LMFDB - Embedded newform 525.2.bb.a.41.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.18
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05761 + 1.45568i) q^{2} +(1.54874 - 0.775505i) q^{3} +(-0.382420 - 1.17697i) q^{4} +(-2.23358 + 0.105508i) q^{5} +(-0.509079 + 3.07465i) q^{6} +(-2.28537 + 1.33307i) q^{7} +(-1.30476 - 0.423944i) q^{8} +(1.79718 - 2.40211i) q^{9} +O(q^{10})$	\(q+(-1.05761 + 1.45568i) q^{2} +(1.54874 - 0.775505i) q^{3} +(-0.382420 - 1.17697i) q^{4} +(-2.23358 + 0.105508i) q^{5} +(-0.509079 + 3.07465i) q^{6} +(-2.28537 + 1.33307i) q^{7} +(-1.30476 - 0.423944i) q^{8} +(1.79718 - 2.40211i) q^{9} +(2.20867 - 3.36295i) q^{10} +(2.25320 - 3.10126i) q^{11} +(-1.50501 - 1.52625i) q^{12} +(-3.81188 - 5.24660i) q^{13} +(0.476515 - 4.73663i) q^{14} +(-3.37741 + 1.89555i) q^{15} +(3.99944 - 2.90576i) q^{16} +(-0.839544 + 2.58385i) q^{17} +(1.59597 + 5.15662i) q^{18} +(2.77292 + 0.900977i) q^{19} +(0.978345 + 2.58850i) q^{20} +(-2.50564 + 3.83689i) q^{21} +(2.13143 + 6.55986i) q^{22} +(5.10006 - 7.01963i) q^{23} +(-2.34951 + 0.355273i) q^{24} +(4.97774 - 0.471322i) q^{25} +11.6688 q^{26} +(0.920522 - 5.11397i) q^{27} +(2.44295 + 2.18002i) q^{28} +(-1.60846 + 0.522622i) q^{29} +(0.812667 - 6.92117i) q^{30} +(-6.85172 - 2.22626i) q^{31} +6.15123i q^{32} +(1.08457 - 6.55041i) q^{33} +(-2.87334 - 3.95482i) q^{34} +(4.96390 - 3.21864i) q^{35} +(-3.51449 - 1.19661i) q^{36} +(-4.27009 + 3.10240i) q^{37} +(-4.24420 + 3.08360i) q^{38} +(-9.97236 - 5.16948i) q^{39} +(2.95902 + 0.809247i) q^{40} +(-1.78524 + 1.29705i) q^{41} +(-2.93529 - 7.70535i) q^{42} -8.54026 q^{43} +(-4.51176 - 1.46596i) q^{44} +(-3.76071 + 5.55491i) q^{45} +(4.82443 + 14.8481i) q^{46} +(-2.92074 - 8.98910i) q^{47} +(3.94065 - 7.60185i) q^{48} +(3.44585 - 6.09312i) q^{49} +(-4.57842 + 7.74445i) q^{50} +(0.703555 + 4.65278i) q^{51} +(-4.71734 + 6.49286i) q^{52} +(6.05684 - 1.96799i) q^{53} +(6.47073 + 6.74857i) q^{54} +(-4.70548 + 7.16464i) q^{55} +(3.54702 - 0.770474i) q^{56} +(4.99324 - 0.755036i) q^{57} +(0.940362 - 2.89414i) q^{58} +(-0.153670 + 0.111648i) q^{59} +(3.52260 + 3.25020i) q^{60} +(-0.0287978 + 0.0396367i) q^{61} +(10.4872 - 7.61938i) q^{62} +(-0.905053 + 7.88549i) q^{63} +(-0.955339 - 0.694094i) q^{64} +(9.06768 + 11.3165i) q^{65} +(8.38823 + 8.50658i) q^{66} +(0.958727 - 2.95066i) q^{67} +3.36217 q^{68} +(2.45490 - 14.8267i) q^{69} +(-0.564579 + 10.6299i) q^{70} +(-0.140481 + 0.0456450i) q^{71} +(-3.36326 + 2.37228i) q^{72} +(-2.85240 + 3.92599i) q^{73} -9.49701i q^{74} +(7.34370 - 4.59021i) q^{75} -3.60819i q^{76} +(-1.01520 + 10.0912i) q^{77} +(18.0720 - 9.04924i) q^{78} +(0.461162 + 1.41931i) q^{79} +(-8.62647 + 6.91222i) q^{80} +(-2.54026 - 8.63407i) q^{81} -3.97050i q^{82} +(-3.80555 + 11.7123i) q^{83} +(5.47411 + 1.48175i) q^{84} +(1.60257 - 5.85981i) q^{85} +(9.03228 - 12.4319i) q^{86} +(-2.08580 + 2.05678i) q^{87} +(-4.25465 + 3.09119i) q^{88} +(-0.931573 - 0.676828i) q^{89} +(-4.10879 - 11.3493i) q^{90} +(15.7056 + 6.90892i) q^{91} +(-10.2122 - 3.31816i) q^{92} +(-12.3380 + 1.86565i) q^{93} +(16.1742 + 5.25533i) q^{94} +(-6.28859 - 1.71984i) q^{95} +(4.77031 + 9.52666i) q^{96} +(0.364241 - 0.118349i) q^{97} +(5.22525 + 11.4602i) q^{98} +(-3.40016 - 10.9860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05761	+	1.45568i	−0.747844	+	1.02932i	0.250285	+	0.968172i	$0.419476\pi$
