LMFDB - Embedded newform 696.2.y.c.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [696,2,Mod(25,696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(696, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("696.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 696 = 2^{3} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	696.y (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.55758798068$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			529.2
Character	$\chi$	$=$	696.529
Dual form			696.2.y.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 - 0.433884i) q^{3} +(-0.301797 - 1.32226i) q^{5} +(-1.69408 - 0.815825i) q^{7} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.900969 - 0.433884i) q^{3} +(-0.301797 - 1.32226i) q^{5} +(-1.69408 - 0.815825i) q^{7} +(0.623490 + 0.781831i) q^{9} +(-2.65781 + 3.33278i) q^{11} +(-2.36397 + 2.96432i) q^{13} +(-0.301797 + 1.32226i) q^{15} +2.91536 q^{17} +(0.896218 - 0.431596i) q^{19} +(1.17234 + 1.47007i) q^{21} +(-1.30359 + 5.71142i) q^{23} +(2.84755 - 1.37131i) q^{25} +(-0.222521 - 0.974928i) q^{27} +(2.51162 + 4.76358i) q^{29} +(0.116687 + 0.511241i) q^{31} +(3.84064 - 1.84956i) q^{33} +(-0.567465 + 2.48623i) q^{35} +(2.24538 + 2.81562i) q^{37} +(3.41603 - 1.64507i) q^{39} -2.67027 q^{41} +(-0.954737 + 4.18298i) q^{43} +(0.845617 - 1.06037i) q^{45} +(-3.66520 + 4.59601i) q^{47} +(-2.16010 - 2.70868i) q^{49} +(-2.62664 - 1.26493i) q^{51} +(2.70341 + 11.8444i) q^{53} +(5.20893 + 2.50849i) q^{55} -0.994727 q^{57} -14.6379 q^{59} +(-7.98350 - 3.84465i) q^{61} +(-0.418403 - 1.83314i) q^{63} +(4.63304 + 2.23116i) q^{65} +(4.72640 + 5.92671i) q^{67} +(3.65259 - 4.58021i) q^{69} +(-3.63276 + 4.55534i) q^{71} +(0.522977 - 2.29131i) q^{73} -3.16055 q^{75} +(7.22150 - 3.47769i) q^{77} +(-6.45931 - 8.09972i) q^{79} +(-0.222521 + 0.974928i) q^{81} +(5.27141 - 2.53858i) q^{83} +(-0.879846 - 3.85486i) q^{85} +(-0.196054 - 5.38159i) q^{87} +(-0.0441638 - 0.193494i) q^{89} +(6.42311 - 3.09321i) q^{91} +(0.116687 - 0.511241i) q^{93} +(-0.841158 - 1.05478i) q^{95} +(15.0982 - 7.27093i) q^{97} -4.26279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9	$ 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9} - 12 q^{11} + 7 q^{13} + q^{15} - 38 q^{17} - 18 q^{19} + 4 q^{21} - 6 q^{23} - 19 q^{25} - 4 q^{27} + 5 q^{29} - 2 q^{31} + 2 q^{33} + 21 q^{35} - 18 q^{37} + 7 q^{39} - 70 q^{41} - q^{43} + q^{45} + 23 q^{47} + 8 q^{49} + 11 q^{51} + 26 q^{53} - 17 q^{55} + 10 q^{57} - 4 q^{59} + 10 q^{61} - 3 q^{63} + 43 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 8 q^{73} + 30 q^{75} - 36 q^{77} + 45 q^{79} - 4 q^{81} - 10 q^{83} - 53 q^{85} - 16 q^{87} + 10 q^{89} + 57 q^{91} - 2 q^{93} - 34 q^{95} + 96 q^{97} + 2 q^{99}+O(q^{100}) $ 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9 - 12 * q^11 + 7 * q^13 + q^15 - 38 * q^17 - 18 * q^19 + 4 * q^21 - 6 * q^23 - 19 * q^25 - 4 * q^27 + 5 * q^29 - 2 * q^31 + 2 * q^33 + 21 * q^35 - 18 * q^37 + 7 * q^39 - 70 * q^41 - q^43 + q^45 + 23 * q^47 + 8 * q^49 + 11 * q^51 + 26 * q^53 - 17 * q^55 + 10 * q^57 - 4 * q^59 + 10 * q^61 - 3 * q^63 + 43 * q^65 + 2 * q^67 + 8 * q^69 + 16 * q^71 + 8 * q^73 + 30 * q^75 - 36 * q^77 + 45 * q^79 - 4 * q^81 - 10 * q^83 - 53 * q^85 - 16 * q^87 + 10 * q^89 + 57 * q^91 - 2 * q^93 - 34 * q^95 + 96 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/696\mathbb{Z}\right)^\times$.

$n$	$175$	$233$	$349$	$553$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{7}\right)$

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
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$		0			0
$5$	−0.301797	−	1.32226i	−0.134968	−	0.591333i	−0.996497	−	0.0836251i	$-0.973350\pi$
$5$	−0.301797	−	1.32226i	−0.134968	−	0.591333i	0.861529	−	0.507708i	$-0.169507\pi$
$6$		0			0
$7$	−1.69408	−	0.815825i	−0.640302	−	0.308353i	0.0854163	−	0.996345i	$-0.472778\pi$
$7$	−1.69408	−	0.815825i	−0.640302	−	0.308353i	−0.725718	+	0.687992i	$0.758492\pi$
$8$		0			0
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$		0			0
$11$	−2.65781	+	3.33278i	−0.801359	+	1.00487i	0.198335	+	0.980134i	$0.436447\pi$
$11$	−2.65781	+	3.33278i	−0.801359	+	1.00487i	−0.999694	+	0.0247380i	$0.992125\pi$
$12$		0			0
$13$	−2.36397	+	2.96432i	−0.655646	+	0.822155i	−0.992861	−	0.119273i	$-0.961944\pi$
$13$	−2.36397	+	2.96432i	−0.655646	+	0.822155i	0.337215	+	0.941428i	$0.390515\pi$
$14$		0			0
$15$	−0.301797	+	1.32226i	−0.0779237	+	0.341406i
$16$		0			0
$17$	2.91536			0.707078			0.353539	−	0.935420i	$-0.384978\pi$
$17$	2.91536			0.707078			0.353539	+	0.935420i	$0.384978\pi$
$18$		0			0
$19$	0.896218	−	0.431596i	0.205607	−	0.0990149i	−0.328247	−	0.944592i	$-0.606458\pi$
$19$	0.896218	−	0.431596i	0.205607	−	0.0990149i	0.533853	+	0.845577i	$0.320743\pi$
$20$		0			0
$21$	1.17234	+	1.47007i	0.255825	+	0.320795i
$22$		0			0
$23$	−1.30359	+	5.71142i	−0.271818	+	1.19091i	0.636046	+	0.771651i	$0.280569\pi$
$23$	−1.30359	+	5.71142i	−0.271818	+	1.19091i	−0.907865	+	0.419263i	$0.862288\pi$
$24$		0			0
$25$	2.84755	−	1.37131i	0.569511	−	0.274262i
$26$		0			0
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$		0			0
$29$	2.51162	+	4.76358i	0.466397	+	0.884576i
$29$	2.51162	+	4.76358i	0.466397	+	0.884576i
$30$		0			0
$31$	0.116687	+	0.511241i	0.0209577	+	0.0918215i	0.984325	−	0.176363i	$-0.0564334\pi$
$31$	0.116687	+	0.511241i	0.0209577	+	0.0918215i	−0.963367	+	0.268185i	$0.913576\pi$
$32$		0			0
$33$	3.84064	−	1.84956i	0.668570	−	0.321966i
$34$		0			0
$35$	−0.567465	+	2.48623i	−0.0959191	+	0.420249i
$36$		0			0
$37$	2.24538	+	2.81562i	0.369139	+	0.462885i	0.931359	−	0.364102i	$-0.118624\pi$
$37$	2.24538	+	2.81562i	0.369139	+	0.462885i	−0.562220	+	0.826988i	$0.690053\pi$
$38$		0			0
$39$	3.41603	−	1.64507i	0.547003	−	0.263423i
$40$		0			0
$41$	−2.67027			−0.417026			−0.208513	−	0.978020i	$-0.566862\pi$
$41$	−2.67027			−0.417026			−0.208513	+	0.978020i	$0.566862\pi$
$42$		0			0
$43$	−0.954737	+	4.18298i	−0.145596	+	0.637898i	0.848481	+	0.529225i	$0.177517\pi$
$43$	−0.954737	+	4.18298i	−0.145596	+	0.637898i	−0.994078	+	0.108673i	$0.965340\pi$
$44$		0			0
$45$	0.845617	−	1.06037i	0.126057	−	0.158071i
$46$		0			0
$47$	−3.66520	+	4.59601i	−0.534624	+	0.670397i	−0.973642	−	0.228081i	$-0.926755\pi$
$47$	−3.66520	+	4.59601i	−0.534624	+	0.670397i	0.439018	+	0.898478i	$0.355326\pi$
$48$		0			0
$49$	−2.16010	−	2.70868i	−0.308585	−	0.386954i
$50$		0			0
$51$	−2.62664	−	1.26493i	−0.367804	−	0.177125i
$52$		0			0
$53$	2.70341	+	11.8444i	0.371342	+	1.62696i	0.723015	+	0.690832i	$0.242756\pi$
$53$	2.70341	+	11.8444i	0.371342	+	1.62696i	−0.351673	+	0.936123i	$0.614387\pi$
$54$		0			0
$55$	5.20893	+	2.50849i	0.702371	+	0.338244i
$56$		0			0
$57$	−0.994727			−0.131755
$58$		0			0
$59$	−14.6379			−1.90569			−0.952846	−	0.303455i	$-0.901860\pi$
$59$	−14.6379			−1.90569			−0.952846	+	0.303455i	$0.901860\pi$
$60$		0			0
$61$	−7.98350	−	3.84465i	−1.02218	−	0.492257i	−0.153774	−	0.988106i	$-0.549143\pi$
