LMFDB - Embedded newform 525.2.bf.g.32.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.16
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.g.443.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78672 + 0.478751i) q^{2} +(-0.293073 + 1.70708i) q^{3} +(1.23113 + 0.710791i) q^{4} +(-1.34091 + 2.90976i) q^{6} +(-0.585067 + 2.58025i) q^{7} +(-0.756555 - 0.756555i) q^{8} +(-2.82822 - 1.00060i) q^{9} +O(q^{10})$	\(q+(1.78672 + 0.478751i) q^{2} +(-0.293073 + 1.70708i) q^{3} +(1.23113 + 0.710791i) q^{4} +(-1.34091 + 2.90976i) q^{6} +(-0.585067 + 2.58025i) q^{7} +(-0.756555 - 0.756555i) q^{8} +(-2.82822 - 1.00060i) q^{9} +(4.61054 + 2.66189i) q^{11} +(-1.57418 + 1.89331i) q^{12} +(-3.44938 + 3.44938i) q^{13} +(-2.28065 + 4.33009i) q^{14} +(-2.41113 - 4.17621i) q^{16} +(1.13091 + 4.22062i) q^{17} +(-4.57420 - 3.14180i) q^{18} +(2.14466 - 1.23822i) q^{19} +(-4.23322 - 1.75496i) q^{21} +(6.96337 + 6.96337i) q^{22} +(0.533436 - 1.99081i) q^{23} +(1.51322 - 1.06977i) q^{24} +(-7.81448 + 4.51169i) q^{26} +(2.53697 - 4.53473i) q^{27} +(-2.55431 + 2.76075i) q^{28} +2.05014 q^{29} +(1.18652 - 2.05512i) q^{31} +(-1.75483 - 6.54911i) q^{32} +(-5.89528 + 7.09041i) q^{33} +8.08250i q^{34} +(-2.77068 - 3.24213i) q^{36} +(1.26256 - 4.71194i) q^{37} +(4.42470 - 1.18560i) q^{38} +(-4.87743 - 6.89928i) q^{39} -4.06556i q^{41} +(-6.72340 - 5.16228i) q^{42} +(-0.254109 + 0.254109i) q^{43} +(3.78410 + 6.55425i) q^{44} +(1.90621 - 3.30165i) q^{46} +(8.31648 + 2.22839i) q^{47} +(7.83574 - 2.89205i) q^{48} +(-6.31539 - 3.01924i) q^{49} +(-7.53635 + 0.693601i) q^{51} +(-6.69841 + 1.79483i) q^{52} +(11.8899 - 3.18590i) q^{53} +(6.70387 - 6.88773i) q^{54} +(2.39474 - 1.50947i) q^{56} +(1.48519 + 4.02398i) q^{57} +(3.66302 + 0.981504i) q^{58} +(-1.70041 + 2.94520i) q^{59} +(3.95741 + 6.85444i) q^{61} +(3.10387 - 3.10387i) q^{62} +(4.23649 - 6.71209i) q^{63} -2.89704i q^{64} +(-13.9278 + 9.84622i) q^{66} +(-2.76544 + 0.740997i) q^{67} +(-1.60768 + 5.99995i) q^{68} +(3.24213 + 1.49407i) q^{69} -14.7384i q^{71} +(1.38269 + 2.89671i) q^{72} +(2.84465 + 10.6164i) q^{73} +(4.51169 - 7.81448i) q^{74} +3.52046 q^{76} +(-9.56583 + 10.3390i) q^{77} +(-5.41159 - 14.6622i) q^{78} +(-5.48749 + 3.16820i) q^{79} +(6.99761 + 5.65981i) q^{81} +(1.94639 - 7.26404i) q^{82} +(1.57660 + 1.57660i) q^{83} +(-3.96422 - 5.16950i) q^{84} +(-0.575678 + 0.332368i) q^{86} +(-0.600840 + 3.49974i) q^{87} +(-1.47425 - 5.50199i) q^{88} +(-4.07820 - 7.06365i) q^{89} +(-6.88215 - 10.9184i) q^{91} +(2.07178 - 2.07178i) q^{92} +(3.16050 + 2.62778i) q^{93} +(13.7924 + 7.96305i) q^{94} +(11.6941 - 1.07626i) q^{96} +(-7.54172 - 7.54172i) q^{97} +(-9.83840 - 8.41804i) q^{98} +(-10.3761 - 12.1417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{6}+O(q^{10}) $ 80 * q + 16 * q^6	$ 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) $ 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.78672	+	0.478751i	1.26340	+	0.338528i	0.827500	−	0.561465i	$-0.189762\pi$
$2$	1.78672	+	0.478751i	1.26340	+	0.338528i	0.435904	+	0.899993i	$0.356429\pi$
$3$	−0.293073	+	1.70708i	−0.169206	+	0.985581i
$3$	−0.293073	+	1.70708i	−0.169206	+	0.985581i
$4$	1.23113	+	0.710791i	0.615563	+	0.355395i
$5$		0			0
$5$		0			0
$6$	−1.34091	+	2.90976i	−0.547422	+	1.18791i
$7$	−0.585067	+	2.58025i	−0.221134	+	0.975243i
$7$	−0.585067	+	2.58025i	−0.221134	+	0.975243i
$8$	−0.756555	−	0.756555i	−0.267482	−	0.267482i
$9$	−2.82822	−	1.00060i	−0.942739	−	0.333532i
$10$		0			0
$11$	4.61054	+	2.66189i	1.39013	+	0.802591i	0.993329	−	0.115314i	$-0.0367874\pi$
$11$	4.61054	+	2.66189i	1.39013	+	0.802591i	0.396800	+	0.917905i	$0.370121\pi$
$12$	−1.57418	+	1.89331i	−0.454428	+	0.546552i
$13$	−3.44938	+	3.44938i	−0.956686	+	0.956686i	−0.999100	−	0.0424138i	$-0.986495\pi$
$13$	−3.44938	+	3.44938i	−0.956686	+	0.956686i	0.0424138	+	0.999100i	$0.486495\pi$
$14$	−2.28065	+	4.33009i	−0.609529	+	1.15727i
$15$		0			0
$16$	−2.41113	−	4.17621i	−0.602784	−	1.04405i
$17$	1.13091	+	4.22062i	0.274286	+	1.02365i	0.956318	+	0.292328i	$0.0944297\pi$
$17$	1.13091	+	4.22062i	0.274286	+	1.02365i	−0.682032	+	0.731322i	$0.738904\pi$
$18$	−4.57420	−	3.14180i	−1.07815	−	0.740529i
$19$	2.14466	−	1.23822i	0.492018	−	0.284067i	−0.233393	−	0.972382i	$-0.574983\pi$
$19$	2.14466	−	1.23822i	0.492018	−	0.284067i	0.725411	+	0.688316i	$0.241650\pi$
$20$		0			0
$21$	−4.23322	−	1.75496i	−0.923764	−	0.382963i
$22$	6.96337	+	6.96337i	1.48459	+	1.48459i
$23$	0.533436	−	1.99081i	0.111229	−	0.415113i	−0.887748	−	0.460330i	$-0.847731\pi$
$23$	0.533436	−	1.99081i	0.111229	−	0.415113i	0.998977	+	0.0452168i	$0.0143979\pi$
$24$	1.51322	−	1.06977i	0.308885	−	0.218366i
$25$		0			0
$26$	−7.81448	+	4.51169i	−1.53255	+	0.884816i
$27$	2.53697	−	4.53473i	0.488240	−	0.872709i
$28$	−2.55431	+	2.76075i	−0.482719	+	0.521734i
$29$	2.05014			0.380701			0.190350	−	0.981716i	$-0.439038\pi$
$29$	2.05014			0.380701			0.190350	+	0.981716i	$0.439038\pi$
$30$		0			0
$31$	1.18652	−	2.05512i	0.213106	−	0.369110i	−0.739579	−	0.673069i	$-0.764975\pi$
$31$	1.18652	−	2.05512i	0.213106	−	0.369110i	0.952685	+	0.303960i	$0.0983088\pi$
$32$	−1.75483	−	6.54911i	−0.310213	−	1.15773i
$33$	−5.89528	+	7.09041i	−1.02624	+	1.23428i
$34$			8.08250i			1.38614i
$35$		0			0
$36$	−2.77068	−	3.24213i	−0.461779	−	0.540355i
$37$	1.26256	−	4.71194i	0.207564	−	0.774639i	−0.781089	−	0.624420i	$-0.785335\pi$
$37$	1.26256	−	4.71194i	0.207564	−	0.774639i	0.988653	−	0.150219i	$-0.0479978\pi$
$38$	4.42470	−	1.18560i	0.717782	−	0.192329i
$39$	−4.87743	−	6.89928i	−0.781015	−	1.10477i
$40$		0			0
$41$		−	4.06556i		−	0.634934i	−0.948269	−	0.317467i	$-0.897168\pi$
$41$		−	4.06556i		−	0.634934i	0.948269	−	0.317467i	$-0.102832\pi$
$42$	−6.72340	−	5.16228i	−1.03744	−	0.796557i
$43$	−0.254109	+	0.254109i	−0.0387513	+	0.0387513i	−0.726217	−	0.687466i	$-0.758723\pi$
$43$	−0.254109	+	0.254109i	−0.0387513	+	0.0387513i	0.687466	+	0.726217i	$0.258723\pi$
$44$	3.78410	+	6.55425i	0.570475	+	0.988091i
$45$		0			0
$46$	1.90621	−	3.30165i	0.281055	−	0.486801i
$47$	8.31648	+	2.22839i	1.21308	+	0.325045i	0.807971	−	0.589222i	$-0.200566\pi$
$47$	8.31648	+	2.22839i	1.21308	+	0.325045i	0.405112	+	0.914267i	$0.367232\pi$
$48$	7.83574	−	2.89205i	1.13099	−	0.417432i
$49$	−6.31539	−	3.01924i	−0.902199	−	0.431320i
$50$		0			0
$51$	−7.53635	+	0.693601i	−1.05530	+	0.0971235i
$52$	−6.69841	+	1.79483i	−0.928903	+	0.248899i
$53$	11.8899	−	3.18590i	1.63321	−	0.437616i	0.678364	−	0.734726i	$-0.262689\pi$
$53$	11.8899	−	3.18590i	1.63321	−	0.437616i	0.954843	+	0.297110i	$0.0960227\pi$
$54$	6.70387	−	6.88773i	0.912281	−	0.937302i
$55$		0			0
$56$	2.39474	−	1.50947i	0.320010	−	0.201711i
$57$	1.48519	+	4.02398i	0.196718	+	0.532989i
$58$	3.66302	+	0.981504i	0.480979	+	0.128878i
$59$	−1.70041	+	2.94520i	−0.221375	+	0.383433i	−0.955226	−	0.295878i	$-0.904388\pi$
$59$	−1.70041	+	2.94520i	−0.221375	+	0.383433i	0.733851	+	0.679311i	$0.237721\pi$
$60$		0			0
$61$	3.95741	+	6.85444i	0.506695	+	0.877621i	0.999970	+	0.00774794i	$0.00246627\pi$
$61$	3.95741	+	6.85444i	0.506695	+	0.877621i	−0.493275	+	0.869873i	$0.664200\pi$
$62$	3.10387	−	3.10387i	0.394193	−	0.394193i
$63$	4.23649	−	6.71209i	0.533747	−	0.845644i
$64$		−	2.89704i		−	0.362130i
$65$		0			0
$66$	−13.9278	+	9.84622i	−1.71439	+	1.21199i
$67$	−2.76544	+	0.740997i	−0.337852	+	0.0905272i	−0.423756	−	0.905776i	$-0.639289\pi$
$67$	−2.76544	+	0.740997i	−0.337852	+	0.0905272i	0.0859043	+	0.996303i	$0.472622\pi$
$68$	−1.60768	+	5.99995i	−0.194960	+	0.727601i
$69$	3.24213	+	1.49407i	0.390307	+	0.179865i
$70$		0			0
$71$		−	14.7384i		−	1.74913i	−0.484910	−	0.874564i	$-0.661148\pi$
$71$		−	14.7384i		−	1.74913i	0.484910	−	0.874564i	$-0.338852\pi$
$72$	1.38269	+	2.89671i	0.162952	+	0.341380i
$73$	2.84465	+	10.6164i	0.332941	+	1.24255i	0.906084	+	0.423098i	$0.139057\pi$
$73$	2.84465	+	10.6164i	0.332941	+	1.24255i	−0.573143	+	0.819456i	$0.694276\pi$
$74$	4.51169	−	7.81448i	0.524474	−	0.908415i
$75$		0			0
$76$	3.52046			0.403824
$77$	−9.56583	+	10.3390i	−1.09013	+	1.17823i
$78$	−5.41159	−	14.6622i	−0.612742	−	1.66016i
$79$	−5.48749	+	3.16820i	−0.617391	+	0.356451i	−0.775853	−	0.630914i	$-0.782680\pi$
$79$	−5.48749	+	3.16820i	−0.617391	+	0.356451i	0.158462	+	0.987365i	$0.449347\pi$