$2$	−1.05761	+	1.45568i	−0.747844	+	1.02932i	−0.998129	+	0.0611469i	$0.980524\pi$
$3$	1.54874	−	0.775505i	0.894165	−	0.447738i
$3$	1.54874	−	0.775505i	0.894165	−	0.447738i
$4$	−0.382420	−	1.17697i	−0.191210	−	0.588484i
$5$	−2.23358	+	0.105508i	−0.998886	+	0.0471847i
$5$	−2.23358	+	0.105508i	−0.998886	+	0.0471847i
$6$	−0.509079	+	3.07465i	−0.207831	+	1.25522i
$7$	−2.28537	+	1.33307i	−0.863789	+	0.503853i
$7$	−2.28537	+	1.33307i	−0.863789	+	0.503853i
$8$	−1.30476	−	0.423944i	−0.461304	−	0.149887i
$9$	1.79718	−	2.40211i	0.599061	−	0.800703i
$10$	2.20867	−	3.36295i	0.698443	−	1.06346i
$11$	2.25320	−	3.10126i	0.679365	−	0.935065i	−0.320561	−	0.947228i	$-0.603871\pi$
$11$	2.25320	−	3.10126i	0.679365	−	0.935065i	0.999926	+	0.0121624i	$0.00387150\pi$
$12$	−1.50501	−	1.52625i	−0.434460	−	0.440590i
$13$	−3.81188	−	5.24660i	−1.05722	−	1.45514i	−0.882374	−	0.470549i	$-0.844056\pi$
$13$	−3.81188	−	5.24660i	−1.05722	−	1.45514i	−0.174850	−	0.984595i	$-0.555944\pi$
$14$	0.476515	−	4.73663i	0.127354	−	1.26592i
$15$	−3.37741	+	1.89555i	−0.872042	+	0.489430i
$16$	3.99944	−	2.90576i	0.999859	−	0.726440i
$17$	−0.839544	+	2.58385i	−0.203619	+	0.626676i	0.796148	+	0.605102i	$0.206868\pi$
$17$	−0.839544	+	2.58385i	−0.203619	+	0.626676i	−0.999767	+	0.0215740i	$0.993132\pi$
$18$	1.59597	+	5.15662i	0.376174	+	1.21543i
$19$	2.77292	+	0.900977i	0.636152	+	0.206698i	0.609298	−	0.792941i	$-0.291451\pi$
$19$	2.77292	+	0.900977i	0.636152	+	0.206698i	0.0268535	+	0.999639i	$0.491451\pi$
$20$	0.978345	+	2.58850i	0.218765	+	0.578807i
$21$	−2.50564	+	3.83689i	−0.546776	+	0.837279i
$22$	2.13143	+	6.55986i	0.454422	+	1.39857i
$23$	5.10006	−	7.01963i	1.06344	−	1.46369i	0.186886	−	0.982382i	$-0.440160\pi$
$23$	5.10006	−	7.01963i	1.06344	−	1.46369i	0.876549	−	0.481312i	$-0.159840\pi$
$24$	−2.34951	+	0.355273i	−0.479592	+	0.0725198i
$25$	4.97774	−	0.471322i	0.995547	−	0.0942643i
$26$	11.6688			2.28845
$27$	0.920522	−	5.11397i	0.177154	−	0.984183i
$28$	2.44295	+	2.18002i	0.461675	+	0.411985i
$29$	−1.60846	+	0.522622i	−0.298684	+	0.0970484i	−0.454526	−	0.890734i	$-0.650191\pi$
$29$	−1.60846	+	0.522622i	−0.298684	+	0.0970484i	0.155841	+	0.987782i	$0.450191\pi$
$30$	0.812667	−	6.92117i	0.148372	−	1.26363i
$31$	−6.85172	−	2.22626i	−1.23061	−	0.399848i	−0.379672	−	0.925121i	$-0.623963\pi$
$31$	−6.85172	−	2.22626i	−1.23061	−	0.399848i	−0.850934	+	0.525273i	$0.823963\pi$
$32$			6.15123i			1.08739i
$33$	1.08457	−	6.55041i	0.188800	−	1.14028i
$34$	−2.87334	−	3.95482i	−0.492774	−	0.678245i
$35$	4.96390	−	3.21864i	0.839053	−	0.544050i
$36$	−3.51449	−	1.19661i	−0.585748	−	0.199436i
$37$	−4.27009	+	3.10240i	−0.701999	+	0.510032i	−0.880583	−	0.473893i	$-0.842848\pi$
$37$	−4.27009	+	3.10240i	−0.701999	+	0.510032i	0.178584	+	0.983925i	$0.442848\pi$
$38$	−4.24420	+	3.08360i	−0.688501	+	0.500225i
$39$	−9.97236	−	5.16948i	−1.59686	−	0.827779i
$40$	2.95902	+	0.809247i	0.467862	+	0.127953i
$41$	−1.78524	+	1.29705i	−0.278807	+	0.202565i	−0.718397	−	0.695633i	$-0.755124\pi$
$41$	−1.78524	+	1.29705i	−0.278807	+	0.202565i	0.439590	+	0.898199i	$0.355124\pi$
$42$	−2.93529	−	7.70535i	−0.452924	−	1.18896i
$43$	−8.54026			−1.30238			−0.651189	−	0.758916i	$-0.725729\pi$
$43$	−8.54026			−1.30238			−0.651189	+	0.758916i	$0.725729\pi$
$44$	−4.51176	−	1.46596i	−0.680173	−	0.221002i
$45$	−3.76071	+	5.55491i	−0.560613	+	0.828078i
$46$	4.82443	+	14.8481i	0.711324	+	2.18923i