$61$	−7.98350	−	3.84465i	−1.02218	−	0.492257i	−0.868409	+	0.495849i	$0.834857\pi$
$62$		0			0
$63$	−0.418403	−	1.83314i	−0.0527138	−	0.230954i
$64$		0			0
$65$	4.63304	+	2.23116i	0.574658	+	0.276741i
$66$		0			0
$67$	4.72640	+	5.92671i	0.577421	+	0.724063i	0.981671	−	0.190586i	$-0.0610387\pi$
$67$	4.72640	+	5.92671i	0.577421	+	0.724063i	−0.404249	+	0.914649i	$0.632467\pi$
$68$		0			0
$69$	3.65259	−	4.58021i	0.439720	−	0.551392i
$70$		0			0
$71$	−3.63276	+	4.55534i	−0.431130	+	0.540620i	−0.949181	−	0.314730i	$-0.898086\pi$
$71$	−3.63276	+	4.55534i	−0.431130	+	0.540620i	0.518052	+	0.855349i	$0.326658\pi$
$72$		0			0
$73$	0.522977	−	2.29131i	0.0612098	−	0.268178i	−0.935058	−	0.354495i	$-0.884653\pi$
$73$	0.522977	−	2.29131i	0.0612098	−	0.268178i	0.996268	+	0.0863173i	$0.0275099\pi$
$74$		0			0
$75$	−3.16055			−0.364949
$76$		0			0
$77$	7.22150	−	3.47769i	0.822967	−	0.396320i
$78$		0			0
$79$	−6.45931	−	8.09972i	−0.726729	−	0.911290i	0.271968	−	0.962306i	$-0.412325\pi$
$79$	−6.45931	−	8.09972i	−0.726729	−	0.911290i	−0.998698	+	0.0510164i	$0.983754\pi$
$80$		0			0
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$		0			0
$83$	5.27141	−	2.53858i	0.578612	−	0.278645i	−0.121601	−	0.992579i	$-0.538803\pi$
$83$	5.27141	−	2.53858i	0.578612	−	0.278645i	0.700213	+	0.713934i	$0.253088\pi$
$84$		0			0
$85$	−0.879846	−	3.85486i	−0.0954327	−	0.418118i
$86$		0			0
$87$	−0.196054	−	5.38159i	−0.0210192	−	0.576968i
$88$		0			0
$89$	−0.0441638	−	0.193494i	−0.00468135	−	0.0205103i	0.972533	−	0.232764i	$-0.0747769\pi$
$89$	−0.0441638	−	0.193494i	−0.00468135	−	0.0205103i	−0.977215	+	0.212253i	$0.931920\pi$
$90$		0			0
$91$	6.42311	−	3.09321i	0.673325	−	0.324256i
$92$		0			0
$93$	0.116687	−	0.511241i	0.0120999	−	0.0530132i
$94$		0			0
$95$	−0.841158	−	1.05478i	−0.0863010	−	0.108218i
$96$		0			0
$97$	15.0982	−	7.27093i	1.53299	−	0.738251i	0.538458	−	0.842652i	$-0.319007\pi$
$97$	15.0982	−	7.27093i	1.53299	−	0.738251i	0.994535	+	0.104401i	$0.0332926\pi$
$98$		0			0
$99$	−4.26279			−0.428427
$100$		0			0
$101$	−2.84811	+	12.4784i	−0.283398	+	1.24165i	0.610007	+	0.792396i	$0.291166\pi$
$101$	−2.84811	+	12.4784i	−0.283398	+	1.24165i	−0.893405	+	0.449252i	$0.851691\pi$
$102$		0			0
$103$	−1.09806	+	1.37692i	−0.108195	+	0.135672i	−0.832980	−	0.553303i	$-0.813367\pi$
$103$	−1.09806	+	1.37692i	−0.108195	+	0.135672i	0.724786	+	0.688974i	$0.241939\pi$
$104$		0			0
$105$	1.59000	−	1.99380i	0.155168	−	0.194575i
$106$		0			0
$107$	−2.85929	−	3.58544i	−0.276418	−	0.346617i	0.624172	−	0.781287i	$-0.285437\pi$
$107$	−2.85929	−	3.58544i	−0.276418	−	0.346617i	−0.900590	+	0.434670i	$0.856865\pi$
$108$		0			0
$109$	2.15698	+	1.03875i	0.206601	+	0.0994939i	0.534323	−	0.845280i	$-0.320567\pi$
$109$	2.15698	+	1.03875i	0.206601	+	0.0994939i	−0.327722	+	0.944774i	$0.606281\pi$
$110$		0			0
$111$	−0.801368	−	3.51102i	−0.0760625	−	0.333252i
$112$		0			0
$113$	−10.7640	−	5.18365i	−1.01259	−	0.487637i	−0.147397	−	0.989077i	$-0.547089\pi$
$113$	−10.7640	−	5.18365i	−1.01259	−	0.487637i	−0.865192	+	0.501440i	$0.832804\pi$
$114$		0			0
$115$	7.94541			0.740913
$116$		0			0
$117$	−3.79151			−0.350525
$118$		0			0
$119$	−4.93884	−	2.37842i	−0.452743	−	0.218030i
$120$		0			0
$121$	−1.59578	−	6.99159i	−0.145071	−	0.635599i
$122$		0			0
$123$	2.40583	+	1.15859i	0.216926	+	0.104466i
$124$		0			0
$125$	−6.90070	−	8.65320i	−0.617217	−	0.773966i
$126$		0			0
$127$	1.23794	−	1.55232i	0.109849	−	0.137746i	−0.723867	−	0.689939i	$-0.757637\pi$
$127$	1.23794	−	1.55232i	0.109849	−	0.137746i	0.833716	+	0.552193i	$0.186209\pi$
$128$		0			0
$129$	2.67511	−	3.35449i	0.235531	−	0.295346i
$130$		0			0
$131$	−1.39064	+	6.09281i	−0.121501	+	0.532332i	0.877141	+	0.480233i	$0.159448\pi$
$131$	−1.39064	+	6.09281i	−0.121501	+	0.532332i	−0.998642	+	0.0520982i	$0.983409\pi$
$132$		0			0
$133$	−1.87037			−0.162182
$134$		0			0
$135$	−1.22195	+	0.588461i	−0.105169	+	0.0506467i
$136$		0			0
$137$	3.91093	+	4.90415i	0.334133	+	0.418989i	0.920308	−	0.391195i	$-0.127938\pi$
$137$	3.91093	+	4.90415i	0.334133	+	0.418989i	−0.586175	+	0.810185i	$0.699367\pi$
$138$		0			0
$139$	−0.636683	+	2.78949i	−0.0540028	+	0.236602i	−0.994725	−	0.102576i	$-0.967292\pi$
$139$	−0.636683	+	2.78949i	−0.0540028	+	0.236602i	0.940722	+	0.339177i	$0.110149\pi$
$140$		0			0
$141$	5.29636	−	2.55059i	0.446034	−	0.214799i
$142$		0			0
$143$	−3.59647	−	15.7572i	−0.300752	−	1.31768i
$144$		0			0
$145$	5.54070	−	4.75866i	0.460130	−	0.395185i
$146$		0			0
$147$	0.770930	+	3.37766i	0.0635852	+	0.278585i
$148$		0			0
$149$	−0.324128	+	0.156092i	−0.0265536	+	0.0127875i	−0.447113	−	0.894477i	$-0.647548\pi$
$149$	−0.324128	+	0.156092i	−0.0265536	+	0.0127875i	0.420560	+	0.907265i	$0.361834\pi$
$150$		0			0
$151$	4.84665	−	21.2345i	0.394414	−	1.72804i	−0.254403	−	0.967098i	$-0.581879\pi$
$151$	4.84665	−	21.2345i	0.394414	−	1.72804i	0.648817	−	0.760944i	$-0.275264\pi$
$152$		0			0
$153$	1.81769	+	2.27932i	0.146952	+	0.184272i
$154$		0			0
$155$	0.640777	−	0.308582i	0.0514685	−	0.0247859i
$156$		0			0
$157$	−23.9464			−1.91113			−0.955565	−	0.294782i	$-0.904753\pi$
$157$	−23.9464			−1.91113			−0.955565	+	0.294782i	$0.904753\pi$
$158$		0			0
$159$	2.70341	−	11.8444i	0.214394	−	0.939323i
$160$		0			0
$161$	6.86792	−	8.61209i	0.541268	−	0.678728i
$162$		0			0
$163$	11.2135	−	14.0612i	0.878306	−	1.10136i	−0.115835	−	0.993268i	$-0.536954\pi$
$163$	11.2135	−	14.0612i	0.878306	−	1.10136i	0.994141	−	0.108092i	$-0.0344743\pi$
$164$		0			0
$165$	−3.60469	−	4.52014i	−0.280625	−	0.351892i
$166$		0			0
$167$	8.05920	+	3.88111i	0.623640	+	0.300329i	0.718890	−	0.695124i	$-0.244651\pi$
$167$	8.05920	+	3.88111i	0.623640	+	0.300329i	−0.0952497	+	0.995453i	$0.530365\pi$
$168$		0			0
$169$	−0.306085	−	1.34105i	−0.0235450	−	0.103157i
$170$		0			0
$171$	0.896218	+	0.431596i	0.0685355	+	0.0330050i
$172$		0			0
$173$	−7.00643			−0.532689			−0.266344	−	0.963878i	$-0.585816\pi$
$173$	−7.00643			−0.532689			−0.266344	+	0.963878i	$0.585816\pi$
$174$		0			0
$175$	−5.94273			−0.449228
$176$		0			0
$177$	13.1883	+	6.35115i	0.991293	+	0.477381i
$178$		0			0
$179$	−1.29236	−	5.66222i	−0.0965958	−	0.423214i	0.903388	−	0.428823i	$-0.141072\pi$
$179$	−1.29236	−	5.66222i	−0.0965958	−	0.423214i	−0.999984	+	0.00560924i	$0.998215\pi$
$180$		0			0
$181$	0.835826	+	0.402513i	0.0621264	+	0.0299185i	0.464689	−	0.885474i	$-0.346166\pi$
$181$	0.835826	+	0.402513i	0.0621264	+	0.0299185i	−0.402563	+	0.915392i	$0.631880\pi$
$182$		0			0
$183$	5.52476	+	6.92782i	0.408402	+	0.512119i
$184$		0			0
$185$	3.04533	−	3.81873i	0.223897	−	0.280758i
$186$		0			0
$187$	−7.74845	+	9.71625i	−0.566623	+	0.710523i
$188$		0			0
$189$	−0.418403	+	1.83314i	−0.0304343	+	0.133342i
$190$		0			0
$191$	6.87070			0.497146			0.248573	−	0.968613i	$-0.420038\pi$
$191$	6.87070			0.497146			0.248573	+	0.968613i	$0.420038\pi$
$192$		0			0