$80$		0			0
$81$	6.99761	+	5.65981i	0.777513	+	0.628867i
$82$	1.94639	−	7.26404i	0.214943	−	0.802179i
$83$	1.57660	+	1.57660i	0.173054	+	0.173054i	0.788320	−	0.615266i	$-0.210951\pi$
$83$	1.57660	+	1.57660i	0.173054	+	0.173054i	−0.615266	+	0.788320i	$0.710951\pi$
$84$	−3.96422	−	5.16950i	−0.432532	−	0.564039i
$85$		0			0
$86$	−0.575678	+	0.332368i	−0.0620770	+	0.0358402i
$87$	−0.600840	+	3.49974i	−0.0644168	+	0.375211i
$88$	−1.47425	−	5.50199i	−0.157156	−	0.586514i
$89$	−4.07820	−	7.06365i	−0.432289	−	0.748746i	0.564781	−	0.825241i	$-0.308960\pi$
$89$	−4.07820	−	7.06365i	−0.432289	−	0.748746i	−0.997070	+	0.0764948i	$0.975627\pi$
$90$		0			0
$91$	−6.88215	−	10.9184i	−0.721446	−	1.14456i
$92$	2.07178	−	2.07178i	0.215998	−	0.215998i
$93$	3.16050	+	2.62778i	0.327729	+	0.272488i
$94$	13.7924	+	7.96305i	1.42258	+	0.821326i
$95$		0			0
$96$	11.6941	−	1.07626i	1.19353	−	0.109845i
$97$	−7.54172	−	7.54172i	−0.765746	−	0.765746i	0.211609	−	0.977354i	$-0.432130\pi$
$97$	−7.54172	−	7.54172i	−0.765746	−	0.765746i	−0.977354	+	0.211609i	$0.932130\pi$
$98$	−9.83840	−	8.41804i	−0.993828	−	0.850351i
$99$	−10.3761	−	12.1417i	−1.04284	−	1.22029i
$100$		0			0
$101$	9.23839	+	5.33378i	0.919254	+	0.530731i	0.883397	−	0.468626i	$-0.155251\pi$
$101$	9.23839	+	5.33378i	0.919254	+	0.530731i	0.0358568	+	0.999357i	$0.488584\pi$
$102$	−13.7974	−	2.36876i	−1.36615	−	0.234543i
$103$	2.37835	+	0.637278i	0.234346	+	0.0627928i	0.374081	−	0.927396i	$-0.377958\pi$
$103$	2.37835	+	0.637278i	0.234346	+	0.0627928i	−0.139735	+	0.990189i	$0.544625\pi$
$104$	5.21929			0.511794
$105$		0			0
$106$	22.7693			2.21155
$107$	−11.9953	−	3.21414i	−1.15963	−	0.310722i	−0.372813	−	0.927907i	$-0.621607\pi$
$107$	−11.9953	−	3.21414i	−1.15963	−	0.310722i	−0.786819	+	0.617184i	$0.788273\pi$
$108$	6.34657	−	3.77957i	0.610699	−	0.363689i
$109$	15.8009	+	9.12263i	1.51345	+	0.873789i	0.999876	+	0.0157428i	$0.00501130\pi$
$109$	15.8009	+	9.12263i	1.51345	+	0.873789i	0.513572	+	0.858047i	$0.328322\pi$
$110$		0			0
$111$	7.67362	+	3.53623i	0.728348	+	0.335644i
$112$	12.1863	−	3.77797i	1.15150	−	0.356985i
$113$	−3.89017	−	3.89017i	−0.365956	−	0.365956i	0.500044	−	0.866000i	$-0.333317\pi$
$113$	−3.89017	−	3.89017i	−0.365956	−	0.365956i	−0.866000	+	0.500044i	$0.833317\pi$
$114$	0.727140	+	7.90077i	0.0681029	+	0.739975i
$115$		0			0
$116$	2.52398	+	1.45722i	0.234345	+	0.135299i
$117$	13.2070	−	6.30416i	1.22099	−	0.582820i
$118$	−4.44819	+	4.44819i	−0.409489	+	0.409489i
$119$	−11.5519	+	0.448692i	−1.05896	+	0.0411315i
$120$		0			0
$121$	8.67136	+	15.0192i	0.788306	+	1.36539i
$122$	3.78923	+	14.1416i	0.343061	+	1.28032i
$123$	6.94022	+	1.19151i	0.625779	+	0.107435i
$124$	2.92152	−	1.68674i	0.262360	−	0.151474i
$125$		0			0
$126$	10.7828	−	9.96443i	0.960612	−	0.887702i
$127$	2.80299	+	2.80299i	0.248725	+	0.248725i	0.820447	−	0.571722i	$-0.193724\pi$
$127$	2.80299	+	2.80299i	0.248725	+	0.248725i	−0.571722	+	0.820447i	$0.693724\pi$
$128$	−2.12270	+	7.92202i	−0.187622	+	0.700214i
$129$	−0.359311	−	0.508257i	−0.0316356	−	0.0447495i
$130$		0			0
$131$	−10.1898	+	5.88311i	−0.890291	+	0.514010i	−0.874038	−	0.485858i	$-0.838507\pi$
$131$	−10.1898	+	5.88311i	−0.890291	+	0.514010i	−0.0162535	+	0.999868i	$0.505174\pi$
$132$	−12.2976	+	4.53887i	−1.07037	+	0.395058i
$133$	1.94015	+	6.25819i	0.168232	+	0.542654i
$134$	−5.29583			−0.457490
$135$		0			0
$136$	2.33753	−	4.04872i	0.200442	−	0.347175i
$137$	−4.71026	−	17.5789i	−0.402425	−	1.50187i	−0.808756	−	0.588144i	$-0.799859\pi$
$137$	−4.71026	−	17.5789i	−0.402425	−	1.50187i	0.406331	−	0.913726i	$-0.366808\pi$
$138$	5.07750	+	4.22166i	0.432226	+	0.359372i
$139$		−	18.0947i		−	1.53478i	−0.641183	−	0.767388i	$-0.721556\pi$
$139$		−	18.0947i		−	1.53478i	0.641183	−	0.767388i	$-0.278444\pi$
$140$		0			0
$141$	−6.24138	+	13.5438i	−0.525619	+	1.14059i
$142$	7.05603	−	26.3335i	0.592129	−	2.20986i
$143$	−25.0854	+	6.72161i	−2.09775	+	0.562089i
$144$	2.64051	+	14.2238i	0.220043	+	1.18532i
$145$		0			0
$146$			20.3304i			1.68256i
$147$	7.00494	−	9.89600i	0.577758	−	0.816208i
$148$	4.90358	−	4.90358i	0.403072	−	0.403072i
$149$	−1.27294	−	2.20479i	−0.104283	−	0.180623i	0.809162	−	0.587586i	$-0.199921\pi$
$149$	−1.27294	−	2.20479i	−0.104283	−	0.180623i	−0.913445	+	0.406962i	$0.866588\pi$
$150$		0			0
$151$	3.21101	−	5.56163i	0.261308	−	0.452599i	−0.705282	−	0.708927i	$-0.749179\pi$
$151$	3.21101	−	5.56163i	0.261308	−	0.452599i	0.966590	+	0.256328i	$0.0825128\pi$
$152$	−2.55933	−	0.685770i	−0.207589	−	0.0556233i
$153$	1.02467	−	13.0684i	0.0828400	−	1.05652i
$154$	−22.0413	+	13.8932i	−1.77614	+	1.11955i
$155$		0			0
$156$	−1.10079	−	11.9607i	−0.0881340	−	0.957624i
$157$	−17.5121	+	4.69234i	−1.39761	+	0.374490i	−0.877487	−	0.479600i	$-0.840782\pi$
$157$	−17.5121	+	4.69234i	−1.39761	+	0.374490i	−0.520127	+	0.854089i	$0.674115\pi$
$158$	−11.3214	+	3.03356i	−0.900683	+	0.241337i
$159$	1.95395	+	21.2307i	0.154958	+	1.68370i
$160$		0			0
$161$	4.82470	+	2.54116i	0.380240	+	0.200271i
$162$	9.79316	+	13.4626i	0.769423	+	1.05772i
$163$	−4.94341	−	1.32458i	−0.387198	−	0.103749i	0.0599682	−	0.998200i	$-0.480900\pi$
$163$	−4.94341	−	1.32458i	−0.387198	−	0.103749i	−0.447166	+	0.894451i	$0.647567\pi$
$164$	2.88977	−	5.00522i	0.225653	−	0.390842i
$165$		0			0
$166$	2.06214	+	3.57174i	0.160053	+	0.277221i
$167$	−7.80577	+	7.80577i	−0.604028	+	0.604028i	−0.941379	−	0.337351i	$-0.890469\pi$
$167$	−7.80577	+	7.80577i	−0.604028	+	0.604028i	0.337351	+	0.941379i	$0.390469\pi$
$168$	1.87494	+	4.53038i	0.144655	+	0.349526i
$169$		−	10.7965i		−	0.830498i
$170$		0			0
$171$	−7.30451	+	1.35601i	−0.558590	+	0.103697i
$172$	−0.493460	+	0.132222i	−0.0376259	+	0.0100818i
$173$	5.26428	−	19.6466i	0.400236	−	1.49370i	−0.412440	−	0.910985i	$-0.635323\pi$
$173$	5.26428	−	19.6466i	0.400236	−	1.49370i	0.812676	−	0.582716i	$-0.198010\pi$
$174$	−2.74904	+	5.96541i	−0.208404	+	0.452236i
$175$		0			0
$176$		−	25.6727i		−	1.93516i
$177$	−4.52934	−	3.76589i	−0.340446	−	0.283062i
$178$	−3.90489	−	14.5732i	−0.292684	−	1.09231i
$179$	−3.30836	+	5.73025i	−0.247279	+	0.428299i	−0.962770	−	0.270323i	$-0.912870\pi$
$179$	−3.30836	+	5.73025i	−0.247279	+	0.428299i	0.715491	+	0.698622i	$0.246203\pi$
$180$		0			0
$181$	−8.70804			−0.647264			−0.323632	−	0.946183i	$-0.604904\pi$
$181$	−8.70804			−0.647264			−0.323632	+	0.946183i	$0.604904\pi$
$182$	−7.06931	−	22.8030i	−0.524012	−	1.69027i
$183$	−12.8609	+	4.74675i	−0.950702	+	0.350890i
$184$	−1.90973	+	1.10258i	−0.140787	+	0.0812836i
$185$		0			0
$186$	4.38889	+	6.20821i	0.321809	+	0.455208i
$187$	−6.02073	+	22.4697i	−0.440279	+	1.64314i
$188$	8.65471	+	8.65471i	0.631210	+	0.631210i
$189$	10.2165	+	9.19914i	0.743137	+	0.669139i
$190$		0			0
$191$	0.256493	−	0.148087i	0.0185592	−	0.0107152i	−0.490692	−	0.871333i	$-0.663256\pi$
$191$	0.256493	−	0.148087i	0.0185592	−	0.0107152i	0.509251	+	0.860618i	$0.329923\pi$
$192$	4.94547	+	0.849045i	0.356908	+	0.0612745i
$193$	2.78610	+	10.3979i	0.200548	+	0.748456i	0.990761	+	0.135623i	$0.0433035\pi$
$193$	2.78610	+	10.3979i	0.200548	+	0.748456i	−0.790212	+	0.612833i	$0.790030\pi$
$194$	−9.86436	−	17.0856i	−0.708220	−	1.22667i
$195$		0			0
$196$	−5.62900	−	8.20599i	−0.402071	−	0.586142i
$197$	0.160785	−	0.160785i	0.0114555	−	0.0114555i	−0.701356	−	0.712811i	$-0.747422\pi$
$197$	0.160785	−	0.160785i	0.0114555	−	0.0114555i	0.712811	+	0.701356i	$0.247422\pi$
$198$	−12.7264	−	26.6614i	−0.904425	−	1.89475i
$199$	5.92757	+	3.42229i	0.420195	+	0.242599i	0.695161	−	0.718854i	$-0.255333\pi$
$199$	5.92757	+	3.42229i	0.420195	+	0.242599i	−0.274966	+	0.961454i	$0.588667\pi$
$200$		0			0
$201$	−0.454462	−	4.93798i	−0.0320553	−	0.348298i
$202$	13.9529	+	13.9529i	0.981721	+	0.981721i
$203$	−1.19947	+	5.28987i	−0.0841860	+	0.371276i
$204$	−9.77120	−	4.50286i	−0.684121	−	0.315263i
$205$		0			0
$206$	3.94436	+	2.27728i	0.274817	+	0.158665i
$207$	−3.50067	+	5.09669i	−0.243314	+	0.354245i
$208$	22.7223	+	6.08841i	1.57550	+	0.422155i
$209$	13.1840			0.911958
$210$		0			0
$211$	−6.49776			−0.447324			−0.223662	−	0.974667i	$-0.571801\pi$
$211$	−6.49776			−0.447324			−0.223662	+	0.974667i	$0.571801\pi$
$212$	16.9025	+	4.52901i	1.16087	+	0.311054i
$213$	25.1596	+	4.31944i	1.72391	+	0.295963i
$214$	−19.8935	−	11.4855i	−1.35989	−	0.785136i