$47$	−2.92074	−	8.98910i	−0.426033	−	1.31120i	−0.902001	−	0.431733i	$-0.857902\pi$
$47$	−2.92074	−	8.98910i	−0.426033	−	1.31120i	0.475968	−	0.879462i	$-0.342098\pi$
$48$	3.94065	−	7.60185i	0.568784	−	1.09723i
$49$	3.44585	−	6.09312i	0.492264	−	0.870446i
$50$	−4.57842	+	7.74445i	−0.647486	+	1.09523i
$51$	0.703555	+	4.65278i	0.0985174	+	0.651520i
$52$	−4.71734	+	6.49286i	−0.654177	+	0.900398i
$53$	6.05684	−	1.96799i	0.831971	−	0.270324i	0.138095	−	0.990419i	$-0.455902\pi$
$53$	6.05684	−	1.96799i	0.831971	−	0.270324i	0.693875	+	0.720095i	$0.255902\pi$
$54$	6.47073	+	6.74857i	0.880555	+	0.918364i
$55$	−4.70548	+	7.16464i	−0.634487	+	0.966080i
$56$	3.54702	−	0.770474i	0.473990	−	0.102959i
$57$	4.99324	−	0.755036i	0.661371	−	0.100007i
$58$	0.940362	−	2.89414i	0.123476	−	0.380019i
$59$	−0.153670	+	0.111648i	−0.0200062	+	0.0145353i	−0.597743	−	0.801687i	$-0.703936\pi$
$59$	−0.153670	+	0.111648i	−0.0200062	+	0.0145353i	0.577737	+	0.816223i	$0.303936\pi$
$60$	3.52260	+	3.25020i	0.454765	+	0.419599i
$61$	−0.0287978	+	0.0396367i	−0.00368717	+	0.00507496i	−0.810857	−	0.585245i	$-0.800998\pi$
$61$	−0.0287978	+	0.0396367i	−0.00368717	+	0.00507496i	0.807169	+	0.590320i	$0.200998\pi$
$62$	10.4872	−	7.61938i	1.33187	−	0.967662i
$63$	−0.905053	+	7.88549i	−0.114026	+	0.993478i
$64$	−0.955339	−	0.694094i	−0.119417	−	0.0867618i
$65$	9.06768	+	11.3165i	1.12471	+	1.40364i
$66$	8.38823	+	8.50658i	1.03252	+	1.04709i
$67$	0.958727	−	2.95066i	0.117127	−	0.360480i	−0.875258	−	0.483657i	$-0.839308\pi$
$67$	0.958727	−	2.95066i	0.117127	−	0.360480i	0.992385	+	0.123177i	$0.0393082\pi$
$68$	3.36217			0.407723
$69$	2.45490	−	14.8267i	0.295536	−	1.78492i
$70$	−0.564579	+	10.6299i	−0.0674800	+	1.27052i
$71$	−0.140481	+	0.0456450i	−0.0166720	+	0.00541707i	−0.317341	−	0.948311i	$-0.602790\pi$
$71$	−0.140481	+	0.0456450i	−0.0166720	+	0.00541707i	0.300669	+	0.953729i	$0.402790\pi$
$72$	−3.36326	+	2.37228i	−0.396364	+	0.279576i
$73$	−2.85240	+	3.92599i	−0.333848	+	0.459502i	−0.942632	−	0.333834i	$-0.891658\pi$
$73$	−2.85240	+	3.92599i	−0.333848	+	0.459502i	0.608784	+	0.793336i	$0.291658\pi$
$74$		−	9.49701i		−	1.10400i
$75$	7.34370	−	4.59021i	0.847978	−	0.530032i
$76$		−	3.60819i		−	0.413888i
$77$	−1.01520	+	10.0912i	−0.115692	+	1.15000i
$78$	18.0720	−	9.04924i	2.04625	−	1.02462i
$79$	0.461162	+	1.41931i	0.0518848	+	0.159685i	0.973642	−	0.228084i	$-0.0732460\pi$
$79$	0.461162	+	1.41931i	0.0518848	+	0.159685i	−0.921757	+	0.387769i	$0.873246\pi$
$80$	−8.62647	+	6.91222i	−0.964469	+	0.772809i
$81$	−2.54026	−	8.63407i	−0.282251	−	0.959341i
$82$		−	3.97050i		−	0.438469i
$83$	−3.80555	+	11.7123i	−0.417714	+	1.28559i	0.492087	+	0.870546i	$0.336234\pi$
$83$	−3.80555	+	11.7123i	−0.417714	+	1.28559i	−0.909801	+	0.415045i	$0.863766\pi$
$84$	5.47411	+	1.48175i	0.597275	+	0.161673i
$85$	1.60257	−	5.85981i	0.173823	−	0.635586i
$86$	9.03228	−	12.4319i	0.973976	−	1.34056i
$87$	−2.08580	+	2.05678i	−0.223621	+	0.220510i
$88$	−4.25465	+	3.09119i	−0.453547	+	0.329521i
$89$	−0.931573	−	0.676828i	−0.0987466	−	0.0717436i	0.537316	−	0.843381i	$-0.319438\pi$
$89$	−0.931573	−	0.676828i	−0.0987466	−	0.0717436i	−0.636063	+	0.771637i	$0.719438\pi$
$90$	−4.10879	−	11.3493i	−0.433105	−	1.19632i
$91$	15.7056	+	6.90892i	1.64640	+	0.724252i
$92$	−10.2122	−	3.31816i	−1.06470	−	0.345942i
$93$	−12.3380	+	1.86565i	−1.27939	+	0.193459i
