LMFDB - Embedded newform 352.2.m.c.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("352.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.2
Root			$0.476925 + 1.46782i$ of defining polynomial
Character	$\chi$	$=$	352.289
Dual form			352.2.m.c.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.476925 + 1.46782i) q^{3} +(0.309017 + 0.224514i) q^{5} +(-0.476925 + 1.46782i) q^{7} +(0.500000 - 0.363271i) q^{9} +(1.54336 + 2.93565i) q^{11} +(-1.30902 + 0.951057i) q^{13} +(-0.182169 + 0.560659i) q^{15} +(0.690983 + 0.502029i) q^{17} +(1.43078 + 4.40347i) q^{19} -2.38197 q^{21} -4.99442 q^{23} +(-1.50000 - 4.61653i) q^{25} +(4.51750 + 3.28216i) q^{27} +(-0.0450850 + 0.138757i) q^{29} +(1.72553 - 1.25367i) q^{31} +(-3.57295 + 3.66547i) q^{33} +(-0.476925 + 0.346506i) q^{35} +(0.572949 - 1.76336i) q^{37} +(-2.02029 - 1.46782i) q^{39} +(0.190983 + 0.587785i) q^{41} +1.90770 q^{43} +0.236068 q^{45} +(-2.97414 - 9.15345i) q^{47} +(3.73607 + 2.71441i) q^{49} +(-0.407343 + 1.25367i) q^{51} +(6.92705 - 5.03280i) q^{53} +(-0.182169 + 1.25367i) q^{55} +(-5.78115 + 4.20025i) q^{57} +(3.19931 - 9.84647i) q^{59} +(10.1631 + 7.38394i) q^{61} +(0.294756 + 0.907165i) q^{63} -0.618034 q^{65} -8.08115 q^{67} +(-2.38197 - 7.33094i) q^{69} +(-8.85283 - 6.43196i) q^{71} +(3.04508 - 9.37181i) q^{73} +(6.06086 - 4.40347i) q^{75} +(-5.04508 + 0.865300i) q^{77} +(12.8934 - 9.36761i) q^{79} +(-2.09017 + 6.43288i) q^{81} +(-8.85283 - 6.43196i) q^{83} +(0.100813 + 0.310271i) q^{85} -0.225173 q^{87} +8.18034 q^{89} +(-0.771681 - 2.37499i) q^{91} +(2.66312 + 1.93487i) q^{93} +(-0.546507 + 1.68198i) q^{95} +(2.54508 - 1.84911i) q^{97} +(1.83812 + 0.907165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} + 4 q^{9} - 6 q^{13} + 10 q^{17} - 28 q^{21} - 12 q^{25} + 22 q^{29} - 42 q^{33} + 18 q^{37} + 6 q^{41} - 16 q^{45} + 12 q^{49} + 42 q^{53} - 6 q^{57} + 50 q^{61} + 4 q^{65} - 28 q^{69} + 2 q^{73}+ \cdots - 2 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 + 4 * q^9 - 6 * q^13 + 10 * q^17 - 28 * q^21 - 12 * q^25 + 22 * q^29 - 42 * q^33 + 18 * q^37 + 6 * q^41 - 16 * q^45 + 12 * q^49 + 42 * q^53 - 6 * q^57 + 50 * q^61 + 4 * q^65 - 28 * q^69 + 2 * q^73 - 18 * q^77 + 28 * q^81 + 50 * q^85 - 24 * q^89 - 10 * q^93 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.476925	+	1.46782i	0.275353	+	0.847449i	0.989126	+	0.147072i	$0.0469848\pi$
$3$	0.476925	+	1.46782i	0.275353	+	0.847449i	−0.713773	+	0.700377i	$0.753015\pi$
$4$		0			0
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	0.654736	−	0.755858i	$-0.272780\pi$
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	−0.516539	+	0.856264i	$0.672780\pi$
$6$		0			0
$7$	−0.476925	+	1.46782i	−0.180261	+	0.554785i	−0.999835	−	0.0181881i	$-0.994210\pi$
$7$	−0.476925	+	1.46782i	−0.180261	+	0.554785i	0.819574	+	0.572974i	$0.194210\pi$
$8$		0			0
$9$	0.500000	−	0.363271i	0.166667	−	0.121090i
$10$		0			0
$11$	1.54336	+	2.93565i	0.465341	+	0.885131i
$11$	1.54336	+	2.93565i	0.465341	+	0.885131i
$12$		0			0
$13$	−1.30902	+	0.951057i	−0.363056	+	0.263776i	−0.754326	−	0.656500i	$-0.772036\pi$
$13$	−1.30902	+	0.951057i	−0.363056	+	0.263776i	0.391270	+	0.920276i	$0.372036\pi$
$14$		0			0
$15$	−0.182169	+	0.560659i	−0.0470359	+	0.144762i
$16$		0			0
$17$	0.690983	+	0.502029i	0.167588	+	0.121760i	0.668418	−	0.743786i	$-0.266972\pi$
$17$	0.690983	+	0.502029i	0.167588	+	0.121760i	−0.500830	+	0.865546i	$0.666972\pi$
$18$		0			0
$19$	1.43078	+	4.40347i	0.328242	+	1.01023i	0.969956	+	0.243282i	$0.0782239\pi$
$19$	1.43078	+	4.40347i	0.328242	+	1.01023i	−0.641713	+	0.766945i	$0.721776\pi$
$20$		0			0
$21$	−2.38197			−0.519788
$22$		0			0
$23$	−4.99442			−1.04141			−0.520705	−	0.853737i	$-0.674331\pi$
$23$	−4.99442			−1.04141			−0.520705	+	0.853737i	$0.674331\pi$
$24$		0			0
$25$	−1.50000	−	4.61653i	−0.300000	−	0.923305i
$26$		0			0
$27$	4.51750	+	3.28216i	0.869393	+	0.631651i
$28$		0			0
$29$	−0.0450850	+	0.138757i	−0.00837207	+	0.0257666i	−0.955155	−	0.296105i	$-0.904312\pi$
$29$	−0.0450850	+	0.138757i	−0.00837207	+	0.0257666i	0.946783	+	0.321872i	$0.104312\pi$
$30$		0			0
$31$	1.72553	−	1.25367i	0.309915	−	0.225166i	−0.421945	−	0.906621i	$-0.638653\pi$
$31$	1.72553	−	1.25367i	0.309915	−	0.225166i	0.731860	+	0.681455i	$0.238653\pi$
$32$		0			0
$33$	−3.57295	+	3.66547i	−0.621971	+	0.638076i
$34$		0			0
$35$	−0.476925	+	0.346506i	−0.0806150	+	0.0585703i
$36$		0			0
$37$	0.572949	−	1.76336i	0.0941922	−	0.289894i	−0.892850	−	0.450354i	$-0.851298\pi$
$37$	0.572949	−	1.76336i	0.0941922	−	0.289894i	0.987042	+	0.160460i	$0.0512978\pi$
$38$		0			0
$39$	−2.02029	−	1.46782i	−0.323505	−	0.235040i
$40$		0			0
$41$	0.190983	+	0.587785i	0.0298265	+	0.0917966i	0.964862	−	0.262759i	$-0.0846323\pi$
$41$	0.190983	+	0.587785i	0.0298265	+	0.0917966i	−0.935035	+	0.354555i	$0.884632\pi$
$42$		0			0
$43$	1.90770			0.290922			0.145461	−	0.989364i	$-0.453534\pi$
$43$	1.90770			0.290922			0.145461	+	0.989364i	$0.453534\pi$
$44$		0			0
$45$	0.236068			0.0351909
$46$		0			0
$47$	−2.97414	−	9.15345i	−0.433822	−	1.33517i	−0.894288	−	0.447491i	$-0.852318\pi$
$47$	−2.97414	−	9.15345i	−0.433822	−	1.33517i	0.460466	−	0.887677i	$-0.347682\pi$
$48$		0			0
$49$	3.73607	+	2.71441i	0.533724	+	0.387773i
$50$		0			0
$51$	−0.407343	+	1.25367i	−0.0570394	+	0.175549i
$52$		0			0
$53$	6.92705	−	5.03280i	0.951504	−	0.691308i	0.000341607	−	1.00000i	$-0.499891\pi$
$53$	6.92705	−	5.03280i	0.951504	−	0.691308i	0.951162	+	0.308692i	$0.0998913\pi$
$54$		0			0
$55$	−0.182169	+	1.25367i	−0.0245637	+	0.169045i
$56$		0			0
$57$	−5.78115	+	4.20025i	−0.765732	+	0.556337i
$58$		0			0
$59$	3.19931	−	9.84647i	0.416515	−	1.28190i	−0.494374	−	0.869249i	$-0.664603\pi$
$59$	3.19931	−	9.84647i	0.416515	−	1.28190i	0.910889	−	0.412651i	$-0.135397\pi$
$60$		0			0
$61$	10.1631	+	7.38394i	1.30125	+	0.945416i	0.999967	−	0.00811711i	$-0.00258378\pi$
$61$	10.1631	+	7.38394i	1.30125	+	0.945416i	0.301287	+	0.953534i	$0.402584\pi$
$62$		0			0
$63$	0.294756	+	0.907165i	0.0371358	+	0.114292i
$64$		0			0
$65$	−0.618034			−0.0766577
$66$		0			0
$67$	−8.08115			−0.987269			−0.493635	−	0.869669i	$-0.664332\pi$
$67$	−8.08115			−0.987269			−0.493635	+	0.869669i	$0.664332\pi$
$68$		0			0
$69$	−2.38197	−	7.33094i	−0.286755	−	0.882541i
$70$		0			0
$71$	−8.85283	−	6.43196i	−1.05064	−	0.763333i	−0.0783039	−	0.996930i	$-0.524950\pi$
$71$	−8.85283	−	6.43196i	−1.05064	−	0.763333i	−0.972334	+	0.233597i	$0.924950\pi$
$72$		0			0
$73$	3.04508	−	9.37181i	0.356400	−	1.09689i	−0.598793	−	0.800904i	$-0.704353\pi$
$73$	3.04508	−	9.37181i	0.356400	−	1.09689i	0.955193	−	0.295983i	$-0.0956473\pi$
$74$		0			0
$75$	6.06086	−	4.40347i	0.699848	−	0.508469i
$76$		0			0
$77$	−5.04508	+	0.865300i	−0.574941	+	0.0986101i