$193$	−12.3523	+	5.94857i	−0.889141	+	0.428188i	−0.821955	−	0.569553i	$-0.807116\pi$
$193$	−12.3523	+	5.94857i	−0.889141	+	0.428188i	−0.0671861	+	0.997740i	$0.521402\pi$
$194$		0			0
$195$	−3.20616	−	4.02040i	−0.229598	−	0.287907i
$196$		0			0
$197$	−1.24401	+	5.45035i	−0.0886319	+	0.388322i	−0.999714	−	0.0239027i	$-0.992391\pi$
$197$	−1.24401	+	5.45035i	−0.0886319	+	0.388322i	0.911082	+	0.412224i	$0.135248\pi$
$198$		0			0
$199$	−7.10179	+	3.42004i	−0.503433	+	0.242440i	−0.668323	−	0.743872i	$-0.732987\pi$
$199$	−7.10179	+	3.42004i	−0.503433	+	0.242440i	0.164890	+	0.986312i	$0.447273\pi$
$200$		0			0
$201$	−1.68683	−	7.39049i	−0.118980	−	0.521285i
$202$		0			0
$203$	−0.368637	−	10.1189i	−0.0258732	−	0.710210i
$204$		0			0
$205$	0.805879	+	3.53079i	0.0562850	+	0.246601i
$206$		0			0
$207$	−5.27815	+	2.54182i	−0.366857	+	0.176669i
$208$		0			0
$209$	−0.943558	+	4.13400i	−0.0652673	+	0.285955i
$210$		0			0
$211$	−5.50798	−	6.90679i	−0.379185	−	0.475483i	0.555216	−	0.831706i	$-0.312636\pi$
$211$	−5.50798	−	6.90679i	−0.379185	−	0.475483i	−0.934401	+	0.356223i	$0.884064\pi$
$212$		0			0
$213$	5.24950	−	2.52802i	0.359690	−	0.173217i
$214$		0			0
$215$	5.81912			0.396861
$216$		0			0
$217$	0.219406	−	0.961279i	0.0148942	−	0.0652558i
$218$		0			0
$219$	−1.46535	+	1.83749i	−0.0990191	+	0.124166i
$220$		0			0
$221$	−6.89180	+	8.64205i	−0.463593	+	0.581327i
$222$		0			0
$223$	17.0449	+	21.3737i	1.14141	+	1.43129i	0.885532	+	0.464579i	$0.153794\pi$
$223$	17.0449	+	21.3737i	1.14141	+	1.43129i	0.255882	+	0.966708i	$0.417634\pi$
$224$		0			0
$225$	2.84755	+	1.37131i	0.189837	+	0.0914207i
$226$		0			0
$227$	1.80263	+	7.89785i	0.119645	+	0.524199i	0.998858	+	0.0477707i	$0.0152117\pi$
$227$	1.80263	+	7.89785i	0.119645	+	0.524199i	−0.879213	+	0.476428i	$0.841931\pi$
$228$		0			0
$229$	−4.39143	−	2.11480i	−0.290194	−	0.139750i	0.283123	−	0.959084i	$-0.408629\pi$
$229$	−4.39143	−	2.11480i	−0.290194	−	0.139750i	−0.573317	+	0.819334i	$0.694344\pi$
$230$		0			0
$231$	−8.01526			−0.527366
$232$		0			0
$233$	14.9577			0.979912			0.489956	−	0.871747i	$-0.337013\pi$
$233$	14.9577			0.979912			0.489956	+	0.871747i	$0.337013\pi$
$234$		0			0
$235$	7.18327	+	3.45928i	0.468585	+	0.225659i
$236$		0			0
$237$	2.30530	+	10.1002i	0.149745	+	0.656078i
$238$		0			0
$239$	11.0139	+	5.30401i	0.712429	+	0.343088i	0.754747	−	0.656016i	$-0.227760\pi$
$239$	11.0139	+	5.30401i	0.712429	+	0.343088i	−0.0423175	+	0.999104i	$0.513474\pi$
$240$		0			0
$241$	−5.08684	−	6.37870i	−0.327672	−	0.410888i	0.590520	−	0.807023i	$-0.298923\pi$
$241$	−5.08684	−	6.37870i	−0.327672	−	0.410888i	−0.918192	+	0.396135i	$0.870351\pi$
$242$		0			0
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$		0			0
$245$	−2.92966	+	3.67368i	−0.187169	+	0.234703i
$246$		0			0
$247$	−0.839241	+	3.67696i	−0.0533996	+	0.233959i
$248$		0			0
$249$	−5.85082			−0.370781
$250$		0			0
$251$	−16.6103	+	7.99911i	−1.04843	+	0.504900i	−0.877097	−	0.480313i	$-0.840523\pi$
$251$	−16.6103	+	7.99911i	−1.04843	+	0.504900i	−0.171337	+	0.985212i	$0.554809\pi$
$252$		0			0
$253$	−15.5702	−	19.5245i	−0.978892	−	1.22749i
$254$		0			0
$255$	−0.879846	+	3.85486i	−0.0550981	+	0.241401i
$256$		0			0
$257$	16.1130	−	7.75962i	1.00510	−	0.484032i	0.142435	−	0.989804i	$-0.454507\pi$
$257$	16.1130	−	7.75962i	1.00510	−	0.484032i	0.862667	+	0.505773i	$0.168792\pi$
$258$		0			0
$259$	−1.50680	−	6.60173i	−0.0936280	−	0.410211i
$260$		0			0
$261$	−2.15835	+	4.93371i	−0.133598	+	0.305389i
$262$		0			0
$263$	1.09837	+	4.81227i	0.0677284	+	0.296737i	0.997436	−	0.0715604i	$-0.0227979\pi$
$263$	1.09837	+	4.81227i	0.0677284	+	0.296737i	−0.929708	+	0.368298i	$0.879941\pi$
$264$		0			0
$265$	14.8455	−	7.14922i	0.911953	−	0.439173i
$266$		0			0
$267$	−0.0441638	+	0.193494i	−0.00270278	+	0.0118417i
$268$		0			0
$269$	−12.9446	−	16.2320i	−0.789247	−	0.989684i	−0.999926	−	0.0121289i	$-0.996139\pi$
$269$	−12.9446	−	16.2320i	−0.789247	−	0.989684i	0.210680	−	0.977555i	$-0.432432\pi$
$270$		0			0
$271$	22.5553	−	10.8621i	1.37014	−	0.659823i	0.403264	−	0.915084i	$-0.367876\pi$
$271$	22.5553	−	10.8621i	1.37014	−	0.659823i	0.966872	+	0.255261i	$0.0821614\pi$
$272$		0			0
$273$	−7.12912			−0.431474
$274$		0			0
$275$	−2.99797	+	13.1350i	−0.180784	+	0.792068i
$276$		0			0
$277$	−20.4940	+	25.6987i	−1.23137	+	1.54408i	−0.492345	+	0.870400i	$0.663860\pi$
$277$	−20.4940	+	25.6987i	−1.23137	+	1.54408i	−0.739020	+	0.673683i	$0.764711\pi$
$278$		0			0
$279$	−0.326951	+	0.409983i	−0.0195740	+	0.0245451i
$280$		0			0
$281$	9.12536	+	11.4428i	0.544373	+	0.682622i	0.975583	−	0.219629i	$-0.0704847\pi$
$281$	9.12536	+	11.4428i	0.544373	+	0.682622i	−0.431210	+	0.902251i	$0.641913\pi$
$282$		0			0
$283$	17.1814	+	8.27412i	1.02133	+	0.491846i	0.868123	−	0.496349i	$-0.165326\pi$
$283$	17.1814	+	8.27412i	1.02133	+	0.491846i	0.153205	+	0.988194i	$0.451041\pi$
$284$		0			0
$285$	0.300206	+	1.31529i	0.0177827	+	0.0779109i
$286$		0			0
$287$	4.52364	+	2.17847i	0.267022	+	0.128591i
$288$		0			0
$289$	−8.50070			−0.500041
$290$		0			0
$291$	−16.7578			−0.982358
$292$		0			0
$293$	−7.52600	−	3.62433i	−0.439673	−	0.211736i	0.200933	−	0.979605i	$-0.435603\pi$
$293$	−7.52600	−	3.62433i	−0.439673	−	0.211736i	−0.640606	+	0.767869i	$0.721317\pi$
$294$		0			0
$295$	4.41768	+	19.3551i	0.257207	+	1.12690i
$296$		0			0
$297$	3.84064	+	1.84956i	0.222857	+	0.107322i
$298$		0			0
$299$	−13.8488	−	17.3659i	−0.800899	−	1.00430i
$300$		0			0
$301$	5.02998	−	6.30740i	0.289923	−	0.363552i
$302$		0			0
$303$	7.98024	−	10.0069i	0.458453	−	0.574881i
$304$		0			0
$305$	−2.67423	+	11.7166i	−0.153126	+	0.670889i
$306$		0			0
$307$	25.5468			1.45803			0.729017	−	0.684495i	$-0.239977\pi$
$307$	25.5468			1.45803			0.729017	+	0.684495i	$0.239977\pi$
$308$		0			0
$309$	1.58674	−	0.764133i	0.0902664	−	0.0434700i
$310$		0			0
$311$	−1.50147	−	1.88278i	−0.0851405	−	0.106763i	0.737437	−	0.675416i	$-0.236036\pi$
$311$	−1.50147	−	1.88278i	−0.0851405	−	0.106763i	−0.822577	+	0.568653i	$0.807465\pi$
$312$		0			0
$313$	4.48997	−	19.6719i	0.253788	−	1.11192i	−0.673976	−	0.738753i	$-0.735415\pi$
$313$	4.48997	−	19.6719i	0.253788	−	1.11192i	0.927764	−	0.373166i	$-0.121728\pi$
$314$		0			0
$315$	−2.29762	+	1.10647i	−0.129456	+	0.0623428i
$316$		0			0
$317$	0.581422	+	2.54738i	0.0326559	+	0.143075i	0.988628	−	0.150384i	$-0.0480509\pi$
$317$	0.581422	+	2.54738i	0.0326559	+	0.143075i	−0.955972	+	0.293459i	$0.905194\pi$
$318$		0			0
$319$	−22.5514	−	4.28998i	−1.26264	−	0.240193i
$320$		0			0
$321$	1.02047	+	4.47097i	0.0569570	+	0.249545i
$322$		0			0
$323$	2.61279	−	1.25826i	0.145380	−	0.0700112i
$324$		0			0
$325$	−2.66652	+	11.6828i	−0.147912	+	0.648045i
$326$		0			0
$327$	−1.49268	−	1.87176i	−0.0825452	−	0.103508i
$328$		0			0
$329$	9.95867	−	4.79584i	0.549039	−	0.264403i
$330$		0			0
$331$	13.1920			0.725098			0.362549	−	0.931965i	$-0.381907\pi$
$331$	13.1920			0.725098			0.362549	+	0.931965i	$0.381907\pi$
$332$		0			0