$94$	16.1742	+	5.25533i	1.66825	+	0.542046i
$95$	−6.28859	−	1.71984i	−0.645196	−	0.176451i
$96$	4.77031	+	9.52666i	0.486868	+	0.972310i
$97$	0.364241	−	0.118349i	0.0369831	−	0.0120165i	−0.290467	−	0.956885i	$-0.593811\pi$
$97$	0.364241	−	0.118349i	0.0369831	−	0.0120165i	0.327450	+	0.944868i	$0.393811\pi$
$98$	5.22525	+	11.4602i	0.527830	+	1.15765i
$99$	−3.40016	−	10.9860i	−0.341728	−	1.10413i
$100$	−2.45832	−	5.67840i	−0.245832	−	0.567840i
$101$	−6.61867			−0.658583			−0.329291	−	0.944228i	$-0.606810\pi$
$101$	−6.61867			−0.658583			−0.329291	+	0.944228i	$0.606810\pi$
$102$	−7.51704	−	3.89669i	−0.744298	−	0.385830i
$103$	−6.73355	+	2.18786i	−0.663477	+	0.215577i	−0.621347	−	0.783535i	$-0.713414\pi$
$103$	−6.73355	+	2.18786i	−0.663477	+	0.215577i	−0.0421297	+	0.999112i	$0.513414\pi$
$104$	2.74934	+	8.46159i	0.269595	+	0.829727i
$105$	5.19172	−	8.83437i	0.506660	−	0.862146i
$106$	−3.54103	+	10.8982i	−0.343935	+	1.05852i
$107$		−	9.82285i		−	0.949611i	−0.880091	−	0.474805i	$-0.842518\pi$
$107$		−	9.82285i		−	0.949611i	0.880091	−	0.474805i	$-0.157482\pi$
$108$	−6.37100	+	0.872259i	−0.613050	+	0.0839331i
$109$	6.02553	−	4.37781i	0.577141	−	0.419318i	−0.260551	−	0.965460i	$-0.583904\pi$
$109$	6.02553	−	4.37781i	0.577141	−	0.419318i	0.837692	+	0.546142i	$0.183904\pi$
$110$	−5.45283	−	14.4271i	−0.519907	−	1.37557i
$111$	−4.20733	+	8.11629i	−0.399342	+	0.770364i
$112$	−5.26661	+	11.9723i	−0.497648	+	1.13127i
$113$	5.10823	+	7.03087i	0.480542	+	0.661409i	0.978609	−	0.205730i	$-0.0659568\pi$
$113$	5.10823	+	7.03087i	0.480542	+	0.661409i	−0.498067	+	0.867138i	$0.665957\pi$
$114$	−4.18182	+	8.06708i	−0.391663	+	0.755552i
$115$	−10.6507	+	16.2170i	−0.993187	+	1.51224i
$116$	1.23022	+	1.69325i	0.114223	+	0.157214i
$117$	−19.4535	−	0.272560i	−1.79848	−	0.0251982i
$118$		−	0.341775i		−	0.0314629i
$119$	−1.52579	−	7.02423i	−0.139869	−	0.643910i
$120$	5.21033	−	1.04142i	0.475636	−	0.0950684i
$121$	−1.14173	−	3.51389i	−0.103794	−	0.319445i
$122$	−0.0272414	−	0.0838405i	−0.00246632	−	0.00759056i
$123$	−1.75900	+	3.39325i	−0.158603	+	0.305959i
$124$			8.91563i			0.800647i
$125$	−11.0684	+	1.57793i	−0.989991	+	0.141134i
$126$	−10.5215	−	9.65724i	−0.937332	−	0.860336i
$127$	4.98085	+	3.61880i	0.441979	+	0.321117i	0.786421	−	0.617691i	$-0.211932\pi$
$127$	4.98085	+	3.61880i	0.441979	+	0.321117i	−0.344442	+	0.938808i	$0.611932\pi$
$128$	−9.67959	+	3.14509i	−0.855563	+	0.277989i
$129$	−13.2266	+	6.62302i	−1.16454	+	0.583124i
$130$	−26.0632	+	1.23116i	−2.28590	+	0.107980i
$131$	1.36951	−	4.21491i	0.119654	−	0.368258i	−0.873235	−	0.487299i	$-0.837982\pi$
$131$	1.36951	−	4.21491i	0.119654	−	0.368258i	0.992889	+	0.119041i	$0.0379821\pi$
$132$	−8.12439	+	1.22850i	−0.707137	+	0.106927i
$133$	−7.53822	+	1.63743i	−0.653647	+	0.141983i
$134$	3.28124	+	4.51625i	0.283456	+	0.390144i
$135$	−1.51649	+	11.5196i	−0.130519	+	0.991446i
$136$	2.19081	−	3.01540i	0.187861	−	0.258568i
$137$	−2.64650	−	3.64259i	−0.226106	−	0.311208i	0.680859	−	0.732415i	$-0.261607\pi$
$137$	−2.64650	−	3.64259i	−0.226106	−	0.311208i	−0.906965	+	0.421207i	$0.861607\pi$
$138$	18.9865	+	19.2544i	1.61624	+	1.63905i
$139$	11.1022	−	15.2808i	0.941674	−	1.29610i	−0.0134545	−	0.999909i	$-0.504283\pi$
$139$	11.1022	−	15.2808i	0.941674	−	1.29610i	0.955128	−	0.296193i	$-0.0957172\pi$
$140$	−5.68654	−	4.61149i	−0.480600	−	0.389742i
$141$	−11.4946	−	11.6567i	−0.968016	−	0.981674i
