73103	+	13.3549i	−0.0642887	+	0.495987i
$726$	30.8484	−	45.9568i	1.14489	−	1.70562i
$727$	−51.1502			−1.89706			−0.948528	−	0.316692i	$-0.897428\pi$
$727$	−51.1502			−1.89706			−0.948528	+	0.316692i	$0.897428\pi$
$728$		0			0
$729$	24.8114	+	10.6487i	0.918941	+	0.394396i
$730$	22.4207	+	1.44701i	0.829829	+	0.0535562i
$731$	−10.5769			−0.391199
$732$	−16.3754	−	10.9919i	−0.605252	−	0.406274i
$733$	−36.5369			−1.34952			−0.674761	−	0.738037i	$-0.735753\pi$
$733$	−36.5369			−1.34952			−0.674761	+	0.738037i	$0.735753\pi$
$734$	21.9252			0.809272
$735$		0			0
$736$	58.6508			2.16190
$737$	29.1892			1.07520
$738$	17.8629	+	43.6471i	0.657544	+	1.60667i
$739$	16.0866			0.591757			0.295878	−	0.955226i	$-0.404388\pi$
$739$	16.0866			0.591757			0.295878	+	0.955226i	$0.404388\pi$
$740$	2.39001	−	37.0321i	0.0878584	−	1.36133i
$741$	13.2658	+	8.90461i	0.487330	+	0.327119i
$742$		0			0
$743$	−27.5407			−1.01037			−0.505186	−	0.863011i	$-0.668576\pi$
$743$	−27.5407			−1.01037			−0.505186	+	0.863011i	$0.668576\pi$
$744$	2.35555	+	1.58116i	0.0863587	+	0.0579681i
$745$	−0.937611	+	14.5279i	−0.0343514	+	0.532259i
$746$			43.7326i			1.60117i
$747$	−33.7504	+	13.8126i	−1.23486	+	0.505378i
$748$	15.2981			0.559353
$749$		0			0
$750$	27.9841	−	28.0336i	1.02184	−	1.02364i
$751$	−38.2761			−1.39671			−0.698357	−	0.715749i	$-0.746085\pi$
$751$	−38.2761			−1.39671			−0.698357	+	0.715749i	$0.746085\pi$
$752$			21.8540i			0.796934i
$753$	−8.50202	+	12.6660i	−0.309831	+	0.461575i
$754$		−	16.4255i		−	0.598182i
$755$	26.2242	+	1.69248i	0.954397	+	0.0615956i
$756$		0			0
$757$			36.0954i			1.31191i	0.754800	+	0.655955i	$0.227734\pi$
$757$			36.0954i			1.31191i	−0.754800	+	0.655955i	$0.772266\pi$
$758$	−49.7139			−1.80569
$759$	53.6450	+	36.0090i	1.94719	+	1.30705i
$760$	−0.167676	+	2.59807i	−0.00608226	+	0.0942419i
$761$	30.2188			1.09543			0.547716	−	0.836664i	$-0.315497\pi$
$761$	30.2188			1.09543			0.547716	+	0.836664i	$0.315497\pi$
$762$	−13.2242	−	8.87670i	−0.479062	−	0.321569i
$763$		0			0
$764$			0.718951i			0.0260108i
$765$	8.63293	−	2.89936i	0.312124	−	0.104826i
$766$			15.1095i			0.545930i
$767$	12.6716			0.457544
$768$	12.2246	−	18.2118i	0.441118	−	0.657162i
$769$		−	16.8667i		−	0.608228i	−0.952636	−	0.304114i	$-0.901640\pi$
$769$		−	16.8667i		−	0.608228i	0.952636	−	0.304114i	$-0.0983603\pi$
$770$		0			0
$771$	16.7292	+	11.2294i	0.602486	+	0.404417i
$772$			17.6093i			0.633772i
$773$			35.6415i			1.28194i	0.767567	+	0.640968i	$0.221467\pi$