$215$		0			0
$216$	−5.35013	+	1.51142i	−0.364030	+	0.102839i
$217$	4.60852	+	4.26390i	0.312847	+	0.289453i
$218$	23.8643	+	23.8643i	1.61629	+	1.61629i
$219$	−18.9567	+	1.74466i	−1.28097	+	0.117893i
$220$		0			0
$221$	−18.4595	−	10.6576i	−1.24172	−	0.716906i
$222$	12.0177	+	9.99202i	0.806573	+	0.670621i
$223$	−0.832465	+	0.832465i	−0.0557460	+	0.0557460i	−0.734430	−	0.678684i	$-0.762551\pi$
$223$	−0.832465	+	0.832465i	−0.0557460	+	0.0557460i	0.678684	+	0.734430i	$0.262551\pi$
$224$	17.9250	−	0.696234i	1.19767	−	0.0465191i
$225$		0			0
$226$	−5.08823	−	8.81308i	−0.338464	−	0.586237i
$227$	−4.01248	−	14.9748i	−0.266318	−	0.993912i	−0.961439	−	0.275019i	$-0.911316\pi$
$227$	−4.01248	−	14.9748i	−0.266318	−	0.993912i	0.695121	−	0.718893i	$-0.255351\pi$
$228$	−1.03175	+	6.00969i	−0.0683294	+	0.398001i
$229$	9.74226	−	5.62470i	0.643787	−	0.371690i	−0.142285	−	0.989826i	$-0.545445\pi$
$229$	9.74226	−	5.62470i	0.643787	−	0.371690i	0.786072	+	0.618135i	$0.212112\pi$
$230$		0			0
$231$	−14.8459	−	19.3597i	−0.976788	−	1.27377i
$232$	−1.55104	−	1.55104i	−0.101831	−	0.101831i
$233$	−6.74201	+	25.1615i	−0.441684	+	1.64839i	0.282863	+	0.959160i	$0.408716\pi$
$233$	−6.74201	+	25.1615i	−0.441684	+	1.64839i	−0.724547	+	0.689226i	$0.757951\pi$
$234$	26.6154	−	4.94090i	1.73991	−	0.322997i
$235$		0			0
$236$	−4.18685	+	2.41728i	−0.272540	+	0.157351i
$237$	−3.80013	−	10.2961i	−0.246845	−	0.668802i
$238$	−20.8549	−	4.72880i	−1.35182	−	0.306523i
$239$	−1.44722			−0.0936127			−0.0468063	−	0.998904i	$-0.514904\pi$
$239$	−1.44722			−0.0936127			−0.0468063	+	0.998904i	$0.514904\pi$
$240$		0			0
$241$	−11.8069	+	20.4502i	−0.760550	+	1.31731i	0.182017	+	0.983295i	$0.441737\pi$
$241$	−11.8069	+	20.4502i	−0.760550	+	1.31731i	−0.942567	+	0.334016i	$0.891596\pi$
$242$	8.30285	+	30.9866i	0.533727	+	1.99190i
$243$	−11.7125	+	10.2867i	−0.751359	+	0.659893i
$244$			11.2516i			0.720308i
$245$		0			0
$246$	11.8298	+	5.45153i	0.754242	+	0.347577i
$247$	−3.12665	+	11.6688i	−0.198944	+	0.742469i
$248$	−2.45248	+	0.657139i	−0.155732	+	0.0417284i
$249$	−3.15343	+	2.22931i	−0.199840	+	0.141277i
$250$		0			0
$251$		−	14.3739i		−	0.907273i	−0.891187	−	0.453637i	$-0.850126\pi$
$251$		−	14.3739i		−	0.907273i	0.891187	−	0.453637i	$-0.149874\pi$
$252$	9.98654	−	5.25218i	0.629093	−	0.330856i
$253$	7.75876	−	7.75876i	0.487789	−	0.487789i
$254$	3.66624	+	6.35011i	0.230040	+	0.398441i
$255$		0			0
$256$	−10.4824	+	18.1560i	−0.655149	+	1.13475i
$257$	−7.36234	−	1.97273i	−0.459250	−	0.123056i	0.0217741	−	0.999763i	$-0.493069\pi$
$257$	−7.36234	−	1.97273i	−0.459250	−	0.123056i	−0.481025	+	0.876707i	$0.659735\pi$
$258$	−0.398662	−	1.08014i	−0.0248196	−	0.0672463i
$259$	11.4193	+	6.01453i	0.709562	+	0.373724i
$260$		0			0
$261$	−5.79823	−	2.05136i	−0.358901	−	0.126976i
$262$	−21.0230	+	5.63309i	−1.29880	+	0.348014i
$263$	19.4637	−	5.21527i	1.20018	−	0.321588i	0.397279	−	0.917698i	$-0.369955\pi$
$263$	19.4637	−	5.21527i	1.20018	−	0.321588i	0.802902	+	0.596110i	$0.203288\pi$
$264$	9.82438	−	0.904177i	0.604649	−	0.0556483i
$265$		0			0
$266$	0.470389	+	12.1105i	0.0288414	+	0.742543i
$267$	13.2534	−	4.89163i	0.811095	−	0.299363i
$268$	−3.93130	−	1.05339i	−0.240142	−	0.0643459i
$269$	7.88383	−	13.6552i	0.480686	−	0.832572i	−0.519069	−	0.854732i	$-0.673721\pi$
$269$	7.88383	−	13.6552i	0.480686	−	0.832572i	0.999754	+	0.0221606i	$0.00705452\pi$
$270$		0			0
$271$	0.445532	+	0.771684i	0.0270641	+	0.0468765i	0.879240	−	0.476379i	$-0.158051\pi$
$271$	0.445532	+	0.771684i	0.0270641	+	0.0468765i	−0.852176	+	0.523255i	$0.824717\pi$
$272$	14.8994	−	14.8994i	0.903408	−	0.903408i
$273$	20.6555	−	8.54847i	1.25013	−	0.517377i
$274$		−	33.6637i		−	2.03370i
$275$		0			0
$276$	2.92950	+	4.14387i	0.176335	+	0.249431i
$277$	20.4274	−	5.47349i	1.22736	−	0.328870i	0.413809	−	0.910364i	$-0.364198\pi$
$277$	20.4274	−	5.47349i	1.22736	−	0.328870i	0.813551	+	0.581493i	$0.197531\pi$
$278$	8.66287	−	32.3303i	0.519565	−	1.93904i
$279$	−5.41208	+	4.62508i	−0.324013	+	0.276896i
$280$		0			0
$281$			15.1742i			0.905215i	0.891710	+	0.452608i	$0.149506\pi$
$281$			15.1742i			0.905215i	−0.891710	+	0.452608i	$0.850494\pi$
$282$	−17.6357	+	21.2109i	−1.05019	+	1.26309i
$283$	−7.34572	−	27.4146i	−0.436658	−	1.62963i	−0.737068	−	0.675819i	$-0.763790\pi$
$283$	−7.34572	−	27.4146i	−0.436658	−	1.62963i	0.300410	−	0.953810i	$-0.402877\pi$
$284$	10.4759	−	18.1449i	0.621632	−	1.07670i
$285$		0			0
$286$	−48.0386			−2.84058
$287$	10.4902	+	2.37863i	0.619215	+	0.140406i
$288$	−1.58998	+	20.2782i	−0.0936906	+	1.19490i
$289$	−1.81221	+	1.04628i	−0.106601	+	0.0615458i
$290$		0			0
$291$	15.0846	−	10.6640i	0.884273	−	0.625136i
$292$	−4.04390	+	15.0921i	−0.236652	+	0.883196i
$293$	−9.07274	−	9.07274i	−0.530035	−	0.530035i	0.390548	−	0.920583i	$-0.372286\pi$
$293$	−9.07274	−	9.07274i	−0.530035	−	0.530035i	−0.920583	+	0.390548i	$0.872286\pi$
$294$	17.2536	−	14.3278i	1.00625	−	0.835614i
$295$		0			0
$296$	−4.52004	+	2.60965i	−0.262722	+	0.151683i
$297$	23.7678	−	14.1544i	1.37915	−	0.821322i
$298$	−1.21884	−	4.54877i	−0.0706055	−	0.263503i
$299$	5.02704	+	8.70710i	0.290721	+	0.503544i
$300$		0			0
$301$	−0.506995	−	0.804337i	−0.0292227	−	0.0463612i
$302$	8.39982	−	8.39982i	0.483355	−	0.483355i
$303$	−11.8127	+	14.2074i	−0.678622	+	0.816196i
$304$	−10.3421	−	5.97102i	−0.593161	−	0.342461i
$305$		0			0
$306$	8.08732	−	22.8590i	0.462321	−	1.30676i
$307$	−5.35299	−	5.35299i	−0.305511	−	0.305511i	0.537654	−	0.843165i	$-0.319311\pi$
$307$	−5.35299	−	5.35299i	−0.305511	−	0.305511i	−0.843165	+	0.537654i	$0.819311\pi$
$308$	−19.1256	+	5.92926i	−1.08978	+	0.337851i
$309$	−1.78491	+	3.87326i	−0.101540	+	0.220342i
$310$		0			0
$311$	1.32067	+	0.762488i	0.0748883	+	0.0432368i	0.536977	−	0.843597i	$-0.319566\pi$
$311$	1.32067	+	0.762488i	0.0748883	+	0.0432368i	−0.462088	+	0.886834i	$0.652900\pi$
$312$	−1.52963	+	8.90973i	−0.0865985	+	0.504414i
$313$	−22.0134	−	5.89848i	−1.24427	−	0.333402i	−0.424151	−	0.905592i	$-0.639427\pi$
$313$	−22.0134	−	5.89848i	−1.24427	−	0.333402i	−0.820121	+	0.572190i	$0.806094\pi$
$314$	−33.5357			−1.89253
$315$		0			0
$316$	−9.00773			−0.506724
$317$	−9.10844	−	2.44060i	−0.511581	−	0.137078i	−0.00621145	−	0.999981i	$-0.501977\pi$
$317$	−9.10844	−	2.44060i	−0.511581	−	0.137078i	−0.505370	+	0.862903i	$0.668644\pi$
$318$	−6.67306	+	38.8688i	−0.374207	+	2.17966i
$319$	9.45222	+	5.45724i	0.529223	+	0.305547i
$320$		0			0
$321$	9.00228	−	19.5349i	0.502458	−	1.09033i
$322$	7.40382	+	6.85017i	0.412599	+	0.381745i
$323$	7.65146	+	7.65146i	0.425738	+	0.425738i
$324$	4.59200	+	11.9418i	0.255111	+	0.663432i
$325$		0			0
$326$	−8.19836	−	4.73333i	−0.454065	−	0.262155i
$327$	−20.2038	+	24.2997i	−1.11727	+	1.34377i
$328$	−3.07582	+	3.07582i	−0.169834	+	0.169834i
$329$	−10.6155	+	20.1548i	−0.585252	+	1.11117i
$330$		0			0
$331$	−2.28471	−	3.95724i	−0.125579	−	0.217510i	0.796380	−	0.604797i	$-0.206746\pi$
$331$	−2.28471	−	3.95724i	−0.125579	−	0.217510i	−0.921959	+	0.387287i	$0.873412\pi$
$332$	0.820358	+	3.06162i	0.0450230	+	0.168028i
$333$	−8.28555	+	12.0631i	−0.454045	+	0.661053i
$334$	−17.6838	+	10.2097i	−0.967612	+	0.558651i
$335$		0			0
$336$	2.87780	+	21.9102i	0.156997	+	1.19530i
$337$	7.88524	+	7.88524i	0.429537	+	0.429537i	0.888470	−	0.458934i	$-0.151768\pi$
$337$	7.88524	+	7.88524i	0.429537	+	0.429537i	−0.458934	+	0.888470i	$0.651768\pi$
$338$	5.16882	−	19.2903i	0.281147	−	1.04925i
$339$	7.78092	−	5.50071i	0.422601	−	0.298758i
$340$		0			0
$341$	10.9410	−	6.31679i	0.592489	−	0.342073i
$342$	−13.7003	−	1.07422i	−0.740829	−	0.0580873i
$343$	11.4853	−	14.5288i	0.620149	−	0.784484i
$344$	0.384495			0.0207306
$345$		0			0
$346$	18.8116	−	32.5827i	1.01132	−	1.75166i
$347$	8.58998	+	32.0582i	0.461134	+	1.72098i	0.669399	+	0.742903i	$0.266552\pi$
$347$	8.58998	+	32.0582i	0.461134	+	1.72098i	−0.208265	+	0.978072i	$0.566782\pi$
$348$	−3.22729	+	3.88155i	−0.173001	+	0.208073i
$349$			31.6736i			1.69545i	0.530437	+	0.847724i	$0.322028\pi$
$349$			31.6736i			1.69545i	−0.530437	+	0.847724i	$0.677972\pi$
$350$		0			0
$351$	6.89105	+	24.3930i	0.367817	+	1.30200i
$352$	9.34234	−	34.8661i	0.497948	−	1.85837i
$353$	3.43985	−	0.921705i	0.183085	−	0.0490574i	−0.166112	−	0.986107i	$-0.553121\pi$
