LMFDB - Embedded newform 735.2.p.g.509.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.24
Character	$\chi$	$=$	735.509
Dual form			735.2.p.g.374.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.451669 - 0.782314i) q^{2} +(1.02385 + 1.39704i) q^{3} +(0.591990 + 1.02536i) q^{4} +(0.0199888 - 2.23598i) q^{5} +(1.55537 - 0.169975i) q^{6} +2.87621 q^{8} +(-0.903447 + 2.86073i) q^{9} +(-1.74021 - 1.02556i) q^{10} +(-3.51985 + 2.03219i) q^{11} +(-0.826354 + 1.87685i) q^{12} +2.88298 q^{13} +(3.14422 - 2.26139i) q^{15} +(0.115117 - 0.199389i) q^{16} +(5.77521 - 3.33432i) q^{17} +(1.82993 + 1.99888i) q^{18} +(4.94242 + 2.85351i) q^{19} +(2.30451 - 1.30318i) q^{20} +3.67151i q^{22} +(0.815927 - 1.41323i) q^{23} +(2.94482 + 4.01819i) q^{24} +(-4.99920 - 0.0893892i) q^{25} +(1.30215 - 2.25540i) q^{26} +(-4.92156 + 1.66682i) q^{27} +5.89707i q^{29} +(-0.348970 - 3.48117i) q^{30} +(1.62006 - 0.935342i) q^{31} +(2.77222 + 4.80163i) q^{32} +(-6.44286 - 2.83671i) q^{33} -6.02404i q^{34} +(-3.46810 + 0.767168i) q^{36} +(-1.38541 - 0.799864i) q^{37} +(4.46468 - 2.57768i) q^{38} +(2.95175 + 4.02764i) q^{39} +(0.0574921 - 6.43115i) q^{40} -9.12244 q^{41} -7.53359i q^{43} +(-4.16743 - 2.40607i) q^{44} +(6.37848 + 2.07727i) q^{45} +(-0.737059 - 1.27662i) q^{46} +(-5.98810 - 3.45723i) q^{47} +(0.396417 - 0.0433215i) q^{48} +(-2.32792 + 3.87057i) q^{50} +(10.5712 + 4.65435i) q^{51} +(1.70670 + 2.95608i) q^{52} +(0.759325 + 1.31519i) q^{53} +(-0.918941 + 4.60305i) q^{54} +(4.47357 + 7.91093i) q^{55} +(1.07385 + 9.82633i) q^{57} +(4.61336 + 2.66353i) q^{58} +(-0.495925 - 0.858968i) q^{59} +(4.18008 + 1.88523i) q^{60} +(-5.33892 - 3.08243i) q^{61} -1.68986i q^{62} +5.46898 q^{64} +(0.0576274 - 6.44628i) q^{65} +(-5.12924 + 3.75908i) q^{66} +(8.73843 - 5.04513i) q^{67} +(6.83773 + 3.94776i) q^{68} +(2.80973 - 0.307054i) q^{69} +4.81213i q^{71} +(-2.59850 + 8.22807i) q^{72} +(0.280309 + 0.485510i) q^{73} +(-1.25149 + 0.722548i) q^{74} +(-4.99357 - 7.07561i) q^{75} +6.75699i q^{76} +(4.48410 - 0.490034i) q^{78} +(-1.89924 + 3.28958i) q^{79} +(-0.443528 - 0.261385i) q^{80} +(-7.36757 - 5.16904i) q^{81} +(-4.12033 + 7.13661i) q^{82} -4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} +(-5.89364 - 3.40269i) q^{86} +(-8.23845 + 6.03774i) q^{87} +(-10.1238 + 5.84500i) q^{88} +(5.20547 - 9.01615i) q^{89} +(4.50604 - 4.05173i) q^{90} +1.93208 q^{92} +(2.96541 + 1.30564i) q^{93} +(-5.40928 + 3.12305i) q^{94} +(6.47917 - 10.9941i) q^{95} +(-3.86972 + 8.78907i) q^{96} -14.5370 q^{97} +(-2.63354 - 11.9053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) $ 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Character values

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

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	0.451669	−	0.782314i	0.319378	−	0.553180i	−0.660980	−	0.750403i	$-0.729859\pi$
$2$	0.451669	−	0.782314i	0.319378	−	0.553180i	0.980358	+	0.197224i	$0.0631926\pi$
$3$	1.02385	+	1.39704i	0.591122	+	0.806582i
$3$	1.02385	+	1.39704i	0.591122	+	0.806582i
$4$	0.591990	+	1.02536i	0.295995	+	0.512678i
$5$	0.0199888	−	2.23598i	0.00893927	−	0.999960i
$5$	0.0199888	−	2.23598i	0.00893927	−	0.999960i
$6$	1.55537	−	0.169975i	0.634976	−	0.0693919i
$7$		0			0
$7$		0			0
$8$	2.87621			1.01689
$9$	−0.903447	+	2.86073i	−0.301149	+	0.953577i
$10$	−1.74021	−	1.02556i	−0.550303	−	0.324311i
$11$	−3.51985	+	2.03219i	−1.06127	+	0.612727i	−0.925785	−	0.378051i	$-0.876594\pi$
$11$	−3.51985	+	2.03219i	−1.06127	+	0.612727i	−0.135490	+	0.990779i	$0.543261\pi$
$12$	−0.826354	+	1.87685i	−0.238548	+	0.541800i
$13$	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
$15$	3.14422	−	2.26139i	0.811834	−	0.583888i
$16$	0.115117	−	0.199389i	0.0287793	−	0.0498472i
$17$	5.77521	−	3.33432i	1.40069	−	0.808691i	0.406230	−	0.913771i	$-0.366843\pi$
$17$	5.77521	−	3.33432i	1.40069	−	0.808691i	0.994464	+	0.105080i	$0.0335097\pi$
$18$	1.82993	+	1.99888i	0.431319	+	0.471141i
$19$	4.94242	+	2.85351i	1.13387	+	0.654639i	0.944905	−	0.327345i	$-0.106154\pi$
$19$	4.94242	+	2.85351i	1.13387	+	0.654639i	0.188964	+	0.981984i	$0.439487\pi$
$20$	2.30451	−	1.30318i	0.515304	−	0.291400i
$21$		0			0
$22$			3.67151i			0.782768i
$23$	0.815927	−	1.41323i	0.170133	−	0.294678i	−0.768333	−	0.640050i	$-0.778914\pi$
$23$	0.815927	−	1.41323i	0.170133	−	0.294678i	0.938466	+	0.345371i	$0.112247\pi$
$24$	2.94482	+	4.01819i	0.601109	+	0.820209i
$25$	−4.99920	−	0.0893892i	−0.999840	−	0.0178778i
$26$	1.30215	−	2.25540i	0.255373	−	0.442320i
$27$	−4.92156	+	1.66682i	−0.947154	+	0.320779i
$28$		0			0
$29$			5.89707i			1.09506i	0.836786	+	0.547530i	$0.184432\pi$
$29$			5.89707i			1.09506i	−0.836786	+	0.547530i	$0.815568\pi$
$30$	−0.348970	−	3.48117i	−0.0637129	−	0.635571i
$31$	1.62006	−	0.935342i	0.290971	−	0.167992i	−0.347409	−	0.937714i	$-0.612938\pi$
$31$	1.62006	−	0.935342i	0.290971	−	0.167992i	0.638380	+	0.769722i	$0.279605\pi$
$32$	2.77222	+	4.80163i	0.490064	+	0.848816i
$33$	−6.44286	−	2.83671i	−1.12156	−	0.493808i
$34$		−	6.02404i		−	1.03311i
$35$		0			0
$36$	−3.46810	+	0.767168i	−0.578017	+	0.127861i
$37$	−1.38541	−	0.799864i	−0.227759	−	0.131497i	0.381779	−	0.924254i	$-0.375312\pi$
$37$	−1.38541	−	0.799864i	−0.227759	−	0.131497i	−0.609538	+	0.792757i	$0.708645\pi$
$38$	4.46468	−	2.57768i	0.724266	−	0.418155i
$39$	2.95175	+	4.02764i	0.472658	+	0.644939i
$40$	0.0574921	−	6.43115i	0.00909030	−	1.01685i
$41$	−9.12244			−1.42469			−0.712343	−	0.701832i	$-0.752366\pi$
$41$	−9.12244			−1.42469			−0.712343	+	0.701832i	$0.752366\pi$
$42$		0			0
$43$		−	7.53359i		−	1.14886i	−0.818553	−	0.574431i	$-0.805223\pi$
$43$		−	7.53359i		−	1.14886i	0.818553	−	0.574431i	$-0.194777\pi$
$44$	−4.16743	−	2.40607i	−0.628264	−	0.362728i
$45$	6.37848	+	2.07727i	0.950847	+	0.309661i
$46$	−0.737059	−	1.27662i	−0.108673	−	0.188228i
$47$	−5.98810	−	3.45723i	−0.873454	−	0.504289i	−0.00495956	−	0.999988i	$-0.501579\pi$
$47$	−5.98810	−	3.45723i	−0.873454	−	0.504289i	−0.868495	+	0.495699i	$0.834912\pi$
$48$	0.396417	−	0.0433215i	0.0572179	−	0.00625292i
$49$		0			0
$50$	−2.32792	+	3.87057i	−0.329217	+	0.547381i
$51$	10.5712	+	4.65435i	1.48026	+	0.651739i
$52$	1.70670	+	2.95608i	0.236676	+	0.409935i
$53$	0.759325	+	1.31519i	0.104301	+	0.180655i	0.913453	−	0.406945i	$-0.133406\pi$
$53$	0.759325	+	1.31519i	0.104301	+	0.180655i	−0.809151	+	0.587600i	$0.800073\pi$
$54$	−0.918941	+	4.60305i	−0.125052	+	0.626396i
$55$	4.47357	+	7.91093i	0.603216	+	1.06671i
$56$		0			0
$57$	1.07385	+	9.82633i	0.142235	+	1.30153i
$58$	4.61336	+	2.66353i	0.605764	+	0.349738i
$59$	−0.495925	−	0.858968i	−0.0645640	−	0.111828i	0.831937	−	0.554871i	$-0.187232\pi$
$59$	−0.495925	−	0.858968i	−0.0645640	−	0.111828i	−0.896500	+	0.443043i	$0.853899\pi$
$60$	4.18008	+	1.88523i	0.539645	+	0.243382i
$61$	−5.33892	−	3.08243i	−0.683578	−	0.394664i	0.117624	−	0.993058i	$-0.462472\pi$
$61$	−5.33892	−	3.08243i	−0.683578	−	0.394664i	−0.801202	+	0.598394i	$0.795806\pi$
$62$		−	1.68986i		−	0.214612i
$63$		0			0
$64$	5.46898			0.683622
$65$	0.0576274	−	6.44628i	0.00714780	−	0.799563i
$66$	−5.12924	+	3.75908i	−0.631366	+	0.462711i
$67$	8.73843	−	5.04513i	1.06757	−	0.616361i	0.140053	−	0.990144i	$-0.455273\pi$
$67$	8.73843	−	5.04513i	1.06757	−	0.616361i	0.927516	+	0.373783i	$0.121939\pi$
$68$	6.83773	+	3.94776i	0.829196	+	0.478737i
$69$	2.80973	−	0.307054i	0.338251	−	0.0369650i
$70$		0			0
$71$			4.81213i			0.571095i	0.958365	+	0.285548i	$0.0921755\pi$
$71$			4.81213i			0.571095i	−0.958365	+	0.285548i	$0.907825\pi$
$72$	−2.59850	+	8.22807i	−0.306237	+	0.969687i
$73$	0.280309	+	0.485510i	0.0328077	+	0.0568246i	0.881963	−	0.471319i	$-0.156222\pi$
$73$	0.280309	+	0.485510i	0.0328077	+	0.0568246i	−0.849155	+	0.528143i	$0.822888\pi$