$78$		0			0
$79$	12.8934	−	9.36761i	1.45062	−	1.05394i	0.464935	−	0.885345i	$-0.346078\pi$
$79$	12.8934	−	9.36761i	1.45062	−	1.05394i	0.985686	−	0.168593i	$-0.0539225\pi$
$80$		0			0
$81$	−2.09017	+	6.43288i	−0.232241	+	0.714765i
$82$		0			0
$83$	−8.85283	−	6.43196i	−0.971724	−	0.705999i	−0.0158803	−	0.999874i	$-0.505055\pi$
$83$	−8.85283	−	6.43196i	−0.971724	−	0.705999i	−0.955844	+	0.293875i	$0.905055\pi$
$84$		0			0
$85$	0.100813	+	0.310271i	0.0109347	+	0.0336536i
$86$		0			0
$87$	−0.225173			−0.0241411
$88$		0			0
$89$	8.18034			0.867114			0.433557	−	0.901126i	$-0.357258\pi$
$89$	8.18034			0.867114			0.433557	+	0.901126i	$0.357258\pi$
$90$		0			0
$91$	−0.771681	−	2.37499i	−0.0808941	−	0.248967i
$92$		0			0
$93$	2.66312	+	1.93487i	0.276153	+	0.200637i
$94$		0			0
$95$	−0.546507	+	1.68198i	−0.0560705	+	0.172567i
$96$		0			0
$97$	2.54508	−	1.84911i	0.258414	−	0.187749i	−0.451033	−	0.892507i	$-0.648944\pi$
$97$	2.54508	−	1.84911i	0.258414	−	0.187749i	0.709448	+	0.704758i	$0.248944\pi$
$98$		0			0
$99$	1.83812	+	0.907165i	0.184738	+	0.0911736i
$100$		0			0
$101$	−12.1631	+	8.83702i	−1.21028	+	0.879317i	−0.995256	−	0.0972930i	$-0.968982\pi$
$101$	−12.1631	+	8.83702i	−1.21028	+	0.879317i	−0.215020	+	0.976610i	$0.568982\pi$
$102$		0			0
$103$	−2.24546	+	6.91082i	−0.221252	+	0.680943i	0.777399	+	0.629008i	$0.216539\pi$
$103$	−2.24546	+	6.91082i	−0.221252	+	0.680943i	−0.998650	+	0.0519348i	$0.983461\pi$
$104$		0			0
$105$	−0.736068	−	0.534785i	−0.0718329	−	0.0521896i
$106$		0			0
$107$	−2.02029	−	6.21780i	−0.195309	−	0.601098i	−0.999973	−	0.00736781i	$-0.997655\pi$
$107$	−2.02029	−	6.21780i	−0.195309	−	0.601098i	0.804664	−	0.593730i	$-0.202345\pi$
$108$		0			0
$109$	−14.4721			−1.38618			−0.693090	−	0.720851i	$-0.743751\pi$
$109$	−14.4721			−1.38618			−0.693090	+	0.720851i	$0.743751\pi$
$110$		0			0
$111$	2.86155			0.271606
$112$		0			0
$113$	−6.04508	−	18.6049i	−0.568674	−	1.75020i	−0.656775	−	0.754086i	$-0.728080\pi$
$113$	−6.04508	−	18.6049i	−0.568674	−	1.75020i	0.0881015	−	0.996112i	$-0.471920\pi$
$114$		0			0
$115$	−1.54336	−	1.12132i	−0.143919	−	0.104563i
$116$		0			0
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$		0			0
$119$	−1.06644	+	0.774812i	−0.0977601	+	0.0710269i
$120$		0			0
$121$	−6.23607	+	9.06154i	−0.566915	+	0.823776i
$122$		0			0
$123$	−0.771681	+	0.560659i	−0.0695801	+	0.0505529i
$124$		0			0
$125$	1.16312	−	3.57971i	0.104033	−	0.320179i
$126$		0			0
$127$	13.8473	+	10.0606i	1.22875	+	0.892736i	0.996795	−	0.0799923i	$-0.0254896\pi$
$127$	13.8473	+	10.0606i	1.22875	+	0.892736i	0.231950	+	0.972728i	$0.425490\pi$
$128$		0			0
$129$	0.909830	+	2.80017i	0.0801061	+	0.246541i
$130$		0			0
$131$	−8.80982			−0.769718			−0.384859	−	0.922975i	$-0.625750\pi$
$131$	−8.80982			−0.769718			−0.384859	+	0.922975i	$0.625750\pi$
$132$		0			0
$133$	−7.14590			−0.619628
$134$		0			0
$135$	0.659094	+	2.02848i	0.0567258	+	0.174584i
$136$		0			0
$137$	8.16312	+	5.93085i	0.697422	+	0.506707i	0.879092	−	0.476653i	$-0.158150\pi$
$137$	8.16312	+	5.93085i	0.697422	+	0.506707i	−0.181669	+	0.983360i	$0.558150\pi$
$138$		0			0
$139$	1.65595	−	5.09649i	0.140456	−	0.432278i	−0.855943	−	0.517070i	$-0.827023\pi$
$139$	1.65595	−	5.09649i	0.140456	−	0.432278i	0.996399	+	0.0847920i	$0.0270226\pi$
$140$		0			0
$141$	12.0172	−	8.73102i	1.01203	−	0.735285i
$142$		0			0
$143$	−4.81225	−	2.37499i	−0.402421	−	0.198607i
$144$		0			0
$145$	−0.0450850	+	0.0327561i	−0.00374410	+	0.00272025i
$146$		0			0
$147$	−2.20246	+	6.77846i	−0.181656	+	0.559078i
$148$		0			0
$149$	16.6353	+	12.0862i	1.36281	+	0.990142i	0.998260	+	0.0589590i	$0.0187781\pi$
$149$	16.6353	+	12.0862i	1.36281	+	0.990142i	0.364553	+	0.931183i	$0.381222\pi$
$150$		0			0
$151$	5.10701	+	15.7178i	0.415603	+	1.27909i	0.911711	+	0.410833i	$0.134762\pi$
$151$	5.10701	+	15.7178i	0.415603	+	1.27909i	−0.496108	+	0.868261i	$0.665238\pi$
$152$		0			0
$153$	0.527864			0.0426753
$154$		0			0
$155$	0.814685			0.0654371
$156$		0			0
$157$	−4.13525	−	12.7270i	−0.330029	−	1.01573i	−0.969119	−	0.246593i	$-0.920689\pi$
$157$	−4.13525	−	12.7270i	−0.330029	−	1.01573i	0.639090	−	0.769132i	$-0.279311\pi$
$158$		0			0
$159$	10.6909	+	7.76743i	0.847847	+	0.615997i
$160$		0			0
$161$	2.38197	−	7.33094i	0.187725	−	0.577759i
$162$		0			0
$163$	−7.30947	+	5.31064i	−0.572522	+	0.415961i	−0.836020	−	0.548698i	$-0.815124\pi$
$163$	−7.30947	+	5.31064i	−0.572522	+	0.415961i	0.263499	+	0.964660i	$0.415124\pi$
$164$		0			0
$165$	−1.92705	+	0.330515i	−0.150021	+	0.0257306i
$166$		0			0
$167$	−4.81225	+	3.49631i	−0.372383	+	0.270552i	−0.758199	−	0.652024i	$-0.773920\pi$
$167$	−4.81225	+	3.49631i	−0.372383	+	0.270552i	0.385815	+	0.922576i	$0.373920\pi$
$168$		0			0
$169$	−3.20820	+	9.87384i	−0.246785	+	0.759526i
$170$		0			0
$171$	2.31504	+	1.68198i	0.177036	+	0.128624i
$172$		0			0
$173$	−0.517221	−	1.59184i	−0.0393236	−	0.121026i	0.929468	−	0.368904i	$-0.120267\pi$
$173$	−0.517221	−	1.59184i	−0.0393236	−	0.121026i	−0.968791	+	0.247878i	$0.920267\pi$
$174$		0			0
$175$	7.49164			0.566314
$176$		0			0
$177$	15.9787			1.20103
$178$		0			0
$179$	0.476925	+	1.46782i	0.0356471	+	0.109710i	0.967297	−	0.253647i	$-0.0816303\pi$
$179$	0.476925	+	1.46782i	0.0356471	+	0.109710i	−0.931650	+	0.363358i	$0.881630\pi$
$180$		0			0
$181$	16.4894	+	11.9802i	1.22564	+	0.890483i	0.996556	−	0.0829230i	$-0.0264255\pi$
$181$	16.4894	+	11.9802i	1.22564	+	0.890483i	0.229088	+	0.973406i	$0.426426\pi$
$182$		0			0
$183$	−5.99128	+	18.4393i	−0.442888	+	1.36307i
$184$		0			0
$185$	0.572949	−	0.416272i	0.0421240	−	0.0306049i
$186$		0			0
$187$	−0.407343	+	2.80330i	−0.0297878	+	0.204997i
$188$		0			0
$189$	−6.97214	+	5.06555i	−0.507148	+	0.368465i
$190$		0			0
$191$	−1.06644	+	3.28216i	−0.0771647	+	0.237488i	−0.982197	−	0.187855i	$-0.939847\pi$
$191$	−1.06644	+	3.28216i	−0.0771647	+	0.237488i	0.905032	+	0.425343i	$0.139847\pi$
$192$		0			0
$193$	−2.69098	−	1.95511i	−0.193701	−	0.140732i	0.486708	−	0.873565i	$-0.338198\pi$
$193$	−2.69098	−	1.95511i	−0.193701	−	0.140732i	−0.680409	+	0.732833i	$0.738198\pi$
$194$		0			0
$195$	−0.294756	−	0.907165i	−0.0211079	−	0.0649635i
$196$		0			0
$197$	−14.1803			−1.01031			−0.505154	−	0.863029i	$-0.668564\pi$
$197$	−14.1803			−1.01031			−0.505154	+	0.863029i	$0.668564\pi$
$198$		0			0
$199$	18.0700			1.28095			0.640474	−	0.767980i	$-0.278738\pi$
$199$	18.0700			1.28095			0.640474	+	0.767980i	$0.278738\pi$
$200$		0			0
$201$	−3.85410	−	11.8617i	−0.271847	−	0.836660i
$202$		0			0
$203$	−0.182169	−	0.132354i	−0.0127858	−	0.00928940i
$204$		0			0
$205$	−0.0729490	+	0.224514i	−0.00509498	+	0.0156807i
$206$		0			0
$207$	−2.49721	+	1.81433i	−0.173568	+	0.126105i
$208$		0			0
$209$	−10.7188	+	10.9964i	−0.741438	+	0.760637i