$333$	−0.801368	+	3.51102i	−0.0439147	+	0.192403i
$334$		0			0
$335$	6.41024	−	8.03819i	0.350229	−	0.439173i
$336$		0			0
$337$	−22.0687	+	27.6733i	−1.20216	+	1.50746i	−0.393347	+	0.919390i	$0.628683\pi$
$337$	−22.0687	+	27.6733i	−1.20216	+	1.50746i	−0.808811	+	0.588069i	$0.799888\pi$
$338$		0			0
$339$	7.44890	+	9.34062i	0.404568	+	0.507313i
$340$		0			0
$341$	−2.01399	−	0.969885i	−0.109064	−	0.0525222i
$342$		0			0
$343$	4.37839	+	19.1830i	0.236411	+	1.03578i
$344$		0			0
$345$	−7.15856	−	3.44738i	−0.385404	−	0.185601i
$346$		0			0
$347$	27.0836			1.45392			0.726961	−	0.686679i	$-0.240932\pi$
$347$	27.0836			1.45392			0.726961	+	0.686679i	$0.240932\pi$
$348$		0			0
$349$	7.17706			0.384179			0.192090	−	0.981377i	$-0.438474\pi$
$349$	7.17706			0.384179			0.192090	+	0.981377i	$0.438474\pi$
$350$		0			0
$351$	3.41603	+	1.64507i	0.182334	+	0.0878075i
$352$		0			0
$353$	−2.39986	−	10.5145i	−0.127732	−	0.559629i	−0.997776	−	0.0666556i	$-0.978767\pi$
$353$	−2.39986	−	10.5145i	−0.127732	−	0.559629i	0.870044	−	0.492973i	$-0.164090\pi$
$354$		0			0
$355$	7.11970	+	3.42867i	0.377875	+	0.181975i
$356$		0			0
$357$	3.41778	+	4.28577i	0.180888	+	0.226827i
$358$		0			0
$359$	−11.2573	+	14.1162i	−0.594137	+	0.745024i	−0.984451	−	0.175657i	$-0.943795\pi$
$359$	−11.2573	+	14.1162i	−0.594137	+	0.745024i	0.390314	+	0.920682i	$0.372366\pi$
$360$		0			0
$361$	−11.2294	+	14.0812i	−0.591020	+	0.741115i
$362$		0			0
$363$	−1.59578	+	6.99159i	−0.0837569	+	0.366963i
$364$		0			0
$365$	−3.18754			−0.166844
$366$		0			0
$367$	−20.8801	+	10.0553i	−1.08993	+	0.524883i	−0.890479	−	0.455025i	$-0.849630\pi$
$367$	−20.8801	+	10.0553i	−1.08993	+	0.524883i	−0.199452	+	0.979908i	$0.563916\pi$
$368$		0			0
$369$	−1.66488	−	2.08770i	−0.0866704	−	0.108681i
$370$		0			0
$371$	5.08318	−	22.2709i	0.263906	−	1.15625i
$372$		0			0
$373$	−16.4232	+	7.90901i	−0.850363	+	0.409513i	−0.807712	−	0.589577i	$-0.799295\pi$
$373$	−16.4232	+	7.90901i	−0.850363	+	0.409513i	−0.0426507	+	0.999090i	$0.513580\pi$
$374$		0			0
$375$	2.46283	+	10.7904i	0.127180	+	0.557212i
$376$		0			0
$377$	−20.0582	−	3.81570i	−1.03305	−	0.196518i
$378$		0			0
$379$	−3.41095	−	14.9443i	−0.175209	−	0.767639i	−0.983800	−	0.179269i	$-0.942627\pi$
$379$	−3.41095	−	14.9443i	−0.175209	−	0.767639i	0.808591	−	0.588371i	$-0.200230\pi$
$380$		0			0
$381$	−1.78887	+	0.861474i	−0.0916465	+	0.0441346i
$382$		0			0
$383$	3.27363	−	14.3427i	0.167275	−	0.732878i	−0.819804	−	0.572644i	$-0.805918\pi$
$383$	3.27363	−	14.3427i	0.167275	−	0.732878i	0.987079	−	0.160234i	$-0.0512250\pi$
$384$		0			0
$385$	−6.77784	−	8.49915i	−0.345431	−	0.433157i
$386$		0			0
$387$	−3.86565	+	1.86160i	−0.196502	+	0.0946305i
$388$		0			0
$389$	−11.7489			−0.595693			−0.297846	−	0.954614i	$-0.596268\pi$
$389$	−11.7489			−0.595693			−0.297846	+	0.954614i	$0.596268\pi$
$390$		0			0
$391$	−3.80044	+	16.6508i	−0.192197	+	0.842069i
$392$		0			0
$393$	3.89650	−	4.88606i	0.196552	−	0.246469i
$394$		0			0
$395$	−8.76053	+	10.9854i	−0.440790	+	0.552734i
$396$		0			0
$397$	16.9525	+	21.2577i	0.850820	+	1.06689i	0.996982	+	0.0776336i	$0.0247364\pi$
$397$	16.9525	+	21.2577i	0.850820	+	1.06689i	−0.146162	+	0.989261i	$0.546692\pi$
$398$		0			0
$399$	1.68515	+	0.811524i	0.0843628	+	0.0406270i
$400$		0			0
$401$	8.45151	+	37.0285i	0.422048	+	1.84911i	0.520345	+	0.853956i	$0.325803\pi$
$401$	8.45151	+	37.0285i	0.422048	+	1.84911i	−0.0982967	+	0.995157i	$0.531339\pi$
$402$		0			0
$403$	−1.79133	−	0.862657i	−0.0892323	−	0.0429720i
$404$		0			0
$405$	1.35626			0.0673933
$406$		0			0
$407$	−15.3517			−0.760953
$408$		0			0
$409$	1.73261	+	0.834383i	0.0856722	+	0.0412576i	0.476229	−	0.879321i	$-0.342003\pi$
$409$	1.73261	+	0.834383i	0.0856722	+	0.0412576i	−0.390557	+	0.920579i	$0.627718\pi$
$410$		0			0
$411$	−1.39579	−	6.11537i	−0.0688494	−	0.301649i
$412$		0			0
$413$	24.7978	+	11.9420i	1.22022	+	0.587626i
$414$		0			0
$415$	−4.94755	−	6.20404i	−0.242866	−	0.304544i
$416$		0			0
$417$	1.78395	−	2.23700i	0.0873603	−	0.109546i
$418$		0			0
$419$	17.6592	−	22.1440i	0.862709	−	1.08180i	−0.133168	−	0.991093i	$-0.542515\pi$
$419$	17.6592	−	22.1440i	0.862709	−	1.08180i	0.995877	−	0.0907097i	$-0.0289135\pi$
$420$		0			0
$421$	−7.07830	+	31.0120i	−0.344975	+	1.51143i	0.443448	+	0.896300i	$0.353755\pi$
$421$	−7.07830	+	31.0120i	−0.344975	+	1.51143i	−0.788423	+	0.615134i	$0.789102\pi$
$422$		0			0
$423$	−5.87852			−0.285823
$424$		0			0
$425$	8.30163	−	3.99786i	0.402688	−	0.193924i
$426$		0			0
$427$	10.3881	+	13.0263i	0.502716	+	0.630386i
$428$		0			0
$429$	−3.59647	+	15.7572i	−0.173639	+	0.760764i
$430$		0			0
$431$	27.4816	−	13.2344i	1.32374	−	0.637481i	0.367491	−	0.930027i	$-0.380217\pi$
$431$	27.4816	−	13.2344i	1.32374	−	0.637481i	0.956251	+	0.292546i	$0.0945025\pi$
$432$		0			0
$433$	2.68749	+	11.7747i	0.129152	+	0.565854i	0.997548	+	0.0699822i	$0.0222943\pi$
$433$	2.68749	+	11.7747i	0.129152	+	0.565854i	−0.868396	+	0.495872i	$0.834849\pi$
$434$		0			0
$435$	−7.05670	+	1.88338i	−0.338343	+	0.0903014i
$436$		0			0
$437$	1.29672	+	5.68131i	0.0620306	+	0.271774i
$438$		0			0
$439$	2.98594	−	1.43795i	0.142511	−	0.0686298i	−0.361269	−	0.932462i	$-0.617656\pi$
$439$	2.98594	−	1.43795i	0.142511	−	0.0686298i	0.503780	+	0.863832i	$0.331942\pi$
$440$		0			0
$441$	0.770930	−	3.37766i	0.0367109	−	0.160841i
$442$		0			0
$443$	−19.9556	−	25.0235i	−0.948117	−	1.18890i	−0.981886	−	0.189472i	$-0.939323\pi$
$443$	−19.9556	−	25.0235i	−0.948117	−	1.18890i	0.0337692	−	0.999430i	$-0.489249\pi$
$444$		0			0
$445$	−0.242521	+	0.116792i	−0.0114966	+	0.00553647i
$446$		0			0
$447$	0.359755			0.0170158
$448$		0			0
$449$	7.67668	−	33.6337i	0.362285	−	1.58727i	−0.385095	−	0.922877i	$-0.625831\pi$
$449$	7.67668	−	33.6337i	0.362285	−	1.58727i	0.747380	−	0.664397i	$-0.231312\pi$
$450$		0			0
$451$	7.09705	−	8.89942i	0.334187	−	0.419057i
$452$		0			0
$453$	−13.5800	+	17.0288i	−0.638044	+	0.800082i
$454$		0			0
$455$	−6.02850	−	7.55951i	−0.282621	−	0.354395i
$456$		0			0
$457$	1.70869	+	0.822862i	0.0799292	+	0.0384919i	0.473421	−	0.880836i	$-0.343019\pi$
$457$	1.70869	+	0.822862i	0.0799292	+	0.0384919i	−0.393492	+	0.919328i	$0.628733\pi$
$458$		0			0
$459$	−0.648728	−	2.84226i	−0.0302800	−	0.132665i
$460$		0			0
$461$	−13.0949	−	6.30619i	−0.609892	−	0.293708i	0.103330	−	0.994647i	$-0.467050\pi$
$461$	−13.0949	−	6.30619i	−0.609892	−	0.293708i	−0.713221	+	0.700939i	$0.752765\pi$
$462$		0			0
$463$	−25.0483			−1.16409			−0.582046	−	0.813156i	$-0.697748\pi$
$463$	−25.0483			−1.16409			−0.582046	+	0.813156i	$0.697748\pi$
$464$		0			0
$465$	−0.711209			−0.0329815
$466$		0			0
$467$	25.3290	+	12.1978i	1.17209	+	0.564447i	0.915596	−	0.402100i	$-0.131720\pi$
$467$	25.3290	+	12.1978i	1.17209	+	0.564447i	0.256490	+	0.966547i	$0.417434\pi$
$468$		0			0
$469$	−3.17172	−	13.8962i	−0.146457	−	0.641668i
$470$		0			0
$471$	21.5749	+	10.3899i	0.994121	+	0.478743i
$472$		0			0
$473$	−11.4035	−	14.2995i	−0.524331	−	0.657491i