$773$			35.6415i			1.28194i	−0.767567	+	0.640968i	$0.778533\pi$
$774$	44.2473	−	18.1085i	1.59043	−	0.650898i
$775$	2.79740	−	21.5819i	0.100485	−	0.775246i
$776$	−7.24441			−0.260059
$777$		0			0
$778$			26.3215i			0.943671i
$779$			23.7778i			0.851927i
$780$	−15.3748	+	19.9905i	−0.550507	+	0.715776i
$781$	−58.1441			−2.08056
$782$			20.0754i			0.717894i
$783$	2.81745	−	13.7084i	0.100687	−	0.489896i
$784$		0			0
$785$	26.7908	+	1.72905i	0.956205	+	0.0617124i
$786$	15.0979	−	22.4923i	0.538524	−	0.802274i
$787$	−1.63639			−0.0583311			−0.0291655	−	0.999575i	$-0.509285\pi$
$787$	−1.63639			−0.0583311			−0.0291655	+	0.999575i	$0.509285\pi$
$788$	20.9983			0.748032
$789$	−0.945729	+	1.40891i	−0.0336689	+	0.0501586i
$790$	54.4499	+	3.51414i	1.93724	+	0.125027i
$791$		0			0
$792$	−5.39121	+	2.20640i	−0.191568	+	0.0784010i
$793$		−	15.5449i		−	0.552017i
$794$	33.2320			1.17936
$795$	14.8571	−	19.3174i	0.526928	−	0.685119i
$796$		−	24.3722i		−	0.863850i
$797$			13.2950i			0.470934i	0.971882	+	0.235467i	$0.0756620\pi$
$797$			13.2950i			0.470934i	−0.971882	+	0.235467i	$0.924338\pi$
$798$		0			0
$799$	−8.24529			−0.291698
$800$	40.2269	+	5.21411i	1.42223	+	0.184347i
$801$	−10.5916	−	25.8800i	−0.374236	−	0.914426i
$802$			20.9061i			0.738220i
$803$			25.3455i			0.894424i
$804$	−17.7678	−	11.9266i	−0.626621	−	0.420618i
$805$		0			0
$806$			26.5442i			0.934980i
$807$	−19.8946	+	29.6382i	−0.700322	+	1.04331i
$808$	−1.95291			−0.0687030
$809$		−	35.5273i		−	1.24907i	−0.780995	−	0.624537i	$-0.785288\pi$
$809$		−	35.5273i		−	1.24907i	0.780995	−	0.624537i	$-0.214712\pi$
$810$	−31.1511	+	26.9095i	−1.09454	+	0.945505i
$811$			31.4512i			1.10440i	0.833711	+	0.552201i	$0.186212\pi$
$811$			31.4512i			1.10440i	−0.833711	+	0.552201i	$0.813788\pi$
$812$		0			0
$813$	3.73864	+	2.50955i	0.131120	+	0.0880138i
$814$	80.1993			2.81098
$815$	2.62065	−	40.6058i	0.0917974	−	1.42236i
$816$	7.02481	+	4.71539i	0.245918	+	0.165072i
$817$	24.1047			0.843317
$818$			37.1578i			1.29919i
$819$		0			0
$820$	−37.4539	−	2.41723i	−1.30795	−	0.0844134i
$821$			48.9716i			1.70912i	0.519351	+	0.854561i	$0.326174\pi$
$821$			48.9716i			1.70912i	−0.519351	+	0.854561i	$0.673826\pi$
$822$	−6.34049	+	9.44583i	−0.221150	+	0.329461i
$823$		−	38.8485i		−	1.35417i	−0.735903	−	0.677087i	$-0.763242\pi$
$823$		−	38.8485i		−	1.35417i	0.735903	−	0.677087i	$-0.236758\pi$
$824$	−1.75405			−0.0611054
$825$	33.5923	+	29.4666i	1.16953	+	1.02590i
$826$		0			0