$142$	0.0821299	−	0.252770i	0.00689218	−	0.0212120i
$143$	−24.8600			−2.07890
$144$	0.207770	−	14.8293i	0.0173142	−	1.23577i
$145$	3.53749	−	1.33702i	0.293773	−	0.111034i
$146$	−2.69825	−	8.30434i	−0.223308	−	0.687272i
$147$	0.611470	−	12.1089i	0.0504332	−	0.998727i
$148$	5.28440	+	3.83934i	0.434375	+	0.315592i
$149$		−	16.6940i		−	1.36762i	−0.729659	−	0.683811i	$-0.760321\pi$
$149$		−	16.6940i		−	1.36762i	0.729659	−	0.683811i	$-0.239679\pi$
$150$	−1.08491	+	15.5447i	−0.0885829	+	1.26922i
$151$	17.5678			1.42965			0.714825	−	0.699303i	$-0.246506\pi$
$151$	17.5678			1.42965			0.714825	+	0.699303i	$0.246506\pi$
$152$	−3.23604	−	2.35112i	−0.262478	−	0.190701i
$153$	4.69788	+	6.66034i	0.379801	+	0.538456i
$154$	−13.6159	−	12.1504i	−1.09720	−	0.979105i
$155$	15.5387	+	4.24961i	1.24810	+	0.341337i
$156$	−2.27068	+	13.7141i	−0.181800	+	1.09800i
$157$		−	1.42614i		−	0.113818i	−0.998379	−	0.0569092i	$-0.981875\pi$
$157$		−	1.42614i		−	0.113818i	0.998379	−	0.0569092i	$-0.0181246\pi$
$158$	−2.55379	−	0.829777i	−0.203169	−	0.0660135i
$159$	7.85428	−	7.74500i	0.622885	−	0.614219i
$160$	−0.649006	−	13.7393i	−0.0513084	−	1.08618i
$161$	−2.29787	+	22.8412i	−0.181097	+	1.80014i
$162$	15.2550	+	5.43369i	1.19855	+	0.426911i
$163$	12.2221	−	8.87989i	0.957310	−	0.695526i	0.00478541	−	0.999989i	$-0.498477\pi$
$163$	12.2221	−	8.87989i	0.957310	−	0.695526i	0.952524	+	0.304462i	$0.0984768\pi$
$164$	2.20930	+	1.60515i	0.172517	+	0.125341i
$165$	−1.73135	+	14.7453i	−0.134786	+	1.14792i
$166$	−13.0245	−	17.9267i	−1.01090	−	1.39138i
$167$	−3.02999	+	9.32534i	−0.234467	+	0.721616i	0.762724	+	0.646724i	$0.223861\pi$
$167$	−3.02999	+	9.32534i	−0.234467	+	0.721616i	−0.997192	+	0.0748926i	$0.976139\pi$
$168$	4.89590	−	3.94399i	0.377727	−	0.304286i
$169$	−8.97916	+	27.6350i	−0.690704	+	2.12577i
$170$	6.83510	+	8.53023i	0.524228	+	0.654239i
$171$	7.14770	−	5.04164i	0.546598	−	0.385544i
$172$	3.26597	+	10.0516i	0.249028	+	0.766429i
$173$	2.63362	+	1.91344i	0.200230	+	0.145476i	0.683382	−	0.730061i	$-0.260508\pi$
$173$	2.63362	+	1.91344i	0.200230	+	0.145476i	−0.483152	+	0.875536i	$0.660508\pi$
$174$	−0.788042	−	5.21152i	−0.0597413	−	0.395084i
$175$	−10.7477	+	7.71282i	−0.812448	+	0.583034i
$176$		−	18.9506i		−	1.42845i
$177$	−0.151412	+	0.292086i	−0.0113808	+	0.0219545i
$178$	1.97048	−	0.640249i	0.147694	−	0.0479887i
$179$	−19.2319	+	6.24882i	−1.43746	+	0.467059i	−0.921105	−	0.389315i	$-0.872712\pi$
$179$	−19.2319	+	6.24882i	−1.43746	+	0.467059i	−0.516355	+	0.856374i	$0.672712\pi$
$180$	7.97613	+	2.30192i	0.594506	+	0.171575i
$181$	−4.97852	−	1.61762i	−0.370051	−	0.120237i	0.118087	−	0.993003i	$-0.462324\pi$
$181$	−4.97852	−	1.61762i	−0.370051	−	0.120237i	−0.488138	+	0.872766i	$0.662324\pi$
$182$	−26.6676	+	15.5554i	−1.97674	+	1.15304i
$183$	−0.0138617	+	0.0837197i	−0.00102469	+	0.00618874i
$184$	−9.63030	+	6.99682i	−0.709955	+	0.515812i
$185$	9.21025	−	7.37999i	0.677151	−	0.542587i
$186$	10.3330	−	19.9333i	0.757655	−	1.46158i
$187$	6.12154	+	8.42558i	0.447651	+	0.616139i
$188$	−9.46294	+	6.87523i	−0.690156	+	0.501428i
$189$	4.71354	+	12.9144i	0.342860	+	0.939387i
$190$	9.15441	−	7.33525i	0.664131	−	0.532155i
$191$	13.9862	+	19.2503i	1.01201	+	1.39291i	0.917660	+	0.397366i	$0.130076\pi$
$191$	13.9862	+	19.2503i	1.01201	+	1.39291i	0.0943454	+	0.995540i	$0.469924\pi$
$192$	−2.01784	−	0.334101i	−0.145625	−	0.0241117i