$474$		0			0
$475$	1.96018	−	2.45799i	0.0899391	−	0.112780i
$476$		0			0
$477$	−7.57479	+	9.49848i	−0.346826	+	0.434906i
$478$		0			0
$479$	0.243510	−	1.06689i	0.0111263	−	0.0487474i	−0.969060	−	0.246825i	$-0.920613\pi$
$479$	0.243510	−	1.06689i	0.0111263	−	0.0487474i	0.980186	+	0.198078i	$0.0634698\pi$
$480$		0			0
$481$	−13.6544			−0.622588
$482$		0			0
$483$	−9.92443	+	4.77935i	−0.451577	+	0.217468i
$484$		0			0
$485$	−14.1707	−	17.7695i	−0.643457	−	0.806869i
$486$		0			0
$487$	−4.43082	+	19.4127i	−0.200779	+	0.879672i	0.769684	+	0.638425i	$0.220414\pi$
$487$	−4.43082	+	19.4127i	−0.200779	+	0.879672i	−0.970464	+	0.241247i	$0.922444\pi$
$488$		0			0
$489$	−16.2039	+	7.80340i	−0.732767	+	0.352882i
$490$		0			0
$491$	8.73658	+	38.2775i	0.394276	+	1.72744i	0.649327	+	0.760510i	$0.275051\pi$
$491$	8.73658	+	38.2775i	0.394276	+	1.72744i	−0.255050	+	0.966928i	$0.582092\pi$
$492$		0			0
$493$	7.32228	+	13.8875i	0.329779	+	0.625464i
$494$		0			0
$495$	1.28650	+	5.63652i	0.0578238	+	0.253343i
$496$		0			0
$497$	9.87055	−	4.75341i	0.442755	−	0.213219i
$498$		0			0
$499$	5.02746	−	22.0267i	0.225060	−	0.986052i	−0.728547	−	0.684996i	$-0.759804\pi$
$499$	5.02746	−	22.0267i	0.225060	−	0.986052i	0.953607	−	0.301056i	$-0.0973390\pi$
$500$		0			0
$501$	−5.57714	−	6.99351i	−0.249168	−	0.312447i
$502$		0			0
$503$	10.6525	−	5.12998i	0.474972	−	0.228735i	−0.181053	−	0.983473i	$-0.557951\pi$
$503$	10.6525	−	5.12998i	0.474972	−	0.228735i	0.656025	+	0.754739i	$0.272236\pi$
$504$		0			0
$505$	17.3592			0.772476
$506$		0			0
$507$	−0.306085	+	1.34105i	−0.0135937	+	0.0595580i
$508$		0			0
$509$	19.0238	−	23.8551i	0.843216	−	1.05736i	−0.154376	−	0.988012i	$-0.549337\pi$
$509$	19.0238	−	23.8551i	0.843216	−	1.05736i	0.997593	−	0.0693477i	$-0.0220918\pi$
$510$		0			0
$511$	−2.75528	+	3.45501i	−0.121886	+	0.152840i
$512$		0			0
$513$	−0.620202	−	0.777709i	−0.0273826	−	0.0343367i
$514$		0			0
$515$	2.15204	+	1.03637i	0.0948300	+	0.0456677i
$516$		0			0
$517$	−5.57613	−	24.4306i	−0.245238	−	1.07446i
$518$		0			0
$519$	6.31257	+	3.03997i	0.277091	+	0.133440i
$520$		0			0
$521$	1.94452			0.0851910			0.0425955	−	0.999092i	$-0.486437\pi$
$521$	1.94452			0.0851910			0.0425955	+	0.999092i	$0.486437\pi$
$522$		0			0
$523$	17.3474			0.758549			0.379274	−	0.925284i	$-0.376174\pi$
$523$	17.3474			0.758549			0.379274	+	0.925284i	$0.376174\pi$
$524$		0			0
$525$	5.35422	+	2.57845i	0.233677	+	0.112533i
$526$		0			0
$527$	0.340185	+	1.49045i	0.0148187	+	0.0649250i
$528$		0			0
$529$	−10.1987	−	4.91144i	−0.443422	−	0.213541i
$530$		0			0
$531$	−9.12658	−	11.4444i	−0.396060	−	0.496643i
$532$		0			0
$533$	6.31242	−	7.91552i	0.273421	−	0.342859i
$534$		0			0
$535$	−3.87795	+	4.86280i	−0.167659	+	0.210237i
$536$		0			0
$537$	−1.29236	+	5.66222i	−0.0557696	+	0.244343i
$538$		0			0
$539$	14.7685			0.636126
$540$		0			0
$541$	23.4435	−	11.2898i	1.00792	−	0.485387i	0.144299	−	0.989534i	$-0.453907\pi$
$541$	23.4435	−	11.2898i	1.00792	−	0.485387i	0.863618	+	0.504147i	$0.168193\pi$
$542$		0			0
$543$	−0.578409	−	0.725302i	−0.0248219	−	0.0311257i
$544$		0			0
$545$	0.722523	−	3.16558i	0.0309495	−	0.135598i
$546$		0			0
$547$	−4.97109	+	2.39395i	−0.212548	+	0.102358i	−0.537129	−	0.843500i	$-0.680491\pi$
$547$	−4.97109	+	2.39395i	−0.212548	+	0.102358i	0.324581	+	0.945858i	$0.394777\pi$
$548$		0			0
$549$	−1.97176	−	8.63885i	−0.0841528	−	0.368697i
$550$		0			0
$551$	4.30691	+	3.18520i	0.183480	+	0.135694i
$552$		0			0
$553$	4.33463	+	18.9912i	0.184327	+	0.807589i
$554$		0			0
$555$	−4.40063	+	2.11923i	−0.186797	+	0.0899565i
$556$		0			0
$557$	−1.06501	+	4.66613i	−0.0451261	+	0.197710i	−0.992466	−	0.122519i	$-0.960903\pi$
$557$	−1.06501	+	4.66613i	−0.0451261	+	0.197710i	0.947340	+	0.320229i	$0.103760\pi$
$558$		0			0
$559$	−10.1427	−	12.7186i	−0.428991	−	0.537938i
$560$		0			0
$561$	11.1968	−	5.39211i	0.472731	−	0.227655i
$562$		0			0
$563$	−30.1260			−1.26966			−0.634831	−	0.772651i	$-0.718930\pi$
$563$	−30.1260			−1.26966			−0.634831	+	0.772651i	$0.718930\pi$
$564$		0			0
$565$	−3.60560	+	15.7972i	−0.151689	+	0.664592i
$566$		0			0
$567$	1.17234	−	1.47007i	0.0492336	−	0.0617370i
$568$		0			0
$569$	17.9590	−	22.5198i	0.752879	−	0.944081i	−0.246809	−	0.969064i	$-0.579382\pi$
$569$	17.9590	−	22.5198i	0.752879	−	0.944081i	0.999688	+	0.0249834i	$0.00795329\pi$
$570$		0			0
$571$	12.2792	+	15.3976i	0.513867	+	0.644369i	0.969294	−	0.245904i	$-0.0790848\pi$
$571$	12.2792	+	15.3976i	0.513867	+	0.644369i	−0.455427	+	0.890273i	$0.650513\pi$
$572$		0			0
$573$	−6.19029	−	2.98108i	−0.258603	−	0.124537i
$574$		0			0
$575$	4.12007	+	18.0512i	0.171819	+	0.752788i
$576$		0			0
$577$	34.0505	+	16.3979i	1.41754	+	0.682652i	0.976636	−	0.214901i	$-0.0689430\pi$
$577$	34.0505	+	16.3979i	1.41754	+	0.682652i	0.440906	+	0.897553i	$0.354657\pi$
$578$		0			0
$579$	13.7101			0.569771
$580$		0			0
$581$	−11.0012			−0.456407
$582$		0			0
$583$	−46.6600	−	22.4703i	−1.93246	−	0.930624i
$584$		0			0
$585$	1.14427	+	5.01336i	0.0473096	+	0.207277i
$586$		0			0
$587$	0.608210	+	0.292899i	0.0251035	+	0.0120892i	0.446393	−	0.894837i	$-0.352708\pi$
$587$	0.608210	+	0.292899i	0.0251035	+	0.0120892i	−0.421290	+	0.906926i	$0.638422\pi$
$588$		0			0
$589$	0.325227	+	0.407821i	0.0134007	+	0.0168040i
$590$		0			0
$591$	3.48563	−	4.37084i	0.143380	−	0.179792i
$592$		0			0
$593$	11.9467	−	14.9807i	0.490593	−	0.615184i	−0.473485	−	0.880802i	$-0.657004\pi$
$593$	11.9467	−	14.9807i	0.490593	−	0.615184i	0.964079	+	0.265617i	$0.0855758\pi$
$594$		0			0
$595$	−1.65436	+	7.24823i	−0.0678222	+	0.297149i
$596$		0			0
$597$	7.88239			0.322605
$598$		0			0
$599$	−25.9655	+	12.5043i	−1.06092	+	0.510912i	−0.881170	−	0.472800i	$-0.843243\pi$
$599$	−25.9655	+	12.5043i	−1.06092	+	0.510912i	−0.179751	+	0.983712i	$0.557529\pi$
$600$		0			0
$601$	−14.8386	−	18.6070i	−0.605278	−	0.758994i	0.380912	−	0.924611i	$-0.375610\pi$
$601$	−14.8386	−	18.6070i	−0.605278	−	0.758994i	−0.986190	+	0.165617i	$0.947039\pi$
$602$		0			0
$603$	−1.68683	+	7.39049i	−0.0686931	+	0.300964i
$604$		0			0
$605$	−8.76309	+	4.22008i	−0.356270	+	0.171571i
$606$		0			0
$607$	−4.31089	−	18.8872i	−0.174974	−	0.766609i	−0.983903	−	0.178703i	$-0.942810\pi$
$607$	−4.31089	−	18.8872i	−0.174974	−	0.766609i	0.808929	−	0.587906i	$-0.200047\pi$
$608$		0			0
$609$	−4.05831	+	9.27679i	−0.164451	+	0.375915i
$610$		0			0
$611$	−4.95965	−	21.7296i	−0.200646	−	0.879087i
$612$		0			0
$613$	40.4196	−	19.4650i	1.63253	−	0.786186i	0.632600	−	0.774479i	$-0.281988\pi$
$613$	40.4196	−	19.4650i	1.63253	−	0.786186i	0.999931	−	0.0117070i	$-0.00372653\pi$
$614$		0			0
$615$	0.805879	−	3.53079i	0.0324962	−	0.142375i
$616$		0			0
$617$	−12.0893	−	15.1595i	−0.486698	−	0.610299i	0.476473	−	0.879189i	$-0.341915\pi$
$617$	−12.0893	−	15.1595i	−0.486698	−	0.610299i	−0.963171	+	0.268889i	$0.913343\pi$
$618$		0			0
$619$	−23.4762	+	11.3055i	−0.943588	+	0.454408i	−0.841434	−	0.540361i	$-0.818288\pi$