$210$		0			0
$211$	−19.4312	+	14.1176i	−1.33770	+	0.971895i	−0.338173	+	0.941084i	$0.609809\pi$
$211$	−19.4312	+	14.1176i	−1.33770	+	0.971895i	−0.999525	+	0.0308107i	$0.990191\pi$
$212$		0			0
$213$	5.21885	−	16.0620i	0.357590	−	1.10055i
$214$		0			0
$215$	0.589512	+	0.428305i	0.0402044	+	0.0292102i
$216$		0			0
$217$	1.01722	+	3.13068i	0.0690535	+	0.212525i
$218$		0			0
$219$	15.2084			1.02769
$220$		0			0
$221$	−1.38197			−0.0929611
$222$		0			0
$223$	6.65037	+	20.4677i	0.445342	+	1.37062i	0.882108	+	0.471047i	$0.156124\pi$
$223$	6.65037	+	20.4677i	0.445342	+	1.37062i	−0.436766	+	0.899575i	$0.643876\pi$
$224$		0			0
$225$	−2.42705	−	1.76336i	−0.161803	−	0.117557i
$226$		0			0
$227$	2.97414	−	9.15345i	0.197400	−	0.607536i	−0.802540	−	0.596599i	$-0.796518\pi$
$227$	2.97414	−	9.15345i	0.197400	−	0.607536i	0.999940	−	0.0109374i	$-0.00348155\pi$
$228$		0			0
$229$	7.01722	−	5.09831i	0.463711	−	0.336906i	−0.331274	−	0.943535i	$-0.607479\pi$
$229$	7.01722	−	5.09831i	0.463711	−	0.336906i	0.794985	+	0.606629i	$0.207479\pi$
$230$		0			0
$231$	−3.67624	−	6.99262i	−0.241879	−	0.460080i
$232$		0			0
$233$	−13.0172	+	9.45756i	−0.852786	+	0.619586i	−0.925913	−	0.377737i	$-0.876702\pi$
$233$	−13.0172	+	9.45756i	−0.852786	+	0.619586i	0.0731264	+	0.997323i	$0.476702\pi$
$234$		0			0
$235$	1.13602	−	3.49631i	0.0741057	−	0.228074i
$236$		0			0
$237$	19.8992	+	14.4576i	1.29259	+	0.939122i
$238$		0			0
$239$	−4.88184	−	15.0248i	−0.315780	−	0.971870i	−0.975432	−	0.220300i	$-0.929297\pi$
$239$	−4.88184	−	15.0248i	−0.315780	−	0.971870i	0.659652	−	0.751571i	$-0.270703\pi$
$240$		0			0
$241$	−7.41641			−0.477733			−0.238866	−	0.971052i	$-0.576776\pi$
$241$	−7.41641			−0.477733			−0.238866	+	0.971052i	$0.576776\pi$
$242$		0			0
$243$	6.31261			0.404954
$244$		0			0
$245$	0.545085	+	1.67760i	0.0348242	+	0.107178i
$246$		0			0
$247$	−6.06086	−	4.40347i	−0.385643	−	0.280186i
$248$		0			0
$249$	5.21885	−	16.0620i	0.330731	−	1.01789i
$250$		0			0
$251$	−11.7144	+	8.51099i	−0.739405	+	0.537209i	−0.892525	−	0.450998i	$-0.851068\pi$
$251$	−11.7144	+	8.51099i	−0.739405	+	0.537209i	0.153120	+	0.988208i	$0.451068\pi$
$252$		0			0
$253$	−7.70820	−	14.6619i	−0.484611	−	0.921784i
$254$		0			0
$255$	−0.407343	+	0.295952i	−0.0255088	+	0.0185332i
$256$		0			0
$257$	−4.42705	+	13.6251i	−0.276152	+	0.849908i	0.712760	+	0.701408i	$0.247445\pi$
$257$	−4.42705	+	13.6251i	−0.276152	+	0.849908i	−0.988912	+	0.148500i	$0.952555\pi$
$258$		0			0
$259$	2.31504	+	1.68198i	0.143850	+	0.104513i
$260$		0			0
$261$	0.0278640	+	0.0857567i	0.00172474	+	0.00530821i
$262$		0			0
$263$	−15.7119			−0.968840			−0.484420	−	0.874835i	$-0.660969\pi$
$263$	−15.7119			−0.968840			−0.484420	+	0.874835i	$0.660969\pi$
$264$		0			0
$265$	3.27051			0.200906
$266$		0			0
$267$	3.90141	+	12.0073i	0.238762	+	0.734835i
$268$		0			0
$269$	−11.1631	−	8.11048i	−0.680627	−	0.494505i	0.192938	−	0.981211i	$-0.438198\pi$
$269$	−11.1631	−	8.11048i	−0.680627	−	0.494505i	−0.873566	+	0.486706i	$0.838198\pi$
$270$		0			0
$271$	7.96856	−	24.5247i	0.484056	−	1.48977i	−0.349288	−	0.937015i	$-0.613577\pi$
$271$	7.96856	−	24.5247i	0.484056	−	1.48977i	0.833344	−	0.552755i	$-0.186423\pi$
$272$		0			0
$273$	3.11803	−	2.26538i	0.188712	−	0.137107i
$274$		0			0
$275$	11.2375	−	11.5284i	0.677644	−	0.695191i
$276$		0			0
$277$	−9.16312	+	6.65740i	−0.550558	+	0.400004i	−0.827991	−	0.560741i	$-0.810516\pi$
$277$	−9.16312	+	6.65740i	−0.550558	+	0.400004i	0.277433	+	0.960745i	$0.410516\pi$
$278$		0			0
$279$	0.407343	−	1.25367i	0.0243870	−	0.0750554i
$280$		0			0
$281$	−11.6353	−	8.45351i	−0.694101	−	0.504294i	0.183905	−	0.982944i	$-0.441126\pi$
$281$	−11.6353	−	8.45351i	−0.694101	−	0.504294i	−0.878006	+	0.478650i	$0.841126\pi$
$282$		0			0
$283$	−6.28603	−	19.3464i	−0.373666	−	1.15003i	−0.944374	−	0.328873i	$-0.893331\pi$
$283$	−6.28603	−	19.3464i	−0.373666	−	1.15003i	0.570708	−	0.821153i	$-0.306669\pi$
$284$		0			0
$285$	−2.72949			−0.161681
$286$		0			0
$287$	−0.953850			−0.0563040
$288$		0			0
$289$	−5.02786	−	15.4742i	−0.295757	−	0.910246i
$290$		0			0
$291$	3.92799	+	2.85385i	0.230263	+	0.167296i
$292$		0			0
$293$	−2.33688	+	7.19218i	−0.136522	+	0.420172i	−0.995824	−	0.0912975i	$-0.970899\pi$
$293$	−2.33688	+	7.19218i	−0.136522	+	0.420172i	0.859302	+	0.511469i	$0.170899\pi$
$294$		0			0
$295$	3.19931	−	2.32444i	0.186271	−	0.135334i
$296$		0			0
$297$	−2.66312	+	18.3273i	−0.154530	+	1.06346i
$298$		0			0
$299$	6.53779	−	4.74998i	0.378090	−	0.274698i
$300$		0			0
$301$	−0.909830	+	2.80017i	−0.0524417	+	0.161399i
$302$		0			0
$303$	−18.7721	−	13.6387i	−1.07843	−	0.783524i
$304$		0			0
$305$	1.48278	+	4.56352i	0.0849037	+	0.261307i
$306$		0			0
$307$	−8.80982			−0.502803			−0.251402	−	0.967883i	$-0.580891\pi$
$307$	−8.80982			−0.502803			−0.251402	+	0.967883i	$0.580891\pi$
$308$		0			0
$309$	−11.2148			−0.637987
$310$		0			0
$311$	−3.78882	−	11.6608i	−0.214844	−	0.661223i	−0.999165	−	0.0408669i	$-0.986988\pi$
$311$	−3.78882	−	11.6608i	−0.214844	−	0.661223i	0.784320	−	0.620356i	$-0.213012\pi$
$312$		0			0
$313$	18.8713	+	13.7108i	1.06667	+	0.774981i	0.975311	−	0.220837i	$-0.0708788\pi$
$313$	18.8713	+	13.7108i	1.06667	+	0.774981i	0.0913594	+	0.995818i	$0.470879\pi$
$314$		0			0
$315$	−0.112587	+	0.346506i	−0.00634354	+	0.0195234i
$316$		0			0
$317$	10.5451	−	7.66145i	0.592271	−	0.430310i	−0.250856	−	0.968024i	$-0.580712\pi$
$317$	10.5451	−	7.66145i	0.592271	−	0.430310i	0.843127	+	0.537714i	$0.180712\pi$
$318$		0			0
$319$	−0.476925	+	0.0817991i	−0.0267027	+	0.00457987i
$320$		0			0
$321$	8.16312	−	5.93085i	0.455621	−	0.331028i
$322$		0			0
$323$	−1.22203	+	3.76102i	−0.0679955	+	0.209268i
$324$		0			0
$325$	6.35410	+	4.61653i	0.352462	+	0.256079i
$326$		0			0
$327$	−6.90212	−	21.2426i	−0.381688	−	1.17472i
$328$		0			0
$329$	14.8541			0.818933
$330$		0			0
$331$	3.81540			0.209713			0.104857	−	0.994487i	$-0.466562\pi$
$331$	3.81540			0.209713			0.104857	+	0.994487i	$0.466562\pi$
$332$		0			0
$333$	−0.354102	−	1.08981i	−0.0194047	−	0.0597214i
$334$		0			0
$335$	−2.49721	−	1.81433i	−0.136437	−	0.0991275i
$336$		0			0
$337$	4.33688	−	13.3475i	0.236245	−	0.727087i	−0.760709	−	0.649093i	$-0.775148\pi$
$337$	4.33688	−	13.3475i	0.236245	−	0.727087i	0.996954	−	0.0779940i	$-0.0248515\pi$
$338$		0			0
$339$	24.4256	−	17.7462i	1.32662	−	0.963844i
$340$		0			0
$341$	6.34346	+	3.13068i	0.343518	+	0.169536i
$342$		0			0
$343$	−14.5063	+	10.5395i	−0.783269	+	0.569078i
$344$		0			0
$345$	0.909830	−	2.80017i	0.0489836	−	0.150756i
$346$		0			0
$347$	14.2116	+	10.3253i	0.762918	+	0.554293i	0.899804	−	0.436294i	$-0.143709\pi$
$347$	14.2116	+	10.3253i	0.762918	+	0.554293i	−0.136886	+	0.990587i	$0.543709\pi$
$348$		0			0