$193$	2.94099			0.211697			0.105849	−	0.994382i	$-0.466244\pi$
$193$	2.94099			0.211697			0.105849	+	0.994382i	$0.466244\pi$
$194$	−0.212947	+	0.655385i	−0.0152887	+	0.0470539i
$195$	22.8195	+	10.4943i	1.63414	+	0.751510i
$196$	−8.48918	−	1.72552i	−0.606370	−	0.123251i
$197$	−9.74661	+	3.16687i	−0.694417	+	0.225630i	−0.634897	−	0.772597i	$-0.718957\pi$
$197$	−9.74661	+	3.16687i	−0.694417	+	0.225630i	−0.0595209	+	0.998227i	$0.518957\pi$
$198$	19.5881	+	6.66935i	1.39206	+	0.473970i
$199$			20.9472i			1.48491i	0.669896	+	0.742455i	$0.266339\pi$
$199$			20.9472i			1.48491i	−0.669896	+	0.742455i	$0.733661\pi$
$200$	−6.69458	−	1.49532i	−0.473379	−	0.105735i
$201$	−0.803432	−	5.31330i	−0.0566697	−	0.374771i
$202$	6.99998	−	9.63465i	0.492517	−	0.677892i
$203$	2.97925	−	3.33858i	0.209102	−	0.234323i
$204$	5.20713	−	2.60738i	0.364572	−	0.182553i
$205$	3.85061	−	3.08542i	0.268938	−	0.215495i
$206$	3.93666	−	12.1158i	0.274280	−	0.844147i
$207$	−7.69617	−	24.8665i	−0.534921	−	1.72834i
$208$	−30.4907	−	9.90703i	−2.11415	−	0.686929i
$209$	9.04211	−	6.56947i	0.625455	−	0.454420i
$210$	7.36917	+	16.9008i	0.508521	+	1.16627i
$211$	−21.0835	−	15.3181i	−1.45145	−	1.05454i	−0.985489	−	0.169736i	$-0.945708\pi$
$211$	−21.0835	−	15.3181i	−1.45145	−	1.05454i	−0.465962	−	0.884805i	$-0.654292\pi$
$212$	−4.63251	−	6.37611i	−0.318162	−	0.437913i
$213$	−0.182170	+	0.179636i	−0.0124821	+	0.0123085i
$214$	14.2989	+	10.3888i	0.977453	+	0.710161i
$215$	19.0753	−	0.901068i	1.30093	−	0.0614523i
$216$	−3.36910	+	6.28227i	−0.229238	+	0.427454i
$217$	18.6265	−	4.04600i	1.26445	−	0.274660i
$218$			13.4012i			0.907647i
$219$	−1.37300	+	8.29238i	−0.0927785	+	0.560347i
$220$	10.2320	+	2.79830i	0.689843	+	0.188662i
$221$	16.7567	−	5.44457i	1.12718	−	0.366241i
$222$	−7.36498	−	14.7084i	−0.494305	−	0.987162i
$223$	8.19237	−	11.2758i	0.548602	−	0.755086i	−0.441220	−	0.897399i	$-0.645454\pi$
$223$	8.19237	−	11.2758i	0.548602	−	0.755086i	0.989822	+	0.142313i	$0.0454541\pi$
$224$	−8.20003	−	14.0579i	−0.547888	−	0.939280i
$225$	7.81374	−	12.8041i	0.520916	−	0.853608i
$226$	−15.6372			−1.04017
$227$	18.4037	+	13.3710i	1.22149	+	0.887467i	0.996223	−	0.0868294i	$-0.0276735\pi$
$227$	18.4037	+	13.3710i	1.22149	+	0.887467i	0.225270	+	0.974296i	$0.427674\pi$
$228$	−2.79817	−	5.58815i	−0.185313	−	0.370084i
$229$	2.39404	−	0.777870i	0.158203	−	0.0514031i	−0.228845	−	0.973463i	$-0.573495\pi$
$229$	2.39404	−	0.777870i	0.158203	−	0.0514031i	0.387048	+	0.922060i	$0.373495\pi$
$230$	−12.3423	−	32.6553i	−0.813830	−	2.15323i
$231$	6.25351	+	16.4159i	0.411451	+	1.08009i
$232$	2.32023			0.152331
$233$	0.145349	+	0.0472269i	0.00952215	+	0.00309393i	0.313774	−	0.949498i	$-0.398407\pi$
$233$	0.145349	+	0.0472269i	0.00952215	+	0.00309393i	−0.304252	+	0.952592i	$0.598407\pi$
$234$	20.9710	−	28.0298i	1.37092	−	1.83237i
$235$	7.47212	+	19.7697i	0.487427	+	1.28963i
$236$	0.190173	+	0.138169i	0.0123792	+	0.00899402i
$237$	1.81490	+	1.84051i	0.117891	+	0.119554i
$238$	11.8387	+	5.20786i	0.767389	+	0.337575i
$239$	−5.07129	+	6.98004i	−0.328035	+	0.451501i	−0.940899	−	0.338687i	$-0.890017\pi$
$239$	−5.07129	+	6.98004i	−0.328035	+	0.451501i	0.612864	+	0.790188i	$0.290017\pi$
$240$	−7.99969	+	17.3951i	−0.516378	+	1.12285i
$241$	−2.45943	−	3.38511i	−0.158426	−	0.218054i	0.722424	−	0.691450i	$-0.243028\pi$
$241$	−2.45943	−	3.38511i	−0.158426	−	0.218054i	−0.880850	+	0.473396i	$0.843028\pi$