$74$	−1.25149	+	0.722548i	−0.145483	+	0.0839946i
$75$	−4.99357	−	7.07561i	−0.576608	−	0.817021i
$76$			6.75699i			0.775079i
$77$		0			0
$78$	4.48410	−	0.490034i	0.507724	−	0.0554854i
$79$	−1.89924	+	3.28958i	−0.213681	+	0.370106i	−0.952864	−	0.303399i	$-0.901879\pi$
$79$	−1.89924	+	3.28958i	−0.213681	+	0.370106i	0.739183	+	0.673505i	$0.235212\pi$
$80$	−0.443528	−	0.261385i	−0.0495879	−	0.0292237i
$81$	−7.36757	−	5.16904i	−0.818619	−	0.574338i
$82$	−4.12033	+	7.13661i	−0.455014	+	0.788107i
$83$		−	4.00431i		−	0.439530i	−0.975553	−	0.219765i	$-0.929471\pi$
$83$		−	4.00431i		−	0.439530i	0.975553	−	0.219765i	$-0.0705291\pi$
$84$		0			0
$85$	−7.34003	−	12.9799i	−0.796138	−	1.40787i
$86$	−5.89364	−	3.40269i	−0.635527	−	0.366922i
$87$	−8.23845	+	6.03774i	−0.883255	+	0.647314i
$88$	−10.1238	+	5.84500i	−1.07920	+	0.623079i
$89$	5.20547	−	9.01615i	0.551779	−	0.955710i	−0.446367	−	0.894850i	$-0.647282\pi$
$89$	5.20547	−	9.01615i	0.551779	−	0.955710i	0.998146	−	0.0608597i	$-0.0193842\pi$
$90$	4.50604	−	4.05173i	0.474978	−	0.427090i
$91$		0			0
$92$	1.93208			0.201433
$93$	2.96541	+	1.30564i	0.307499	+	0.135388i
$94$	−5.40928	+	3.12305i	−0.557925	+	0.322118i
$95$	6.47917	−	10.9941i	0.664749	−	1.12797i
$96$	−3.86972	+	8.78907i	−0.394952	+	0.897031i
$97$	−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
$100$	−2.86782	−	5.17888i	−0.286782	−	0.517888i
$101$	−6.89867	−	11.9488i	−0.686443	−	1.18895i	−0.972981	−	0.230886i	$-0.925838\pi$
$101$	−6.89867	−	11.9488i	−0.686443	−	1.18895i	0.286538	−	0.958069i	$-0.407496\pi$
$102$	8.41583	−	6.16773i	0.833291	−	0.610697i
$103$	4.15679	−	7.19978i	0.409581	−	0.709415i	−0.585262	−	0.810844i	$-0.699008\pi$
$103$	4.15679	−	7.19978i	0.409581	−	0.709415i	0.994843	+	0.101429i	$0.0323416\pi$
$104$	8.29206			0.813104
$105$		0			0
$106$	1.37186			0.133246
$107$	5.36854	−	9.29858i	0.518996	−	0.898927i	−0.480760	−	0.876852i	$-0.659639\pi$
$107$	5.36854	−	9.29858i	0.518996	−	0.898927i	0.999756	−	0.0220754i	$-0.00702739\pi$
$108$	−4.62259	−	4.05961i	−0.444809	−	0.390636i
$109$	−0.268338	−	0.464774i	−0.0257021	−	0.0445173i	0.852888	−	0.522093i	$-0.174849\pi$
$109$	−0.268338	−	0.464774i	−0.0257021	−	0.0445173i	−0.878590	+	0.477576i	$0.841515\pi$
$110$	8.20941	+	0.0733891i	0.782736	+	0.00699737i
$111$	−0.301010	−	2.75441i	−0.0285706	−	0.261437i
$112$		0			0
$113$	−12.1028			−1.13854			−0.569270	−	0.822151i	$-0.692774\pi$
$113$	−12.1028			−1.13854			−0.569270	+	0.822151i	$0.692774\pi$
$114$	8.17230	+	3.59817i	0.765406	+	0.336999i
$115$	−3.14364	−	1.85264i	−0.293146	−	0.172760i
$116$	−6.04660	+	3.49101i	−0.561413	+	0.324132i
$117$	−2.60462	+	8.24743i	−0.240797	+	0.762476i
$118$	−0.895977			−0.0824813
$119$		0			0
$120$	9.04344	−	6.50424i	0.825549	−	0.593753i
$121$	2.75956	−	4.77971i	0.250870	−	0.434519i
$122$	−4.82285	+	2.78447i	−0.436640	+	0.252094i
$123$	−9.34004	−	12.7444i	−0.842163	−	1.14913i
$124$	1.91812	+	1.10743i	0.172252	+	0.0994497i
$125$	−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	$0.547508\pi$
$128$	−3.07427	+	5.32480i	−0.271730	+	0.470650i
$129$	10.5247	−	7.71330i	0.926651	−	0.679118i
$130$	−5.01699	−	2.95667i	−0.440019	−	0.259317i
$131$	0.0570895	−	0.0988819i	0.00498793	−	0.00863935i	−0.863521	−	0.504313i	$-0.831746\pi$
$131$	0.0570895	−	0.0988819i	0.00498793	−	0.00863935i	0.868509	+	0.495674i	$0.165079\pi$
$132$	−0.905465	−	8.28553i	−0.0788106	−	0.721163i
$133$		0			0
$134$		−	9.11493i		−	0.787410i
$135$	3.62859	+	11.0378i	0.312300	+	0.949984i
$136$	16.6107	−	9.59021i	1.42436	−	0.822353i
$137$	−6.27188	−	10.8632i	−0.535842	−	0.928106i	−0.999122	−	0.0418942i	$-0.986661\pi$
$137$	−6.27188	−	10.8632i	−0.535842	−	0.928106i	0.463280	−	0.886212i	$-0.346673\pi$
$138$	1.02885	−	2.33678i	0.0875819	−	0.198920i
$139$			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
$142$	3.76460	+	2.17349i	0.315918	+	0.182395i
$143$	−10.1477	+	5.85876i	−0.848590	+	0.489934i
$144$	0.466395	+	0.509456i	0.0388663	+	0.0424547i
$145$	13.1857	+	0.117876i	1.09502	+	0.00978903i
$146$	0.506428			0.0419123
$147$		0			0
$148$		−	1.89405i		−	0.155690i
$149$	−14.2621	−	8.23423i	−1.16840	−	0.674575i	−0.215096	−	0.976593i	$-0.569006\pi$
$149$	−14.2621	−	8.23423i	−1.16840	−	0.674575i	−0.953302	+	0.302018i	$0.902340\pi$
$150$	−7.79079	+	0.710705i	−0.636116	+	0.0580288i
$151$	6.57364	+	11.3859i	0.534955	+	0.926569i	0.999166	+	0.0408444i	$0.0130048\pi$
$151$	6.57364	+	11.3859i	0.534955	+	0.926569i	−0.464211	+	0.885725i	$0.653662\pi$
$152$	14.2154	+	8.20729i	1.15302	+	0.665699i
$153$	4.32099	+	19.5337i	0.349332	+	1.57921i
$154$		0			0
$155$	−2.05902	−	3.64111i	−0.165385	−	0.292461i
$156$	−2.38236	+	5.41092i	−0.190742	+	0.433220i
$157$	1.59406	+	2.76100i	0.127220	+	0.220352i	0.922599	−	0.385761i	$-0.126061\pi$
$157$	1.59406	+	2.76100i	0.127220	+	0.220352i	−0.795378	+	0.606113i	$0.792728\pi$
$158$	1.71565	+	2.97160i	0.136490	+	0.236408i
$159$	−1.05994	+	2.40737i	−0.0840584	+	0.190917i
$160$	10.7918	−	6.10265i	0.853163	−	0.482457i
$161$		0			0
$162$	−7.37152	+	3.42906i	−0.579161	+	0.269412i
$163$	−16.6965	−	9.63970i	−1.30777	−	0.755040i	−0.326044	−	0.945354i	$-0.605716\pi$
$163$	−16.6965	−	9.63970i	−1.30777	−	0.755040i	−0.981723	+	0.190314i	$0.939049\pi$
$164$	−5.40039	−	9.35375i	−0.421700	−	0.730405i
$165$	−6.47162	+	14.3494i	−0.503815	+	1.11710i
$166$	−3.13263	−	1.80863i	−0.243139	−	0.140377i
$167$			0.883913i			0.0683993i	0.999415	+	0.0341996i	$0.0108882\pi$
$167$			0.883913i			0.0683993i	−0.999415	+	0.0341996i	$0.989112\pi$
$168$		0			0
$169$	−4.68842			−0.360648
$170$	−13.4696	−	0.120413i	−1.03307	−	0.00923529i
$171$	−12.6283	+	11.5609i	−0.965712	+	0.884087i
$172$	7.72462	−	4.45981i	0.588996	−	0.340057i
$173$	10.8393	+	6.25807i	0.824097	+	0.475793i	0.851827	−	0.523823i	$-0.175495\pi$
$173$	10.8393	+	6.25807i	0.824097	+	0.475793i	−0.0277303	+	0.999615i	$0.508828\pi$
$174$	1.00235	+	9.17212i	0.0759882	+	0.695337i
$175$		0			0
$176$			0.935758i			0.0705354i
$177$	0.692258	−	1.57228i	0.0520333	−	0.118180i
$178$	−4.70231	−	8.14463i	−0.352453	−	0.610466i
$179$	10.5358	−	6.08284i	0.787481	−	0.454653i	−0.0515938	−	0.998668i	$-0.516430\pi$
$179$	10.5358	−	6.08284i	0.787481	−	0.454653i	0.839075	+	0.544016i	$0.183097\pi$
$180$	1.64605	+	7.76993i	0.122689	+	0.579137i
$181$		−	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
$184$	2.34678	−	4.06474i	0.173007	−	0.299657i
$185$	−1.81617	+	3.08175i	−0.133528	+	0.226575i
$186$	2.36080	−	1.73017i	0.173103	−	0.126862i
$187$	−13.5519	+	23.4726i	−0.991014	+	1.71649i
$188$		−	8.18658i		−	0.597068i
$189$		0			0
$190$	−5.67440	−	10.0344i	−0.411664	−	0.727975i
$191$	7.16890	+	4.13896i	0.518723	+	0.299485i	0.736412	−	0.676533i	$-0.236518\pi$
$191$	7.16890	+	4.13896i	0.518723	+	0.299485i	−0.217689	+	0.976018i	$0.569852\pi$
$192$	5.59943	+	7.64039i	0.404104	+	0.551397i
$193$	13.7918	−	7.96267i	0.992752	−	0.573166i	0.0866562	−	0.996238i	$-0.472382\pi$
$193$	13.7918	−	7.96267i	0.992752	−	0.573166i	0.906096	+	0.423073i	$0.139048\pi$
$194$	−6.56593	+	11.3725i	−0.471406	+	0.816499i
$195$	9.06473	−	6.51954i	0.649138	−	0.466874i
$196$		0			0
$197$	−23.8738			−1.70094			−0.850468	−	0.526027i	$-0.823681\pi$
$197$	−23.8738			−1.70094			−0.850468	+	0.526027i	$0.823681\pi$
$198$	−10.5032	−	3.31701i	−0.746429	−	0.235730i
$199$	−10.5891	+	6.11364i	−0.750643	+	0.433384i	−0.825926	−	0.563778i	$-0.809347\pi$
$199$	−10.5891	+	6.11364i	−0.750643	+	0.433384i	0.0752829	+	0.997162i	$0.476014\pi$
$200$	−14.3788	−	0.257102i	−1.01673	−	0.0181799i
$201$	15.9951	+	7.04246i	1.12821	+	0.496737i
$202$	−12.4637			−0.876941
$203$		0			0
$204$	1.48565	+	13.5945i	0.104016	+	0.951807i
$205$	−0.182347	+	20.3976i	−0.0127357	+	1.42463i
$206$	−3.75499	−	6.50384i	−0.261623	−	0.453144i