$349$	3.10081	+	9.54332i	0.165983	+	0.510842i	0.999107	−	0.0422430i	$-0.0134504\pi$
$349$	3.10081	+	9.54332i	0.165983	+	0.510842i	−0.833125	+	0.553085i	$0.813450\pi$
$350$		0			0
$351$	−9.03500			−0.482253
$352$		0			0
$353$	19.7082			1.04896			0.524481	−	0.851422i	$-0.324259\pi$
$353$	19.7082			1.04896			0.524481	+	0.851422i	$0.324259\pi$
$354$		0			0
$355$	−1.29161	−	3.97517i	−0.0685516	−	0.210980i
$356$		0			0
$357$	−1.64590	−	1.19581i	−0.0871102	−	0.0632892i
$358$		0			0
$359$	9.14758	−	28.1534i	0.482791	−	1.48588i	−0.352364	−	0.935863i	$-0.614622\pi$
$359$	9.14758	−	28.1534i	0.482791	−	1.48588i	0.835155	−	0.550015i	$-0.185378\pi$
$360$		0			0
$361$	−1.97214	+	1.43284i	−0.103797	+	0.0754127i
$362$		0			0
$363$	−16.2749	−	4.83178i	−0.854210	−	0.253603i
$364$		0			0
$365$	3.04508	−	2.21238i	0.159387	−	0.115801i
$366$		0			0
$367$	8.33290	−	25.6460i	0.434974	−	1.33871i	−0.458140	−	0.888880i	$-0.651484\pi$
$367$	8.33290	−	25.6460i	0.434974	−	1.33871i	0.893113	−	0.449832i	$-0.148516\pi$
$368$		0			0
$369$	0.309017	+	0.224514i	0.0160868	+	0.0116877i
$370$		0			0
$371$	4.08358	+	12.5680i	0.212009	+	0.652496i
$372$		0			0
$373$	−6.29180			−0.325777			−0.162888	−	0.986644i	$-0.552081\pi$
$373$	−6.29180			−0.325777			−0.162888	+	0.986644i	$0.552081\pi$
$374$		0			0
$375$	5.80911			0.299981
$376$		0			0
$377$	−0.0729490	−	0.224514i	−0.00375707	−	0.0115631i
$378$		0			0
$379$	−2.67938	−	1.94668i	−0.137631	−	0.0999945i	0.516840	−	0.856082i	$-0.327108\pi$
$379$	−2.67938	−	1.94668i	−0.137631	−	0.0999945i	−0.654470	+	0.756088i	$0.727108\pi$
$380$		0			0
$381$	−8.16312	+	25.1235i	−0.418209	+	1.28712i
$382$		0			0
$383$	−21.3389	+	15.5036i	−1.09037	+	0.792197i	−0.979461	−	0.201633i	$-0.935375\pi$
$383$	−21.3389	+	15.5036i	−1.09037	+	0.792197i	−0.110905	+	0.993831i	$0.535375\pi$
$384$		0			0
$385$	−1.75329	−	0.865300i	−0.0893559	−	0.0440998i
$386$		0			0
$387$	0.953850	−	0.693013i	0.0484869	−	0.0352278i
$388$		0			0
$389$	7.28115	−	22.4091i	0.369169	−	1.13619i	−0.578160	−	0.815924i	$-0.696229\pi$
$389$	7.28115	−	22.4091i	0.369169	−	1.13619i	0.947329	−	0.320262i	$-0.103771\pi$
$390$		0			0
$391$	−3.45106	−	2.50734i	−0.174528	−	0.126802i
$392$		0			0
$393$	−4.20163	−	12.9313i	−0.211944	−	0.652297i
$394$		0			0
$395$	6.08744			0.306292
$396$		0			0
$397$	−14.1803			−0.711691			−0.355845	−	0.934545i	$-0.615807\pi$
$397$	−14.1803			−0.711691			−0.355845	+	0.934545i	$0.615807\pi$
$398$		0			0
$399$	−3.40806	−	10.4889i	−0.170616	−	0.525103i
$400$		0			0
$401$	−11.8713	−	8.62502i	−0.592826	−	0.430713i	0.250500	−	0.968117i	$-0.419405\pi$
$401$	−11.8713	−	8.62502i	−0.592826	−	0.430713i	−0.843325	+	0.537404i	$0.819405\pi$
$402$		0			0
$403$	−1.06644	+	3.28216i	−0.0531230	+	0.163496i
$404$		0			0
$405$	−2.09017	+	1.51860i	−0.103861	+	0.0754597i
$406$		0			0
$407$	6.06086	−	1.03952i	0.300426	−	0.0515270i
$408$		0			0
$409$	3.69098	−	2.68166i	0.182507	−	0.132599i	−0.492780	−	0.870154i	$-0.664019\pi$
$409$	3.69098	−	2.68166i	0.182507	−	0.132599i	0.675288	+	0.737554i	$0.264019\pi$
$410$		0			0
$411$	−4.81225	+	14.8106i	−0.237371	+	0.730553i
$412$		0			0
$413$	12.9271	+	9.39205i	0.636099	+	0.462153i
$414$		0			0
$415$	−1.29161	−	3.97517i	−0.0634027	−	0.195133i
$416$		0			0
$417$	8.27051			0.405009
$418$		0			0
$419$	27.3302			1.33517			0.667583	−	0.744535i	$-0.267329\pi$
$419$	27.3302			1.33517			0.667583	+	0.744535i	$0.267329\pi$
$420$		0			0
$421$	2.57295	+	7.91872i	0.125398	+	0.385935i	0.993973	−	0.109622i	$-0.0349640\pi$
$421$	2.57295	+	7.91872i	0.125398	+	0.385935i	−0.868575	+	0.495557i	$0.834964\pi$
$422$		0			0
$423$	−4.81225	−	3.49631i	−0.233980	−	0.169996i
$424$		0			0
$425$	1.28115	−	3.94298i	0.0621450	−	0.191263i
$426$		0			0
$427$	−15.6854	+	11.3961i	−0.759068	+	0.551495i
$428$		0			0
$429$	1.19098	−	8.19624i	0.0575012	−	0.395718i
$430$		0			0
$431$	−7.67381	+	5.57535i	−0.369634	+	0.268555i	−0.757059	−	0.653346i	$-0.773365\pi$
$431$	−7.67381	+	5.57535i	−0.369634	+	0.268555i	0.387425	+	0.921901i	$0.373365\pi$
$432$		0			0
$433$	−10.2254	+	31.4706i	−0.491403	+	1.51238i	0.331086	+	0.943600i	$0.392585\pi$
$433$	−10.2254	+	31.4706i	−0.491403	+	1.51238i	−0.822489	+	0.568781i	$0.807415\pi$
$434$		0			0
$435$	−0.0695824	−	0.0505546i	−0.00333622	−	0.00242391i
$436$		0			0
$437$	−7.14590	−	21.9928i	−0.341835	−	1.05206i
$438$		0			0
$439$	19.6994			0.940199			0.470100	−	0.882613i	$-0.344218\pi$
$439$	19.6994			0.940199			0.470100	+	0.882613i	$0.344218\pi$
$440$		0			0
$441$	2.85410			0.135910
$442$		0			0
$443$	1.79511	+	5.52479i	0.0852884	+	0.262491i	0.984601	−	0.174815i	$-0.0559327\pi$
$443$	1.79511	+	5.52479i	0.0852884	+	0.262491i	−0.899313	+	0.437306i	$0.855933\pi$
$444$		0			0
$445$	2.52786	+	1.83660i	0.119832	+	0.0870632i
$446$		0			0
$447$	−9.80668	+	30.1819i	−0.463840	+	1.42755i
$448$		0			0
$449$	−20.8713	+	15.1639i	−0.984979	+	0.715629i	−0.958816	−	0.284029i	$-0.908329\pi$
$449$	−20.8713	+	15.1639i	−0.984979	+	0.715629i	−0.0261629	+	0.999658i	$0.508329\pi$
$450$		0			0
$451$	−1.43078	+	1.46782i	−0.0673726	+	0.0691172i
$452$		0			0
$453$	−20.6353	+	14.9924i	−0.969529	+	0.704404i
$454$		0			0
$455$	0.294756	−	0.907165i	0.0138184	−	0.0425286i
$456$		0			0
$457$	−23.2533	−	16.8945i	−1.08774	−	0.790292i	−0.108726	−	0.994072i	$-0.534677\pi$
$457$	−23.2533	−	16.8945i	−1.08774	−	0.790292i	−0.979017	+	0.203780i	$0.934677\pi$
$458$		0			0
$459$	1.47378	+	4.53583i	0.0687901	+	0.211714i
$460$		0			0
$461$	−2.76393			−0.128729			−0.0643646	−	0.997926i	$-0.520502\pi$
$461$	−2.76393			−0.128729			−0.0643646	+	0.997926i	$0.520502\pi$
$462$		0			0
$463$	−31.8742			−1.48132			−0.740661	−	0.671879i	$-0.765487\pi$
$463$	−31.8742			−1.48132			−0.740661	+	0.671879i	$0.765487\pi$
$464$		0			0
$465$	0.388544	+	1.19581i	0.0180183	+	0.0554546i
$466$		0			0
$467$	−3.26889	−	2.37499i	−0.151266	−	0.109901i	0.509578	−	0.860425i	$-0.329802\pi$
$467$	−3.26889	−	2.37499i	−0.151266	−	0.109901i	−0.660844	+	0.750523i	$0.729802\pi$
$468$		0			0
$469$	3.85410	−	11.8617i	0.177966	−	0.547723i
$470$		0			0
$471$	16.7088	−	12.1397i	0.769901	−	0.559366i
$472$		0			0
$473$	2.94427	+	5.60034i	0.135378	+	0.257504i
$474$		0			0
$475$	18.1826	−	13.2104i	0.834274	−	0.606136i
$476$		0			0
$477$	1.63525	−	5.03280i	0.0748732	−	0.230436i
$478$		0			0
$479$	15.3906	+	11.1819i	0.703215	+	0.510916i	0.880978	−	0.473158i	$-0.156886\pi$
$479$	15.3906	+	11.1819i	0.703215	+	0.510916i	−0.177763	+	0.984073i	$0.556886\pi$
$480$		0			0
$481$	0.927051	+	2.85317i	0.0422699	+	0.130093i
$482$		0			0
$483$	11.8965			0.541312
$484$		0			0
$485$	1.20163			0.0545630
$486$		0			0
$487$	2.97414	+	9.15345i	0.134771	+	0.414783i	0.995554	−	0.0941891i	$-0.0300258\pi$
$487$	2.97414	+	9.15345i	0.134771	+	0.414783i	−0.860783	+	0.508972i	$0.830026\pi$