$353$	3.43985	−	0.921705i	0.183085	−	0.0490574i	0.349196	+	0.937050i	$0.386455\pi$
$354$	−6.28975	−	8.89704i	−0.334296	−	0.472872i
$355$		0			0
$356$		−	11.5950i		−	0.614534i
$357$	2.61960	−	19.8515i	0.138644	−	1.05065i
$358$	−8.65449	+	8.65449i	−0.457404	+	0.457404i
$359$	3.21386	+	5.56657i	0.169621	+	0.293792i	0.938287	−	0.345859i	$-0.112412\pi$
$359$	3.21386	+	5.56657i	0.169621	+	0.293792i	−0.768666	+	0.639651i	$0.779079\pi$
$360$		0			0
$361$	−6.43363	+	11.1434i	−0.338612	+	0.586494i
$362$	−15.5589	−	4.16898i	−0.817756	−	0.219117i
$363$	−28.1803	+	10.4009i	−1.47908	+	0.545908i
$364$	−0.712106	−	18.3337i	−0.0373245	−	0.960946i
$365$		0			0
$366$	−25.2513	+	2.32398i	−1.31991	+	0.121476i
$367$	−16.8145	+	4.50544i	−0.877712	+	0.235182i	−0.669420	−	0.742884i	$-0.733457\pi$
$367$	−16.8145	+	4.50544i	−0.877712	+	0.235182i	−0.208292	+	0.978067i	$0.566790\pi$
$368$	−9.60023	+	2.57237i	−0.500447	+	0.134094i
$369$	−4.06799	+	11.4983i	−0.211771	+	0.598577i
$370$		0			0
$371$	1.26401	+	32.5430i	0.0656243	+	1.68955i
$372$	2.02317	+	5.48159i	0.104897	+	0.284207i
$373$	16.4184	+	4.39929i	0.850111	+	0.227787i	0.657468	−	0.753482i	$-0.271627\pi$
$373$	16.4184	+	4.39929i	0.850111	+	0.227787i	0.192643	+	0.981269i	$0.438294\pi$
$374$	−21.5148	+	37.2646i	−1.11250	+	1.92691i
$375$		0			0
$376$	−4.60597	−	7.97777i	−0.237535	−	0.411422i
$377$	−7.07170	+	7.07170i	−0.364211	+	0.364211i
$378$	13.8499	+	21.3274i	0.712361	+	1.09697i
$379$			0.345401i			0.0177420i	0.999961	+	0.00887102i	$0.00282377\pi$
$379$			0.345401i			0.0177420i	−0.999961	+	0.00887102i	$0.997176\pi$
$380$		0			0
$381$	−5.60640	+	3.96344i	−0.287225	+	0.203053i
$382$	0.529179	−	0.141793i	0.0270752	−	0.00725477i
$383$	2.21949	−	8.28324i	0.113411	−	0.423254i	−0.885753	−	0.464158i	$-0.846357\pi$
$383$	2.21949	−	8.28324i	0.113411	−	0.423254i	0.999163	+	0.0409038i	$0.0130237\pi$
$384$	−12.9014	−	5.94534i	−0.658371	−	0.303397i
$385$		0			0
$386$			19.9120i			1.01349i
$387$	0.972938	−	0.464416i	0.0494572	−	0.0236076i
$388$	−3.92422	−	14.6454i	−0.199222	−	0.743507i
$389$	−9.20300	+	15.9401i	−0.466611	+	0.808193i	−0.999273	−	0.0381349i	$-0.987858\pi$
$389$	−9.20300	+	15.9401i	−0.466611	+	0.808193i	0.532662	+	0.846328i	$0.321192\pi$
$390$		0			0
$391$	9.00572			0.455439
$392$	2.49372	+	7.06216i	0.125952	+	0.356693i
$393$	−7.05655	−	19.1190i	−0.355956	−	0.964427i
$394$	0.364254	−	0.210302i	0.0183509	−	0.0105949i
$395$		0			0
$396$	−4.14409	−	22.3232i	−0.208248	−	1.12178i
$397$	6.02986	−	22.5038i	0.302630	−	1.12943i	−0.632336	−	0.774694i	$-0.717904\pi$
$397$	6.02986	−	22.5038i	0.302630	−	1.12943i	0.934966	−	0.354737i	$-0.115430\pi$
$398$	8.95251	+	8.95251i	0.448749	+	0.448749i
$399$	−11.2518	+	1.47787i	−0.563295	+	0.0739860i
$400$		0			0
$401$	28.1317	−	16.2419i	1.40483	−	0.811080i	0.409949	−	0.912109i	$-0.365547\pi$
$401$	28.1317	−	16.2419i	1.40483	−	0.811080i	0.994884	+	0.101028i	$0.0322133\pi$
$402$	1.55206	−	9.04038i	0.0774099	−	0.450893i
$403$	2.99611	+	11.1816i	0.149247	+	0.556997i
$404$	7.58241	+	13.1331i	0.377239	+	0.653397i
$405$		0			0
$406$	−4.67564	+	8.87728i	−0.232048	+	0.440572i
$407$	18.3638	−	18.3638i	0.910259	−	0.910259i
$408$	6.22641	+	5.17692i	0.308253	+	0.256295i
$409$	−3.74989	−	2.16500i	−0.185420	−	0.107052i	0.404417	−	0.914575i	$-0.367475\pi$
$409$	−3.74989	−	2.16500i	−0.185420	−	0.107052i	−0.589837	+	0.807523i	$0.700808\pi$
$410$		0			0
$411$	31.3890	−	2.88886i	1.54831	−	0.142497i
$412$	2.47508	+	2.47508i	0.121938	+	0.121938i
$413$	−6.60451	−	6.11063i	−0.324987	−	0.300685i
$414$	−8.69478	+	7.43043i	−0.427325	+	0.365186i
$415$		0			0
$416$	28.6435	+	16.5373i	1.40436	+	0.810808i
$417$	30.8891	+	5.30308i	1.51265	+	0.259693i
$418$	23.5562	+	6.31186i	1.15217	+	0.308723i
$419$	33.4081			1.63209			0.816046	−	0.577986i	$-0.196161\pi$
$419$	33.4081			1.63209			0.816046	+	0.577986i	$0.196161\pi$
$420$		0			0
$421$	17.3681			0.846471			0.423236	−	0.906020i	$-0.360894\pi$
$421$	17.3681			0.846471			0.423236	+	0.906020i	$0.360894\pi$
$422$	−11.6097	−	3.11081i	−0.565152	−	0.151432i
$423$	−21.2911	−	14.6238i	−1.03521	−	0.711035i
$424$	−11.4057	−	6.58507i	−0.553909	−	0.319800i
$425$		0			0
$426$	42.8853	+	19.7628i	2.07780	+	0.957512i
$427$	−20.0015	+	6.20082i	−0.967942	+	0.300079i
$428$	−12.4832	−	12.4832i	−0.603397	−	0.603397i
$429$	−4.12244	−	44.7926i	−0.199033	−	2.16261i
$430$		0			0
$431$	−19.4574	−	11.2337i	−0.937228	−	0.541109i	−0.0481375	−	0.998841i	$-0.515329\pi$
$431$	−19.4574	−	11.2337i	−0.937228	−	0.541109i	−0.889090	+	0.457732i	$0.848662\pi$
$432$	−25.0550	+	0.338941i	−1.20546	+	0.0163073i
$433$	−7.76189	+	7.76189i	−0.373013	+	0.373013i	−0.868573	−	0.495561i	$-0.834963\pi$
$433$	−7.76189	+	7.76189i	−0.373013	+	0.373013i	0.495561	+	0.868573i	$0.334963\pi$
$434$	6.19280	+	9.82475i	0.297264	+	0.471603i
$435$		0			0
$436$	12.9686	+	22.4622i	0.621082	+	1.07575i
$437$	−1.32102	−	4.93012i	−0.0631930	−	0.235839i
$438$	−34.7056	−	5.95830i	−1.65830	−	0.284699i
$439$	−4.35444	+	2.51404i	−0.207826	+	0.119988i	−0.600301	−	0.799774i	$-0.704952\pi$
$439$	−4.35444	+	2.51404i	−0.207826	+	0.119988i	0.392475	+	0.919763i	$0.371619\pi$
$440$		0			0
$441$	14.8403	+	14.8582i	0.706679	+	0.707534i
$442$	−27.8796	−	27.8796i	−1.32610	−	1.32610i
$443$	2.56800	−	9.58391i	0.122009	−	0.455345i	−0.877706	−	0.479199i	$-0.840927\pi$
$443$	2.56800	−	9.58391i	0.122009	−	0.455345i	0.999715	+	0.0238542i	$0.00759373\pi$
$444$	6.93367	+	9.80789i	0.329058	+	0.465462i
$445$		0			0
$446$	−1.88593	+	1.08884i	−0.0893013	+	0.0515581i
$447$	4.13681	−	1.52683i	0.195664	−	0.0722168i
$448$	7.47509	+	1.69496i	0.353165	+	0.0800794i
$449$	3.59510			0.169663			0.0848317	−	0.996395i	$-0.472965\pi$
$449$	3.59510			0.169663			0.0848317	+	0.996395i	$0.472965\pi$
$450$		0			0
$451$	10.8221	−	18.7444i	0.509593	−	0.882641i
$452$	−2.02419	−	7.55439i	−0.0952100	−	0.355328i
$453$	8.55306	+	7.11140i	0.401858	+	0.334123i
$454$		−	28.6768i		−	1.34587i
$455$		0			0
$456$	1.92073	−	4.16799i	0.0899465	−	0.195184i
$457$	1.77045	−	6.60740i	0.0828181	−	0.309081i	−0.912074	−	0.410026i	$-0.865520\pi$
$457$	1.77045	−	6.60740i	0.0828181	−	0.309081i	0.994892	+	0.100944i	$0.0321864\pi$
$458$	20.0996	−	5.38566i	0.939190	−	0.251655i
$459$	22.0084	+	5.57919i	1.02727	+	0.260414i
$460$		0			0
$461$		−	2.00072i		−	0.0931829i	−0.998914	−	0.0465915i	$-0.985164\pi$
$461$		−	2.00072i		−	0.0931829i	0.998914	−	0.0465915i	$-0.0148359\pi$
$462$	−17.2570	−	41.6978i	−0.802870	−	1.93996i
$463$	29.2416	−	29.2416i	1.35897	−	1.35897i	0.483786	−	0.875186i	$-0.339261\pi$
$463$	29.2416	−	29.2416i	1.35897	−	1.35897i	0.875186	−	0.483786i	$-0.160739\pi$
$464$	−4.94315	−	8.56179i	−0.229480	−	0.397471i
$465$		0			0
$466$	−24.0922	+	41.7289i	−1.11605	+	1.93306i
$467$	13.6417	+	3.65529i	0.631265	+	0.169147i	0.560244	−	0.828328i	$-0.310708\pi$
$467$	13.6417	+	3.65529i	0.631265	+	0.169147i	0.0710212	+	0.997475i	$0.477374\pi$
$468$	20.7405	+	1.62623i	0.958728	+	0.0751725i
$469$	−0.293993	−	7.56906i	−0.0135753	−	0.349507i
$470$		0			0
$471$	−2.87787	−	31.2696i	−0.132605	−	1.44083i
$472$	3.51466	−	0.941751i	0.161775	−	0.0433476i
$473$	−1.84799	+	0.495168i	−0.0849708	+	0.0227679i
$474$	−1.86052	−	20.2156i	−0.0854565	−	0.928531i
$475$		0			0
$476$	−14.5408	−	7.65860i	−0.666476	−	0.351031i
$477$	−36.8151	−	2.88662i	−1.68565	−	0.132169i
$478$	−2.58578	−	0.692856i	−0.118271	−	0.0316905i
$479$	8.02039	−	13.8917i	0.366461	−	0.634729i	−0.622548	−	0.782581i	$-0.713903\pi$
$479$	8.02039	−	13.8917i	0.366461	−	0.634729i	0.989009	+	0.147852i	$0.0472360\pi$
$480$		0			0
$481$	11.8982	+	20.6083i	0.542513	+	0.939660i
$482$	−30.8862	+	30.8862i	−1.40683	+	1.40683i
$483$	−5.75194	+	7.49138i	−0.261722	+	0.340870i
$484$			24.6541i			1.12064i
$485$		0			0
$486$	−25.8518	+	12.7721i	−1.17266	+	0.579356i
$487$	4.68754	−	1.25602i	0.212413	−	0.0569158i	−0.151044	−	0.988527i	$-0.548263\pi$
$487$	4.68754	−	1.25602i	0.212413	−	0.0569158i	0.363456	+	0.931611i	$0.381597\pi$
$488$	2.19176	−	8.17976i	0.0992163	−	0.370280i
$489$	3.70995	−	8.05058i	0.167770	−	0.364060i
$490$		0			0
$491$		−	15.9243i		−	0.718652i	−0.933212	−	0.359326i	$-0.883007\pi$
$491$		−	15.9243i		−	0.718652i	0.933212	−	0.359326i	$-0.116993\pi$
$492$	7.69738	+	6.39995i	0.347025	+	0.288532i