$619$	−23.4762	+	11.3055i	−0.943588	+	0.454408i	−0.102154	+	0.994769i	$0.532574\pi$
$620$		0			0
$621$	5.85830			0.235086
$622$		0			0
$623$	−0.0830406	+	0.363824i	−0.00332695	+	0.0145763i
$624$		0			0
$625$	0.493673	−	0.619046i	0.0197469	−	0.0247619i
$626$		0			0
$627$	2.64379	−	3.31521i	0.105583	−	0.132397i
$628$		0			0
$629$	6.54609	+	8.20854i	0.261010	+	0.327296i
$630$		0			0
$631$	−8.56468	−	4.12453i	−0.340955	−	0.164195i	0.255569	−	0.966791i	$-0.417737\pi$
$631$	−8.56468	−	4.12453i	−0.340955	−	0.164195i	−0.596523	+	0.802596i	$0.703452\pi$
$632$		0			0
$633$	1.96578	+	8.61263i	0.0781326	+	0.342321i
$634$		0			0
$635$	−2.42618	−	1.16839i	−0.0962800	−	0.0463660i
$636$		0			0
$637$	13.1358			0.520458
$638$		0			0
$639$	−5.82650			−0.230493
$640$		0			0
$641$	19.6947	+	9.48448i	0.777895	+	0.374614i	0.780318	−	0.625383i	$-0.215057\pi$
$641$	19.6947	+	9.48448i	0.777895	+	0.374614i	−0.00242360	+	0.999997i	$0.500771\pi$
$642$		0			0
$643$	−10.5080	−	46.0386i	−0.414395	−	1.81558i	−0.562722	−	0.826646i	$-0.690246\pi$
$643$	−10.5080	−	46.0386i	−0.414395	−	1.81558i	0.148327	−	0.988938i	$-0.452611\pi$
$644$		0			0
$645$	−5.24285	−	2.52482i	−0.206437	−	0.0994148i
$646$		0			0
$647$	−6.10026	−	7.64949i	−0.239826	−	0.300732i	0.647323	−	0.762216i	$-0.275889\pi$
$647$	−6.10026	−	7.64949i	−0.239826	−	0.300732i	−0.887149	+	0.461484i	$0.847317\pi$
$648$		0			0
$649$	38.9047	−	48.7850i	1.52714	−	1.91498i
$650$		0			0
$651$	−0.614761	+	0.770886i	−0.0240944	+	0.0302134i
$652$		0			0
$653$	−4.30147	+	18.8460i	−0.168329	+	0.737499i	0.818336	+	0.574740i	$0.194897\pi$
$653$	−4.30147	+	18.8460i	−0.168329	+	0.737499i	−0.986666	+	0.162760i	$0.947961\pi$
$654$		0			0
$655$	8.47598			0.331184
$656$		0			0
$657$	2.11749	−	1.01973i	0.0826112	−	0.0397835i
$658$		0			0
$659$	−20.8311	−	26.1214i	−0.811465	−	1.01754i	−0.999375	−	0.0353584i	$-0.988743\pi$
$659$	−20.8311	−	26.1214i	−0.811465	−	1.01754i	0.187910	−	0.982186i	$-0.439829\pi$
$660$		0			0
$661$	1.57980	−	6.92157i	0.0614473	−	0.269218i	−0.934867	−	0.354999i	$-0.884481\pi$
$661$	1.57980	−	6.92157i	0.0614473	−	0.269218i	0.996314	+	0.0857807i	$0.0273384\pi$
$662$		0			0
$663$	9.95894	−	4.79598i	0.386773	−	0.186260i
$664$		0			0
$665$	0.564473	+	2.47312i	0.0218893	+	0.0959034i
$666$		0			0
$667$	−30.4810	+	8.13517i	−1.18023	+	0.314995i
$668$		0			0
$669$	−6.08327	−	26.6525i	−0.235193	−	1.03045i
$670$		0			0
$671$	34.0320	−	16.3889i	1.31379	−	0.632688i
$672$		0			0
$673$	−0.00525292	+	0.0230145i	−0.000202485	+	0.000887145i	−0.975029	−	0.222077i	$-0.928716\pi$
$673$	−0.00525292	+	0.0230145i	−0.000202485	+	0.000887145i	0.974827	+	0.222964i	$0.0715734\pi$
$674$		0			0
$675$	−1.97057	−	2.47101i	−0.0758472	−	0.0951094i
$676$		0			0
$677$	33.5176	−	16.1412i	1.28819	−	0.620358i	0.340706	−	0.940170i	$-0.389334\pi$
$677$	33.5176	−	16.1412i	1.28819	−	0.620358i	0.947481	+	0.319812i	$0.103620\pi$
$678$		0			0
$679$	−31.5094			−1.20922
$680$		0			0
$681$	1.80263	−	7.89785i	0.0690771	−	0.302646i
$682$		0			0
$683$	−23.5864	+	29.5765i	−0.902510	+	1.13171i	0.0882519	+	0.996098i	$0.471872\pi$
$683$	−23.5864	+	29.5765i	−0.902510	+	1.13171i	−0.990762	+	0.135613i	$0.956699\pi$
$684$		0			0
$685$	5.30425	−	6.65132i	0.202665	−	0.254134i
$686$		0			0
$687$	3.03896	+	3.81074i	0.115944	+	0.145389i
$688$		0			0
$689$	−41.5014	−	19.9860i	−1.58108	−	0.761407i
$690$		0			0
$691$	0.249542	+	1.09332i	0.00949303	+	0.0415917i	0.979453	−	0.201674i	$-0.0646383\pi$
$691$	0.249542	+	1.09332i	0.00949303	+	0.0415917i	−0.969960	+	0.243266i	$0.921781\pi$
$692$		0			0
$693$	7.22150	+	3.47769i	0.274322	+	0.132107i
$694$		0			0
$695$	3.88058			0.147199
$696$		0			0
$697$	−7.78478			−0.294869
$698$		0			0
$699$	−13.4764	−	6.48991i	−0.509725	−	0.245471i
$700$		0			0
$701$	−2.93047	−	12.8392i	−0.110682	−	0.484930i	−0.999637	−	0.0269356i	$-0.991425\pi$
$701$	−2.93047	−	12.8392i	−0.110682	−	0.484930i	0.888955	−	0.457994i	$-0.151432\pi$
$702$		0			0
$703$	3.22756	+	1.55431i	0.121730	+	0.0586220i
$704$		0			0
$705$	−4.97098	−	6.23341i	−0.187218	−	0.234764i
$706$		0			0
$707$	15.0051	−	18.8158i	0.564326	−	0.707642i
$708$		0			0
$709$	12.0185	−	15.0707i	0.451365	−	0.565994i	−0.503134	−	0.864208i	$-0.667820\pi$
$709$	12.0185	−	15.0707i	0.451365	−	0.565994i	0.954499	+	0.298215i	$0.0963912\pi$
$710$		0			0
$711$	2.30530	−	10.1002i	0.0864556	−	0.378787i
$712$		0			0
$713$	−3.07202			−0.115048
$714$		0			0
$715$	−19.7497	+	9.51095i	−0.738596	+	0.355689i
$716$		0			0
$717$	−7.62185	−	9.55749i	−0.284643	−	0.356931i
$718$		0			0
$719$	4.53938	−	19.8883i	0.169290	−	0.741708i	−0.816993	−	0.576647i	$-0.804361\pi$
$719$	4.53938	−	19.8883i	0.169290	−	0.741708i	0.986283	−	0.165061i	$-0.0527822\pi$
$720$		0			0
$721$	2.98352	−	1.43679i	0.111112	−	0.0535088i
$722$		0			0
$723$	1.81547	+	7.95411i	0.0675182	+	0.295816i
$724$		0			0
$725$	13.6843	+	10.1204i	0.508224	+	0.375860i
$726$		0			0
$727$	−2.91037	−	12.7512i	−0.107940	−	0.472915i	−0.999788	−	0.0205807i	$-0.993448\pi$
$727$	−2.91037	−	12.7512i	−0.107940	−	0.472915i	0.891848	−	0.452334i	$-0.149409\pi$
$728$		0			0
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$		0			0
$731$	−2.78340	+	12.1949i	−0.102948	+	0.451044i
$732$		0			0
$733$	−19.7669	−	24.7869i	−0.730108	−	0.915527i	0.268754	−	0.963209i	$-0.413388\pi$
$733$	−19.7669	−	24.7869i	−0.730108	−	0.915527i	−0.998863	+	0.0476819i	$0.984817\pi$
$734$		0			0
$735$	4.23348	−	2.03874i	0.156154	−	0.0752000i
$736$		0			0
$737$	−32.3143			−1.19031
$738$		0			0
$739$	−8.48412	+	37.1714i	−0.312094	+	1.36737i	0.538977	+	0.842320i	$0.318811\pi$
$739$	−8.48412	+	37.1714i	−0.312094	+	1.36737i	−0.851071	+	0.525051i	$0.824046\pi$
$740$		0			0
$741$	2.35150	−	2.94869i	0.0863846	−	0.108323i
$742$		0			0
$743$	9.70598	−	12.1709i	0.356078	−	0.446508i	−0.571239	−	0.820783i	$-0.693537\pi$
$743$	9.70598	−	12.1709i	0.356078	−	0.446508i	0.927317	+	0.374276i	$0.122109\pi$
$744$		0			0
$745$	0.304215	+	0.381473i	0.0111456	+	0.0139761i
$746$		0			0
$747$	5.27141	+	2.53858i	0.192871	+	0.0928817i
$748$		0			0
$749$	1.91877	+	8.40670i	0.0701105	+	0.307174i
$750$		0			0
$751$	−21.6211	−	10.4122i	−0.788966	−	0.379946i	−0.00439945	−	0.999990i	$-0.501400\pi$
$751$	−21.6211	−	10.4122i	−0.788966	−	0.379946i	−0.784567	+	0.620044i	$0.787115\pi$
$752$		0			0
$753$	18.4361			0.671848
$754$		0			0
$755$	−29.5403			−1.07508
$756$		0			0
$757$	−17.0407	−	8.20636i	−0.619354	−	0.298265i	0.0977719	−	0.995209i	$-0.468828\pi$
$757$	−17.0407	−	8.20636i	−0.619354	−	0.298265i	−0.717126	+	0.696944i	$0.754543\pi$
$758$		0			0
$759$	5.55695	+	24.3466i	0.201705	+	0.883726i
$760$		0			0
$761$	0.370152	+	0.178256i	0.0134180	+	0.00646177i	0.440581	−	0.897713i	$-0.354773\pi$
$761$	0.370152	+	0.178256i	0.0134180	+	0.00646177i	−0.427163	+	0.904175i	$0.640487\pi$
$762$		0			0
$763$	−2.80666	−	3.51944i	−0.101608	−	0.127412i
$764$		0			0
$765$	2.46527	−	3.09136i	0.0891322	−	0.111768i
$766$		0			0