$488$		0			0
$489$	−11.2812	−	8.19624i	−0.510151	−	0.370647i
$490$		0			0
$491$	−10.2406	+	31.5173i	−0.462152	+	1.42236i	0.400378	+	0.916350i	$0.368879\pi$
$491$	−10.2406	+	31.5173i	−0.462152	+	1.42236i	−0.862530	+	0.506007i	$0.831121\pi$
$492$		0			0
$493$	−0.100813	+	0.0732450i	−0.00454039	+	0.00329879i
$494$		0			0
$495$	0.364338	+	0.693013i	0.0163758	+	0.0311486i
$496$		0			0
$497$	13.6631	−	9.92684i	0.612875	−	0.445279i
$498$		0			0
$499$	−2.74896	+	8.46044i	−0.123061	+	0.378741i	−0.993543	−	0.113459i	$-0.963807\pi$
$499$	−2.74896	+	8.46044i	−0.123061	+	0.378741i	0.870482	+	0.492200i	$0.163807\pi$
$500$		0			0
$501$	−7.42705	−	5.39607i	−0.331816	−	0.241079i
$502$		0			0
$503$	12.1483	+	37.3886i	0.541666	+	1.66708i	0.728788	+	0.684740i	$0.240084\pi$
$503$	12.1483	+	37.3886i	0.541666	+	1.66708i	−0.187122	+	0.982337i	$0.559916\pi$
$504$		0			0
$505$	−5.74265			−0.255544
$506$		0			0
$507$	−16.0231			−0.711612
$508$		0			0
$509$	3.42705	+	10.5474i	0.151901	+	0.467504i	0.997834	−	0.0657858i	$-0.0209554\pi$
$509$	3.42705	+	10.5474i	0.151901	+	0.467504i	−0.845932	+	0.533290i	$0.820955\pi$
$510$		0			0
$511$	12.3039	+	8.93930i	0.544292	+	0.395451i
$512$		0			0
$513$	−7.98936	+	24.5887i	−0.352739	+	1.08562i
$514$		0			0
$515$	−2.24546	+	1.63142i	−0.0989468	+	0.0718891i
$516$		0			0
$517$	22.2812	−	22.8581i	0.979924	−	1.00530i
$518$		0			0
$519$	2.08987	−	1.51838i	0.0917351	−	0.0666494i
$520$		0			0
$521$	4.13525	−	12.7270i	0.181169	−	0.557580i	−0.818693	−	0.574232i	$-0.805301\pi$
$521$	4.13525	−	12.7270i	0.181169	−	0.557580i	0.999861	+	0.0166519i	$0.00530070\pi$
$522$		0			0
$523$	−2.90455	−	2.11028i	−0.127007	−	0.0922762i	0.522468	−	0.852659i	$-0.325011\pi$
$523$	−2.90455	−	2.11028i	−0.127007	−	0.0922762i	−0.649475	+	0.760383i	$0.725011\pi$
$524$		0			0
$525$	3.57295	+	10.9964i	0.155936	+	0.479923i
$526$		0			0
$527$	1.82169			0.0793541
$528$		0			0
$529$	1.94427			0.0845336
$530$		0			0
$531$	−1.97728	−	6.08545i	−0.0858068	−	0.264086i
$532$		0			0
$533$	−0.809017	−	0.587785i	−0.0350424	−	0.0254598i
$534$		0			0
$535$	0.771681	−	2.37499i	0.0333627	−	0.102680i
$536$		0			0
$537$	−1.92705	+	1.40008i	−0.0831584	+	0.0604181i
$538$		0			0
$539$	−2.20246	+	15.1571i	−0.0948665	+	0.652863i
$540$		0			0
$541$	29.9615	−	21.7683i	1.28815	−	0.935892i	0.288379	−	0.957516i	$-0.406884\pi$
$541$	29.9615	−	21.7683i	1.28815	−	0.935892i	0.999766	+	0.0216241i	$0.00688369\pi$
$542$		0			0
$543$	−9.72067	+	29.9171i	−0.417154	+	1.28387i
$544$		0			0
$545$	−4.47214	−	3.24920i	−0.191565	−	0.139180i
$546$		0			0
$547$	9.59793	+	29.5394i	0.410378	+	1.26301i	0.916320	+	0.400446i	$0.131145\pi$
$547$	9.59793	+	29.5394i	0.410378	+	1.26301i	−0.505942	+	0.862567i	$0.668855\pi$
$548$		0			0
$549$	7.76393			0.331357
$550$		0			0
$551$	−0.675520			−0.0287781
$552$		0			0
$553$	7.60081	+	23.3929i	0.323219	+	0.994767i
$554$		0			0
$555$	0.884268	+	0.642458i	0.0375351	+	0.0272708i
$556$		0			0
$557$	−6.13525	+	18.8824i	−0.259959	+	0.800072i	0.732853	+	0.680387i	$0.238188\pi$
$557$	−6.13525	+	18.8824i	−0.259959	+	0.800072i	−0.992812	+	0.119685i	$0.961812\pi$
$558$		0			0
$559$	−2.49721	+	1.81433i	−0.105621	+	0.0767380i
$560$		0			0
$561$	−4.30902	+	0.739054i	−0.181927	+	0.0312029i
$562$		0			0
$563$	29.4200	−	21.3749i	1.23991	−	0.900845i	0.242315	−	0.970198i	$-0.422093\pi$
$563$	29.4200	−	21.3749i	1.23991	−	0.900845i	0.997592	+	0.0693528i	$0.0220934\pi$
$564$		0			0
$565$	2.30902	−	7.10642i	0.0971411	−	0.298969i
$566$		0			0
$567$	−8.44549	−	6.13600i	−0.354677	−	0.257688i
$568$		0			0
$569$	1.98936	+	6.12261i	0.0833982	+	0.256673i	0.984057	−	0.177854i	$-0.0569155\pi$
$569$	1.98936	+	6.12261i	0.0833982	+	0.256673i	−0.900659	+	0.434527i	$0.856915\pi$
$570$		0			0
$571$	−39.6771			−1.66043			−0.830217	−	0.557441i	$-0.811783\pi$
$571$	−39.6771			−1.66043			−0.830217	+	0.557441i	$0.811783\pi$
$572$		0			0
$573$	−5.32624			−0.222507
$574$		0			0
$575$	7.49164	+	23.0569i	0.312423	+	0.961539i
$576$		0			0
$577$	−0.309017	−	0.224514i	−0.0128645	−	0.00934664i	0.581334	−	0.813665i	$-0.302531\pi$
$577$	−0.309017	−	0.224514i	−0.0128645	−	0.00934664i	−0.594199	+	0.804318i	$0.702531\pi$
$578$		0			0
$579$	1.58637	−	4.88233i	0.0659271	−	0.202903i
$580$		0			0
$581$	13.6631	−	9.92684i	0.566842	−	0.411835i
$582$		0			0
$583$	25.4655	+	12.5680i	1.05467	+	0.520512i
$584$		0			0
$585$	−0.309017	+	0.224514i	−0.0127763	+	0.00928251i
$586$		0			0
$587$	−0.476925	+	1.46782i	−0.0196848	+	0.0605836i	−0.960416	−	0.278568i	$-0.910140\pi$
$587$	−0.476925	+	1.46782i	−0.0196848	+	0.0605836i	0.940732	+	0.339152i	$0.110140\pi$
$588$		0			0
$589$	7.98936	+	5.80461i	0.329196	+	0.239175i
$590$		0			0
$591$	−6.76296	−	20.8142i	−0.278191	−	0.856184i
$592$		0			0
$593$	38.6525			1.58727			0.793633	−	0.608396i	$-0.208187\pi$
$593$	38.6525			1.58727			0.793633	+	0.608396i	$0.208187\pi$
$594$		0			0
$595$	−0.503503			−0.0206416
$596$		0			0
$597$	8.61803	+	26.5236i	0.352713	+	1.08554i
$598$		0			0
$599$	21.3389	+	15.5036i	0.871883	+	0.633460i	0.931092	−	0.364785i	$-0.118858\pi$
$599$	21.3389	+	15.5036i	0.871883	+	0.633460i	−0.0592083	+	0.998246i	$0.518858\pi$
$600$		0			0
$601$	8.31559	−	25.5928i	0.339200	−	1.04395i	−0.625416	−	0.780292i	$-0.715071\pi$
$601$	8.31559	−	25.5928i	0.339200	−	1.04395i	0.964616	−	0.263659i	$-0.0849294\pi$
$602$		0			0
$603$	−4.04057	+	2.93565i	−0.164545	+	0.119549i
$604$		0			0
$605$	−3.96149	+	1.40008i	−0.161058	+	0.0569215i
$606$		0			0
$607$	−0.771681	+	0.560659i	−0.0313216	+	0.0227564i	−0.603336	−	0.797487i	$-0.706162\pi$
$607$	−0.771681	+	0.560659i	−0.0313216	+	0.0227564i	0.572014	+	0.820244i	$0.306162\pi$
$608$		0			0
$609$	0.107391	−	0.330515i	0.00435170	−	0.0133931i
$610$		0			0
$611$	12.5986	+	9.15345i	0.509687	+	0.370309i
$612$		0			0
$613$	5.51722	+	16.9803i	0.222838	+	0.685826i	0.998504	+	0.0546819i	$0.0174145\pi$
$613$	5.51722	+	16.9803i	0.222838	+	0.685826i	−0.775665	+	0.631144i	$0.782586\pi$
$614$		0			0
$615$	−0.364338			−0.0146915
$616$		0			0
$617$	−10.0689			−0.405358			−0.202679	−	0.979245i	$-0.564965\pi$
$617$	−10.0689			−0.405358			−0.202679	+	0.979245i	$0.564965\pi$
$618$		0			0
$619$	−11.2805	−	34.7177i	−0.453400	−	1.39542i	−0.873003	−	0.487714i	$-0.837831\pi$
$619$	−11.2805	−	34.7177i	−0.453400	−	1.39542i	0.419604	−	0.907707i	$-0.362169\pi$
$620$		0			0
$621$	−22.5623	−	16.3925i	−0.905394	−	0.657807i
$622$		0			0
$623$	−3.90141	+	12.0073i	−0.156307	+	0.481062i
$624$		0			0
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$		0			0
$627$	−21.2529	−	10.4889i	−0.848758	−	0.418887i
$628$		0			0
$629$	1.28115	−	0.930812i	0.0510829	−	0.0371139i
$630$		0			0
$631$	1.29161	−	3.97517i	0.0514182	−	0.158249i	−0.922050	−	0.387070i	$-0.873487\pi$