$493$	2.31852	+	8.65284i	0.104421	+	0.389704i
$494$	−11.1729	+	19.3521i	−0.502694	+	0.870691i
$495$		0			0
$496$	−11.4435			−0.513826
$497$	38.0288	+	8.62296i	1.70583	+	0.386793i
$498$	−6.70159	+	2.47345i	−0.300305	+	0.110838i
$499$	9.09769	−	5.25255i	0.407268	−	0.235137i	−0.282347	−	0.959312i	$-0.591113\pi$
$499$	9.09769	−	5.25255i	0.407268	−	0.235137i	0.689615	+	0.724176i	$0.257780\pi$
$500$		0			0
$501$	−11.0374	−	15.6127i	−0.493114	−	0.697524i
$502$	6.88153	−	25.6822i	0.307138	−	1.14625i
$503$	−9.84893	−	9.84893i	−0.439142	−	0.439142i	0.452581	−	0.891723i	$-0.350503\pi$
$503$	−9.84893	−	9.84893i	−0.439142	−	0.439142i	−0.891723	+	0.452581i	$0.850503\pi$
$504$	−8.28320	+	1.87293i	−0.368963	+	0.0834270i
$505$		0			0
$506$	17.5773	−	10.1482i	0.781405	−	0.451144i
$507$	18.4304	+	3.16416i	0.818522	+	0.140525i
$508$	1.45850	+	5.44318i	0.0647103	+	0.241502i
$509$	−12.0330	−	20.8417i	−0.533352	−	0.923793i	−0.999241	−	0.0389500i	$-0.987599\pi$
$509$	−12.0330	−	20.8417i	−0.533352	−	0.923793i	0.465889	−	0.884843i	$-0.345735\pi$
$510$		0			0
$511$	−29.0572	+	1.12862i	−1.28542	+	0.0499274i
$512$	−15.8227	+	15.8227i	−0.699271	+	0.699271i
$513$	−0.174060	−	12.8668i	−0.00768494	−	0.568081i
$514$	−12.2100	−	7.04946i	−0.538561	−	0.310938i
$515$		0			0
$516$	−0.0810934	−	0.881124i	−0.00356994	−	0.0387893i
$517$	32.4117	+	32.4117i	1.42546	+	1.42546i
$518$	17.5237	+	16.2133i	0.769947	+	0.712372i
$519$	31.9954	+	14.7444i	1.40444	+	0.647208i
$520$		0			0
$521$	0.396615	+	0.228986i	0.0173760	+	0.0100320i	0.508663	−	0.860966i	$-0.330140\pi$
$521$	0.396615	+	0.228986i	0.0173760	+	0.0100320i	−0.491287	+	0.870998i	$0.663473\pi$
$522$	−9.37774	−	6.44112i	−0.410452	−	0.281920i
$523$	−38.0113	−	10.1851i	−1.66212	−	0.445364i	−0.699150	−	0.714975i	$-0.746438\pi$
$523$	−38.0113	−	10.1851i	−1.66212	−	0.445364i	−0.962969	+	0.269611i	$0.913105\pi$
$524$	−16.7267			−0.730707
$525$		0			0
$526$	37.2730			1.62518
$527$	10.0157	+	2.68370i	0.436291	+	0.116904i
$528$	43.8253	+	7.52399i	1.90725	+	0.327440i
$529$	16.2398	+	9.37606i	0.706079	+	0.407655i
$530$		0			0
$531$	7.75610	−	6.62824i	0.336586	−	0.287641i
$532$	−2.05970	+	9.08366i	−0.0892994	+	0.393827i
$533$	14.0237	+	14.0237i	0.607433	+	0.607433i
$534$	26.0220	−	2.39491i	1.12608	−	0.103638i
$535$		0			0
$536$	2.65281	+	1.53160i	0.114584	+	0.0661551i
$537$	−8.81238	−	7.32701i	−0.380282	−	0.316184i
$538$	20.6237	−	20.6237i	0.889149	−	0.889149i
$539$	−21.0805	−	30.7312i	−0.908000	−	1.32369i
$540$		0			0
$541$	12.8403	+	22.2400i	0.552046	+	0.956172i	0.998127	+	0.0611795i	$0.0194862\pi$
$541$	12.8403	+	22.2400i	0.552046	+	0.956172i	−0.446080	+	0.894993i	$0.647180\pi$
$542$	0.426598	+	1.59208i	0.0183239	+	0.0683859i
$543$	2.55209	−	14.8653i	0.109521	−	0.637931i
$544$	25.6567	−	14.8129i	1.10002	−	0.635099i
$545$		0			0
$546$	40.9982	−	5.38491i	1.75456	−	0.230453i
$547$	−23.9536	−	23.9536i	−1.02418	−	1.02418i	−0.999700	−	0.0244811i	$-0.992207\pi$
$547$	−23.9536	−	23.9536i	−1.02418	−	1.02418i	−0.0244811	−	0.999700i	$-0.507793\pi$
$548$	6.69602	−	24.9899i	0.286040	−	1.06752i
$549$	−4.33389	−	23.3456i	−0.184966	−	0.996367i
$550$		0			0
$551$	4.39684	−	2.53851i	0.187312	−	0.108144i
$552$	−1.32250	−	3.58320i	−0.0562895	−	0.152511i
$553$	−4.96422	−	16.0127i	−0.211100	−	0.680930i
$554$	39.1185			1.66198
$555$		0			0
$556$	12.8616	−	22.2769i	0.545452	−	0.944751i
$557$	−7.02893	−	26.2323i	−0.297825	−	1.11150i	−0.938947	−	0.344061i	$-0.888197\pi$
$557$	−7.02893	−	26.2323i	−0.297825	−	1.11150i	0.641122	−	0.767439i	$-0.278469\pi$
$558$	−11.8842	+	5.67270i	−0.503096	+	0.240145i
$559$		−	1.75304i		−	0.0741457i
$560$		0			0
$561$	−36.5929	−	16.8631i	−1.54495	−	0.711961i
$562$	−7.26465	+	27.1120i	−0.306441	+	1.14365i
$563$	1.54034	−	0.412734i	0.0649177	−	0.0173947i	−0.226214	−	0.974078i	$-0.572635\pi$
$563$	1.54034	−	0.412734i	0.0649177	−	0.0173947i	0.291132	+	0.956683i	$0.405968\pi$
$564$	−17.3107	+	12.2378i	−0.728913	+	0.515304i
$565$		0			0
$566$		−	52.4991i		−	2.20670i
$567$	−18.6978	+	14.7442i	−0.785234	+	0.619200i
$568$	−11.1504	+	11.1504i	−0.467861	+	0.467861i
$569$	−6.46955	−	11.2056i	−0.271218	−	0.469763i	0.697956	−	0.716140i	$-0.254093\pi$
$569$	−6.46955	−	11.2056i	−0.271218	−	0.469763i	−0.969174	+	0.246378i	$0.920760\pi$
$570$		0			0
$571$	3.63645	−	6.29852i	0.152181	−	0.263585i	−0.779848	−	0.625969i	$-0.784704\pi$
$571$	3.63645	−	6.29852i	0.152181	−	0.263585i	0.932029	+	0.362384i	$0.118037\pi$
$572$	−35.6609	−	9.55532i	−1.49106	−	0.399528i
$573$	0.177624	+	0.481254i	0.00742033	+	0.0201047i
$574$	17.6043	+	9.27213i	0.734788	+	0.387011i
$575$		0			0
$576$	−2.89877	+	8.19346i	−0.120782	+	0.341394i
$577$	−17.6275	+	4.72328i	−0.733843	+	0.196633i	−0.606340	−	0.795206i	$-0.707363\pi$
$577$	−17.6275	+	4.72328i	−0.733843	+	0.196633i	−0.127503	+	0.991838i	$0.540696\pi$
$578$	−3.73882	+	1.00181i	−0.155515	+	0.0416700i
$579$	−18.5665	+	1.70875i	−0.771598	+	0.0710132i
$580$		0			0
$581$	−4.99043	+	3.14560i	−0.207038	+	0.130501i
$582$	32.0574	−	11.8319i	1.32882	−	0.490448i
$583$	63.2995	+	16.9610i	2.62160	+	0.702454i
$584$	5.87974	−	10.1840i	0.243305	−	0.421417i
$585$		0			0
$586$	−11.8669	−	20.5541i	−0.490217	−	0.849080i
$587$	−5.12734	+	5.12734i	−0.211628	+	0.211628i	−0.804959	−	0.593331i	$-0.797813\pi$
$587$	−5.12734	+	5.12734i	−0.211628	+	0.211628i	0.593331	+	0.804959i	$0.297813\pi$
$588$	15.6580	−	7.20417i	0.645723	−	0.297095i
$589$		−	5.87669i		−	0.242145i
$590$		0			0
$591$	0.227350	+	0.321594i	0.00935195	+	0.0132286i
$592$	−22.7223	+	6.08841i	−0.933879	+	0.250232i
$593$	−3.03836	+	11.3393i	−0.124770	+	0.465650i	−0.999831	−	0.0183632i	$-0.994154\pi$
$593$	−3.03836	+	11.3393i	−0.124770	+	0.465650i	0.875061	+	0.484013i	$0.160821\pi$
$594$	49.2428	−	13.9112i	2.02046	−	0.570782i
$595$		0			0
$596$		−	3.61917i		−	0.148247i
$597$	−7.57932	+	9.11584i	−0.310201	+	0.373086i
$598$	4.81340	+	17.9639i	0.196835	+	0.734597i
$599$	4.87896	−	8.45060i	0.199349	−	0.345282i	−0.748969	−	0.662605i	$-0.769451\pi$
$599$	4.87896	−	8.45060i	0.199349	−	0.345282i	0.948317	+	0.317323i	$0.102784\pi$
$600$		0			0
$601$	37.0872			1.51282			0.756408	−	0.654100i	$-0.226952\pi$
$601$	37.0872			1.51282			0.756408	+	0.654100i	$0.226952\pi$
$602$	−0.520783	−	1.67985i	−0.0212255	−	0.0684657i
$603$	8.56270	+	0.671388i	0.348700	+	0.0273410i
$604$	7.90631	−	4.56471i	0.321703	−	0.185735i
$605$		0			0
$606$	−27.9078	+	19.7294i	−1.13368	+	0.801453i
$607$	4.36982	−	16.3084i	0.177366	−	0.661937i	−0.818771	−	0.574120i	$-0.805344\pi$
$607$	4.36982	−	16.3084i	0.177366	−	0.661937i	0.996137	−	0.0878171i	$-0.0279891\pi$
$608$	−11.8727	−	11.8727i	−0.481503	−	0.481503i
$609$	−8.67867	−	3.59790i	−0.351677	−	0.145794i
$610$		0			0
$611$	−36.3733	+	21.0001i	−1.47151	+	0.849574i
$612$	10.5504	−	15.3605i	0.426475	−	0.620912i
$613$	−2.74436	−	10.2421i	−0.110844	−	0.413674i	0.888099	−	0.459653i	$-0.152026\pi$
$613$	−2.74436	−	10.2421i	−0.110844	−	0.413674i	−0.998942	+	0.0459784i	$0.985359\pi$
$614$	−7.00156	−	12.1271i	−0.282560	−	0.489408i
$615$		0			0
$616$	15.0591	−	0.584914i	0.606747	−	0.0235669i
$617$	18.4282	−	18.4282i	0.741892	−	0.741892i	−0.231050	−	0.972942i	$-0.574216\pi$
$617$	18.4282	−	18.4282i	0.741892	−	0.741892i	0.972942	+	0.231050i	$0.0742161\pi$
$618$	−5.04347	+	6.06591i	−0.202878	+	0.244007i
$619$	−27.8270	−	16.0659i	−1.11846	−	0.645745i	−0.177455	−	0.984129i	$-0.556786\pi$
$619$	−27.8270	−	16.0659i	−1.11846	−	0.645745i	−0.941008	+	0.338384i	$0.890120\pi$
$620$		0			0
$621$	−7.67449	−	7.46962i	−0.307967	−	0.299745i
$622$	1.99463	+	1.99463i	0.0799773	+	0.0799773i
$623$	20.6120	−	6.39008i	0.825803	−	0.256013i
$624$	−17.0527	+	37.0043i	−0.682653	+	1.48136i
$625$		0			0
$626$	−36.5080	−	21.0779i	−1.45915	−	0.842442i
$627$	−3.86388	+	22.5061i	−0.154309	+	0.898808i
$628$	−24.8948	−	6.67055i	−0.993411	−	0.266184i
$629$	21.3151			0.849891
$630$		0			0
$631$	−33.8314			−1.34681			−0.673404	−	0.739274i	$-0.735169\pi$
$631$	−33.8314			−1.34681			−0.673404	+	0.739274i	$0.735169\pi$
$632$	6.54851	+	1.75467i	0.260486	+	0.0697969i
$633$	1.90432	−	11.0922i	0.0756899	−	0.440874i
$634$	−15.1058	−	8.72135i	−0.599929	−	0.346369i
$635$		0			0
$636$	−12.6850	+	27.5265i	−0.502995	+	1.09150i
$637$	32.1987	−	11.3697i	1.27576	−	0.450484i