$207$	3.30572	+	3.61093i	0.229763	+	0.250977i
$208$	0.331880	−	0.574834i	0.0230118	−	0.0398576i
$209$	−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	$0.275051\pi$
$212$	−0.899025	+	1.55716i	−0.0617453	+	0.106946i
$213$	−6.72275	+	4.92692i	−0.460635	+	0.337587i
$214$	−4.84961	−	8.39976i	−0.331512	−	0.574196i
$215$	−16.8450	−	0.150588i	−1.14882	−	0.0102700i
$216$	−14.1554	+	4.79412i	−0.963156	+	0.326199i
$217$		0			0
$218$	−0.484799			−0.0328348
$219$	−0.391282	+	0.888695i	−0.0264404	+	0.0600524i
$220$	−5.46322	+	9.27019i	−0.368330	+	0.624996i
$221$	16.6498	−	9.61278i	1.11999	−	0.646625i
$222$	−2.29077	−	1.00860i	−0.153747	−	0.0676928i
$223$	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
$225$	4.77223	−	14.2206i	0.318149	−	0.948041i
$226$	−5.46649	+	9.46823i	−0.363625	+	0.629817i
$227$	−9.96079	+	5.75087i	−0.661121	+	0.381698i	−0.792704	−	0.609607i	$-0.791327\pi$
$227$	−9.96079	+	5.75087i	−0.661121	+	0.381698i	0.131583	+	0.991305i	$0.457994\pi$
$228$	−9.43979	+	6.91816i	−0.625165	+	0.458167i
$229$	−15.0457	−	8.68661i	−0.994245	−	0.574028i	−0.0877044	−	0.996147i	$-0.527953\pi$
$229$	−15.0457	−	8.68661i	−0.994245	−	0.574028i	−0.906540	+	0.422119i	$0.861286\pi$
$230$	−2.86923	+	1.62253i	−0.189192	+	0.106986i
$231$		0			0
$232$			16.9612i			1.11356i
$233$	−0.231425	+	0.400840i	−0.0151611	+	0.0262599i	−0.873506	−	0.486813i	$-0.838159\pi$
$233$	−0.231425	+	0.400840i	−0.0151611	+	0.0262599i	0.858345	+	0.513072i	$0.171493\pi$
$234$	5.27566	+	5.76274i	0.344881	+	0.376722i
$235$	−7.84999	+	13.3202i	−0.512077	+	0.868911i
$236$	0.587165	−	1.01700i	0.0382212	−	0.0662011i
$237$	−6.54021	+	0.714732i	−0.424833	+	0.0464268i
$238$		0			0
$239$			17.3055i			1.11940i	0.828696	+	0.559699i	$0.189083\pi$
$239$			17.3055i			1.11940i	−0.828696	+	0.559699i	$0.810917\pi$
$240$	−0.0889421	−	0.887246i	−0.00574119	−	0.0572715i
$241$	3.70606	−	2.13970i	0.238729	−	0.137830i	−0.375864	−	0.926675i	$-0.622654\pi$
$241$	3.70606	−	2.13970i	0.238729	−	0.137830i	0.614592	+	0.788845i	$0.289321\pi$
$242$	−2.49282	−	4.31769i	−0.160245	−	0.277552i
$243$	−0.321951	−	15.5851i	−0.0206532	−	0.999787i
$244$		−	7.29906i		−	0.467274i
$245$		0			0
$246$	−14.1888	+	1.55058i	−0.904642	+	0.0988617i
$247$	14.2489	+	8.22661i	0.906636	+	0.523446i
$248$	4.65963	−	2.69024i	0.295887	−	0.170830i
$249$	5.59419	−	4.09983i	0.354517	−	0.259816i
$250$	8.60798	+	5.28254i	0.544417	+	0.334097i
$251$	17.4145			1.09919			0.549597	−	0.835430i	$-0.314781\pi$
$251$	17.4145			1.09919			0.549597	+	0.835430i	$0.314781\pi$
$252$		0			0
$253$			6.63247i			0.416980i
$254$	17.4364	+	10.0669i	1.09406	+	0.631656i
$255$	10.6183	−	23.5438i	0.664946	−	1.47437i
$256$	8.24609	+	14.2826i	0.515381	+	0.892665i
$257$	−13.3507	−	7.70805i	−0.832796	−	0.480815i	0.0220130	−	0.999758i	$-0.492992\pi$
$257$	−13.3507	−	7.70805i	−0.832796	−	0.480815i	−0.854809	+	0.518943i	$0.826326\pi$
$258$	−1.28052	−	11.7175i	−0.0797217	−	0.729500i
$259$		0			0
$260$	6.64385	−	3.75704i	0.412034	−	0.233002i
$261$	−16.8699	−	5.32769i	−1.04422	−	0.329776i
$262$	−0.0515711	−	0.0893238i	−0.00318607	−	0.00551844i
$263$	3.10585	+	5.37949i	0.191515	+	0.331714i	0.945752	−	0.324888i	$-0.105327\pi$
$263$	3.10585	+	5.37949i	0.191515	+	0.331714i	−0.754238	+	0.656602i	$0.771993\pi$
$264$	−18.5310	−	8.15899i	−1.14051	−	0.502151i
$265$	2.95591	−	1.67155i	0.181580	−	0.102682i
$266$		0			0
$267$	17.9256	−	1.95895i	1.09703	−	0.119886i
$268$	10.3461	+	5.97333i	0.631990	+	0.364879i
$269$	2.99535	+	5.18810i	0.182630	+	0.316324i	0.942775	−	0.333429i	$-0.108206\pi$
$269$	2.99535	+	5.18810i	0.182630	+	0.316324i	−0.760146	+	0.649753i	$0.774872\pi$
$270$	10.2740	+	2.14674i	0.625253	+	0.130647i
$271$	−5.40846	−	3.12257i	−0.328540	−	0.189683i	0.326652	−	0.945145i	$-0.394079\pi$
$271$	−5.40846	−	3.12257i	−0.328540	−	0.189683i	−0.655193	+	0.755462i	$0.727413\pi$
$272$		−	1.53535i		−	0.0930942i
$273$		0			0
$274$	−11.3313			−0.684546
$275$	17.7781	−	9.84467i	1.07206	−	0.593656i
$276$	1.97817	+	2.69920i	0.119072	+	0.162473i
$277$	7.53810	−	4.35212i	0.452920	−	0.261494i	−0.256142	−	0.966639i	$-0.582452\pi$
$277$	7.53810	−	4.35212i	0.452920	−	0.261494i	0.709063	+	0.705145i	$0.249118\pi$
$278$	1.85909	+	1.07335i	0.111501	+	0.0643751i
$279$	1.21212	+	5.47959i	0.0725679	+	0.328054i
$280$		0			0
$281$			4.36274i			0.260259i	0.991497	+	0.130130i	$0.0415393\pi$
$281$			4.36274i			0.260259i	−0.991497	+	0.130130i	$0.958461\pi$
$282$	−9.90134	−	4.35944i	−0.589616	−	0.259601i
$283$	3.76038	+	6.51316i	0.223531	+	0.387167i	0.955878	−	0.293765i	$-0.0949082\pi$
$283$	3.76038	+	6.51316i	0.223531	+	0.387167i	−0.732347	+	0.680932i	$0.761575\pi$
$284$	−4.93415	+	2.84873i	−0.292788	+	0.169041i
$285$	21.9929	−	2.20468i	1.30275	−	0.130594i
$286$			10.5849i			0.625897i
$287$		0			0
$288$	−16.2407	+	3.59256i	−0.956994	+	0.211694i
$289$	13.7354	−	23.7904i	0.807963	−	1.39943i
$290$	6.04781	−	10.2621i	0.355139	−	0.602614i
$291$	−14.8838	−	20.3088i	−0.872503	−	1.19052i
$292$	−0.331880	+	0.574834i	−0.0194218	+	0.0336396i
$293$		−	0.105885i		−	0.00618587i	−0.999995	−	0.00309293i	$-0.999015\pi$
$293$		−	0.105885i		−	0.00618587i	0.999995	−	0.00309293i	$-0.000984513\pi$
$294$		0			0
$295$	−1.93055	+	1.09171i	−0.112401	+	0.0635617i
$296$	−3.98472	−	2.30058i	−0.231607	−	0.133718i
$297$	13.9359	−	15.8685i	0.808641	−	0.920782i
$298$	−12.8835	+	7.43830i	−0.746322	+	0.430889i
$299$	2.35230	−	4.07431i	0.136037	−	0.235623i
$300$	4.29888	−	9.30888i	0.248196	−	0.537448i
$301$		0			0
$302$	11.8764			0.683412
$303$	9.62980	−	21.8716i	0.553218	−	1.25649i
$304$	1.13791	−	0.656975i	0.0652638	−	0.0376801i
$305$	−6.99896	+	11.8761i	−0.400759	+	0.680023i
$306$	17.2332	+	5.44240i	0.985154	+	0.311121i
$307$	−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
$310$	−3.77849	−	0.0337783i	−0.214604	−	0.00191848i
$311$	12.6572	+	21.9228i	0.717722	+	1.24313i	0.961900	+	0.273400i	$0.0881483\pi$
$311$	12.6572	+	21.9228i	0.717722	+	1.24313i	−0.244179	+	0.969730i	$0.578518\pi$
$312$	8.48986	+	11.5844i	0.480644	+	0.655835i
$313$	3.82491	−	6.62494i	0.216197	−	0.374464i	−0.737445	−	0.675407i	$-0.763968\pi$
$313$	3.82491	−	6.62494i	0.216197	−	0.374464i	0.953642	+	0.300943i	$0.0973014\pi$
$314$	2.87996			0.162526
$315$		0			0
$316$	−4.49732			−0.252994
$317$	−12.3732	+	21.4311i	−0.694950	+	1.20369i	0.275247	+	0.961374i	$0.411240\pi$
$317$	−12.3732	+	21.4311i	−0.694950	+	1.20369i	−0.970197	+	0.242316i	$0.922093\pi$
$318$	1.40458	+	1.91654i	0.0787649	+	0.107474i
$319$	−11.9840	−	20.7568i	−0.670973	−	1.16216i
$320$	0.109318	−	12.2285i	0.00611109	−	0.683595i
$321$	18.4871	−	2.02032i	1.03185	−	0.112763i
$322$		0			0
$323$	38.0580			2.11760
$324$	0.938583	−	10.6144i	0.0521435	−	0.589689i
$325$	−14.4126	−	0.257707i	−0.799467	−	0.0142950i
$326$	−15.0826	+	8.70792i	−0.835346	+	0.482287i
$327$	0.374570	−	0.850740i	0.0207138	−	0.0470460i
$328$	−26.2381			−1.44875
$329$		0			0
$330$	8.30270	+	11.5440i	0.457049	+	0.635477i
$331$	8.17810	−	14.1649i	0.449509	−	0.778573i	−0.548845	−	0.835924i	$-0.684932\pi$
$331$	8.17810	−	14.1649i	0.449509	−	0.778573i	0.998354	+	0.0573514i	$0.0182655\pi$
$332$	4.10585	−	2.37051i	0.225338	−	0.130099i
$333$	3.53984	−	3.24064i	0.193982	−	0.177586i
$334$	0.691498	+	0.399237i	0.0378371	+	0.0218453i
$335$	−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	$0.968804\pi$
$338$	−2.11762	+	3.66782i	−0.115183	+	0.199503i
$339$	−12.3915	−	16.9082i	−0.673017	−	0.918326i
$340$	8.96380	−	15.2101i	0.486130	−	0.824884i
$341$	−3.80158	+	6.58453i	−0.205867	+	0.356572i
$342$	3.34046	+	15.1010i	0.180631	+	0.816571i
$343$		0			0
$344$		−	21.6682i		−	1.16827i
$345$	−0.630404	−	6.28863i	−0.0339398	−	0.338568i
$346$	9.79156	−	5.65316i	0.526398	−	0.303916i