$631$	1.29161	−	3.97517i	0.0514182	−	0.158249i	0.973468	+	0.228821i	$0.0734871\pi$
$632$		0			0
$633$	−29.9894	−	21.7885i	−1.19197	−	0.866017i
$634$		0			0
$635$	2.02029	+	6.21780i	0.0801726	+	0.246746i
$636$		0			0
$637$	−7.47214			−0.296057
$638$		0			0
$639$	−6.76296			−0.267539
$640$		0			0
$641$	3.39261	+	10.4414i	0.134000	+	0.412410i	0.995433	−	0.0954614i	$-0.0304327\pi$
$641$	3.39261	+	10.4414i	0.134000	+	0.412410i	−0.861433	+	0.507871i	$0.830433\pi$
$642$		0			0
$643$	−35.9578	−	26.1249i	−1.41804	−	1.03026i	−0.992092	−	0.125517i	$-0.959941\pi$
$643$	−35.9578	−	26.1249i	−1.41804	−	1.03026i	−0.425947	−	0.904748i	$-0.640059\pi$
$644$		0			0
$645$	−0.347524	+	1.06957i	−0.0136838	+	0.0421143i
$646$		0			0
$647$	37.5012	−	27.2462i	1.47432	−	1.07116i	0.494992	−	0.868897i	$-0.335171\pi$
$647$	37.5012	−	27.2462i	1.47432	−	1.07116i	0.979332	−	0.202261i	$-0.0648291\pi$
$648$		0			0
$649$	33.8435	−	5.80461i	1.32847	−	0.227851i
$650$		0			0
$651$	−4.11016	+	2.98620i	−0.161090	+	0.117039i
$652$		0			0
$653$	−3.33688	+	10.2699i	−0.130582	+	0.401891i	−0.994877	−	0.101095i	$-0.967765\pi$
$653$	−3.33688	+	10.2699i	−0.130582	+	0.401891i	0.864295	+	0.502986i	$0.167765\pi$
$654$		0			0
$655$	−2.72239	−	1.97793i	−0.106372	−	0.0772841i
$656$		0			0
$657$	−1.88197	−	5.79210i	−0.0734225	−	0.225971i
$658$		0			0
$659$	11.1679			0.435039			0.217519	−	0.976056i	$-0.430204\pi$
$659$	11.1679			0.435039			0.217519	+	0.976056i	$0.430204\pi$
$660$		0			0
$661$	−31.4164			−1.22196			−0.610978	−	0.791647i	$-0.709224\pi$
$661$	−31.4164			−1.22196			−0.610978	+	0.791647i	$0.709224\pi$
$662$		0			0
$663$	−0.659094	−	2.02848i	−0.0255971	−	0.0787798i
$664$		0			0
$665$	−2.20820	−	1.60435i	−0.0856305	−	0.0622142i
$666$		0			0
$667$	0.225173	−	0.693013i	0.00871875	−	0.0268336i
$668$		0			0
$669$	−26.8713	+	19.5232i	−1.03891	+	0.754809i
$670$		0			0
$671$	−5.99128	+	41.2314i	−0.231291	+	1.59172i
$672$		0			0
$673$	35.9058	−	26.0871i	1.38407	−	1.00558i	0.387578	−	0.921837i	$-0.373312\pi$
$673$	35.9058	−	26.0871i	1.38407	−	1.00558i	0.996487	−	0.0837457i	$-0.0266883\pi$
$674$		0			0
$675$	8.37590	−	25.7784i	0.322389	−	0.992210i
$676$		0			0
$677$	−19.3992	−	14.0943i	−0.745571	−	0.541689i	0.148880	−	0.988855i	$-0.452433\pi$
$677$	−19.3992	−	14.0943i	−0.745571	−	0.541689i	−0.894451	+	0.447166i	$0.852433\pi$
$678$		0			0
$679$	1.50036	+	4.61763i	0.0575784	+	0.177208i
$680$		0			0
$681$	14.8541			0.569210
$682$		0			0
$683$	−26.1511			−1.00065			−0.500323	−	0.865839i	$-0.666785\pi$
$683$	−26.1511			−1.00065			−0.500323	+	0.865839i	$0.666785\pi$
$684$		0			0
$685$	1.19098	+	3.66547i	0.0455051	+	0.140050i
$686$		0			0
$687$	10.8301	+	7.86854i	0.413195	+	0.300203i
$688$		0			0
$689$	−4.28115	+	13.1760i	−0.163099	+	0.501967i
$690$		0			0
$691$	16.3445	−	11.8749i	0.621773	−	0.451744i	−0.231768	−	0.972771i	$-0.574451\pi$
$691$	16.3445	−	11.8749i	0.621773	−	0.451744i	0.853540	+	0.521027i	$0.174451\pi$
$692$		0			0
$693$	−2.20820	+	2.26538i	−0.0838827	+	0.0860548i
$694$		0			0
$695$	1.65595	−	1.20312i	0.0628137	−	0.0456368i
$696$		0			0
$697$	−0.163119	+	0.502029i	−0.00617857	+	0.0190157i
$698$		0			0
$699$	−20.0903	−	14.5964i	−0.759884	−	0.552088i
$700$		0			0
$701$	−7.33688	−	22.5806i	−0.277110	−	0.852857i	−0.988653	−	0.150215i	$-0.952003\pi$
$701$	−7.33688	−	22.5806i	−0.277110	−	0.852857i	0.711543	−	0.702642i	$-0.247997\pi$
$702$		0			0
$703$	8.58465			0.323776
$704$		0			0
$705$	5.67376			0.213686
$706$		0			0
$707$	−7.17030	−	22.0679i	−0.269667	−	0.829950i
$708$		0			0
$709$	9.39919	+	6.82891i	0.352994	+	0.256465i	0.750124	−	0.661297i	$-0.229994\pi$
$709$	9.39919	+	6.82891i	0.352994	+	0.256465i	−0.397130	+	0.917762i	$0.629994\pi$
$710$		0			0
$711$	3.04372	−	9.36761i	0.114148	−	0.351313i
$712$		0			0
$713$	−8.61803	+	6.26137i	−0.322748	+	0.234490i
$714$		0			0
$715$	−0.953850	−	1.81433i	−0.0356720	−	0.0678521i
$716$		0			0
$717$	19.7254	−	14.3314i	0.736659	−	0.535214i
$718$		0			0
$719$	7.37905	−	22.7104i	0.275192	−	0.846954i	−0.713976	−	0.700170i	$-0.753108\pi$
$719$	7.37905	−	22.7104i	0.275192	−	0.846954i	0.989169	−	0.146784i	$-0.0468924\pi$
$720$		0			0
$721$	−9.07295	−	6.59188i	−0.337894	−	0.245495i
$722$		0			0
$723$	−3.53707	−	10.8860i	−0.131545	−	0.404854i
$724$		0			0
$725$	0.708204			0.0263020
$726$		0			0
$727$	−11.4462			−0.424516			−0.212258	−	0.977214i	$-0.568082\pi$
$727$	−11.4462			−0.424516			−0.212258	+	0.977214i	$0.568082\pi$
$728$		0			0
$729$	9.28115	+	28.5645i	0.343746	+	1.05794i
$730$		0			0
$731$	1.31819	+	0.957720i	0.0487550	+	0.0354226i
$732$		0			0
$733$	−1.98936	+	6.12261i	−0.0734786	+	0.226144i	−0.981050	−	0.193753i	$-0.937934\pi$
$733$	−1.98936	+	6.12261i	−0.0734786	+	0.226144i	0.907572	+	0.419897i	$0.137934\pi$
$734$		0			0
$735$	−2.20246	+	1.60018i	−0.0812388	+	0.0590235i
$736$		0			0
$737$	−12.4721	−	23.7234i	−0.459417	−	0.873863i
$738$		0			0
$739$	14.0724	−	10.2242i	0.517663	−	0.376104i	−0.298060	−	0.954547i	$-0.596340\pi$
$739$	14.0724	−	10.2242i	0.517663	−	0.376104i	0.815723	+	0.578443i	$0.196340\pi$
$740$		0			0
$741$	3.57295	−	10.9964i	0.131256	−	0.403963i
$742$		0			0
$743$	−10.0319	−	7.28857i	−0.368033	−	0.267392i	0.388362	−	0.921507i	$-0.373041\pi$
$743$	−10.0319	−	7.28857i	−0.368033	−	0.267392i	−0.756395	+	0.654115i	$0.773041\pi$
$744$		0			0
$745$	2.42705	+	7.46969i	0.0889203	+	0.273668i
$746$		0			0
$747$	−6.76296			−0.247444
$748$		0			0
$749$	10.0902			0.368687
$750$		0			0
$751$	−13.7777	−	42.4033i	−0.502754	−	1.54732i	−0.804513	−	0.593935i	$-0.797574\pi$
$751$	−13.7777	−	42.4033i	−0.502754	−	1.54732i	0.301759	−	0.953384i	$-0.402426\pi$
$752$		0			0
$753$	−18.0795	−	13.1355i	−0.658855	−	0.478686i
$754$		0			0
$755$	−1.95070	+	6.00365i	−0.0709934	+	0.218495i
$756$		0			0
$757$	−26.0172	+	18.9026i	−0.945612	+	0.687027i	−0.949765	−	0.312964i	$-0.898678\pi$
$757$	−26.0172	+	18.9026i	−0.945612	+	0.687027i	0.00415299	+	0.999991i	$0.498678\pi$
$758$		0			0
$759$	17.8448	−	18.3069i	0.647726	−	0.664499i
$760$		0			0
$761$	−15.2533	+	11.0822i	−0.552931	+	0.401728i	−0.828865	−	0.559449i	$-0.811013\pi$
$761$	−15.2533	+	11.0822i	−0.552931	+	0.401728i	0.275934	+	0.961177i	$0.411013\pi$
$762$		0			0
$763$	6.90212	−	21.2426i	0.249874	−	0.769032i
$764$		0			0
$765$	0.163119	+	0.118513i	0.00589758	+	0.00428484i
$766$		0			0
$767$	5.17659	+	15.9319i	0.186916	+	0.575268i
$768$		0			0
$769$	−25.1246			−0.906017			−0.453008	−	0.891506i	$-0.649649\pi$
$769$	−25.1246			−0.906017			−0.453008	+	0.891506i	$0.649649\pi$
$770$		0			0
$771$	−22.1106			−0.796293
$772$		0			0
$773$	16.7533	+	51.5613i	0.602574	+	1.85453i	0.512679	+	0.858581i	$0.328653\pi$
$773$	16.7533	+	51.5613i	0.602574	+	1.85453i	0.0898953	+	0.995951i	$0.471347\pi$
$774$		0			0