$638$	14.2758	+	14.2758i	0.565186	+	0.565186i
$639$	−14.7472	+	41.6834i	−0.583391	+	1.64897i
$640$		0			0
$641$	16.3821	+	9.45823i	0.647055	+	0.373577i	0.787327	−	0.616536i	$-0.211464\pi$
$641$	16.3821	+	9.45823i	0.647055	+	0.373577i	−0.140272	+	0.990113i	$0.544798\pi$
$642$	25.4370	−	30.5937i	1.00392	−	1.20744i
$643$	2.39355	−	2.39355i	0.0943926	−	0.0943926i	−0.658334	−	0.752726i	$-0.728738\pi$
$643$	2.39355	−	2.39355i	0.0943926	−	0.0943926i	0.752726	+	0.658334i	$0.228738\pi$
$644$	4.13358	+	6.55784i	0.162886	+	0.258415i
$645$		0			0
$646$	10.0079	+	17.3342i	0.393755	+	0.682004i
$647$	−0.609034	−	2.27295i	−0.0239436	−	0.0893588i	0.952920	−	0.303221i	$-0.0980622\pi$
$647$	−0.609034	−	2.27295i	−0.0239436	−	0.0893588i	−0.976864	+	0.213863i	$0.931396\pi$
$648$	−1.01212	−	9.57603i	−0.0397600	−	0.376182i
$649$	−15.6796	+	9.05264i	−0.615480	+	0.355347i
$650$		0			0
$651$	−8.62944	+	6.61746i	−0.338215	+	0.259359i
$652$	−5.14446	−	5.14446i	−0.201473	−	0.201473i
$653$	−6.42731	+	23.9871i	−0.251520	+	0.938686i	0.718473	+	0.695555i	$0.244841\pi$
$653$	−6.42731	+	23.9871i	−0.251520	+	0.938686i	−0.969993	+	0.243132i	$0.921825\pi$
$654$	−47.7321	+	33.7442i	−1.86647	+	1.31950i
$655$		0			0
$656$	−16.9786	+	9.80262i	−0.662904	+	0.382728i
$657$	2.57743	−	32.8718i	0.100555	−	1.28245i
$658$	−28.6161	+	30.9289i	−1.11557	+	1.20574i
$659$	10.2106			0.397748			0.198874	−	0.980025i	$-0.436271\pi$
$659$	10.2106			0.397748			0.198874	+	0.980025i	$0.436271\pi$
$660$		0			0
$661$	−1.16075	+	2.01047i	−0.0451478	+	0.0781982i	−0.887716	−	0.460391i	$-0.847709\pi$
$661$	−1.16075	+	2.01047i	−0.0451478	+	0.0781982i	0.842568	+	0.538589i	$0.181043\pi$
$662$	−2.18762	−	8.16430i	−0.0850242	−	0.317315i
$663$	23.6033	−	28.3882i	0.916675	−	1.10251i
$664$		−	2.38556i		−	0.0925778i
$665$		0			0
$666$	−20.5792	+	17.5867i	−0.797428	+	0.681469i
$667$	1.09362	−	4.08143i	0.0423450	−	0.158034i
$668$	−15.1582	+	4.06161i	−0.586487	+	0.157149i
$669$	−1.17711	−	1.66505i	−0.0455096	−	0.0643747i
$670$		0			0
$671$			42.1369i			1.62668i
$672$	−4.06483	+	30.8035i	−0.156804	+	1.18827i
$673$	−1.14714	+	1.14714i	−0.0442189	+	0.0442189i	−0.728870	−	0.684652i	$-0.759954\pi$
$673$	−1.14714	+	1.14714i	−0.0442189	+	0.0442189i	0.684652	+	0.728870i	$0.259954\pi$
$674$	10.3137	+	17.8638i	0.397268	+	0.688089i
$675$		0			0
$676$	7.67403	−	13.2918i	0.295155	−	0.511224i
$677$	2.42261	+	0.649136i	0.0931084	+	0.0249483i	0.305072	−	0.952329i	$-0.401319\pi$
$677$	2.42261	+	0.649136i	0.0931084	+	0.0249483i	−0.211964	+	0.977277i	$0.567986\pi$
$678$	16.5358	−	6.10312i	0.635054	−	0.234389i
$679$	23.8719	−	15.0471i	0.916121	−	0.577456i
$680$		0			0
$681$	26.7391	−	2.46090i	1.02464	−	0.0943020i
$682$	22.5727	−	6.04834i	0.864354	−	0.231603i
$683$	−26.8414	+	7.19213i	−1.02706	+	0.275199i	−0.732740	−	0.680509i	$-0.761759\pi$
$683$	−26.8414	+	7.19213i	−1.02706	+	0.275199i	−0.294317	+	0.955708i	$0.595092\pi$
$684$	−9.95661	−	3.52256i	−0.380701	−	0.134688i
$685$		0			0
$686$	27.4768	−	20.4604i	1.04907	−	0.781182i
$687$	6.74659	+	18.2792i	0.257398	+	0.697396i
$688$	1.67391	+	0.448522i	0.0638171	+	0.0170997i
$689$	−30.0235	+	52.0023i	−1.14381	+	1.98113i
$690$		0			0
$691$	−21.0048	−	36.3813i	−0.799059	−	1.38401i	−0.920230	−	0.391379i	$-0.871998\pi$
$691$	−21.0048	−	36.3813i	−0.799059	−	1.38401i	0.121171	−	0.992632i	$-0.461335\pi$
$692$	20.4456	−	20.4456i	0.777225	−	0.777225i
$693$	37.3994	−	19.6693i	1.42068	−	0.747174i
$694$			61.3916i			2.33039i
$695$		0			0
$696$	3.10231	−	2.19317i	0.117593	−	0.0831321i
$697$	17.1592	−	4.59779i	0.649950	−	0.174154i
$698$	−15.1638	+	56.5919i	−0.573957	+	2.14204i
$699$	−40.9767	−	18.8833i	−1.54988	−	0.714232i
$700$		0			0
$701$			12.5905i			0.475538i	0.971322	+	0.237769i	$0.0764161\pi$
$701$			12.5905i			0.475538i	−0.971322	+	0.237769i	$0.923584\pi$
$702$	0.634223	+	46.8826i	0.0239372	+	1.76947i
$703$	−3.12665	−	11.6688i	−0.117924	−	0.440098i
$704$	7.71162	−	13.3569i	0.290642	−	0.503407i
$705$		0			0
$706$	6.58733			0.247917
$707$	−19.1676	+	20.7167i	−0.720871	+	0.779133i
$708$	−2.89942	−	7.85570i	−0.108967	−	0.295235i
$709$	13.5078	−	7.79873i	0.507296	−	0.292887i	−0.224426	−	0.974491i	$-0.572051\pi$
$709$	13.5078	−	7.79873i	0.507296	−	0.292887i	0.731721	+	0.681604i	$0.238717\pi$
$710$		0			0
$711$	18.6899	−	3.46960i	0.700926	−	0.130120i
$712$	−2.25866	+	8.42942i	−0.0846468	+	0.315906i
$713$	−3.45842	−	3.45842i	−0.129519	−	0.129519i
$714$	14.1844	−	34.2150i	0.530839	−	1.28046i
$715$		0			0
$716$	−8.14602	+	4.70311i	−0.304431	+	0.175763i
$717$	0.424140	−	2.47051i	0.0158398	−	0.0922628i
$718$	3.07728	+	11.4846i	0.114843	+	0.428600i
$719$	0.580808	+	1.00599i	0.0216605	+	0.0375171i	0.876652	−	0.481124i	$-0.159771\pi$
$719$	0.580808	+	1.00599i	0.0216605	+	0.0375171i	−0.854992	+	0.518641i	$0.826438\pi$
$720$		0			0
$721$	−3.03583	+	5.76390i	−0.113060	+	0.214659i
$722$	−16.8300	+	16.8300i	−0.626349	+	0.626349i
$723$	−31.4497	−	26.1487i	−1.16963	−	0.972481i
$724$	−10.7207	−	6.18960i	−0.398432	−	0.230035i
$725$		0			0
$726$	−55.3299	+	5.09223i	−2.05349	+	0.188990i
$727$	29.8756	+	29.8756i	1.10803	+	1.10803i	0.993410	+	0.114616i	$0.0365637\pi$
$727$	29.8756	+	29.8756i	1.10803	+	1.10803i	0.114616	+	0.993410i	$0.463436\pi$
$728$	−3.05363	+	13.4671i	−0.113175	+	0.499123i
$729$	−14.1276	−	23.0089i	−0.523244	−	0.852183i
$730$		0			0
$731$	−1.35987	−	0.785123i	−0.0502967	−	0.0290388i
$732$	−19.2073	−	3.29754i	−0.709922	−	0.121880i
$733$	−10.9604	−	2.93683i	−0.404831	−	0.108474i	0.0506569	−	0.998716i	$-0.483869\pi$
$733$	−10.9604	−	2.93683i	−0.404831	−	0.108474i	−0.455488	+	0.890242i	$0.650535\pi$
$734$	−32.1999			−1.18852
$735$		0			0
$736$	−13.9741			−0.515094
$737$	−14.7226	−	3.94491i	−0.542314	−	0.145313i
$738$	−12.7732	+	18.5967i	−0.470188	+	0.684554i
$739$	13.2799	+	7.66718i	0.488511	+	0.282042i	0.723956	−	0.689846i	$-0.242322\pi$
$739$	13.2799	+	7.66718i	0.488511	+	0.282042i	−0.235446	+	0.971888i	$0.575655\pi$
$740$		0			0
$741$	−19.0032	−	8.75725i	−0.698101	−	0.321706i
$742$	−13.3215	+	58.7504i	−0.489049	+	2.15680i
$743$	−29.6061	−	29.6061i	−1.08614	−	1.08614i	−0.995922	−	0.0902205i	$-0.971243\pi$
$743$	−29.6061	−	29.6061i	−1.08614	−	1.08614i	−0.0902205	−	0.995922i	$-0.528757\pi$
$744$	−0.403031	−	4.37915i	−0.0147758	−	0.160548i
$745$		0			0
$746$	27.2289	+	15.7206i	0.996922	+	0.575573i
$747$	−2.88142	−	6.03649i	−0.105426	−	0.220864i
$748$	−23.3835	+	23.3835i	−0.854986	+	0.854986i
$749$	15.3113	−	29.0705i	0.559464	−	1.06221i
$750$		0			0
$751$	−5.18864	−	8.98698i	−0.189336	−	0.327940i	0.755693	−	0.654926i	$-0.227300\pi$
$751$	−5.18864	−	8.98698i	−0.189336	−	0.327940i	−0.945029	+	0.326986i	$0.893967\pi$
$752$	−10.7459	−	40.1043i	−0.391863	−	1.46245i
$753$	24.5374	+	4.21261i	0.894191	+	0.153516i
$754$	−16.0208	+	9.24959i	−0.583441	+	0.336850i
$755$		0			0
$756$	6.03908	+	18.5871i	0.219639	+	0.676005i
$757$	1.14687	+	1.14687i	0.0416838	+	0.0416838i	0.727641	−	0.685958i	$-0.240616\pi$
$757$	1.14687	+	1.14687i	0.0416838	+	0.0416838i	−0.685958	+	0.727641i	$0.740616\pi$
$758$	−0.165361	+	0.617135i	−0.00600618	+	0.0224154i
$759$	10.9709	+	15.5187i	0.398219	+	0.563292i
$760$		0			0
$761$	11.5360	−	6.66031i	0.418180	−	0.241436i	−0.276119	−	0.961124i	$-0.589048\pi$
$761$	11.5360	−	6.66031i	0.418180	−	0.241436i	0.694298	+	0.719687i	$0.255715\pi$
$762$	−11.9146	+	4.39750i	−0.431620	+	0.159304i
$763$	−32.7832	+	35.4328i	−1.18683	+	1.28275i
$764$	0.421034			0.0152325
$765$		0			0
$766$	7.93122	−	13.7373i	0.286567	−	0.496348i
$767$	−4.29375	−	16.0245i	−0.155038	−	0.578611i
$768$	−27.9216	−	23.2153i	−1.00753	−	0.837709i
$769$			47.7620i			1.72234i	0.508315	+	0.861171i	$0.330269\pi$
$769$			47.7620i			1.72234i	−0.508315	+	0.861171i	$0.669731\pi$
$770$		0			0
$771$	5.52531	−	11.9899i	0.198989	−	0.431807i
$772$	−3.96067	+	14.7814i	−0.142548	+	0.531996i
$773$	−4.71423	+	1.26317i	−0.169559	+	0.0454332i	−0.342600	−	0.939481i	$-0.611307\pi$
$773$	−4.71423	+	1.26317i	−0.169559	+	0.0454332i	0.173041	+	0.984915i	$0.444641\pi$
$774$	1.96071	−	0.363987i	0.0704762	−	0.0130832i
$775$		0			0
$776$			11.4115i			0.409647i
$777$	−13.6139	+	17.7309i	−0.488398	+	0.636094i
$778$	−24.0745	+	24.0745i	−0.863114	+	0.863114i
$779$	−5.03405	−	8.71924i	−0.180364	−	0.312399i
$780$		0			0