$347$	9.46440	+	16.3928i	0.508075	+	0.880012i	0.999956	+	0.00934990i	$0.00297621\pi$
$347$	9.46440	+	16.3928i	0.508075	+	0.880012i	−0.491881	+	0.870662i	$0.663690\pi$
$348$	−11.0679	−	4.87307i	−0.593302	−	0.261224i
$349$			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
$352$	−19.5156	−	11.2673i	−1.04019	−	0.600551i
$353$	27.8032	−	16.0522i	1.47982	−	0.854373i	0.480078	−	0.877226i	$-0.340608\pi$
$353$	27.8032	−	16.0522i	1.47982	−	0.854373i	0.999739	+	0.0228526i	$0.00727484\pi$
$354$	−0.917349	−	1.25172i	−0.0487566	−	0.0665280i
$355$	10.7598	+	0.0961889i	0.571072	+	0.00510518i
$356$	12.3263			0.653295
$357$		0			0
$358$		−	10.9897i		−	0.580825i
$359$	14.7805	+	8.53352i	0.780085	+	0.450382i	0.836460	−	0.548027i	$-0.184621\pi$
$359$	14.7805	+	8.53352i	0.780085	+	0.450382i	−0.0563756	+	0.998410i	$0.517954\pi$
$360$	18.3458	+	5.97467i	0.966911	+	0.314893i
$361$	6.78500	+	11.7520i	0.357105	+	0.618524i
$362$	−12.6557	−	7.30678i	−0.665169	−	0.384036i
$363$	9.50284	−	1.03850i	0.498770	−	0.0545069i
$364$		0			0
$365$	1.09119	−	0.617061i	0.0571157	−	0.0322984i
$366$	−8.82792	−	3.88683i	−0.461443	−	0.203168i
$367$	7.83753	+	13.5750i	0.409116	+	0.708609i	0.994791	−	0.101937i	$-0.0325040\pi$
$367$	7.83753	+	13.5750i	0.409116	+	0.708609i	−0.585675	+	0.810546i	$0.699171\pi$
$368$	−0.187854	−	0.325373i	−0.00979259	−	0.0169613i
$369$	8.24164	−	26.0968i	0.429043	−	1.35855i
$370$	1.59059	+	2.81275i	0.0826907	+	0.146228i
$371$		0			0
$372$	0.416753	+	3.81353i	0.0216076	+	0.197722i
$373$	0.908235	+	0.524370i	0.0470266	+	0.0271508i	0.523329	−	0.852131i	$-0.324690\pi$
$373$	0.908235	+	0.524370i	0.0470266	+	0.0271508i	−0.476302	+	0.879282i	$0.658023\pi$
$374$	12.2420	+	21.2037i	0.633017	+	1.09642i
$375$	−15.9207	+	11.0241i	−0.822143	+	0.569281i
$376$	−17.2230	−	9.94373i	−0.888211	−	0.512809i
$377$			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	$0.669037\pi$
$380$	15.1085	+	0.135064i	0.775048	+	0.00692865i
$381$	−31.1376	+	22.8199i	−1.59523	+	1.16910i
$382$	6.47594	−	3.73889i	0.331338	−	0.191298i
$383$	−2.38931	−	1.37947i	−0.122088	−	0.0704876i	0.437712	−	0.899115i	$-0.355789\pi$
$383$	−2.38931	−	1.37947i	−0.122088	−	0.0704876i	−0.559800	+	0.828628i	$0.689122\pi$
$384$	−10.5866	+	1.15693i	−0.540244	+	0.0590392i
$385$		0			0
$386$		−	14.3860i		−	0.732227i
$387$	21.5516	+	6.80620i	1.09553	+	0.345979i
$388$	−8.60577	−	14.9056i	−0.436892	−	0.756719i
$389$	−27.6283	+	15.9512i	−1.40081	+	0.808758i	−0.994476	−	0.104966i	$-0.966527\pi$
$389$	−27.6283	+	15.9512i	−1.40081	+	0.808758i	−0.406335	+	0.913724i	$0.633193\pi$
$390$	−1.00607	−	10.0361i	−0.0509445	−	0.508200i
$391$		−	10.8822i		−	0.550339i
$392$		0			0
$393$	0.196593	−	0.0214842i	0.00991682	−	0.00108374i
$394$	−10.7831	+	18.6768i	−0.543242	+	0.940923i
$395$	7.31746	+	4.31241i	0.368181	+	0.216981i
$396$	10.6482	−	9.74814i	0.535090	−	0.489863i
$397$	9.41023	−	16.2990i	0.472286	−	0.818023i	−0.527211	−	0.849734i	$-0.676762\pi$
$397$	9.41023	−	16.2990i	0.472286	−	0.818023i	0.999497	+	0.0317111i	$0.0100957\pi$
$398$			11.0454i			0.553654i
$399$		0			0
$400$	−0.593317	+	0.986494i	−0.0296658	+	0.0493247i
$401$	2.84850	+	1.64458i	0.142247	+	0.0821266i	0.569435	−	0.822037i	$-0.307162\pi$
$401$	2.84850	+	1.64458i	0.142247	+	0.0821266i	−0.427187	+	0.904163i	$0.640495\pi$
$402$	12.7339	−	9.33235i	0.635111	−	0.465455i
$403$	4.67060	−	2.69657i	0.232659	−	0.134326i
$404$	8.16788	−	14.1472i	0.406367	−	0.703849i
$405$	−11.7051	+	16.3704i	−0.581633	+	0.813452i
$406$		0			0
$407$	6.50190			0.322287
$408$	30.4049	+	13.3869i	1.50527	+	0.662750i
$409$	3.59326	−	2.07457i	0.177675	−	0.102581i	−0.408525	−	0.912747i	$-0.633957\pi$
$409$	3.59326	−	2.07457i	0.177675	−	0.102581i	0.586200	+	0.810166i	$0.300623\pi$
$410$	15.8750	+	9.35561i	0.784008	+	0.462041i
$411$	8.75486	−	19.8844i	0.431845	−	0.980825i
$412$	9.84311			0.484935
$413$		0			0
$414$	4.31797	−	0.955165i	0.212217	−	0.0469438i
$415$	−8.95356	−	0.0800415i	−0.439513	−	0.00392908i
$416$	7.99226	+	13.8430i	0.391853	+	0.678709i
$417$	−3.31993	+	2.43309i	−0.162578	+	0.119149i
$418$	−10.4767	+	18.1461i	−0.512430	+	0.887555i
$419$	22.6231			1.10521			0.552606	−	0.833443i	$-0.313633\pi$
$419$	22.6231			1.10521			0.552606	+	0.833443i	$0.313633\pi$
$420$		0			0
$421$	31.9233			1.55584			0.777922	−	0.628360i	$-0.216274\pi$
$421$	31.9233			1.55584			0.777922	+	0.628360i	$0.216274\pi$
$422$	8.52030	−	14.7576i	0.414762	−	0.718389i
$423$	15.3001	−	14.0069i	0.743918	−	0.681040i
$424$	2.18398	+	3.78276i	0.106063	+	0.183707i
$425$	−29.1695	+	16.1527i	−1.41493	+	0.783521i
$426$	0.817941	+	7.48464i	0.0396294	+	0.362632i
$427$		0			0
$428$	12.7125			0.614481
$429$	−18.5746	−	8.17819i	−0.896792	−	0.394847i
$430$	−7.72615	+	13.1100i	−0.372588	+	0.632222i
$431$	21.6894	−	12.5224i	1.04474	−	0.603182i	0.123569	−	0.992336i	$-0.460566\pi$
$431$	21.6894	−	12.5224i	1.04474	−	0.603182i	0.921173	+	0.389154i	$0.127233\pi$
$432$	−0.234211	+	1.17318i	−0.0112685	+	0.0564447i
$433$	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
$435$	13.3356	+	18.5417i	0.639392	+	0.889006i
$436$	0.317706	−	0.550283i	0.0152154	−	0.0263538i
$437$	8.06531	−	4.65651i	0.385816	−	0.222751i
$438$	0.518509	+	0.707501i	0.0247753	+	0.0338057i
$439$	9.77568	+	5.64399i	0.466568	+	0.269373i	0.714802	−	0.699327i	$-0.246517\pi$
$439$	9.77568	+	5.64399i	0.466568	+	0.269373i	−0.248234	+	0.968700i	$0.579850\pi$
$440$	12.8669	+	22.7535i	0.613407	+	1.08473i
$441$		0			0
$442$		−	17.3672i		−	0.826073i
$443$	−10.9591	+	18.9817i	−0.520681	+	0.901847i	0.479029	+	0.877799i	$0.340989\pi$
$443$	−10.9591	+	18.9817i	−0.520681	+	0.901847i	−0.999711	+	0.0240479i	$0.992345\pi$
$444$	2.64606	−	1.93923i	0.125576	−	0.0920316i
$445$	−20.0559	−	11.8196i	−0.950739	−	0.560301i
$446$	8.70725	−	15.0814i	0.412300	−	0.714125i
$447$	−3.09875	−	28.3554i	−0.146566	−	1.34116i
$448$		0			0
$449$			0.449397i			0.0212083i	0.999944	+	0.0106042i	$0.00337548\pi$
$449$			0.449397i			0.0212083i	−0.999944	+	0.0106042i	$0.996625\pi$
$450$	−8.96952	−	10.1564i	−0.422827	−	0.478777i
$451$	32.1096	−	18.5385i	1.51198	−	0.872944i
$452$	−7.16476	−	12.4097i	−0.337002	−	0.583705i
$453$	−9.17609	+	20.8411i	−0.431130	+	0.979201i
$454$			10.3900i			0.487625i
$455$		0			0
$456$	3.08861	+	28.2626i	0.144638	+	1.32352i
$457$	−8.04787	−	4.64644i	−0.376463	−	0.217351i	0.299815	−	0.953997i	$-0.403075\pi$
$457$	−8.04787	−	4.64644i	−0.376463	−	0.217351i	−0.676278	+	0.736646i	$0.736408\pi$
$458$	−13.5913	+	7.84695i	−0.635081	+	0.366664i
$459$	−22.8653	+	26.0363i	−1.06726	+	1.21527i
$460$	0.0386201	−	4.32009i	0.00180067	−	0.201425i
$461$	−20.8668			−0.971863			−0.485931	−	0.873997i	$-0.661519\pi$
$461$	−20.8668			−0.971863			−0.485931	+	0.873997i	$0.661519\pi$
$462$		0			0
$463$		−	2.45294i		−	0.113998i	−0.998374	−	0.0569989i	$-0.981847\pi$
$463$		−	2.45294i		−	0.113998i	0.998374	−	0.0569989i	$-0.0181532\pi$
$464$	1.17581	+	0.678854i	0.0545856	+	0.0315150i
$465$	2.97865	−	6.60450i	0.138132	−	0.306277i
$466$	0.209055	+	0.362094i	0.00968429	+	0.0167737i
$467$	6.91084	+	3.98997i	0.319795	+	0.184634i	0.651301	−	0.758819i	$-0.274223\pi$
$467$	6.91084	+	3.98997i	0.319795	+	0.184634i	−0.331506	+	0.943453i	$0.607557\pi$
$468$	−9.99847	+	2.21173i	−0.462179	+	0.102237i
$469$		0			0
$470$	6.87495	+	12.1575i	0.317118	+	0.560782i
$471$	−2.22514	+	5.05384i	−0.102529	+	0.232868i
$472$	−1.42639	−	2.47057i	−0.0656547	−	0.113717i
$473$	15.3097	+	26.5171i	0.703939	+	1.21926i
$474$	−2.39487	+	5.43932i	−0.110000	+	0.249836i
$475$	−24.4531	−	14.7071i	−1.12198	−	0.674806i
$476$		0			0
$477$	−4.44841	+	0.984021i	−0.203679	+	0.0450552i
$478$	13.5383	+	7.81635i	0.619228	+	0.357511i
$479$	−6.94646	−	12.0316i	−0.317392	−	0.549739i	0.662551	−	0.749017i	$-0.269474\pi$