$827$	−44.6506			−1.55265			−0.776327	−	0.630330i	$-0.782919\pi$
$827$	−44.6506			−1.55265			−0.776327	+	0.630330i	$0.782919\pi$
$828$	−17.9411	−	43.8382i	−0.623497	−	1.52348i
$829$		−	42.1358i		−	1.46344i	−0.681606	−	0.731719i	$-0.738718\pi$
$829$		−	42.1358i		−	1.46344i	0.681606	−	0.731719i	$-0.261282\pi$
$830$	3.58083	−	55.4833i	0.124292	−	1.92585i
$831$	27.5390	+	18.4855i	0.955319	+	0.641255i
$832$	−28.0200			−0.971419
$833$		0			0
$834$	−29.7385	−	19.9619i	−1.02976	−	0.691223i
$835$	2.97290	−	46.0638i	0.102882	−	1.59410i
$836$	−34.8643			−1.20581
$837$	−4.55309	+	22.1532i	−0.157378	+	0.765725i
$838$	−6.93381			−0.239525
$839$	25.5067			0.880588			0.440294	−	0.897854i	$-0.354874\pi$
$839$	25.5067			0.880588			0.440294	+	0.897854i	$0.354874\pi$
$840$		0			0
$841$	21.7460			0.749863
$842$	10.4816			0.361220
$843$	21.3140	+	14.3069i	0.734092	+	0.492757i
$844$	2.63614			0.0907397
$845$	9.17243	+	0.591978i	0.315541	+	0.0203647i
$846$	34.4934	−	14.1167i	1.18591	−	0.485342i
$847$		0			0
$848$	22.6410			0.777494
$849$	−2.20659	+	3.28729i	−0.0757299	+	0.112820i
$850$	−1.78472	+	13.7691i	−0.0612154	+	0.472277i
$851$			54.9360i			1.88318i
$852$	35.3929	+	23.7574i	1.21254	+	0.813915i
$853$	−6.38527			−0.218628			−0.109314	−	0.994007i	$-0.534865\pi$
$853$	−6.38527			−0.218628			−0.109314	+	0.994007i	$0.534865\pi$
$854$		0			0
$855$	−19.6745	+	6.60765i	−0.672853	+	0.225977i
$856$	−0.331111			−0.0113171
$857$		−	55.7512i		−	1.90442i	−0.305437	−	0.952212i	$-0.598803\pi$
$857$		−	55.7512i		−	1.90442i	0.305437	−	0.952212i	$-0.401197\pi$
$858$	−45.2534	−	30.3762i	−1.54493	−	1.03703i
$859$		−	27.2608i		−	0.930128i	−0.885277	−	0.465064i	$-0.846031\pi$
$859$		−	27.2608i		−	0.930128i	0.885277	−	0.465064i	$-0.153969\pi$
$860$	−2.45047	+	37.9689i	−0.0835603	+	1.29473i
$861$		0			0
$862$		−	26.8793i		−	0.915513i
$863$	−22.1972			−0.755602			−0.377801	−	0.925887i	$-0.623320\pi$
$863$	−22.1972			−0.755602			−0.377801	+	0.925887i	$0.623320\pi$
$864$	−41.2916	−	8.48658i	−1.40477	−	0.288719i
$865$	−2.65494	+	41.1370i	−0.0902705	+	1.39870i
$866$	9.74677			0.331209
$867$	14.6315	−	21.7974i	0.496910	−	0.740279i
$868$		0			0
$869$			61.5529i			2.08804i
$870$	16.9130	+	13.0079i	0.573406	+	0.441009i
$871$		−	16.8667i		−	0.571507i
$872$	−2.21187			−0.0749033
$873$	−21.8741	−	53.4482i	−0.740327	−	1.80895i
$874$		−	45.7519i		−	1.54758i
$875$		0			0
$876$	10.3561	−	15.4281i	0.349899	−	0.521267i
$877$		−	28.3910i		−	0.958697i	−0.877625	−	0.479348i	$-0.840873\pi$