$775$	−8.37590	−	6.08545i	−0.300871	−	0.218596i
$776$		0			0
$777$	−1.36475	+	4.20025i	−0.0489600	+	0.150683i
$778$		0			0
$779$	−2.31504	+	1.68198i	−0.0829450	+	0.0602631i
$780$		0			0
$781$	5.21885	−	35.9156i	0.186745	−	1.28516i
$782$		0			0
$783$	−0.659094	+	0.478860i	−0.0235541	+	0.0171131i
$784$		0			0
$785$	1.57953	−	4.86128i	0.0563757	−	0.173507i
$786$		0			0
$787$	−14.8011	−	10.7536i	−0.527602	−	0.383326i	0.291858	−	0.956462i	$-0.405727\pi$
$787$	−14.8011	−	10.7536i	−0.527602	−	0.383326i	−0.819460	+	0.573136i	$0.805727\pi$
$788$		0			0
$789$	−7.49342	−	23.0624i	−0.266773	−	0.821043i
$790$		0			0
$791$	30.1917			1.07349
$792$		0			0
$793$	−20.3262			−0.721806
$794$		0			0
$795$	1.55979	+	4.80053i	0.0553200	+	0.170257i
$796$		0			0
$797$	−30.7254	−	22.3233i	−1.08835	−	0.790733i	−0.109230	−	0.994016i	$-0.534839\pi$
$797$	−30.7254	−	22.3233i	−1.08835	−	0.790733i	−0.979120	+	0.203284i	$0.934839\pi$
$798$		0			0
$799$	2.54022	−	7.81798i	0.0898664	−	0.276580i
$800$		0			0
$801$	4.09017	−	2.97168i	0.144519	−	0.104999i
$802$		0			0
$803$	32.2120	−	5.52479i	1.13674	−	0.194966i
$804$		0			0
$805$	2.38197	−	1.73060i	0.0839533	−	0.0609956i
$806$		0			0
$807$	6.58079	−	20.2536i	0.231655	−	0.712960i
$808$		0			0
$809$	−6.30902	−	4.58377i	−0.221813	−	0.161157i	0.471329	−	0.881957i	$-0.343774\pi$
$809$	−6.30902	−	4.58377i	−0.221813	−	0.161157i	−0.693143	+	0.720801i	$0.743774\pi$
$810$		0			0
$811$	−6.56436	−	20.2030i	−0.230506	−	0.709425i	−0.997686	−	0.0679925i	$-0.978341\pi$
$811$	−6.56436	−	20.2030i	−0.230506	−	0.709425i	0.767180	−	0.641432i	$-0.221659\pi$
$812$		0			0
$813$	39.7984			1.39579
$814$		0			0
$815$	−3.45106			−0.120885
$816$		0			0
$817$	2.72949	+	8.40051i	0.0954928	+	0.293897i
$818$		0			0
$819$	−1.24861	−	0.907165i	−0.0436298	−	0.0316989i
$820$		0			0
$821$	−4.66312	+	14.3516i	−0.162744	+	0.500874i	−0.998863	−	0.0476737i	$-0.984819\pi$
$821$	−4.66312	+	14.3516i	−0.162744	+	0.500874i	0.836119	+	0.548548i	$0.184819\pi$
$822$		0			0
$823$	−36.1830	+	26.2885i	−1.26126	+	0.916359i	−0.998819	−	0.0485890i	$-0.984528\pi$
$823$	−36.1830	+	26.2885i	−1.26126	+	0.916359i	−0.262441	+	0.964948i	$0.584528\pi$
$824$		0			0
$825$	22.2812	+	10.9964i	0.775730	+	0.382846i
$826$		0			0
$827$	−14.8011	+	10.7536i	−0.514685	+	0.373940i	−0.814598	−	0.580026i	$-0.803042\pi$
$827$	−14.8011	+	10.7536i	−0.514685	+	0.373940i	0.299913	+	0.953967i	$0.403042\pi$
$828$		0			0
$829$	−4.06637	+	12.5150i	−0.141231	+	0.434664i	−0.996507	−	0.0835084i	$-0.973387\pi$
$829$	−4.06637	+	12.5150i	−0.141231	+	0.434664i	0.855276	+	0.518172i	$0.173387\pi$
$830$		0			0
$831$	−14.1420	−	10.2748i	−0.490581	−	0.356428i
$832$		0			0
$833$	1.21885	+	3.75123i	0.0422305	+	0.129972i
$834$		0			0
$835$	−2.27204			−0.0786271
$836$		0			0
$837$	11.9098			0.411664
$838$		0			0
$839$	5.24618	+	16.1461i	0.181118	+	0.557424i	0.999860	−	0.0167377i	$-0.00532801\pi$
$839$	5.24618	+	16.1461i	0.181118	+	0.557424i	−0.818742	+	0.574162i	$0.805328\pi$
$840$		0			0
$841$	23.4443	+	17.0333i	0.808423	+	0.587354i
$842$		0			0
$843$	6.85912	−	21.1102i	0.236241	−	0.727074i
$844$		0			0
$845$	−3.20820	+	2.33090i	−0.110366	+	0.0801853i
$846$		0			0
$847$	−10.3266	−	13.4751i	−0.354826	−	0.463011i
$848$		0			0
$849$	25.3992	−	18.4536i	0.871698	−	0.633326i
$850$		0			0
$851$	−2.86155	+	8.80695i	−0.0980927	+	0.301898i
$852$		0			0
$853$	−28.1074	−	20.4212i	−0.962379	−	0.699209i	−0.00867675	−	0.999962i	$-0.502762\pi$
$853$	−28.1074	−	20.4212i	−0.962379	−	0.699209i	−0.953702	+	0.300753i	$0.902762\pi$
$854$		0			0
$855$	0.337760	+	1.03952i	0.0115512	+	0.0355508i
$856$		0			0
$857$	31.1246			1.06320			0.531598	−	0.846997i	$-0.321592\pi$
$857$	31.1246			1.06320			0.531598	+	0.846997i	$0.321592\pi$
$858$		0			0
$859$	3.81540			0.130180			0.0650899	−	0.997879i	$-0.479267\pi$
$859$	3.81540			0.130180			0.0650899	+	0.997879i	$0.479267\pi$
$860$		0			0
$861$	−0.454915	−	1.40008i	−0.0155035	−	0.0477148i
$862$		0			0
$863$	−9.21717	−	6.69666i	−0.313756	−	0.227957i	0.419750	−	0.907640i	$-0.362118\pi$
$863$	−9.21717	−	6.69666i	−0.313756	−	0.227957i	−0.733506	+	0.679682i	$0.762118\pi$
$864$		0			0
$865$	0.197561	−	0.608030i	0.00671727	−	0.0206736i
$866$		0			0
$867$	20.3155	−	14.7600i	0.689949	−	0.501277i
$868$		0			0
$869$	47.3992	+	23.3929i	1.60791	+	0.793550i
$870$		0			0
$871$	10.5784	−	7.68563i	0.358434	−	0.260418i
$872$		0			0
$873$	0.600813	−	1.84911i	0.0203344	−	0.0625830i
$874$		0			0
$875$	4.69967	+	3.41451i	0.158878	+	0.115431i
$876$		0			0
$877$	7.62868	+	23.4787i	0.257602	+	0.792818i	0.993306	+	0.115514i	$0.0368516\pi$
$877$	7.62868	+	23.4787i	0.257602	+	0.792818i	−0.735704	+	0.677304i	$0.763148\pi$
$878$		0			0
$879$	−11.6714			−0.393666
$880$		0			0
$881$	−1.23607			−0.0416442			−0.0208221	−	0.999783i	$-0.506628\pi$
$881$	−1.23607			−0.0416442			−0.0208221	+	0.999783i	$0.506628\pi$
$882$		0			0
$883$	6.42520	+	19.7747i	0.216225	+	0.665473i	0.999064	+	0.0432485i	$0.0137707\pi$
$883$	6.42520	+	19.7747i	0.216225	+	0.665473i	−0.782839	+	0.622224i	$0.786229\pi$
$884$		0			0
$885$	4.93769	+	3.58744i	0.165979	+	0.120591i
$886$		0			0
$887$	4.65666	−	14.3317i	0.156355	−	0.481213i	−0.841940	−	0.539571i	$-0.818587\pi$
$887$	4.65666	−	14.3317i	0.156355	−	0.481213i	0.998296	+	0.0583581i	$0.0185865\pi$
$888$		0			0
$889$	−21.3713	+	15.5272i	−0.716771	+	0.520765i
$890$		0			0
$891$	−22.1106	+	3.79226i	−0.740732	+	0.127045i
$892$		0			0
$893$	36.0517	−	26.1931i	1.20642	−	0.876518i
$894$		0			0
$895$	−0.182169	+	0.560659i	−0.00608924	+	0.0187408i
$896$		0			0
$897$	10.0902	+	7.33094i	0.336901	+	0.244773i
$898$		0			0
$899$	0.0961606	+	0.295952i	0.00320713	+	0.00987054i
$900$		0			0
$901$	7.31308			0.243634
$902$		0			0
$903$	−4.54408			−0.151217
$904$		0			0
$905$	2.40576	+	7.40418i	0.0799703	+	0.246123i
$906$		0			0
$907$	35.3683	+	25.6966i	1.17439	+	0.853241i	0.991527	−	0.129898i	$-0.0414651\pi$
$907$	35.3683	+	25.6966i	1.17439	+	0.853241i	0.182858	+	0.983139i	$0.441465\pi$
$908$		0			0
$909$	−2.87132	+	8.83702i	−0.0952358	+	0.293106i
$910$		0			0
$911$	1.95070	−	1.41727i	0.0646297	−	0.0469562i	−0.555001	−	0.831849i	$-0.687282\pi$
$911$	1.95070	−	1.41727i	0.0646297	−	0.0469562i	0.619631	+	0.784893i	$0.287282\pi$
$912$		0			0
$913$	5.21885	−	35.9156i	0.172719	−	1.18863i
$914$		0			0
$915$	−5.99128	+	4.35292i	−0.198066	+	0.143903i
$916$		0			0
$917$	4.20163	−	12.9313i	0.138750	−	0.427028i
$918$		0			0
$919$	−1.13602	−	0.825366i	−0.0374738	−	0.0272263i	0.568891	−	0.822413i	$-0.307373\pi$
$919$	−1.13602	−	0.825366i	−0.0374738	−	0.0272263i	−0.606364	+	0.795187i	$0.707373\pi$
$920$		0			0
$921$	−4.20163	−	12.9313i	−0.138448	−	0.426100i
$922$		0			0
$923$	17.7057			0.582789
$924$		0			0
$925$	−9.00000			−0.295918