$479$	−6.94646	−	12.0316i	−0.317392	−	0.549739i	−0.979943	+	0.199278i	$0.936140\pi$
$480$	19.5748	+	8.82830i	0.893465	+	0.402955i
$481$	−3.99410	−	2.30599i	−0.182115	−	0.105144i
$482$		−	3.86574i		−	0.176080i
$483$		0			0
$484$	6.53454			0.297024
$485$	−0.290578	+	32.5045i	−0.0131945	+	1.47595i
$486$	−12.3379	−	6.78746i	−0.559658	−	0.307885i
$487$	−22.9590	+	13.2554i	−1.04037	+	0.600659i	−0.919939	−	0.392062i	$-0.871762\pi$
$487$	−22.9590	+	13.2554i	−1.04037	+	0.600659i	−0.120433	+	0.992721i	$0.538428\pi$
$488$	−15.3559	−	8.86571i	−0.695127	−	0.401332i
$489$	−3.62767	−	33.1953i	−0.164049	−	1.50114i
$490$		0			0
$491$		−	2.54611i		−	0.114905i	−0.998348	−	0.0574523i	$-0.981702\pi$
$491$		−	2.54611i		−	0.114905i	0.998348	−	0.0574523i	$-0.0182977\pi$
$492$	7.53836	−	17.1214i	0.339856	−	0.771894i
$493$	19.6627	+	34.0568i	0.885565	+	1.53384i
$494$	12.8716	−	7.43141i	0.579120	−	0.334355i
$495$	−26.6727	+	5.65057i	−1.19885	+	0.253974i
$496$		−	0.430695i		−	0.0193388i
$497$		0			0
$498$	−0.680632	−	6.22818i	−0.0304999	−	0.279091i
$499$	−14.8248	+	25.6773i	−0.663649	+	1.14947i	0.316001	+	0.948759i	$0.397660\pi$
$499$	−14.8248	+	25.6773i	−0.663649	+	1.14947i	−0.979650	+	0.200714i	$0.935674\pi$
$500$	−11.6372	+	6.30886i	−0.520431	+	0.282141i
$501$	−1.23486	+	0.904998i	−0.0551696	+	0.0404323i
$502$	7.86560	−	13.6236i	0.351059	−	0.608052i
$503$		−	31.2378i		−	1.39283i	−0.717642	−	0.696413i	$-0.754778\pi$
$503$		−	31.2378i		−	1.39283i	0.717642	−	0.696413i	$-0.245222\pi$
$504$		0			0
$505$	−26.8553	+	15.1864i	−1.19504	+	0.675787i
$506$	5.18867	+	2.99568i	0.230665	+	0.133174i
$507$	−4.80026	−	6.54992i	−0.213187	−	0.290892i
$508$	−22.8534	+	13.1944i	−1.01396	+	0.585408i
$509$	−19.0072	+	32.9214i	−0.842478	+	1.45921i	0.0453160	+	0.998973i	$0.485571\pi$
$509$	−19.0072	+	32.9214i	−0.842478	+	1.45921i	−0.887794	+	0.460242i	$0.847763\pi$
$510$	−13.6227	−	18.9409i	−0.603223	−	0.838717i
$511$		0			0
$512$	2.60093			0.114946
$513$	−29.0807	−	5.80558i	−1.28394	−	0.256323i
$514$	−12.0602	+	6.96298i	−0.531954	+	0.307124i
$515$	−16.0155	−	9.43841i	−0.705725	−	0.415906i
$516$	14.1394	+	6.22541i	0.622453	+	0.274059i
$517$	28.1030			1.23597
$518$		0			0
$519$	2.35507	+	21.5503i	0.103376	+	0.945953i
$520$	0.165749	−	18.5409i	0.00726856	−	0.813071i
$521$	19.5707	+	33.8974i	0.857407	+	1.48507i	0.874394	+	0.485217i	$0.161259\pi$
$521$	19.5707	+	33.8974i	0.857407	+	1.48507i	−0.0169866	+	0.999856i	$0.505407\pi$
$522$	−11.7876	+	10.7912i	−0.515928	+	0.472320i
$523$	3.98588	−	6.90375i	0.174290	−	0.301880i	−0.765625	−	0.643287i	$-0.777570\pi$
$523$	3.98588	−	6.90375i	0.174290	−	0.301880i	0.939915	+	0.341407i	$0.110904\pi$
$524$	0.135186			0.00590561
$525$		0			0
$526$	5.61127			0.244663
$527$	6.23745	−	10.8036i	0.271708	−	0.470612i
$528$	−1.30729	+	0.958079i	−0.0568926	+	0.0416950i
$529$	10.1685	+	17.6124i	0.442110	+	0.765757i
$530$	0.0274218	−	3.06744i	0.00119113	−	0.133241i
$531$	2.90532	−	0.642677i	0.126080	−	0.0278898i
$532$		0			0
$533$	−26.2998			−1.13917
$534$	6.56391	−	14.9082i	0.284048	−	0.645142i
$535$	−20.6841	−	12.1898i	−0.894252	−	0.527011i
$536$	25.1336	−	14.5109i	1.08560	−	0.626774i
$537$	19.2851	+	8.49098i	0.832212	+	0.366413i
$538$	5.41163			0.233312
$539$		0			0
$540$	−9.16960	+	10.2549i	−0.394597	+	0.441299i
$541$	4.04174	−	7.00049i	0.173768	−	0.300975i	−0.765966	−	0.642881i	$-0.777739\pi$
$541$	4.04174	−	7.00049i	0.173768	−	0.300975i	0.939734	+	0.341906i	$0.111072\pi$
$542$	−4.88567	+	2.82074i	−0.209857	+	0.121161i
$543$	22.6003	−	16.5632i	0.969872	−	0.710793i
$544$	32.0203	+	18.4869i	1.37286	+	0.792621i
$545$	−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	$-0.290919\pi$
$548$	7.42577	−	12.8618i	0.317213	−	0.549429i
$549$	13.6414	−	12.4884i	0.582202	−	0.532992i
$550$	0.328193	−	18.3546i	0.0139942	−	0.782642i
$551$	−16.8273	+	29.1458i	−0.716869	+	1.24165i
$552$	8.08137	−	0.883153i	0.343966	−	0.0375895i
$553$		0			0
$554$		−	7.86288i		−	0.334062i
$555$	−6.16483	+	0.617993i	−0.261682	+	0.0262324i
$556$	−2.43666	+	1.40680i	−0.103337	+	0.0596618i
$557$	4.44428	+	7.69772i	0.188310	+	0.326163i	0.944687	−	0.327973i	$-0.106366\pi$
$557$	4.44428	+	7.69772i	0.188310	+	0.326163i	−0.756377	+	0.654136i	$0.773032\pi$
$558$	4.83424	+	1.52670i	0.204650	+	0.0646303i
$559$		−	21.7192i		−	0.918624i
$560$		0			0
$561$	−46.6674	+	5.09993i	−1.97030	+	0.215319i
$562$	3.41303	+	1.97051i	0.143970	+	0.0831211i
$563$	−34.1282	+	19.7039i	−1.43833	+	0.830421i	−0.997734	−	0.0672831i	$-0.978567\pi$
$563$	−34.1282	+	19.7039i	−1.43833	+	0.830421i	−0.440598	+	0.897704i	$0.645234\pi$
$564$	11.4370	−	8.38186i	0.481584	−	0.352940i
$565$	−0.241922	+	27.0617i	−0.0101777	+	1.13849i
$566$	6.79378			0.285564
$567$		0			0
$568$			13.8407i			0.580744i
$569$	15.1146	+	8.72640i	0.633636	+	0.365830i	0.782159	−	0.623079i	$-0.214119\pi$
$569$	15.1146	+	8.72640i	0.633636	+	0.365830i	−0.148523	+	0.988909i	$0.547452\pi$
$570$	8.20878	−	18.2012i	0.343828	−	0.762363i
$571$	9.69444	+	16.7913i	0.405700	+	0.702692i	0.994403	−	0.105657i	$-0.0336946\pi$
$571$	9.69444	+	16.7913i	0.405700	+	0.702692i	−0.588703	+	0.808349i	$0.700361\pi$
$572$	−12.0146	−	6.93665i	−0.502357	−	0.290036i
$573$	1.55760	+	14.2529i	0.0650696	+	0.595425i
$574$		0			0
$575$	−4.20531	+	6.99207i	−0.175374	+	0.291590i
$576$	−4.94093	+	15.6453i	−0.205872	+	0.651887i
$577$	−20.8653	−	36.1397i	−0.868633	−	1.50452i	−0.863394	−	0.504531i	$-0.831665\pi$
$577$	−20.8653	−	36.1397i	−0.868633	−	1.50452i	−0.00523985	−	0.999986i	$-0.501668\pi$
$578$	−12.4077	−	21.4907i	−0.516092	−	0.893897i
$579$	25.2449	+	11.1150i	1.04914	+	0.461925i
$580$	7.68495	+	13.5899i	0.319100	+	0.564288i
$581$		0			0
$582$	−22.6104	+	2.47093i	−0.937232	+	0.102423i
$583$	−5.34542	−	3.08618i	−0.221385	−	0.127817i
$584$	0.806229	+	1.39643i	0.0333620	+	0.0577847i
$585$	18.3890	+	5.98873i	0.760293	+	0.247604i
$586$	−0.0828353	−	0.0478250i	−0.00342190	−	0.00197563i
$587$		−	19.5477i		−	0.806820i	−0.915019	−	0.403410i	$-0.867825\pi$
$587$		−	19.5477i		−	0.806820i	0.915019	−	0.403410i	$-0.132175\pi$
$588$		0			0
$589$	10.6760			0.439897
$590$	−0.0179095	+	2.00338i	−0.000737323	+	0.0824780i
$591$	−24.4433	−	33.3526i	−1.00546	−	1.37194i
$592$	−0.318968	+	0.184156i	−0.0131095	+	0.00756877i
$593$	−2.27890	−	1.31572i	−0.0935832	−	0.0540303i	0.452478	−	0.891776i	$-0.350540\pi$
$593$	−2.27890	−	1.31572i	−0.0935832	−	0.0540303i	−0.546061	+	0.837745i	$0.683873\pi$
$594$	−6.11973	−	18.0695i	−0.251096	−	0.741401i
$595$		0			0
$596$		−	19.4983i		−	0.798683i
$597$	−19.3827	−	8.53398i	−0.793282	−	0.349272i
$598$	−2.12493	−	3.68048i	−0.0868947	−	0.150506i
$599$	27.0326	−	15.6073i	1.10452	−	0.637697i	0.167118	−	0.985937i	$-0.446554\pi$
$599$	27.0326	−	15.6073i	1.10452	−	0.637697i	0.937405	+	0.348240i	$0.113221\pi$
$600$	−14.3626	−	20.3510i	−0.586349	−	0.830824i
$601$			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
$604$	−7.78305	+	13.4806i	−0.316688	+	0.548519i
$605$	−10.6322	−	6.26587i	−0.432259	−	0.254744i
$606$	−12.7610	−	17.4123i	−0.518379	−	0.707325i
$607$	2.40692	−	4.16891i	0.0976940	−	0.169211i	−0.813036	−	0.582214i	$-0.802187\pi$
$607$	2.40692	−	4.16891i	0.0976940	−	0.169211i	0.910730	+	0.413003i	$0.135520\pi$
$608$			31.6422i			1.28326i
$609$		0			0
$610$	6.12962	+	10.8394i	0.248181	+	0.438876i
$611$	−17.2636	−	9.96713i	−0.698410	−	0.403227i
$612$	−17.4710	+	15.9943i	−0.706224	+	0.646532i
$613$	34.7031	−	20.0359i	1.40165	−	0.809240i	0.407084	−	0.913391i	$-0.366546\pi$
$613$	34.7031	−	20.0359i	1.40165	−	0.809240i	0.994562	+	0.104150i	$0.0332123\pi$
$614$	−4.20626	+	7.28546i	−0.169751	+	0.294017i
$615$	−28.6830	+	20.6294i	−1.15661	+	0.831857i
$616$		0			0
$617$	18.4205			0.741583			0.370791	−	0.928716i	$-0.379087\pi$