$767$	34.6035	−	43.3914i	1.24946	−	1.56677i
$768$		0			0
$769$	−8.72329	+	38.2192i	−0.314570	+	1.37822i	0.532361	+	0.846517i	$0.321305\pi$
$769$	−8.72329	+	38.2192i	−0.314570	+	1.37822i	−0.846931	+	0.531703i	$0.821552\pi$
$770$		0			0
$771$	−17.8841			−0.644080
$772$		0			0
$773$	19.1816	−	9.23739i	0.689916	−	0.332246i	−0.0558641	−	0.998438i	$-0.517791\pi$
$773$	19.1816	−	9.23739i	0.689916	−	0.332246i	0.745780	+	0.666192i	$0.232077\pi$
$774$		0			0
$775$	1.03334	+	1.29577i	0.0371188	+	0.0465455i
$776$		0			0
$777$	−1.50680	+	6.60173i	−0.0540562	+	0.236836i
$778$		0			0
$779$	−2.39314	+	1.15248i	−0.0857432	+	0.0412917i
$780$		0			0
$781$	−5.52679	−	24.2144i	−0.197764	−	0.866461i
$782$		0			0
$783$	4.08526	−	3.50865i	0.145995	−	0.125389i
$784$		0			0
$785$	7.22695	+	31.6633i	0.257941	+	1.13011i
$786$		0			0
$787$	43.7159	−	21.0525i	1.55830	−	0.750440i	0.561288	−	0.827621i	$-0.310306\pi$
$787$	43.7159	−	21.0525i	1.55830	−	0.750440i	0.997017	+	0.0771809i	$0.0245919\pi$
$788$		0			0
$789$	1.09837	−	4.81227i	0.0391030	−	0.171321i
$790$		0			0
$791$	14.0061	+	17.5630i	0.497998	+	0.624470i
$792$		0			0
$793$	30.2695	−	14.5770i	1.07490	−	0.517646i
$794$		0			0
$795$	−16.4773			−0.584389
$796$		0			0
$797$	−3.42705	+	15.0149i	−0.121392	+	0.531855i	0.877263	+	0.480011i	$0.159367\pi$
$797$	−3.42705	+	15.0149i	−0.121392	+	0.531855i	−0.998655	+	0.0518446i	$0.983490\pi$
$798$		0			0
$799$	−10.6854	+	13.3990i	−0.378021	+	0.474023i
$800$		0			0
$801$	0.123744	−	0.155170i	0.00437229	−	0.00548267i
$802$		0			0
$803$	6.24648	+	7.83284i	0.220433	+	0.276415i
$804$		0			0
$805$	−13.4601	−	6.48207i	−0.474408	−	0.228463i
$806$		0			0
$807$	4.61988	+	20.2410i	0.162627	+	0.712517i
$808$		0			0
$809$	−8.98836	−	4.32856i	−0.316014	−	0.152184i	0.269152	−	0.963098i	$-0.413256\pi$
$809$	−8.98836	−	4.32856i	−0.316014	−	0.152184i	−0.585166	+	0.810913i	$0.698971\pi$
$810$		0			0
$811$	10.5296			0.369743			0.184871	−	0.982763i	$-0.440813\pi$
$811$	10.5296			0.369743			0.184871	+	0.982763i	$0.440813\pi$
$812$		0			0
$813$	−25.0345			−0.877997
$814$		0			0
$815$	−21.9768	−	10.5835i	−0.769814	−	0.370723i
$816$		0			0
$817$	0.949703	+	4.16092i	0.0332259	+	0.145572i
$818$		0			0
$819$	6.42311	+	3.09321i	0.224442	+	0.108085i
$820$		0			0
$821$	17.6902	+	22.1828i	0.617392	+	0.774185i	0.987975	−	0.154615i	$-0.0494136\pi$
$821$	17.6902	+	22.1828i	0.617392	+	0.774185i	−0.370583	+	0.928799i	$0.620842\pi$
$822$		0			0
$823$	−10.9506	+	13.7317i	−0.381716	+	0.478656i	−0.935158	−	0.354231i	$-0.884743\pi$
$823$	−10.9506	+	13.7317i	−0.381716	+	0.478656i	0.553442	+	0.832888i	$0.313314\pi$
$824$		0			0
$825$	8.40012	−	10.5334i	0.292455	−	0.366727i
$826$		0			0
$827$	−8.15189	+	35.7158i	−0.283469	+	1.24196i	0.609843	+	0.792522i	$0.291232\pi$
$827$	−8.15189	+	35.7158i	−0.283469	+	1.24196i	−0.893312	+	0.449437i	$0.851625\pi$
$828$		0			0
$829$	41.8000			1.45177			0.725886	−	0.687815i	$-0.241430\pi$
$829$	41.8000			1.45177			0.725886	+	0.687815i	$0.241430\pi$
$830$		0			0
$831$	29.6147	−	14.2617i	1.02732	−	0.494732i
$832$		0			0
$833$	−6.29745	−	7.89675i	−0.218194	−	0.273606i
$834$		0			0
$835$	2.69959	−	11.8277i	0.0934231	−	0.409313i
$836$		0			0
$837$	0.472457	−	0.227524i	0.0163305	−	0.00786436i
$838$		0			0
$839$	−1.94617	−	8.52671i	−0.0671891	−	0.294375i	0.930159	−	0.367158i	$-0.119669\pi$
$839$	−1.94617	−	8.52671i	−0.0671891	−	0.294375i	−0.997348	+	0.0727831i	$0.976812\pi$
$840$		0			0
$841$	−16.3835	+	23.9287i	−0.564948	+	0.825127i
$842$		0			0
$843$	−3.25680	−	14.2690i	−0.112170	−	0.491450i
$844$		0			0
$845$	−1.68084	+	0.809449i	−0.0578226	+	0.0278459i
$846$		0			0
$847$	−3.00053	+	13.1462i	−0.103099	+	0.451708i
$848$		0			0
$849$	−11.8899	−	14.9095i	−0.408060	−	0.511691i
$850$		0			0
$851$	−19.0083	+	9.15390i	−0.651595	+	0.313792i
$852$		0			0
$853$	6.28719			0.215269			0.107635	−	0.994191i	$-0.465672\pi$
$853$	6.28719			0.215269			0.107635	+	0.994191i	$0.465672\pi$
$854$		0			0
$855$	0.300206	−	1.31529i	0.0102668	−	0.0449819i
$856$		0			0
$857$	−22.0153	+	27.6064i	−0.752029	+	0.943015i	−0.999666	−	0.0258379i	$-0.991775\pi$
$857$	−22.0153	+	27.6064i	−0.752029	+	0.943015i	0.247637	+	0.968853i	$0.420346\pi$
$858$		0			0
$859$	−1.72717	+	2.16580i	−0.0589303	+	0.0738963i	−0.810423	−	0.585845i	$-0.800763\pi$
$859$	−1.72717	+	2.16580i	−0.0589303	+	0.0738963i	0.751493	+	0.659741i	$0.229334\pi$
$860$		0			0
$861$	−3.13046	−	3.92547i	−0.106686	−	0.133780i
$862$		0			0
$863$	35.7599	+	17.2210i	1.21728	+	0.586211i	0.928553	−	0.371200i	$-0.121054\pi$
$863$	35.7599	+	17.2210i	1.21728	+	0.586211i	0.288727	+	0.957411i	$0.406768\pi$
$864$		0			0
$865$	2.11452	+	9.26432i	0.0718959	+	0.314996i
$866$		0			0
$867$	7.65887	+	3.68832i	0.260109	+	0.125262i
$868$		0			0
$869$	44.1622			1.49810
$870$		0			0
$871$	−28.7417			−0.973876
$872$		0			0
$873$	15.0982	+	7.27093i	0.510998	+	0.246084i
$874$		0			0
$875$	4.63082	+	20.2890i	0.156550	+	0.685892i
$876$		0			0
$877$	47.0669	+	22.6662i	1.58934	+	0.765383i	0.999123	−	0.0418650i	$-0.0133299\pi$
$877$	47.0669	+	22.6662i	1.58934	+	0.765383i	0.590212	+	0.807248i	$0.299044\pi$
$878$		0			0
$879$	5.20815	+	6.53082i	0.175667	+	0.220279i
$880$		0			0
$881$	11.8673	−	14.8812i	0.399820	−	0.501359i	−0.540644	−	0.841252i	$-0.681819\pi$
$881$	11.8673	−	14.8812i	0.399820	−	0.501359i	0.940464	+	0.339893i	$0.110391\pi$
$882$		0			0
$883$	28.3478	−	35.5471i	0.953980	−	1.19625i	−0.0265025	−	0.999649i	$-0.508437\pi$
$883$	28.3478	−	35.5471i	0.953980	−	1.19625i	0.980483	−	0.196605i	$-0.0629916\pi$
$884$		0			0
$885$	4.41768	−	19.3551i	0.148499	−	0.650615i
$886$		0			0
$887$	−10.3941			−0.349001			−0.174500	−	0.984657i	$-0.555831\pi$
$887$	−10.3941			−0.349001			−0.174500	+	0.984657i	$0.555831\pi$
$888$		0			0
$889$	−3.36358	+	1.61982i	−0.112811	+	0.0543269i
$890$		0			0
$891$	−2.65781	−	3.33278i	−0.0890399	−	0.111652i
$892$		0			0
$893$	−1.30120	+	5.70091i	−0.0435429	+	0.190774i
$894$		0			0
$895$	−7.09689	+	3.41768i	−0.237223	+	0.114241i
$896$		0			0
$897$	4.94259	+	21.6549i	0.165028	+	0.723036i
$898$		0			0
$899$	−2.14226	+	1.83989i	−0.0714485	+	0.0613639i
$900$		0			0
$901$	7.88140	+	34.5307i	0.262568	+	1.15038i
$902$		0			0
$903$	−7.26853	+	3.50034i	−0.241882	+	0.116484i
$904$		0			0
$905$	0.279976	−	1.22666i	0.00930673	−	0.0407754i
$906$		0			0
$907$	15.0028	+	18.8130i	0.498161	+	0.624674i	0.965813	−	0.259239i	$-0.0834716\pi$
$907$	15.0028	+	18.8130i	0.498161	+	0.624674i	−0.467653	+	0.883912i	$0.654900\pi$
$908$		0			0
$909$	−11.5318	+	5.55341i	−0.382485	+	0.184195i
$910$		0			0
$911$	−51.8755			−1.71871			−0.859356	−	0.511377i	$-0.829135\pi$
$911$	−51.8755			−1.71871			−0.859356	+	0.511377i	$0.829135\pi$
$912$		0			0
$913$	−5.54986	+	24.3155i	−0.183673	+	0.804726i
$914$		0			0
$915$	7.49303	−	9.39596i	0.247712	−	0.310621i
$916$		0			0
$917$	7.32653	−	9.18718i	0.241943	−	0.303388i
$918$		0			0
$919$	23.9480	+	30.0298i	0.789971	+	0.990593i	0.999917	+	0.0128796i	$0.00409982\pi$