$781$	39.2321	−	67.9520i	1.40384	−	2.43151i
$782$	16.0907	+	4.31150i	0.575403	+	0.154179i
$783$	5.20113	−	9.29681i	0.185873	−	0.332241i
$784$	2.61830	+	33.6542i	0.0935107	+	1.20194i
$785$		0			0
$786$	−3.45484	−	37.5387i	−0.123230	−	1.33896i
$787$	5.59964	−	1.50042i	0.199606	−	0.0534842i	−0.157631	−	0.987498i	$-0.550386\pi$
$787$	5.59964	−	1.50042i	0.199606	−	0.0534842i	0.357237	+	0.934014i	$0.383719\pi$
$788$	0.312231	−	0.0836621i	0.0111228	−	0.00298034i
$789$	3.19859	+	34.7544i	0.113873	+	1.23729i
$790$		0			0
$791$	12.3136	−	7.76161i	0.437822	−	0.275971i
$792$	−1.33576	+	17.0360i	−0.0474643	+	0.605346i
$793$	−37.2942	−	9.99295i	−1.32436	−	0.354860i
$794$	21.5474	−	37.3212i	0.764688	−	1.32448i
$795$		0			0
$796$	4.86506	+	8.42653i	0.172438	+	0.298671i
$797$	25.7650	−	25.7650i	0.912644	−	0.912644i	−0.0838353	−	0.996480i	$-0.526717\pi$
$797$	25.7650	−	25.7650i	0.912644	−	0.912644i	0.996480	+	0.0838353i	$0.0267170\pi$
$798$	−20.8114	−	2.74628i	−0.736716	−	0.0972171i
$799$			37.6208i			1.33093i
$800$		0			0
$801$	4.46617	+	24.0582i	0.157804	+	0.850054i
$802$	58.0394	−	15.5516i	2.04944	−	0.549147i
$803$	−15.1443	+	56.5194i	−0.534432	+	1.99453i
$804$	2.95037	−	6.40230i	0.104052	−	0.225792i
$805$		0			0
$806$			21.4129i			0.754237i
$807$	20.9999	+	17.4603i	0.739232	+	0.614630i
$808$	−2.95404	−	11.0246i	−0.103923	−	0.387846i
$809$	13.1923	−	22.8498i	0.463818	−	0.803356i	−0.535330	−	0.844643i	$-0.679813\pi$
$809$	13.1923	−	22.8498i	0.463818	−	0.803356i	0.999147	+	0.0412873i	$0.0131459\pi$
$810$		0			0
$811$	−21.9075			−0.769276			−0.384638	−	0.923067i	$-0.625674\pi$
$811$	−21.9075			−0.769276			−0.384638	+	0.923067i	$0.625674\pi$
$812$	−5.23668	+	5.65992i	−0.183772	+	0.198624i
$813$	−1.44790	+	0.534397i	−0.0507799	+	0.0187421i
$814$	41.6027	−	24.0193i	1.45817	−	0.841876i
$815$		0			0
$816$	21.0678	+	29.8010i	0.737520	+	1.04324i
$817$	−0.230335	+	0.859620i	−0.00805839	+	0.0300743i
$818$	−5.66352	−	5.66352i	−0.198020	−	0.198020i
$819$	8.53931	+	37.7658i	0.298388	+	1.31964i
$820$		0			0
$821$	−29.6181	+	17.1000i	−1.03368	+	0.596794i	−0.918036	−	0.396497i	$-0.870226\pi$
$821$	−29.6181	+	17.1000i	−1.03368	+	0.596794i	−0.115642	+	0.993291i	$0.536893\pi$
$822$	57.4665	+	9.86594i	2.00438	+	0.344114i
$823$	10.4901	+	39.1497i	0.365663	+	1.36467i	0.866520	+	0.499142i	$0.166351\pi$
$823$	10.4901	+	39.1497i	0.365663	+	1.36467i	−0.500858	+	0.865530i	$0.666982\pi$
$824$	−1.31722	−	2.28149i	−0.0458875	−	0.0794795i
$825$		0			0
$826$	−8.87495	−	14.0799i	−0.308799	−	0.489903i
$827$	−33.6571	+	33.6571i	−1.17037	+	1.17037i	−0.188249	+	0.982121i	$0.560281\pi$
$827$	−33.6571	+	33.6571i	−1.17037	+	1.17037i	−0.982121	+	0.188249i	$0.939719\pi$
$828$	−7.93245	+	3.78642i	−0.275672	+	0.131587i
$829$	−14.9735	−	8.64496i	−0.520051	−	0.300252i	0.216904	−	0.976193i	$-0.430404\pi$
$829$	−14.9735	−	8.64496i	−0.520051	−	0.300252i	−0.736956	+	0.675941i	$0.763737\pi$
$830$		0			0
$831$	3.35696	+	36.4752i	0.116452	+	1.26531i
$832$	9.99300	+	9.99300i	0.346445	+	0.346445i
$833$	5.60090	−	30.0693i	0.194060	−	1.04184i
$834$	52.6514	+	24.2633i	1.82317	+	0.840170i
$835$		0			0
$836$	16.2312	+	9.37108i	0.561367	+	0.324106i
$837$	−6.30923	−	10.5943i	−0.218079	−	0.366193i
$838$	59.6910	+	15.9942i	2.06199	+	0.552509i
$839$	−29.2813			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$839$	−29.2813			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$840$		0			0
$841$	−24.7969			−0.855067
$842$	31.0321	+	8.31501i	1.06944	+	0.286554i
$843$	−25.9035	−	4.44714i	−0.892162	−	0.153168i
$844$	−7.99957	−	4.61855i	−0.275356	−	0.158977i
$845$		0			0
$846$	−31.0401	−	36.3218i	−1.06718	−	1.24877i
$847$	−43.8267	+	13.5870i	−1.50590	+	0.466856i
$848$	−41.9732	−	41.9732i	−1.44136	−	1.44136i
$849$	48.9516	−	4.50522i	1.68002	−	0.154619i
$850$		0			0
$851$	−8.70710	−	5.02704i	−0.298475	−	0.172325i
$852$	27.9044	+	23.2010i	0.955990	+	0.794853i
$853$	−16.2493	+	16.2493i	−0.556365	+	0.556365i	−0.928271	−	0.371905i	$-0.878705\pi$
$853$	−16.2493	+	16.2493i	−0.556365	+	0.556365i	0.371905	+	0.928271i	$0.378705\pi$
$854$	−38.7058	+	1.50339i	−1.32449	+	0.0514449i
$855$		0			0
$856$	6.64345	+	11.5068i	0.227068	+	0.393294i
$857$	9.04935	+	33.7726i	0.309120	+	1.15365i	0.929341	+	0.369224i	$0.120376\pi$
$857$	9.04935	+	33.7726i	0.309120	+	1.15365i	−0.620221	+	0.784427i	$0.712957\pi$
$858$	14.0788	−	82.0056i	0.480643	−	2.79962i
$859$	47.9023	−	27.6564i	1.63441	−	0.943625i	0.651695	−	0.758481i	$-0.274058\pi$
$859$	47.9023	−	27.6564i	1.63441	−	0.943625i	0.982712	−	0.185143i	$-0.0592750\pi$
$860$		0			0
$861$	−7.13488	+	17.2104i	−0.243156	+	0.586529i
$862$	−29.3868	−	29.3868i	−1.00092	−	1.00092i
$863$	−8.09450	+	30.2091i	−0.275540	+	1.02833i	0.679939	+	0.733269i	$0.262006\pi$
$863$	−8.09450	+	30.2091i	−0.275540	+	1.02833i	−0.955479	+	0.295060i	$0.904660\pi$
$864$	−34.1504	−	8.65721i	−1.16182	−	0.294524i
$865$		0			0
$866$	−17.5844	+	10.1523i	−0.597541	+	0.344991i
$867$	−1.25497	−	3.40021i	−0.0426210	−	0.115477i
$868$	2.64293	+	8.52510i	0.0897068	+	0.289361i
$869$	−33.7337			−1.14434
$870$		0			0
$871$	6.98307	−	12.0950i	0.236612	−	0.409825i
$872$	−5.05245	−	18.8560i	−0.171097	−	0.638544i
$873$	13.7834	+	28.8758i	0.466497	+	0.977299i
$874$		−	9.44119i		−	0.319353i
$875$		0			0
$876$	−24.5781	−	11.3263i	−0.830418	−	0.382681i
$877$	−5.81291	+	21.6941i	−0.196288	+	0.732556i	0.795642	+	0.605767i	$0.207134\pi$
$877$	−5.81291	+	21.6941i	−0.196288	+	0.732556i	−0.991930	+	0.126789i	$0.959533\pi$
$878$	−8.98378	+	2.40720i	−0.303188	+	0.0812389i
$879$	18.1468	−	12.8289i	0.612078	−	0.432707i
$880$		0			0
$881$			47.2694i			1.59254i	0.604938	+	0.796272i	$0.293198\pi$
$881$			47.2694i			1.59254i	−0.604938	+	0.796272i	$0.706802\pi$
$882$	19.4020	+	33.6523i	0.653301	+	1.13313i
$883$	2.23535	−	2.23535i	0.0752257	−	0.0752257i	−0.668493	−	0.743719i	$-0.733060\pi$
$883$	2.23535	−	2.23535i	0.0752257	−	0.0752257i	0.743719	+	0.668493i	$0.233060\pi$
$884$	−15.1506	−	26.2416i	−0.509570	−	0.882602i
$885$		0			0
$886$	9.17661	−	15.8944i	0.308294	−	0.533981i
$887$	40.3902	+	10.8225i	1.35617	+	0.363384i	0.862408	−	0.506213i	$-0.168955\pi$
$887$	40.3902	+	10.8225i	1.35617	+	0.363384i	0.493761	+	0.869598i	$0.335622\pi$
$888$	−3.13016	−	8.48087i	−0.105041	−	0.284599i
$889$	−8.87236	+	5.59249i	−0.297569	+	0.187566i
$890$		0			0
$891$	17.1969	+	44.7216i	0.576119	+	1.49823i
$892$	−1.61658	+	0.433161i	−0.0541270	+	0.0145033i
$893$	20.5952	−	5.51847i	0.689193	−	0.184669i
$894$	8.12230	−	0.747528i	0.271650	−	0.0250011i
$895$		0			0
$896$	−19.1989	−	10.1120i	−0.641389	−	0.337818i
$897$	−16.3370	+	6.02973i	−0.545475	+	0.201327i
$898$	6.42346	+	1.72116i	0.214354	+	0.0574358i
$899$	2.43253	−	4.21327i	0.0811294	−	0.140520i
$900$		0			0
$901$	26.8929	+	46.5798i	0.895932	+	1.55180i
$902$	28.3100	−	28.3100i	0.942620	−	0.942620i
$903$	1.52165	−	0.629750i	0.0506374	−	0.0209568i
$904$			5.88625i			0.195774i
$905$		0			0
$906$	11.8774	+	16.8009i	0.394599	+	0.558172i
$907$	−40.3556	+	10.8133i	−1.33999	+	0.359048i	−0.856429	−	0.516265i	$-0.827322\pi$
$907$	−40.3556	+	10.8133i	−1.33999	+	0.359048i	−0.483557	+	0.875313i	$0.660655\pi$
$908$	5.70408	−	21.2879i	0.189296	−	0.706464i
$909$	−20.7912	−	24.3290i	−0.689600	−	0.806942i
$910$		0			0
$911$			14.8509i			0.492031i	0.969266	+	0.246016i	$0.0791215\pi$
$911$			14.8509i			0.492031i	−0.969266	+	0.246016i	$0.920879\pi$
$912$	13.2240	−	15.9048i	0.437890	−	0.526661i
$913$	3.07222	+	11.4657i	0.101676	+	0.379459i
$914$	6.32660	−	10.9580i	0.209265	−	0.362458i
$915$		0			0
$916$	15.9919			0.528388
$917$	−9.21817	−	29.7344i	−0.304411	−	0.981916i
$918$	36.6520	+	20.5050i	1.20969	+	0.676767i
$919$	−48.8849	+	28.2237i	−1.61257	+	0.931015i	−0.623792	+	0.781590i	$0.714409\pi$
$919$	−48.8849	+	28.2237i	−1.61257	+	0.931015i	−0.988773	+	0.149425i	$0.952258\pi$
$920$		0			0
$921$	10.7068	−	7.56914i	0.352800	−	0.249412i
$922$	0.957848	−	3.57474i	0.0315450	−	0.117728i
$923$	50.8384	+	50.8384i	1.67337	+	1.67337i
$924$	−4.51649	−	34.3865i	−0.148582	−	1.13123i
$925$		0			0
$926$	66.2461	−	38.2472i	2.17698	−	1.25688i
$927$	−6.08884	−	4.18213i	−0.199984	−	0.137359i
$928$	−3.59764	−	13.4266i	−0.118098	−	0.440749i
$929$	26.8842	+	46.5647i	0.882041	+	1.52774i	0.849068	+	0.528283i	$0.177164\pi$