$877$		−	28.3910i		−	0.958697i	0.877625	−	0.479348i	$-0.159127\pi$
$878$		−	58.5596i		−	1.97629i
$879$	−42.3189	−	28.4065i	−1.42738	−	0.958126i
$880$	−2.67372	+	41.4281i	−0.0901312	+	1.39654i
$881$	20.0653			0.676017			0.338009	−	0.941143i	$-0.390247\pi$
$881$	20.0653			0.676017			0.338009	+	0.941143i	$0.390247\pi$
$882$		0			0
$883$			31.1643i			1.04876i	0.851484	+	0.524381i	$0.175703\pi$
$883$			31.1643i			1.04876i	−0.851484	+	0.524381i	$0.824297\pi$
$884$		−	8.83985i		−	0.297316i
$885$	−10.0350	+	13.0477i	−0.337324	+	0.438593i
$886$	−58.2421			−1.95668
$887$			12.7773i			0.429020i	0.976722	+	0.214510i	$0.0688154\pi$
$887$			12.7773i			0.429020i	−0.976722	+	0.214510i	$0.931185\pi$
$888$	−4.11246	−	2.76048i	−0.138005	−	0.0926356i
$889$		0			0
$890$	42.5449	+	2.74580i	1.42611	+	0.0920394i
$891$	−32.5570	−	33.1135i	−1.09070	−	1.10934i
$892$	−9.40378			−0.314862
$893$	18.7911			0.628819
$894$	19.1516	+	12.8555i	0.640525	+	0.429951i
$895$	2.35170	−	36.4385i	0.0786085	−	1.21800i
$896$		0			0
$897$	20.8075	−	30.9983i	0.694742	−	1.03500i
$898$			7.26569i			0.242459i
$899$	11.7226			0.390972
$900$	−8.40805	−	31.6623i	−0.280268	−	1.05541i
$901$			8.54220i			0.284582i
$902$		−	81.1129i		−	2.70076i
$903$		0			0
$904$	−1.13077			−0.0376088
$905$	0.512686	−	7.94384i	0.0170423	−	0.264062i
$906$	23.2054	−	34.5705i	0.770946	−	1.14853i
$907$			0.340207i			0.0112964i	0.999984	+	0.00564819i	$0.00179788\pi$
$907$			0.340207i			0.0112964i	−0.999984	+	0.00564819i	$0.998202\pi$
$908$			8.84019i			0.293372i
$909$	−5.89670	−	14.4083i	−0.195581	−	0.477892i
$910$		0			0
$911$		−	34.4235i		−	1.14050i	−0.821471	−	0.570250i	$-0.806846\pi$
$911$		−	34.4235i		−	1.14050i	0.821471	−	0.570250i	$-0.193154\pi$
$912$	−16.0096	−	10.7464i	−0.530130	−	0.355848i
$913$	62.7211			2.07576
$914$			59.8089i			1.97830i
$915$	16.0063	+	12.3105i	0.529153	+	0.406974i
$916$			18.7218i			0.618585i
$917$		0			0
$918$	2.90484	−	14.1336i	0.0958741	−	0.466477i
$919$	−39.3723			−1.29877			−0.649386	−	0.760459i	$-0.724974\pi$
$919$	−39.3723			−1.29877			−0.649386	+	0.760459i	$0.724974\pi$
$920$	6.07094	+	0.391811i	0.200153	+	0.0129176i
$921$	−18.9905	+	28.2913i	−0.625757	+	0.932230i
$922$	57.9376			1.90807
$923$			33.5980i			1.10589i
$924$		0			0
$925$	−4.88386	+	37.6790i	−0.160580	+	1.23888i
$926$			81.0945i			2.66493i
$927$	−5.29628	−	12.9412i	−0.173953	−	0.425044i
$928$			21.8500i			0.717262i
$929$	−44.9750			−1.47558			−0.737791	−	0.675030i	$-0.764131\pi$