$919$	23.9480	+	30.0298i	0.789971	+	0.990593i	−0.209946	+	0.977713i	$0.567329\pi$
$920$		0			0
$921$	−23.0169	−	11.0844i	−0.758433	−	0.365242i
$922$		0			0
$923$	−4.91576	−	21.5374i	−0.161804	−	0.708911i
$924$		0			0
$925$	10.2549	+	4.93852i	0.337180	+	0.162378i
$926$		0			0
$927$	−1.76115			−0.0578436
$928$		0			0
$929$	−6.82478			−0.223914			−0.111957	−	0.993713i	$-0.535712\pi$
$929$	−6.82478			−0.223914			−0.111957	+	0.993713i	$0.535712\pi$
$930$		0			0
$931$	−3.10497	−	1.49528i	−0.101761	−	0.0490057i
$932$		0			0
$933$	0.535868	+	2.34779i	0.0175435	+	0.0768632i
$934$		0			0
$935$	15.1859	+	7.31313i	0.496631	+	0.239165i
$936$		0			0
$937$	24.0641	+	30.1754i	0.786140	+	0.985788i	0.999960	+	0.00891539i	$0.00283790\pi$
$937$	24.0641	+	30.1754i	0.786140	+	0.985788i	−0.213820	+	0.976873i	$0.568591\pi$
$938$		0			0
$939$	−12.5806	+	15.7756i	−0.410553	+	0.514818i
$940$		0			0
$941$	−27.3619	+	34.3107i	−0.891973	+	1.11850i	0.100366	+	0.994951i	$0.467999\pi$
$941$	−27.3619	+	34.3107i	−0.891973	+	1.11850i	−0.992339	+	0.123548i	$0.960573\pi$
$942$		0			0
$943$	3.48095	−	15.2510i	0.113355	−	0.496642i
$944$		0			0
$945$	2.55016			0.0829569
$946$		0			0
$947$	−41.8254	+	20.1421i	−1.35914	+	0.654529i	−0.964446	−	0.264281i	$-0.914865\pi$
$947$	−41.8254	+	20.1421i	−1.35914	+	0.654529i	−0.394699	+	0.918811i	$0.629151\pi$
$948$		0			0
$949$	5.55588	+	6.96686i	0.180352	+	0.226154i
$950$		0			0
$951$	0.581422	−	2.54738i	0.0188539	−	0.0826043i
$952$		0			0
$953$	−50.5832	+	24.3596i	−1.63855	+	0.789085i	−0.638745	+	0.769418i	$0.720546\pi$
$953$	−50.5832	+	24.3596i	−1.63855	+	0.789085i	−0.999807	+	0.0196665i	$0.993740\pi$
$954$		0			0
$955$	−2.07356	−	9.08485i	−0.0670988	−	0.293979i
$956$		0			0
$957$	18.4568	+	13.6498i	0.596623	+	0.441236i
$958$		0			0
$959$	−2.62449	−	11.4986i	−0.0847492	−	0.371310i
$960$		0			0
$961$	27.6823	−	13.3311i	0.892977	−	0.430035i
$962$		0			0
$963$	1.02047	−	4.47097i	0.0328842	−	0.144075i
$964$		0			0
$965$	11.5935	+	14.5377i	0.373207	+	0.467986i
$966$		0			0
$967$	22.7227	−	10.9427i	0.730713	−	0.351893i	−0.0312518	−	0.999512i	$-0.509949\pi$
$967$	22.7227	−	10.9427i	0.730713	−	0.351893i	0.761964	+	0.647619i	$0.224235\pi$
$968$		0			0
$969$	−2.89998			−0.0931609
$970$		0			0
$971$	−11.7819	+	51.6201i	−0.378101	+	1.65657i	0.325178	+	0.945653i	$0.394576\pi$
$971$	−11.7819	+	51.6201i	−0.378101	+	1.65657i	−0.703278	+	0.710915i	$0.748281\pi$
$972$		0			0
$973$	3.35433	−	4.20620i	0.107535	−	0.134844i
$974$		0			0
$975$	7.47143	−	9.36887i	0.239277	−	0.300044i
$976$		0			0
$977$	−5.87748	−	7.37013i	−0.188037	−	0.235791i	0.678873	−	0.734256i	$-0.262469\pi$
$977$	−5.87748	−	7.37013i	−0.188037	−	0.235791i	−0.866910	+	0.498465i	$0.833897\pi$
$978$		0			0
$979$	0.762253	+	0.367082i	0.0243617	+	0.0117320i
$980$		0			0
$981$	0.532730	+	2.33404i	0.0170088	+	0.0745202i
$982$		0			0
$983$	29.2973	+	14.1088i	0.934439	+	0.450002i	0.838204	−	0.545357i	$-0.183606\pi$
$983$	29.2973	+	14.1088i	0.934439	+	0.450002i	0.0962346	+	0.995359i	$0.469320\pi$
$984$		0			0
$985$	7.58222			0.241590
$986$		0			0
$987$	−11.0533			−0.351830
$988$		0			0
$989$	−22.6462	−	10.9058i	−0.720106	−	0.346785i
$990$		0			0
$991$	−8.56577	−	37.5291i	−0.272101	−	1.19215i	−0.907528	−	0.419991i	$-0.862033\pi$
$991$	−8.56577	−	37.5291i	−0.272101	−	1.19215i	0.635428	−	0.772160i	$-0.280824\pi$
$992$		0			0
$993$	−11.8856	−	5.72380i	−0.377178	−	0.181639i
$994$		0			0
$995$	6.66549	+	8.35825i	0.211310	+	0.264974i
$996$		0			0
$997$	6.37391	−	7.99263i	0.201864	−	0.253129i	−0.670587	−	0.741831i	$-0.733958\pi$
$997$	6.37391	−	7.99263i	0.201864	−	0.253129i	0.872451	+	0.488701i	$0.162529\pi$
$998$		0			0
$999$	2.24538	−	2.81562i	0.0710408	−	0.0890823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	696.2.y.c.529.2	yes	24
29.25	even	7	inner	696.2.y.c.25.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
696.2.y.c.25.2	✓	24	29.25	even	7	inner
696.2.y.c.529.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.y (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 - 0.433884i) q^{3} +(-0.301797 - 1.32226i) q^{5} +(-1.69408 - 0.815825i) q^{7} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.900969 - 0.433884i) q^{3} +(-0.301797 - 1.32226i) q^{5} +(-1.69408 - 0.815825i) q^{7} +(0.623490 + 0.781831i) q^{9} +(-2.65781 + 3.33278i) q^{11} +(-2.36397 + 2.96432i) q^{13} +(-0.301797 + 1.32226i) q^{15} +2.91536 q^{17} +(0.896218 - 0.431596i) q^{19} +(1.17234 + 1.47007i) q^{21} +(-1.30359 + 5.71142i) q^{23} +(2.84755 - 1.37131i) q^{25} +(-0.222521 - 0.974928i) q^{27} +(2.51162 + 4.76358i) q^{29} +(0.116687 + 0.511241i) q^{31} +(3.84064 - 1.84956i) q^{33} +(-0.567465 + 2.48623i) q^{35} +(2.24538 + 2.81562i) q^{37} +(3.41603 - 1.64507i) q^{39} -2.67027 q^{41} +(-0.954737 + 4.18298i) q^{43} +(0.845617 - 1.06037i) q^{45} +(-3.66520 + 4.59601i) q^{47} +(-2.16010 - 2.70868i) q^{49} +(-2.62664 - 1.26493i) q^{51} +(2.70341 + 11.8444i) q^{53} +(5.20893 + 2.50849i) q^{55} -0.994727 q^{57} -14.6379 q^{59} +(-7.98350 - 3.84465i) q^{61} +(-0.418403 - 1.83314i) q^{63} +(4.63304 + 2.23116i) q^{65} +(4.72640 + 5.92671i) q^{67} +(3.65259 - 4.58021i) q^{69} +(-3.63276 + 4.55534i) q^{71} +(0.522977 - 2.29131i) q^{73} -3.16055 q^{75} +(7.22150 - 3.47769i) q^{77} +(-6.45931 - 8.09972i) q^{79} +(-0.222521 + 0.974928i) q^{81} +(5.27141 - 2.53858i) q^{83} +(-0.879846 - 3.85486i) q^{85} +(-0.196054 - 5.38159i) q^{87} +(-0.0441638 - 0.193494i) q^{89} +(6.42311 - 3.09321i) q^{91} +(0.116687 - 0.511241i) q^{93} +(-0.841158 - 1.05478i) q^{95} +(15.0982 - 7.27093i) q^{97} -4.26279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9	\( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9} - 12 q^{11} + 7 q^{13} + q^{15} - 38 q^{17} - 18 q^{19} + 4 q^{21} - 6 q^{23} - 19 q^{25} - 4 q^{27} + 5 q^{29} - 2 q^{31} + 2 q^{33} + 21 q^{35} - 18 q^{37} + 7 q^{39} - 70 q^{41} - q^{43} + q^{45} + 23 q^{47} + 8 q^{49} + 11 q^{51} + 26 q^{53} - 17 q^{55} + 10 q^{57} - 4 q^{59} + 10 q^{61} - 3 q^{63} + 43 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 8 q^{73} + 30 q^{75} - 36 q^{77} + 45 q^{79} - 4 q^{81} - 10 q^{83} - 53 q^{85} - 16 q^{87} + 10 q^{89} + 57 q^{91} - 2 q^{93} - 34 q^{95} + 96 q^{97} + 2 q^{99}+O(q^{100}) \) 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9 - 12 * q^11 + 7 * q^13 + q^15 - 38 * q^17 - 18 * q^19 + 4 * q^21 - 6 * q^23 - 19 * q^25 - 4 * q^27 + 5 * q^29 - 2 * q^31 + 2 * q^33 + 21 * q^35 - 18 * q^37 + 7 * q^39 - 70 * q^41 - q^43 + q^45 + 23 * q^47 + 8 * q^49 + 11 * q^51 + 26 * q^53 - 17 * q^55 + 10 * q^57 - 4 * q^59 + 10 * q^61 - 3 * q^63 + 43 * q^65 + 2 * q^67 + 8 * q^69 + 16 * q^71 + 8 * q^73 + 30 * q^75 - 36 * q^77 + 45 * q^79 - 4 * q^81 - 10 * q^83 - 53 * q^85 - 16 * q^87 + 10 * q^89 + 57 * q^91 - 2 * q^93 - 34 * q^95 + 96 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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