$242$	6.32260	+	2.05434i	0.406432	+	0.132058i
$243$	−10.6300	−	11.4019i	−0.681912	−	0.731434i
$244$	0.0576640	+	0.0187362i	0.00369156	+	0.00119946i
$245$	−7.05369	+	13.9730i	−0.450644	+	0.892704i
$246$	−3.07914	−	6.14927i	−0.196319	−	0.392063i
$247$	−5.84297	−	17.9828i	−0.371779	−	1.14422i
$248$	7.99607	+	5.80949i	0.507751	+	0.368903i
$249$	3.18913	+	21.0905i	0.202103	+	1.33656i
$250$	9.40915	−	17.7809i	0.595087	−	1.12456i
$251$	24.7536			1.56243			0.781217	−	0.624260i	$-0.214599\pi$
$251$	24.7536			1.56243			0.781217	+	0.624260i	$0.214599\pi$
$252$	9.62708	−	1.95035i	0.606449	−	0.122861i
$253$	−10.2783	−	31.6332i	−0.646188	−	1.98876i
$254$	−10.5356	+	3.42323i	−0.661063	+	0.214793i
$255$	−2.06235	−	10.3181i	−0.129149	−	0.646146i
$256$	6.38882	−	19.6628i	0.399301	−	1.22892i
$257$	3.71383			0.231662			0.115831	−	0.993269i	$-0.463047\pi$
$257$	3.71383			0.231662			0.115831	+	0.993269i	$0.463047\pi$
$258$	4.34767	−	26.2583i	0.270674	−	1.63477i
$259$	5.62302	−	12.7825i	0.349398	−	0.794264i
$260$	9.85149	−	15.0000i	0.610964	−	0.930262i
$261$	−1.63531	+	4.80296i	−0.101223	+	0.297296i
$262$	4.68714	+	6.45129i	0.289572	+	0.398562i
$263$	12.3699	+	17.0257i	0.762759	+	1.04985i	0.996980	+	0.0776648i	$0.0247464\pi$
$263$	12.3699	+	17.0257i	0.762759	+	1.04985i	−0.234220	+	0.972184i	$0.575254\pi$
$264$	−4.19211	+	8.08694i	−0.258007	+	0.497717i
$265$	−13.3208	+	5.03469i	−0.818289	+	0.309279i
$266$	5.58893	−	12.7050i	0.342680	−	0.778993i
$267$	−1.96765	−	0.325790i	−0.120418	−	0.0199380i
$268$	−3.83947			−0.234533
$269$	7.54932	−	23.2344i	0.460290	−	1.41663i	−0.404520	−	0.914529i	$-0.632561\pi$
$269$	7.54932	−	23.2344i	0.460290	−	1.41663i	0.864810	−	0.502099i	$-0.167439\pi$
$270$	−15.1649	−	14.3907i	−0.922907	−	0.875793i
$271$	11.9066	−	3.86869i	0.723274	−	0.235006i	0.0758320	−	0.997121i	$-0.475839\pi$
$271$	11.9066	−	3.86869i	0.723274	−	0.235006i	0.647442	+	0.762115i	$0.275839\pi$
$272$	4.15035	+	12.7735i	0.251652	+	0.774505i
$273$	29.6818	−	1.47968i	1.79643	−	0.0895542i
$274$	8.10141			0.489424
$275$	9.75413	−	16.4992i	0.588196	−	0.994942i
$276$	−18.3894	+	2.78068i	−1.10691	+	0.167377i
$277$	−9.18493	−	6.67324i	−0.551869	−	0.400956i	0.276605	−	0.960984i	$-0.410791\pi$
$277$	−9.18493	−	6.67324i	−0.551869	−	0.400956i	−0.828474	+	0.560028i	$0.810791\pi$
$278$	10.5022	+	32.3223i	0.629878	+	1.93857i
$279$	−17.6615	+	12.4576i	−1.05737	+	0.745816i
$280$	−7.84125	+	2.09515i	−0.468604	+	0.125209i
$281$	−13.1640	−	4.27723i	−0.785296	−	0.255158i	−0.111196	−	0.993798i	$-0.535468\pi$
$281$	−13.1640	−	4.27723i	−0.785296	−	0.255158i	−0.674100	+	0.738640i	$0.735468\pi$
$282$	29.1252	−	4.40407i	1.73438	−	0.262258i
$283$	6.51920	+	2.11822i	0.387526	+	0.125915i	0.496299	−	0.868152i	$-0.334692\pi$
$283$	6.51920	+	2.11822i	0.387526	+	0.125915i	−0.108773	+	0.994067i	$0.534692\pi$
$284$	0.107446	+	0.147886i	0.00637572	+	0.00877543i
$285$	−11.0731	+	2.21326i	−0.655916	+	0.131102i
$286$	26.2922	−	36.1881i	1.55469	−	2.13985i
$287$	2.35087	−	5.34409i	0.138767	−	0.315451i
$288$	14.7759	+	11.0549i	0.870680	+	0.651416i
$289$	7.78183	+	5.65383i	0.457755	+	0.332578i
$290$	−1.79502	+	6.56349i	−0.105407	+	0.385422i
$291$	0.472334	−	0.465762i	0.0276887	−	0.0273035i
$292$	5.71158	+	1.85581i	0.334245	+	0.108603i
$293$	25.7327			1.50332			0.751660	−	0.659551i	$-0.229254\pi$
$293$	25.7327			1.50332			0.751660	+	0.659551i	$0.229254\pi$