$929$	−44.9750			−1.47558			−0.737791	+	0.675030i	$0.764131\pi$
$930$	−27.3320	−	21.0212i	−0.896253	−	0.689313i
$931$		0			0
$932$	19.9160			0.652369
$933$	−7.49529	+	11.1662i	−0.245385	+	0.365565i
$934$			41.9699i			1.37330i
$935$	−15.6304	−	1.00877i	−0.511169	−	0.0329903i
$936$	1.27495	+	3.11527i	0.0416730	+	0.101826i
$937$	−30.0270			−0.980941			−0.490470	−	0.871458i	$-0.663175\pi$
$937$	−30.0270			−0.980941			−0.490470	+	0.871458i	$0.663175\pi$
$938$		0			0
$939$	14.8554	−	22.1311i	0.484789	−	0.722221i
$940$	−1.91029	+	29.5990i	−0.0623067	+	0.965414i
$941$	−4.09261			−0.133415			−0.0667077	−	0.997773i	$-0.521250\pi$
$941$	−4.09261			−0.133415			−0.0667077	+	0.997773i	$0.521250\pi$
$942$	23.7067	−	35.3174i	0.772407	−	1.15070i
$943$	55.5618			1.80934
$944$	−15.2925			−0.497728
$945$		0			0
$946$	−82.2282			−2.67347
$947$	−1.75027			−0.0568760			−0.0284380	−	0.999596i	$-0.509053\pi$
$947$	−1.75027			−0.0568760			−0.0284380	+	0.999596i	$0.509053\pi$
$948$	25.1502	−	37.4679i	0.816842	−	1.21690i
$949$	14.6457			0.475419
$950$	4.06738	−	31.3799i	0.131963	−	1.01810i
$951$	1.55851	−	2.32181i	0.0505380	−	0.0752897i
$952$		0			0
$953$	−33.2268			−1.07632			−0.538161	−	0.842842i	$-0.680881\pi$
$953$	−33.2268			−1.07632			−0.538161	+	0.842842i	$0.680881\pi$
$954$	−14.6250	−	35.7355i	−0.473503	−	1.15698i
$955$	0.0474083	−	0.734570i	0.00153410	−	0.0237701i
$956$		−	38.7718i		−	1.25397i
$957$	−13.4150	+	19.9851i	−0.433644	+	0.646027i
$958$	13.5385			0.437409
$959$		0			0
$960$	22.1899	−	28.8516i	0.716177	−	0.931183i
$961$	12.0558			0.388897
$962$		−	46.3425i		−	1.49414i
$963$	−0.999773	−	2.44289i	−0.0322172	−	0.0787210i
$964$			52.4519i			1.68936i
$965$	1.16117	−	17.9918i	0.0373794	−	0.579178i
$966$		0			0
$967$			4.20353i			0.135176i	0.997713	+	0.0675882i	$0.0215304\pi$
$967$			4.20353i			0.135176i	−0.997713	+	0.0675882i	$0.978470\pi$
$968$	5.87934			0.188969
$969$	4.05450	−	6.04025i	0.130249	−	0.194041i
$970$	87.8650	+	5.67071i	2.82118	+	0.182075i
$971$	−51.5343			−1.65381			−0.826907	−	0.562339i	$-0.809902\pi$
$971$	−51.5343			−1.65381			−0.826907	+	0.562339i	$0.809902\pi$
$972$	6.28776	+	33.4592i	0.201680	+	1.07320i
$973$		0			0
$974$		−	40.5821i		−	1.30033i
$975$	17.0270	−	19.4110i	0.545302	−	0.621650i
$976$			18.7602i			0.600498i
$977$	−49.6186			−1.58744			−0.793720	−	0.608284i	$-0.791858\pi$
$977$	−49.6186			−1.58744			−0.793720	+	0.608284i	$0.791858\pi$
$978$	−53.5293	−	35.9314i	−1.71168	−	1.14896i