$617$	18.4205			0.741583			0.370791	+	0.928716i	$0.379087\pi$
$618$	5.24156	−	11.9049i	0.210847	−	0.478883i
$619$	−9.54440	+	5.51046i	−0.383622	+	0.221484i	−0.679393	−	0.733775i	$-0.737757\pi$
$619$	−9.54440	+	5.51046i	−0.383622	+	0.221484i	0.295771	+	0.955259i	$0.404423\pi$
$620$	2.51452	−	4.26673i	0.100986	−	0.171356i
$621$	−1.66004	+	8.31528i	−0.0666151	+	0.333681i
$622$	22.8674			0.916899
$623$		0			0
$624$	1.14286	−	0.124895i	0.0457512	−	0.00499981i
$625$	24.9840	+	0.893749i	0.999361	+	0.0357500i
$626$	−3.45519	−	5.98457i	−0.138097	−	0.239191i
$627$	−23.7487	−	32.4050i	−0.948433	−	1.29413i
$628$	−1.88734	+	3.26897i	−0.0753131	+	0.130446i
$629$	−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	$0.396425\pi$
$632$	−5.46261	+	9.46152i	−0.217291	+	0.376359i
$633$	19.3140	+	26.3538i	0.767663	+	1.04747i
$634$	11.1772	+	19.3595i	0.443904	+	0.768865i
$635$	49.8361	+	0.445517i	1.97769	+	0.0176798i
$636$	−3.09588	+	0.338326i	−0.122760	+	0.0134155i
$637$		0			0
$638$	−21.6511			−0.857177
$639$	−13.7662	−	4.34751i	−0.544583	−	0.171985i
$640$	11.8447	+	6.98045i	0.468202	+	0.275926i
$641$	−34.4615	+	19.8964i	−1.36115	+	0.785859i	−0.989777	−	0.142625i	$-0.954446\pi$
$641$	−34.4615	+	19.8964i	−1.36115	+	0.785859i	−0.371372	+	0.928484i	$0.621112\pi$
$642$	6.76953	−	15.3752i	0.267172	−	0.606812i
$643$	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
$645$	−17.0364	−	23.6873i	−0.670807	−	0.932685i
$646$	17.1896	−	29.7733i	0.676317	−	1.17142i
$647$	−22.1456	+	12.7858i	−0.870633	+	0.502660i	−0.867558	−	0.497335i	$-0.834312\pi$
$647$	−22.1456	+	12.7858i	−0.870633	+	0.502660i	−0.00307433	+	0.999995i	$0.500979\pi$
$648$	−21.1907	−	14.8672i	−0.832449	−	0.584041i
$649$	3.49116	+	2.01563i	0.137040	+	0.0791202i
$650$	−6.71134	+	11.1588i	−0.263240	+	0.437684i
$651$		0			0
$652$		−	22.8264i		−	0.893952i
$653$	−8.49921	+	14.7211i	−0.332600	+	0.576080i	−0.983021	−	0.183494i	$-0.941259\pi$
$653$	−8.49921	+	14.7211i	−0.332600	+	0.576080i	0.650421	+	0.759574i	$0.274592\pi$
$654$	−0.496364	−	0.677285i	−0.0194094	−	0.0264839i
$655$	−0.219957	−	0.129627i	−0.00859442	−	0.00506496i
$656$	−1.05015	+	1.81891i	−0.0410014	+	0.0710166i
$657$	−1.64216	+	0.363257i	−0.0640667	+	0.0141720i
$658$		0			0
$659$			2.82840i			0.110179i	0.998481	+	0.0550894i	$0.0175444\pi$
$659$			2.82840i			0.110179i	−0.998481	+	0.0550894i	$0.982456\pi$
$660$	−18.5444	+	1.85898i	−0.721839	+	0.0723608i
$661$	12.6301	−	7.29200i	0.491254	−	0.283626i	−0.233840	−	0.972275i	$-0.575129\pi$
$661$	12.6301	−	7.29200i	0.491254	−	0.283626i	0.725095	+	0.688649i	$0.241796\pi$
$662$	−7.38760	−	12.7957i	−0.287127	−	0.497319i
$663$	30.4764	+	13.4184i	1.18361	+	0.521128i
$664$		−	11.5172i		−	0.446956i
$665$		0			0
$666$	−0.936361	−	4.23296i	−0.0362833	−	0.164024i
$667$	8.33391	+	4.81158i	0.322690	+	0.186305i
$668$	−0.906326	+	0.523268i	−0.0350668	+	0.0202458i
$669$	19.7378	+	26.9321i	0.763107	+	1.04125i
$670$	−20.3808	−	0.182197i	−0.787378	−	0.00703887i
$671$	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	$-0.0823043\pi$
$674$	2.81051	+	1.62265i	0.108257	+	0.0625022i
$675$	24.7528	−	7.89282i	0.952737	−	0.303795i
$676$	−2.77550	−	4.80730i	−0.106750	−	0.184896i
$677$	23.6762	+	13.6695i	0.909950	+	0.525360i	0.880415	−	0.474204i	$-0.157264\pi$
$677$	23.6762	+	13.6695i	0.909950	+	0.525360i	0.0295351	+	0.999564i	$0.490597\pi$
$678$	−18.8244	+	2.05718i	−0.722946	+	0.0790055i
$679$		0			0
$680$	−21.1115	−	37.3329i	−0.809588	−	1.43165i
$681$	−18.2326	−	8.02759i	−0.698674	−	0.307618i
$682$	3.43411	+	5.94806i	0.131499	+	0.227763i
$683$	2.53669	+	4.39367i	0.0970637	+	0.168119i	0.910468	−	0.413579i	$-0.135722\pi$
$683$	2.53669	+	4.39367i	0.0970637	+	0.168119i	−0.813404	+	0.581699i	$0.802388\pi$
$684$	−19.3299	−	6.10458i	−0.739098	−	0.233414i
$685$	−24.4153	+	13.8066i	−0.932859	+	0.527524i
$686$		0			0
$687$	−3.26900	−	29.9132i	−0.124720	−	1.14126i
$688$	−1.50211	−	0.867245i	−0.0572675	−	0.0330634i
$689$	2.18912	+	3.79167i	0.0833988	+	0.144451i
$690$	−5.20442	−	2.34721i	−0.198129	−	0.0893566i
$691$	−29.6673	−	17.1284i	−1.12860	−	0.651596i	−0.185016	−	0.982736i	$-0.559234\pi$
$691$	−29.6673	−	17.1284i	−1.12860	−	0.651596i	−0.943582	+	0.331140i	$0.892567\pi$
$692$			14.8189i			0.563329i
$693$		0			0
$694$	17.0991			0.649073
$695$	5.31358	+	0.0475014i	0.201556	+	0.00180183i
$696$	−23.6955	+	17.3658i	−0.898177	+	0.658250i
$697$	−52.6840	+	30.4171i	−1.99555	+	1.15213i
$698$	18.9125	+	10.9192i	0.715850	+	0.413296i
$699$	−0.796935	+	0.0870911i	−0.0301428	+	0.00329409i
$700$		0			0
$701$		−	17.6912i		−	0.668188i	−0.942540	−	0.334094i	$-0.891570\pi$
$701$		−	17.6912i		−	0.668188i	0.942540	−	0.334094i	$-0.108430\pi$
$702$	−2.64929	+	13.2705i	−0.0999910	+	0.500863i
$703$	−4.56484	−	7.90653i	−0.172166	−	0.298200i
$704$	−19.2500	+	11.1140i	−0.725511	+	0.418874i
$705$	−26.6460	+	2.67113i	−1.00355	+	0.100601i
$706$		−	29.0012i		−	1.09147i
$707$		0			0
$708$	2.02196	−	0.220965i	0.0759900	−	0.00830439i
$709$	−7.80875	+	13.5251i	−0.293264	+	0.507948i	−0.974579	−	0.224042i	$-0.928075\pi$
$709$	−7.80875	+	13.5251i	−0.293264	+	0.507948i	0.681316	+	0.731990i	$0.261408\pi$
$710$	4.93513	−	8.37412i	0.185212	−	0.314275i
$711$	−7.69473	−	8.40517i	−0.288575	−	0.315218i
$712$	14.9720	−	25.9323i	0.561101	−	0.971856i
$713$		−	3.05268i		−	0.114324i
$714$		0			0
$715$	12.8972	+	22.8071i	0.482328	+	0.852936i
$716$	12.4741	+	7.20195i	0.466181	+	0.269150i
$717$	−24.1764	+	17.7183i	−0.902886	+	0.661701i
$718$	13.3518	−	7.70866i	0.498284	−	0.287685i
$719$	−8.07179	+	13.9808i	−0.301027	+	0.521394i	−0.976369	−	0.216111i	$-0.930663\pi$
$719$	−8.07179	+	13.9808i	−0.301027	+	0.521394i	0.675342	+	0.737505i	$0.263996\pi$
$720$	1.14846	−	1.03267i	0.0428004	−	0.0384852i
$721$		0			0
$722$	12.2583			0.456207
$723$	6.78371	+	2.98679i	0.252289	+	0.111080i
$724$	16.5875	−	9.57678i	0.616468	−	0.355918i
$725$	0.527135	−	29.4807i	0.0195773	−	1.09488i
$726$	3.47971	−	7.90326i	0.129144	−	0.293318i
$727$	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
$730$	0.0101229	−	1.13236i	0.000374666	−	0.0419106i
$731$	−25.1194	−	43.5081i	−0.929075	−	1.60920i
$732$	10.1971	−	7.47316i	0.376895	−	0.276216i
$733$	−11.0872	+	19.2035i	−0.409514	+	0.709299i	−0.994835	−	0.101503i	$-0.967635\pi$
$733$	−11.0872	+	19.2035i	−0.409514	+	0.709299i	0.585321	+	0.810801i	$0.300968\pi$
$734$	14.1599			0.522651
$735$		0			0
$736$	9.04773			0.333504
$737$	−20.5053	+	35.5162i	−0.755323	+	1.30826i
$738$	−16.6934	−	18.2347i	−0.614494	−	0.671229i
$739$	−21.2262	−	36.7649i	−0.780820	−	1.35242i	−0.931465	−	0.363831i	$-0.881468\pi$
$739$	−21.2262	−	36.7649i	−0.780820	−	1.35242i	0.150645	−	0.988588i	$-0.451865\pi$
$740$	−4.23505	−	0.0378598i	−0.155683	−	0.00139175i
$741$	3.09588	+	28.3291i	0.113730	+	1.04070i
$742$		0			0
$743$	−24.5486			−0.900600			−0.450300	−	0.892877i	$-0.648683\pi$
$743$	−24.5486			−0.900600			−0.450300	+	0.892877i	$0.648683\pi$
$744$	8.52916	+	3.75529i	0.312694	+	0.137675i
$745$	−18.6967	+	31.7252i	−0.684992	+	1.16232i
$746$	0.820444	−	0.473684i	0.0300386	−	0.0173428i
$747$	11.4553	+	3.61768i	0.419126	+	0.132364i
$748$	−32.0904			−1.17334
$749$		0			0
$750$	1.43339	+	17.4343i	0.0523401	+	0.636609i
$751$	−12.6883	+	21.9768i	−0.463003	+	0.801944i	−0.999109	−	0.0422062i	$-0.986561\pi$
$751$	−12.6883	+	21.9768i	−0.463003	+	0.801944i	0.536106	+	0.844151i	$0.319895\pi$
$752$	−1.37867	+	0.795973i	−0.0502748	+	0.0290261i
$753$	17.8299	+	24.3288i	0.649758	+	0.886590i
$754$	13.3002	+	7.67890i	0.484366	+	0.279649i
$755$	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	$-0.111733\pi$
$758$	−8.90625	+	15.4261i	−0.323489	+	0.560300i
$759$	−9.26583	+	6.79068i	−0.336328	+	0.246486i
$760$	18.6355	−	31.6214i	0.675980	−	1.14703i