$926$		0			0
$927$	1.38777	+	4.27112i	0.0455804	+	0.140282i
$928$		0			0
$929$	−40.9615	−	29.7603i	−1.34390	−	0.976403i	−0.999291	−	0.0376576i	$-0.988010\pi$
$929$	−40.9615	−	29.7603i	−1.34390	−	0.976403i	−0.344612	−	0.938745i	$-0.611990\pi$
$930$		0			0
$931$	−6.60737	+	20.3354i	−0.216548	+	0.666465i
$932$		0			0
$933$	15.3090	−	11.1227i	0.501195	−	0.364139i
$934$		0			0
$935$	−0.755255	+	0.774812i	−0.0246995	+	0.0253391i
$936$		0			0
$937$	0.163119	−	0.118513i	0.00532886	−	0.00387165i	−0.585118	−	0.810948i	$-0.698952\pi$
$937$	0.163119	−	0.118513i	0.00532886	−	0.00387165i	0.590446	+	0.807077i	$0.298952\pi$
$938$		0			0
$939$	−11.1249	+	34.2388i	−0.363046	+	1.11734i
$940$		0			0
$941$	−19.0172	−	13.8168i	−0.619944	−	0.450415i	0.232958	−	0.972487i	$-0.425159\pi$
$941$	−19.0172	−	13.8168i	−0.619944	−	0.450415i	−0.852902	+	0.522071i	$0.825159\pi$
$942$		0			0
$943$	−0.953850	−	2.93565i	−0.0310616	−	0.0955979i
$944$		0			0
$945$	−3.29180			−0.107082
$946$		0			0
$947$	23.7931			0.773172			0.386586	−	0.922253i	$-0.373654\pi$
$947$	23.7931			0.773172			0.386586	+	0.922253i	$0.373654\pi$
$948$		0			0
$949$	4.92705	+	15.1639i	0.159939	+	0.492241i
$950$		0			0
$951$	16.2749	+	11.8244i	0.527749	+	0.383432i
$952$		0			0
$953$	−13.8647	+	42.6713i	−0.449123	+	1.38226i	0.428775	+	0.903411i	$0.358945\pi$
$953$	−13.8647	+	42.6713i	−0.449123	+	1.38226i	−0.877898	+	0.478848i	$0.841055\pi$
$954$		0			0
$955$	−1.06644	+	0.774812i	−0.0345091	+	0.0250723i
$956$		0			0
$957$	−0.347524	−	0.661030i	−0.0112339	−	0.0213681i
$958$		0			0
$959$	−12.5986	+	9.15345i	−0.406832	+	0.295580i
$960$		0			0
$961$	−8.17376	+	25.1563i	−0.263670	+	0.811492i
$962$		0			0
$963$	−3.26889	−	2.37499i	−0.105339	−	0.0765330i
$964$		0			0
$965$	−0.392609	−	1.20833i	−0.0126385	−	0.0388974i
$966$		0			0
$967$	−60.3834			−1.94180			−0.970900	−	0.239484i	$-0.923022\pi$
$967$	−60.3834			−1.94180			−0.970900	+	0.239484i	$0.923022\pi$
$968$		0			0
$969$	−6.10333			−0.196067
$970$		0			0
$971$	5.69652	+	17.5321i	0.182810	+	0.562632i	0.999904	−	0.0138733i	$-0.00441615\pi$
$971$	5.69652	+	17.5321i	0.182810	+	0.562632i	−0.817094	+	0.576505i	$0.804416\pi$
$972$		0			0
$973$	6.69098	+	4.86128i	0.214503	+	0.155846i
$974$		0			0
$975$	−3.74582	+	11.5284i	−0.119962	+	0.369206i
$976$		0			0
$977$	−7.30902	+	5.31031i	−0.233836	+	0.169892i	−0.698533	−	0.715578i	$-0.746163\pi$
$977$	−7.30902	+	5.31031i	−0.233836	+	0.169892i	0.464697	+	0.885470i	$0.346163\pi$
$978$		0			0
$979$	12.6252	+	24.0146i	0.403504	+	0.767510i
$980$		0			0
$981$	−7.23607	+	5.25731i	−0.231030	+	0.167853i
$982$		0			0
$983$	0.0265781	−	0.0817991i	0.000847710	−	0.00260898i	−0.950632	−	0.310321i	$-0.899563\pi$
$983$	0.0265781	−	0.0817991i	0.000847710	−	0.00260898i	0.951479	+	0.307712i	$0.0995634\pi$
$984$		0			0
$985$	−4.38197	−	3.18368i	−0.139621	−	0.101441i
$986$		0			0
$987$	7.08429	+	21.8032i	0.225496	+	0.694004i
$988$		0			0
$989$	−9.52786			−0.302968
$990$		0			0
$991$	15.2616			0.484801			0.242400	−	0.970176i	$-0.422065\pi$
$991$	15.2616			0.484801			0.242400	+	0.970176i	$0.422065\pi$
$992$		0			0
$993$	1.81966	+	5.60034i	0.0577452	+	0.177721i
$994$		0			0
$995$	5.58394	+	4.05697i	0.177023	+	0.128614i
$996$		0			0
$997$	8.40576	−	25.8703i	0.266213	−	0.819320i	−0.725198	−	0.688540i	$-0.758252\pi$
$997$	8.40576	−	25.8703i	0.266213	−	0.819320i	0.991411	−	0.130780i	$-0.0417481\pi$
$998$		0			0
$999$	8.37590	−	6.08545i	0.265002	−	0.192535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.c.289.2	yes	8
4.3	odd	2	inner	352.2.m.c.289.1	yes	8
8.3	odd	2		704.2.m.k.641.2		8
8.5	even	2		704.2.m.k.641.1		8
11.2	odd	10		3872.2.a.bf.1.3		4
11.4	even	5	inner	352.2.m.c.257.2	yes	8
11.9	even	5		3872.2.a.bg.1.3		4
44.15	odd	10	inner	352.2.m.c.257.1	✓	8
44.31	odd	10		3872.2.a.bg.1.2		4
44.35	even	10		3872.2.a.bf.1.2		4
88.13	odd	10		7744.2.a.dq.1.2		4
88.35	even	10		7744.2.a.dq.1.3		4
88.37	even	10		704.2.m.k.257.1		8
88.53	even	10		7744.2.a.dp.1.2		4
88.59	odd	10		704.2.m.k.257.2		8
88.75	odd	10		7744.2.a.dp.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.c.257.1	✓	8	44.15	odd	10	inner
352.2.m.c.257.2	yes	8	11.4	even	5	inner
352.2.m.c.289.1	yes	8	4.3	odd	2	inner
352.2.m.c.289.2	yes	8	1.1	even	1	trivial
704.2.m.k.257.1		8	88.37	even	10
704.2.m.k.257.2		8	88.59	odd	10
704.2.m.k.641.1		8	8.5	even	2
704.2.m.k.641.2		8	8.3	odd	2
3872.2.a.bf.1.2		4	44.35	even	10
3872.2.a.bf.1.3		4	11.2	odd	10
3872.2.a.bg.1.2		4	44.31	odd	10
3872.2.a.bg.1.3		4	11.9	even	5
7744.2.a.dp.1.2		4	88.53	even	10
7744.2.a.dp.1.3		4	88.75	odd	10
7744.2.a.dq.1.2		4	88.13	odd	10
7744.2.a.dq.1.3		4	88.35	even	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.476925 + 1.46782i) q^{3} +(0.309017 + 0.224514i) q^{5} +(-0.476925 + 1.46782i) q^{7} +(0.500000 - 0.363271i) q^{9} +(1.54336 + 2.93565i) q^{11} +(-1.30902 + 0.951057i) q^{13} +(-0.182169 + 0.560659i) q^{15} +(0.690983 + 0.502029i) q^{17} +(1.43078 + 4.40347i) q^{19} -2.38197 q^{21} -4.99442 q^{23} +(-1.50000 - 4.61653i) q^{25} +(4.51750 + 3.28216i) q^{27} +(-0.0450850 + 0.138757i) q^{29} +(1.72553 - 1.25367i) q^{31} +(-3.57295 + 3.66547i) q^{33} +(-0.476925 + 0.346506i) q^{35} +(0.572949 - 1.76336i) q^{37} +(-2.02029 - 1.46782i) q^{39} +(0.190983 + 0.587785i) q^{41} +1.90770 q^{43} +0.236068 q^{45} +(-2.97414 - 9.15345i) q^{47} +(3.73607 + 2.71441i) q^{49} +(-0.407343 + 1.25367i) q^{51} +(6.92705 - 5.03280i) q^{53} +(-0.182169 + 1.25367i) q^{55} +(-5.78115 + 4.20025i) q^{57} +(3.19931 - 9.84647i) q^{59} +(10.1631 + 7.38394i) q^{61} +(0.294756 + 0.907165i) q^{63} -0.618034 q^{65} -8.08115 q^{67} +(-2.38197 - 7.33094i) q^{69} +(-8.85283 - 6.43196i) q^{71} +(3.04508 - 9.37181i) q^{73} +(6.06086 - 4.40347i) q^{75} +(-5.04508 + 0.865300i) q^{77} +(12.8934 - 9.36761i) q^{79} +(-2.09017 + 6.43288i) q^{81} +(-8.85283 - 6.43196i) q^{83} +(0.100813 + 0.310271i) q^{85} -0.225173 q^{87} +8.18034 q^{89} +(-0.771681 - 2.37499i) q^{91} +(2.66312 + 1.93487i) q^{93} +(-0.546507 + 1.68198i) q^{95} +(2.54508 - 1.84911i) q^{97} +(1.83812 + 0.907165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} + 4 q^{9} - 6 q^{13} + 10 q^{17} - 28 q^{21} - 12 q^{25} + 22 q^{29} - 42 q^{33} + 18 q^{37} + 6 q^{41} - 16 q^{45} + 12 q^{49} + 42 q^{53} - 6 q^{57} + 50 q^{61} + 4 q^{65} - 28 q^{69} + 2 q^{73}+ \cdots - 2 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 + 4 * q^9 - 6 * q^13 + 10 * q^17 - 28 * q^21 - 12 * q^25 + 22 * q^29 - 42 * q^33 + 18 * q^37 + 6 * q^41 - 16 * q^45 + 12 * q^49 + 42 * q^53 - 6 * q^57 + 50 * q^61 + 4 * q^65 - 28 * q^69 + 2 * q^73 - 18 * q^77 + 28 * q^81 + 50 * q^85 - 24 * q^89 - 10 * q^93 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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