$979$			48.0949i			1.53712i
$980$		0			0
$981$	−6.67862	−	16.3189i	−0.213232	−	0.521021i
$982$		−	23.8614i		−	0.761448i
$983$			21.7102i			0.692447i	0.938152	+	0.346224i	$0.112536\pi$
$983$			21.7102i			0.692447i	−0.938152	+	0.346224i	$0.887464\pi$
$984$	−2.79192	+	4.15931i	−0.0890033	+	0.132594i
$985$	−21.4544	−	1.38464i	−0.683595	−	0.0441184i
$986$	−7.47897			−0.238179
$987$		0			0
$988$			20.1461i			0.640931i
$989$		−	56.3257i		−	1.79105i
$990$	67.1154	−	22.5406i	2.13307	−	0.716387i
$991$	−16.3479			−0.519309			−0.259655	−	0.965702i	$-0.583609\pi$
$991$	−16.3479			−0.519309			−0.259655	+	0.965702i	$0.583609\pi$
$992$		−	35.3104i		−	1.12111i
$993$	29.4006	−	43.8000i	0.933000	−	1.38995i
$994$		0			0
$995$	−1.60713	+	24.9017i	−0.0509493	+	0.789437i
$996$	−38.1790	−	25.6275i	−1.20975	−	0.812040i
$997$	−32.9021			−1.04202			−0.521010	−	0.853550i	$-0.674445\pi$
$997$	−32.9021			−1.04202			−0.521010	+	0.853550i	$0.674445\pi$
$998$	30.5821			0.968060
$999$	7.94906	−	38.6763i	0.251497	−	1.22366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.c.734.7	yes	32
3.2	odd	2	inner	735.2.g.c.734.28	yes	32
5.4	even	2	inner	735.2.g.c.734.26	yes	32
7.2	even	3		735.2.p.g.374.27		64
7.3	odd	6		735.2.p.g.509.28		64
7.4	even	3		735.2.p.g.509.25		64
7.5	odd	6		735.2.p.g.374.26		64
7.6	odd	2	inner	735.2.g.c.734.6	yes	32
15.14	odd	2	inner	735.2.g.c.734.5	✓	32
21.2	odd	6		735.2.p.g.374.5		64
21.5	even	6		735.2.p.g.374.8		64
21.11	odd	6		735.2.p.g.509.7		64
21.17	even	6		735.2.p.g.509.6		64
21.20	even	2	inner	735.2.g.c.734.25	yes	32
35.4	even	6		735.2.p.g.509.8		64
35.9	even	6		735.2.p.g.374.6		64
35.19	odd	6		735.2.p.g.374.7		64
35.24	odd	6		735.2.p.g.509.5		64
35.34	odd	2	inner	735.2.g.c.734.27	yes	32
105.44	odd	6		735.2.p.g.374.28		64
105.59	even	6		735.2.p.g.509.27		64
105.74	odd	6		735.2.p.g.509.26		64
105.89	even	6		735.2.p.g.374.25		64
105.104	even	2	inner	735.2.g.c.734.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.5	✓	32	15.14	odd	2	inner
735.2.g.c.734.6	yes	32	7.6	odd	2	inner
735.2.g.c.734.7	yes	32	1.1	even	1	trivial
735.2.g.c.734.8	yes	32	105.104	even	2	inner
735.2.g.c.734.25	yes	32	21.20	even	2	inner
735.2.g.c.734.26	yes	32	5.4	even	2	inner
735.2.g.c.734.27	yes	32	35.34	odd	2	inner
735.2.g.c.734.28	yes	32	3.2	odd	2	inner
735.2.p.g.374.5		64	21.2	odd	6
735.2.p.g.374.6		64	35.9	even	6
735.2.p.g.374.7		64	35.19	odd	6
735.2.p.g.374.8		64	21.5	even	6
735.2.p.g.374.25		64	105.89	even	6
735.2.p.g.374.26		64	7.5	odd	6