$761$	5.12909	−	8.88384i	0.185929	−	0.322039i	−0.757960	−	0.652301i	$-0.773804\pi$
$761$	5.12909	−	8.88384i	0.185929	−	0.322039i	0.943889	+	0.330262i	$0.107137\pi$
$762$	3.78845	+	34.6665i	0.137241	+	1.25583i
$763$		0			0
$764$			9.80090i			0.354584i
$765$	43.7633	−	9.27119i	1.58227	−	0.335201i
$766$	−2.15836	+	1.24613i	−0.0779846	+	0.0450244i
$767$	−1.42974	−	2.47639i	−0.0516250	−	0.0894172i
$768$	−11.5107	+	26.1435i	−0.415355	+	0.943371i
$769$			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
$772$	16.3291	+	9.42764i	0.587699	+	0.339308i
$773$	−8.93898	+	5.16092i	−0.321513	+	0.185626i	−0.652067	−	0.758162i	$-0.726098\pi$
$773$	−8.93898	+	5.16092i	−0.321513	+	0.185626i	0.330554	+	0.943787i	$0.392764\pi$
$774$	15.0588	−	13.7860i	0.541277	−	0.495526i
$775$	−8.18261	+	4.53114i	−0.293928	+	0.162764i
$776$	−41.8116			−1.50095
$777$		0			0
$778$			28.8187i			1.03320i
$779$	−45.0869	−	26.0309i	−1.61541	−	0.932655i
$780$	12.0511	+	5.43507i	0.431498	+	0.194607i
$781$	−9.77915	−	16.9380i	−0.349926	−	0.606089i
$782$	−8.51334	−	4.91518i	−0.304436	−	0.175766i
$783$	−9.82935	−	29.0228i	−0.351272	−	1.03719i
$784$		0			0
$785$	6.20540	−	3.50911i	0.221480	−	0.125245i
$786$	0.0719877	−	0.163501i	0.00256772	−	0.00583191i
$787$	−6.26338	−	10.8485i	−0.223265	−	0.386707i	0.732532	−	0.680732i	$-0.238338\pi$
$787$	−6.26338	−	10.8485i	−0.223265	−	0.386707i	−0.955798	+	0.294025i	$0.905005\pi$
$788$	−14.1330	−	24.4791i	−0.503468	−	0.872033i
$789$	−4.33543	+	9.84681i	−0.154345	+	0.350556i
$790$	6.67873	−	3.77677i	0.237619	−	0.134371i
$791$		0			0
$792$	−7.57462	−	34.2422i	−0.269152	−	1.21674i
$793$	−15.3920	−	8.88657i	−0.546586	−	0.315571i
$794$	−8.50062	−	14.7235i	−0.301676	−	0.522518i
$795$	5.36164	+	2.41811i	0.190158	+	0.0857617i
$796$	−12.5373	−	7.23842i	−0.444373	−	0.256559i
$797$			23.4184i			0.829521i	0.909931	+	0.414761i	$0.136135\pi$
$797$			23.4184i			0.829521i	−0.909931	+	0.414761i	$0.863865\pi$
$798$		0			0
$799$	−46.1100			−1.63126
$800$	−13.4297	−	24.2521i	−0.474811	−	0.857442i
$801$	21.0899	+	23.0371i	0.745175	+	0.813975i
$802$	2.57316	−	1.48562i	0.0908615	−	0.0524589i
$803$	−1.97329	−	1.13928i	−0.0696360	−	0.0402044i
$804$	2.24792	+	20.5698i	0.0792780	+	0.725440i
$805$		0			0
$806$		−	4.87184i		−	0.171603i
$807$	−4.18118	+	9.49648i	−0.147185	+	0.334292i
$808$	−19.8420	−	34.3674i	−0.698040	−	1.20904i
$809$	9.50469	−	5.48754i	0.334167	−	0.192932i	−0.323522	−	0.946220i	$-0.604867\pi$
$809$	9.50469	−	5.48754i	0.334167	−	0.192932i	0.657690	+	0.753289i	$0.271534\pi$
$810$	7.51995	+	16.5511i	0.264224	+	0.581546i
$811$			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
$814$	2.93671	−	5.08653i	0.102932	−	0.178283i
$815$	−21.8879	+	37.1402i	−0.766700	+	1.30097i
$816$	2.14495	−	1.57197i	0.0750881	−	0.0550300i
$817$	21.4972	−	37.2342i	0.752090	−	1.30266i
$818$		−	3.74808i		−	0.131048i
$819$		0			0
$820$	−21.0227	+	11.8882i	−0.734146	+	0.415154i
$821$	39.5091	+	22.8106i	1.37888	+	0.796094i	0.992024	−	0.126048i	$-0.0402293\pi$
$821$	39.5091	+	22.8106i	1.37888	+	0.796094i	0.386851	+	0.922142i	$0.373563\pi$
$822$	−11.6015	−	15.8302i	−0.404650	−	0.552143i
$823$	12.0190	−	6.93918i	0.418956	−	0.241885i	−0.275674	−	0.961251i	$-0.588901\pi$
$823$	12.0190	−	6.93918i	0.418956	−	0.241885i	0.694631	+	0.719366i	$0.255568\pi$
$824$	11.9558	−	20.7081i	0.416501	−	0.721400i
$825$	31.9556	+	14.7572i	1.11255	+	0.513781i
$826$		0			0
$827$	−12.3739			−0.430283			−0.215141	−	0.976583i	$-0.569021\pi$
$827$	−12.3739			−0.430283			−0.215141	+	0.976583i	$0.569021\pi$
$828$	−1.74553	+	5.52717i	−0.0606615	+	0.192082i
$829$	9.24010	−	5.33478i	0.320922	−	0.185284i	−0.330881	−	0.943672i	$-0.607346\pi$
$829$	9.24010	−	5.33478i	0.320922	−	0.185284i	0.651803	+	0.758388i	$0.274013\pi$
$830$	−4.10666	+	6.96834i	−0.142544	+	0.241875i
$831$	13.7980	+	6.07509i	0.478647	+	0.210743i
$832$	15.7670			0.546621
$833$		0			0
$834$	0.403928	+	3.69618i	0.0139869	+	0.127988i
$835$	1.97641	+	0.0176684i	0.0683965	+	0.000611440i
$836$	−13.7315	−	23.7836i	−0.474912	−	0.822572i
$837$	−6.41417	+	7.30368i	−0.221706	+	0.252452i
$838$	10.2182	−	17.6984i	0.352981	−	0.611381i
$839$	−17.5497			−0.605883			−0.302941	−	0.953009i	$-0.597969\pi$
$839$	−17.5497			−0.605883			−0.302941	+	0.953009i	$0.597969\pi$
$840$		0			0
$841$	−5.77548			−0.199154
$842$	14.4188	−	24.9740i	0.496903	−	0.860662i
$843$	−6.09492	+	4.46680i	−0.209920	+	0.153845i
$844$	11.1673	+	19.3424i	0.384395	+	0.665791i
$845$	−0.0937160	+	10.4832i	−0.00322393	+	0.360633i
$846$	−4.04721	−	18.2960i	−0.139146	−	0.629030i
$847$		0			0
$848$	0.349645			0.0120069
$849$	−5.24908	+	11.9219i	−0.180148	+	0.409159i
$850$	−0.538484	+	30.1154i	−0.0184698	+	1.03295i
$851$	−2.26078	+	1.30526i	−0.0774986	+	0.0447438i
$852$	−9.03165	−	3.97653i	−0.309419	−	0.136234i
$853$	−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
$855$	25.5976	+	28.4678i	0.875419	+	0.973577i
$856$	15.4410	−	26.7447i	0.527764	−	0.914114i
$857$	38.6264	−	22.3010i	1.31945	−	0.761787i	0.335812	−	0.941929i	$-0.390989\pi$
$857$	38.6264	−	22.3010i	1.31945	−	0.761787i	0.983641	+	0.180142i	$0.0576558\pi$
$858$	−14.7875	+	10.8374i	−0.504837	+	0.369982i
$859$	−5.57093	−	3.21638i	−0.190078	−	0.109741i	0.401941	−	0.915665i	$-0.368336\pi$
$859$	−5.57093	−	3.21638i	−0.190078	−	0.109741i	−0.592019	+	0.805924i	$0.701669\pi$
$860$	−9.81763	−	17.3612i	−0.334778	−	0.592013i
$861$		0			0
$862$		−	22.6239i		−	0.770573i
$863$	26.6755	−	46.2033i	0.908045	−	1.57278i	0.0912683	−	0.995826i	$-0.470908\pi$
$863$	26.6755	−	46.2033i	0.908045	−	1.57278i	0.816777	−	0.576954i	$-0.195759\pi$
$864$	−21.6471	−	19.0107i	−0.736449	−	0.646757i
$865$	14.2096	−	24.1114i	0.483140	−	0.819811i
$866$	2.30451	−	3.99152i	0.0783104	−	0.135638i
$867$	47.2991	−	5.16897i	1.60636	−	0.175547i
$868$		0			0
$869$		−	15.4384i		−	0.523713i
$870$	20.5287	−	2.05790i	0.695988	−	0.0697694i
$871$	25.1927	−	14.5450i	0.853623	−	0.492839i
$872$	−0.771796	−	1.33679i	−0.0261363	−	0.0452694i
$873$	13.1334	−	41.5865i	0.444499	−	1.40749i
$874$		−	8.41281i		−	0.284567i
$875$		0			0
$876$	−1.14286	+	0.124895i	−0.0386138	+	0.00421982i
$877$	−30.7320	−	17.7431i	−1.03774	−	0.599142i	−0.118551	−	0.992948i	$-0.537825\pi$
$877$	−30.7320	−	17.7431i	−1.03774	−	0.599142i	−0.919194	+	0.393806i	$0.871158\pi$
$878$	8.83075	−	5.09844i	0.298023	−	0.172064i
$879$	0.147926	−	0.108411i	0.00498941	−	0.00365660i
$880$	2.09233	+	0.0187047i	0.0705326	+	0.000630535i
$881$	−25.0114			−0.842655			−0.421327	−	0.906909i	$-0.638436\pi$
$881$	−25.0114			−0.842655			−0.421327	+	0.906909i	$0.638436\pi$
$882$		0			0
$883$			30.1344i			1.01410i	0.861916	+	0.507051i	$0.169264\pi$
$883$			30.1344i			1.01410i	−0.861916	+	0.507051i	$0.830736\pi$
$884$	19.7130	+	11.3813i	0.663021	+	0.382796i
$885$	−3.50176	−	1.57930i	−0.117710	−	0.0530877i
$886$	9.89976	+	17.1469i	0.332589	+	0.576061i
$887$	7.84535	+	4.52951i	0.263421	+	0.152086i	0.625894	−	0.779908i	$-0.284734\pi$
$887$	7.84535	+	4.52951i	0.263421	+	0.152086i	−0.362473	+	0.931994i	$0.618068\pi$
$888$	−0.865767	−	7.92227i	−0.0290532	−	0.265854i
$889$		0			0
$890$	−18.3052	+	10.3515i	−0.613592	+	0.346982i
$891$	36.4372	+	3.22197i	1.22069	+	0.107940i
$892$	11.4123	+	19.7668i	0.382113	+	0.661840i
$893$	−19.7305	−	34.1742i	−0.660255	−	1.14359i
$894$	−23.5824	−	10.3831i	−0.788715	−	0.347262i
$895$	−13.3905	−	23.6794i	−0.447595	−	0.791514i
$896$		0			0
$897$	8.10039	−	0.885232i	0.270464	−	0.0295570i
$898$	0.351569	+	0.202979i	0.0117320	+	0.00677349i
$899$	5.51578	+	9.55361i	0.183962	+	0.318631i
$900$	17.4063	−	3.52522i	0.580210	−	0.117507i
$901$	8.77052	+	5.06366i	0.292188	+	0.168695i
$902$		−	33.4931i		−	1.11520i
$903$		0			0
$904$	−34.8104			−1.15778
$905$	−36.1720	−	0.323365i	−1.20240	−	0.0107490i