$929$	26.8842	+	46.5647i	0.882041	+	1.52774i	0.0329723	+	0.999456i	$0.489503\pi$
$930$		0			0
$931$	−17.2828	+	1.34461i	−0.566422	+	0.0440677i
$932$	−26.1848	+	26.1848i	−0.857713	+	0.857713i
$933$	−1.68868	+	2.03102i	−0.0552848	+	0.0664925i
$934$	22.6240	+	13.0620i	0.740281	+	0.427402i
$935$		0			0
$936$	−14.7613	−	5.22240i	−0.482488	−	0.170700i
$937$	−29.0463	−	29.0463i	−0.948901	−	0.948901i	0.0498553	−	0.998756i	$-0.484124\pi$
$937$	−29.0463	−	29.0463i	−0.948901	−	0.948901i	−0.998756	+	0.0498553i	$0.984124\pi$
$938$	3.09841	−	13.6646i	0.101167	−	0.446164i
$939$	16.5207	−	35.8499i	0.539132	−	1.16992i
$940$		0			0
$941$	−41.3850	−	23.8937i	−1.34911	−	0.778911i	−0.360989	−	0.932570i	$-0.617561\pi$
$941$	−41.3850	−	23.8937i	−1.34911	−	0.778911i	−0.988124	+	0.153659i	$0.950894\pi$
$942$	9.82840	−	57.2479i	0.320227	−	1.86524i
$943$	−8.09377	−	2.16872i	−0.263569	−	0.0706232i
$944$	16.3997			0.533765
$945$		0			0
$946$	−3.53892			−0.115060
$947$	−4.63306	−	1.24142i	−0.150554	−	0.0403409i	0.182755	−	0.983159i	$-0.441499\pi$
$947$	−4.63306	−	1.24142i	−0.150554	−	0.0403409i	−0.333309	+	0.942818i	$0.608165\pi$
$948$	2.63992	−	15.3769i	0.0857407	−	0.499418i
$949$	−46.4322	−	26.8077i	−1.50725	−	0.870214i
$950$		0			0
$951$	6.83573	−	14.8335i	0.221664	−	0.481010i
$952$	9.07911	+	8.40019i	0.294256	+	0.272252i
$953$	−3.13902	−	3.13902i	−0.101683	−	0.101683i	0.654435	−	0.756118i	$-0.272906\pi$
$953$	−3.13902	−	3.13902i	−0.101683	−	0.101683i	−0.756118	+	0.654435i	$0.772906\pi$
$954$	−64.3964	−	22.7828i	−2.08491	−	0.737622i
$955$		0			0
$956$	−1.78171	−	1.02867i	−0.0576245	−	0.0332695i
$957$	−12.0861	+	14.5363i	−0.390689	+	0.469892i
$958$	20.9809	−	20.9809i	0.677862	−	0.677862i
$959$	48.1139	−	1.86881i	1.55368	−	0.0603470i
$960$		0			0
$961$	12.6843	+	21.9699i	0.409172	+	0.708707i
$962$	11.3926	+	42.5177i	0.367312	+	1.37083i
$963$	30.7093	+	21.0928i	0.989594	+	0.679704i
$964$	−29.0716	+	16.7845i	−0.936333	+	0.540592i
$965$		0			0
$966$	−13.8636	+	10.6313i	−0.446055	+	0.342056i
$967$	17.3509	+	17.3509i	0.557968	+	0.557968i	0.928729	−	0.370760i	$-0.120903\pi$
$967$	17.3509	+	17.3509i	0.557968	+	0.557968i	−0.370760	+	0.928729i	$0.620903\pi$
$968$	4.80252	−	17.9232i	0.154359	−	0.576075i
$969$	−15.3041	+	10.8192i	−0.491637	+	0.347562i
$970$		0			0
$971$	2.99257	−	1.72776i	0.0960363	−	0.0554466i	−0.451213	−	0.892416i	$-0.649008\pi$
$971$	2.99257	−	1.72776i	0.0960363	−	0.0554466i	0.547249	+	0.836970i	$0.315675\pi$
$972$	−21.7313	+	4.33909i	−0.697032	+	0.139176i
$973$	46.6890	+	10.5866i	1.49678	+	0.339392i
$974$	8.97665			0.287630
$975$		0			0
$976$	19.0837	−	33.0540i	0.610855	−	1.05803i
$977$	−1.13275	−	4.22749i	−0.0362399	−	0.135249i	0.945436	−	0.325809i	$-0.105637\pi$
$977$	−1.13275	−	4.22749i	−0.0362399	−	0.135249i	−0.981676	+	0.190559i	$0.938970\pi$
$978$	10.4829	−	12.6080i	0.335205	−	0.403160i
$979$		−	43.4230i		−	1.38780i
$980$		0			0
$981$	−35.5602	−	41.6111i	−1.13535	−	1.32854i
$982$	7.62375	−	28.4522i	0.243284	−	0.907947i
$983$	25.7749	−	6.90637i	0.822093	−	0.220279i	0.176831	−	0.984241i	$-0.443415\pi$
$983$	25.7749	−	6.90637i	0.822093	−	0.220279i	0.645261	+	0.763962i	$0.276749\pi$
$984$	−4.34922	−	6.15210i	−0.138648	−	0.196122i
$985$		0			0
$986$			16.5702i			0.527703i
$987$	−31.2947	−	24.0283i	−0.996122	−	0.764830i
$988$	−12.1434	+	12.1434i	−0.386333	+	0.386333i
$989$	0.370333	+	0.641435i	0.0117759	+	0.0203965i
$990$		0			0
$991$	−4.20000	+	7.27461i	−0.133417	+	0.231086i	−0.924992	−	0.379987i	$-0.875928\pi$
$991$	−4.20000	+	7.27461i	−0.133417	+	0.231086i	0.791574	+	0.611073i	$0.209262\pi$
$992$	−15.5413	−	4.16429i	−0.493438	−	0.132216i
$993$	7.42490	−	2.74042i	0.235622	−	0.0869645i
$994$	63.8187	+	33.6132i	2.02421	+	1.06615i
$995$		0			0
$996$	−5.46684	+	0.503135i	−0.173223	+	0.0159425i
$997$	18.5787	−	4.97815i	0.588393	−	0.157659i	0.0476744	−	0.998863i	$-0.484819\pi$
$997$	18.5787	−	4.97815i	0.588393	−	0.157659i	0.540719	+	0.841203i	$0.318152\pi$
$998$	18.7697	−	5.02933i	0.594145	−	0.159201i
$999$	−18.1643	−	17.6794i	−0.574694	−	0.559352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.g.32.16	yes	80
3.2	odd	2	inner	525.2.bf.g.32.6	yes	80
5.2	odd	4	inner	525.2.bf.g.368.6	yes	80
5.3	odd	4	inner	525.2.bf.g.368.15	yes	80
5.4	even	2	inner	525.2.bf.g.32.5	✓	80
7.2	even	3	inner	525.2.bf.g.107.5	yes	80
15.2	even	4	inner	525.2.bf.g.368.16	yes	80
15.8	even	4	inner	525.2.bf.g.368.5	yes	80
15.14	odd	2	inner	525.2.bf.g.32.15	yes	80
21.2	odd	6	inner	525.2.bf.g.107.15	yes	80
35.2	odd	12	inner	525.2.bf.g.443.15	yes	80
35.9	even	6	inner	525.2.bf.g.107.16	yes	80
35.23	odd	12	inner	525.2.bf.g.443.6	yes	80
105.2	even	12	inner	525.2.bf.g.443.5	yes	80
105.23	even	12	inner	525.2.bf.g.443.16	yes	80
105.44	odd	6	inner	525.2.bf.g.107.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.g.32.5	✓	80	5.4	even	2	inner
525.2.bf.g.32.6	yes	80	3.2	odd	2	inner
525.2.bf.g.32.15	yes	80	15.14	odd	2	inner
525.2.bf.g.32.16	yes	80	1.1	even	1	trivial
525.2.bf.g.107.5	yes	80	7.2	even	3	inner
525.2.bf.g.107.6	yes	80	105.44	odd	6	inner
525.2.bf.g.107.15	yes	80	21.2	odd	6	inner
525.2.bf.g.107.16	yes	80	35.9	even	6	inner
525.2.bf.g.368.5	yes	80	15.8	even	4	inner
525.2.bf.g.368.6	yes	80	5.2	odd	4	inner
525.2.bf.g.368.15	yes	80	5.3	odd	4	inner
525.2.bf.g.368.16	yes	80	15.2	even	4	inner
525.2.bf.g.443.5	yes	80	105.2	even	12	inner
525.2.bf.g.443.6	yes	80	35.23	odd	12	inner
525.2.bf.g.443.15	yes	80	35.2	odd	12	inner
525.2.bf.g.443.16	yes	80	105.23	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78672 + 0.478751i) q^{2} +(-0.293073 + 1.70708i) q^{3} +(1.23113 + 0.710791i) q^{4} +(-1.34091 + 2.90976i) q^{6} +(-0.585067 + 2.58025i) q^{7} +(-0.756555 - 0.756555i) q^{8} +(-2.82822 - 1.00060i) q^{9} +O(q^{10})\)	\(q+(1.78672 + 0.478751i) q^{2} +(-0.293073 + 1.70708i) q^{3} +(1.23113 + 0.710791i) q^{4} +(-1.34091 + 2.90976i) q^{6} +(-0.585067 + 2.58025i) q^{7} +(-0.756555 - 0.756555i) q^{8} +(-2.82822 - 1.00060i) q^{9} +(4.61054 + 2.66189i) q^{11} +(-1.57418 + 1.89331i) q^{12} +(-3.44938 + 3.44938i) q^{13} +(-2.28065 + 4.33009i) q^{14} +(-2.41113 - 4.17621i) q^{16} +(1.13091 + 4.22062i) q^{17} +(-4.57420 - 3.14180i) q^{18} +(2.14466 - 1.23822i) q^{19} +(-4.23322 - 1.75496i) q^{21} +(6.96337 + 6.96337i) q^{22} +(0.533436 - 1.99081i) q^{23} +(1.51322 - 1.06977i) q^{24} +(-7.81448 + 4.51169i) q^{26} +(2.53697 - 4.53473i) q^{27} +(-2.55431 + 2.76075i) q^{28} +2.05014 q^{29} +(1.18652 - 2.05512i) q^{31} +(-1.75483 - 6.54911i) q^{32} +(-5.89528 + 7.09041i) q^{33} +8.08250i q^{34} +(-2.77068 - 3.24213i) q^{36} +(1.26256 - 4.71194i) q^{37} +(4.42470 - 1.18560i) q^{38} +(-4.87743 - 6.89928i) q^{39} -4.06556i q^{41} +(-6.72340 - 5.16228i) q^{42} +(-0.254109 + 0.254109i) q^{43} +(3.78410 + 6.55425i) q^{44} +(1.90621 - 3.30165i) q^{46} +(8.31648 + 2.22839i) q^{47} +(7.83574 - 2.89205i) q^{48} +(-6.31539 - 3.01924i) q^{49} +(-7.53635 + 0.693601i) q^{51} +(-6.69841 + 1.79483i) q^{52} +(11.8899 - 3.18590i) q^{53} +(6.70387 - 6.88773i) q^{54} +(2.39474 - 1.50947i) q^{56} +(1.48519 + 4.02398i) q^{57} +(3.66302 + 0.981504i) q^{58} +(-1.70041 + 2.94520i) q^{59} +(3.95741 + 6.85444i) q^{61} +(3.10387 - 3.10387i) q^{62} +(4.23649 - 6.71209i) q^{63} -2.89704i q^{64} +(-13.9278 + 9.84622i) q^{66} +(-2.76544 + 0.740997i) q^{67} +(-1.60768 + 5.99995i) q^{68} +(3.24213 + 1.49407i) q^{69} -14.7384i q^{71} +(1.38269 + 2.89671i) q^{72} +(2.84465 + 10.6164i) q^{73} +(4.51169 - 7.81448i) q^{74} +3.52046 q^{76} +(-9.56583 + 10.3390i) q^{77} +(-5.41159 - 14.6622i) q^{78} +(-5.48749 + 3.16820i) q^{79} +(6.99761 + 5.65981i) q^{81} +(1.94639 - 7.26404i) q^{82} +(1.57660 + 1.57660i) q^{83} +(-3.96422 - 5.16950i) q^{84} +(-0.575678 + 0.332368i) q^{86} +(-0.600840 + 3.49974i) q^{87} +(-1.47425 - 5.50199i) q^{88} +(-4.07820 - 7.06365i) q^{89} +(-6.88215 - 10.9184i) q^{91} +(2.07178 - 2.07178i) q^{92} +(3.16050 + 2.62778i) q^{93} +(13.7924 + 7.96305i) q^{94} +(11.6941 - 1.07626i) q^{96} +(-7.54172 - 7.54172i) q^{97} +(-9.83840 - 8.41804i) q^{98} +(-10.3761 - 12.1417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{6}+O(q^{10}) \) 80 * q + 16 * q^6	\( 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) \) 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more