735.2.p.g.374.27		64	7.2	even	3
735.2.p.g.374.28		64	105.44	odd	6
735.2.p.g.509.5		64	35.24	odd	6
735.2.p.g.509.6		64	21.17	even	6
735.2.p.g.509.7		64	21.11	odd	6
735.2.p.g.509.8		64	35.4	even	6
735.2.p.g.509.25		64	7.4	even	3
735.2.p.g.509.26		64	105.74	odd	6
735.2.p.g.509.27		64	105.59	even	6
735.2.p.g.509.28		64	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q-2.04548 q^{2} +(0.965325 - 1.43811i) q^{3} +2.18398 q^{4} +(-2.23143 - 0.144014i) q^{5} +(-1.97455 + 2.94161i) q^{6} -0.376326 q^{8} +(-1.13630 - 2.77648i) q^{9} +(4.56433 + 0.294577i) q^{10} +5.15975i q^{11} +(2.10825 - 3.14079i) q^{12} +2.98151 q^{13} +(-2.36116 + 3.07001i) q^{15} -3.59819 q^{16} -1.35756i q^{17} +(2.32427 + 5.67922i) q^{18} +3.09389i q^{19} +(-4.87339 - 0.314523i) q^{20} -10.5542i q^{22} +7.22952 q^{23} +(-0.363276 + 0.541196i) q^{24} +(4.95852 + 0.642711i) q^{25} -6.09862 q^{26} +(-5.08976 - 1.04609i) q^{27} +2.69332i q^{29} +(4.82969 - 6.27963i) q^{30} -4.35249i q^{31} +8.11267 q^{32} +(7.42026 + 4.98083i) q^{33} +2.77686i q^{34} +(-2.48165 - 6.06377i) q^{36} +7.59884i q^{37} -6.32848i q^{38} +(2.87813 - 4.28773i) q^{39} +(0.839743 + 0.0541960i) q^{40} +7.68540 q^{41} -7.79107i q^{43} +11.2688i q^{44} +(2.13571 + 6.35915i) q^{45} -14.7878 q^{46} -6.07361i q^{47} +(-3.47342 + 5.17458i) q^{48} +(-10.1425 - 1.31465i) q^{50} +(-1.95232 - 1.31049i) q^{51} +6.51157 q^{52} -6.29231 q^{53} +(10.4110 + 2.13975i) q^{54} +(0.743074 - 11.5136i) q^{55} +(4.44934 + 2.98661i) q^{57} -5.50912i q^{58} +4.25005 q^{59} +(-5.15672 + 6.70483i) q^{60} -5.21377i q^{61} +8.90293i q^{62} -9.39791 q^{64} +(-6.65303 - 0.429379i) q^{65} +(-15.1780 - 10.1882i) q^{66} -5.65710i q^{67} -2.96489i q^{68} +(6.97884 - 10.3968i) q^{69} +11.2688i q^{71} +(0.427617 + 1.04486i) q^{72} +4.91216 q^{73} -15.5433i q^{74} +(5.71087 - 6.51045i) q^{75} +6.75699i q^{76} +(-5.88715 + 8.77046i) q^{78} +11.9294 q^{79} +(8.02910 + 0.518189i) q^{80} +(-6.41766 + 6.30980i) q^{81} -15.7203 q^{82} -12.1558i q^{83} +(-0.195507 + 3.02930i) q^{85} +15.9365i q^{86} +(3.87328 + 2.59993i) q^{87} -1.94175i q^{88} +9.32117 q^{89} +(-4.36855 - 13.0075i) q^{90} +15.7891 q^{92} +(-6.25935 - 4.20157i) q^{93} +12.4234i q^{94} +(0.445562 - 6.90378i) q^{95} +(7.83137 - 11.6669i) q^{96} +19.2504 q^{97} +(14.3259 - 5.86300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) \) 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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