$906$	12.1597	+	16.5919i	0.403980	+	0.551228i
$907$	−8.21292	+	4.74173i	−0.272705	+	0.157447i	−0.630116	−	0.776501i	$-0.716993\pi$
$907$	−8.21292	+	4.74173i	−0.272705	+	0.157447i	0.357411	+	0.933947i	$0.383660\pi$
$908$	−11.7934	−	6.80891i	−0.391377	−	0.225962i
$909$	40.4150	−	8.94009i	1.34048	−	0.296524i
$910$		0			0
$911$			56.8415i			1.88324i	0.336672	+	0.941622i	$0.390699\pi$
$911$			56.8415i			1.88324i	−0.336672	+	0.941622i	$0.609301\pi$
$912$	2.08288	+	0.917066i	0.0689710	+	0.0303671i
$913$	8.13751	+	14.0946i	0.269312	+	0.466463i
$914$	−7.26995	+	4.19731i	−0.240469	+	0.138835i
$915$	−23.7573	+	2.38155i	−0.785392	+	0.0787317i
$916$		−	20.5695i		−	0.679637i
$917$		0			0
$918$	10.0410	+	29.6476i	0.331402	+	0.978518i
$919$	28.6839	−	49.6820i	0.946195	−	1.63886i	0.192853	−	0.981228i	$-0.438226\pi$
$919$	28.6839	−	49.6820i	0.946195	−	1.63886i	0.753341	−	0.657630i	$-0.228441\pi$
$920$	−9.04177	−	5.32860i	−0.298098	−	0.175679i
$921$	−9.53485	−	13.0102i	−0.314184	−	0.428702i
$922$	−9.42488	+	16.3244i	−0.310392	+	0.537615i
$923$			13.8733i			0.456645i
$924$		0			0
$925$	6.85442	+	4.12252i	0.225372	+	0.135548i
$926$	−1.91897	−	1.10792i	−0.0630613	−	0.0364084i
$927$	16.8412	+	18.3961i	0.553137	+	0.604207i
$928$	−28.3156	+	16.3480i	−0.929504	+	0.536649i
$929$	5.14668	−	8.91430i	0.168857	−	0.292469i	−0.769161	−	0.639055i	$-0.779326\pi$
$929$	5.14668	−	8.91430i	0.168857	−	0.292469i	0.938018	+	0.346586i	$0.112659\pi$
$930$	−3.82143	−	5.31329i	−0.125310	−	0.174230i
$931$		0			0
$932$	−0.548005			−0.0179505
$933$	−17.6680	+	40.1284i	−0.578425	+	1.31374i
$934$	6.24283	−	3.60430i	0.204271	−	0.117936i
$935$	52.2134	+	30.7710i	1.70756	+	1.00632i
$936$	−7.49144	+	23.7214i	−0.244865	+	0.775357i
$937$	−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
$940$	−18.3050	−	0.163640i	−0.597044	−	0.00533735i
$941$	−7.48583	−	12.9658i	−0.244031	−	0.422674i	0.717828	−	0.696221i	$-0.245137\pi$
$941$	−7.48583	−	12.9658i	−0.244031	−	0.422674i	−0.961859	+	0.273546i	$0.911803\pi$
$942$	2.94866	+	4.02342i	0.0960725	+	0.131090i
$943$	−7.44325	+	12.8921i	−0.242386	+	0.419824i
$944$	−0.228358			−0.00743242
$945$		0			0
$946$	27.6596			0.899292
$947$	7.25429	−	12.5648i	0.235733	−	0.408301i	−0.723753	−	0.690059i	$-0.757584\pi$
$947$	7.25429	−	12.5648i	0.235733	−	0.408301i	0.959485	+	0.281758i	$0.0909177\pi$
$948$	−4.60459	−	6.28294i	−0.149550	−	0.204060i
$949$	0.808126	+	1.39972i	0.0262329	+	0.0454367i
$950$	−22.5502	+	12.4873i	−0.731626	+	0.405140i
$951$	−42.6085	+	4.65637i	−1.38167	+	0.150993i
$952$		0			0
$953$	34.9591			1.13244			0.566218	−	0.824256i	$-0.308406\pi$
$953$	34.9591			1.13244			0.566218	+	0.824256i	$0.308406\pi$
$954$	−1.23940	+	3.92451i	−0.0401270	+	0.127061i
$955$	9.39793	−	15.9468i	0.304110	−	0.516025i
$956$	−17.7443	+	10.2447i	−0.573891	+	0.331336i
$957$	16.7283	−	37.9940i	0.540749	−	1.22817i
$958$	−12.5500			−0.405473
$959$		0			0
$960$	17.1957	−	12.3675i	0.554988	−	0.399159i
$961$	−13.7503	+	23.8162i	−0.443557	+	0.768264i
$962$	−3.60802	+	2.08309i	−0.116327	+	0.0671616i
$963$	21.7505	+	23.7587i	0.700901	+	0.765614i
$964$	4.38790	+	2.53336i	0.141325	+	0.0815939i
$965$	−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	$-0.270226\pi$
$968$	7.93709	−	13.7474i	0.255108	−	0.441860i
$969$	38.9658	+	53.1686i	1.25176	+	1.70802i
$970$	25.2975	+	14.9086i	0.812253	+	0.478686i
$971$	0.656690	−	1.13742i	0.0210742	−	0.0365016i	−0.855296	−	0.518140i	$-0.826625\pi$
$971$	0.656690	−	1.13742i	0.0210742	−	0.0365016i	0.876370	+	0.481638i	$0.159958\pi$
$972$	15.7897	−	9.55635i	0.506456	−	0.306520i
$973$		0			0
$974$			23.9482i			0.767350i
$975$	−14.3964	−	20.3988i	−0.461053	−	0.653286i
$976$	−1.22920	+	0.709680i	−0.0393458	+	0.0227163i
$977$	26.5376	+	45.9645i	0.849013	+	1.47053i	0.882090	+	0.471081i	$0.156136\pi$
$977$	26.5376	+	45.9645i	0.849013	+	1.47053i	−0.0330769	+	0.999453i	$0.510531\pi$
$978$	−27.6076	−	12.1553i	−0.882795	−	0.388684i
$979$			42.3140i			1.35236i
$980$		0			0
$981$	1.57202	−	0.347743i	0.0501908	−	0.0111026i
$982$	−1.99186	−	1.15000i	−0.0635629	−	0.0366980i
$983$	18.2849	−	10.5568i	0.583198	−	0.336709i	−0.179206	−	0.983812i	$-0.557353\pi$
$983$	18.2849	−	10.5568i	0.583198	−	0.336709i	0.762403	+	0.647102i	$0.224019\pi$
$984$	−26.8639	−	36.6557i	−0.856391	−	1.16854i
$985$	−0.477209	+	53.3812i	−0.0152051	+	1.70087i
$986$	35.5242			1.13132
$987$		0			0
$988$			19.4803i			0.619750i
$989$	−10.6467	−	6.14686i	−0.338545	−	0.195459i
$990$	−7.62671	+	23.4186i	−0.242393	+	0.744292i
$991$	26.8174	+	46.4491i	0.851883	+	1.47551i	0.879507	+	0.475887i	$0.157873\pi$
$991$	26.8174	+	46.4491i	0.851883	+	1.47551i	−0.0276234	+	0.999618i	$0.508794\pi$
$992$	8.98233	+	5.18595i	0.285189	+	0.164654i
$993$	28.1621	−	3.07763i	0.893698	−	0.0976657i
$994$		0			0
$995$	13.4583	+	23.7993i	0.426657	+	0.754488i
$996$	7.51549	+	3.30898i	0.238137	+	0.104849i
$997$	−19.4435	−	33.6771i	−0.615781	−	1.06656i	−0.990247	−	0.139323i	$-0.955507\pi$
$997$	−19.4435	−	33.6771i	−0.615781	−	1.06656i	0.374466	−	0.927241i	$-0.377826\pi$
$998$	13.3918	+	23.1953i	0.423910	+	0.734234i
$999$	8.15158	+	1.62736i	0.257905	+	0.0514874i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.451669 - 0.782314i) q^{2} +(1.02385 + 1.39704i) q^{3} +(0.591990 + 1.02536i) q^{4} +(0.0199888 - 2.23598i) q^{5} +(1.55537 - 0.169975i) q^{6} +2.87621 q^{8} +(-0.903447 + 2.86073i) q^{9} +(-1.74021 - 1.02556i) q^{10} +(-3.51985 + 2.03219i) q^{11} +(-0.826354 + 1.87685i) q^{12} +2.88298 q^{13} +(3.14422 - 2.26139i) q^{15} +(0.115117 - 0.199389i) q^{16} +(5.77521 - 3.33432i) q^{17} +(1.82993 + 1.99888i) q^{18} +(4.94242 + 2.85351i) q^{19} +(2.30451 - 1.30318i) q^{20} +3.67151i q^{22} +(0.815927 - 1.41323i) q^{23} +(2.94482 + 4.01819i) q^{24} +(-4.99920 - 0.0893892i) q^{25} +(1.30215 - 2.25540i) q^{26} +(-4.92156 + 1.66682i) q^{27} +5.89707i q^{29} +(-0.348970 - 3.48117i) q^{30} +(1.62006 - 0.935342i) q^{31} +(2.77222 + 4.80163i) q^{32} +(-6.44286 - 2.83671i) q^{33} -6.02404i q^{34} +(-3.46810 + 0.767168i) q^{36} +(-1.38541 - 0.799864i) q^{37} +(4.46468 - 2.57768i) q^{38} +(2.95175 + 4.02764i) q^{39} +(0.0574921 - 6.43115i) q^{40} -9.12244 q^{41} -7.53359i q^{43} +(-4.16743 - 2.40607i) q^{44} +(6.37848 + 2.07727i) q^{45} +(-0.737059 - 1.27662i) q^{46} +(-5.98810 - 3.45723i) q^{47} +(0.396417 - 0.0433215i) q^{48} +(-2.32792 + 3.87057i) q^{50} +(10.5712 + 4.65435i) q^{51} +(1.70670 + 2.95608i) q^{52} +(0.759325 + 1.31519i) q^{53} +(-0.918941 + 4.60305i) q^{54} +(4.47357 + 7.91093i) q^{55} +(1.07385 + 9.82633i) q^{57} +(4.61336 + 2.66353i) q^{58} +(-0.495925 - 0.858968i) q^{59} +(4.18008 + 1.88523i) q^{60} +(-5.33892 - 3.08243i) q^{61} -1.68986i q^{62} +5.46898 q^{64} +(0.0576274 - 6.44628i) q^{65} +(-5.12924 + 3.75908i) q^{66} +(8.73843 - 5.04513i) q^{67} +(6.83773 + 3.94776i) q^{68} +(2.80973 - 0.307054i) q^{69} +4.81213i q^{71} +(-2.59850 + 8.22807i) q^{72} +(0.280309 + 0.485510i) q^{73} +(-1.25149 + 0.722548i) q^{74} +(-4.99357 - 7.07561i) q^{75} +6.75699i q^{76} +(4.48410 - 0.490034i) q^{78} +(-1.89924 + 3.28958i) q^{79} +(-0.443528 - 0.261385i) q^{80} +(-7.36757 - 5.16904i) q^{81} +(-4.12033 + 7.13661i) q^{82} -4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} +(-5.89364 - 3.40269i) q^{86} +(-8.23845 + 6.03774i) q^{87} +(-10.1238 + 5.84500i) q^{88} +(5.20547 - 9.01615i) q^{89} +(4.50604 - 4.05173i) q^{90} +1.93208 q^{92} +(2.96541 + 1.30564i) q^{93} +(-5.40928 + 3.12305i) q^{94} +(6.47917 - 10.9941i) q^{95} +(-3.86972 + 8.78907i) q^{96} -14.5370 q^{97} +(-2.63354 - 11.9053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) \) 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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