$294$	16.9800	+	13.6966i	0.990293	+	0.798804i
$295$	0.331455	−	0.265588i	0.0192981	−	0.0154631i
$296$	6.88670	−	2.23763i	0.400282	−	0.130059i
$297$	−13.7856	−	14.3776i	−0.799923	−	0.834270i
$298$	24.3010	+	17.6557i	1.40772	+	1.02277i
$299$	−56.2699			−3.25417
$300$	−8.21092	−	6.88792i	−0.474057	−	0.397674i
$301$	19.5177	−	11.3848i	1.12498	−	0.656207i
$302$	−18.5799	+	25.5731i	−1.06916	+	1.47157i
$303$	−10.2506	+	5.13281i	−0.588881	+	0.294872i
$304$	13.7081	−	4.45405i	0.786216	−	0.255457i
$305$	0.0601400	−	0.0915700i	0.00344361	−	0.00524329i
$306$	−14.6638	−	0.205452i	−0.838275	−	0.0117449i
$307$		−	10.2409i		−	0.584478i	−0.956345	−	0.292239i	$-0.905600\pi$
$307$		−	10.2409i		−	0.584478i	0.956345	−	0.292239i	$-0.0944002\pi$
$308$	12.2653	−	2.66423i	0.698878	−	0.151809i
$309$	−8.73182	+	8.61033i	−0.496736	+	0.489825i
$310$	−22.6200	+	18.1250i	−1.28473	+	1.02943i
$311$	−5.82425	−	4.23156i	−0.330263	−	0.239950i	0.410279	−	0.911960i	$-0.365431\pi$
$311$	−5.82425	−	4.23156i	−0.330263	−	0.239950i	−0.740542	+	0.672010i	$0.765431\pi$
$312$	10.8200	+	10.9727i	0.612562	+	0.621205i
$313$	5.77397	+	7.94719i	0.326364	+	0.449202i	0.940397	−	0.340079i	$-0.110454\pi$
$313$	5.77397	+	7.94719i	0.326364	+	0.449202i	−0.614033	+	0.789281i	$0.710454\pi$
$314$	2.07600	+	1.50830i	0.117155	+	0.0851184i
$315$	1.18952	−	17.7083i	0.0670220	−	0.997751i
$316$	1.49413	−	1.08555i	0.0840512	−	0.0610668i
$317$	−7.33671	−	2.38384i	−0.412071	−	0.133890i	0.0956431	−	0.995416i	$-0.469509\pi$
$317$	−7.33671	−	2.38384i	−0.412071	−	0.133890i	−0.507714	+	0.861526i	$0.669509\pi$
$318$	2.96745	+	19.6245i	0.166406	+	1.10049i
$319$	−2.00340	+	6.16584i	−0.112169	+	0.345221i
$320$	2.20706	+	1.44952i	0.123378	+	0.0810305i
$321$	−7.61767	−	15.2130i	−0.425177	−	0.849109i
$322$	−30.8192	−	27.5021i	−1.71748	−	1.53263i
$323$	−4.65598	+	6.40841i	−0.259066	+	0.356573i
$324$	−9.19058	+	6.29164i	−0.510588	+	0.349536i
$325$	−21.4473	−	24.3196i	−1.18968	−	1.34901i
$326$			27.1829i			1.50552i
$327$	5.93697	−	11.4529i	0.328315	−	0.633347i
$328$	2.87919	−	0.935505i	0.158977	−	0.0516546i
$329$	18.6581	+	16.6499i	1.02865	+	0.917938i
$330$	−19.6333	−	18.1151i	−1.08078	−	0.997202i
$331$	−4.62680	+	14.2398i	−0.254312	+	0.782692i	0.739652	+	0.672989i	$0.234990\pi$
$331$	−4.62680	+	14.2398i	−0.254312	+	0.782692i	−0.993964	+	0.109703i	$0.965010\pi$
$332$	15.2403			0.836421
$333$	−0.221830	+	15.8328i	−0.0121562	+	0.867633i
$334$	−10.3701	−	14.2733i	−0.567429	−	0.780998i
$335$	−1.83007	+	6.69168i	−0.0999875	+	0.365605i
$336$	1.12795	+	22.6262i	0.0615345	+	1.23436i
$337$	24.0334	−	17.4613i	1.30918	−	0.951176i	0.309182	−	0.951003i	$-0.399945\pi$
$337$	24.0334	−	17.4613i	1.30918	−	0.951176i	1.00000		0.000173133i	$-5.51101e-5\pi$
$338$	−30.7312	−	42.2979i	−1.67156	−	2.30070i
$339$	13.3638	+	6.92753i	0.725821	+	0.376252i
$340$	−7.50967	+	0.354737i	−0.407269	+	0.0192383i
$341$	−22.3425	+	16.2328i	−1.20991	+	0.879054i
$342$	−0.220486	+	15.7368i	−0.0119225	+	0.850950i
$343$	0.247523	+	18.5186i	0.0133650	+	0.999911i
$344$	11.1430	+	3.62059i	0.600792	+	0.195209i
$345$	−3.91888	+	33.3756i	−0.210985	+	1.79688i
$346$	−5.57069	+	1.81003i	−0.299482	+	0.0973077i
$347$	22.4033	−	7.27926i	1.20267	−	0.390771i	0.361927	−	0.932206i	$-0.382119\pi$
$347$	22.4033	−	7.27926i	1.20267	−	0.390771i	0.840743	+	0.541435i	$0.182119\pi$
$348$	3.21841	+	1.66836i	0.172525	+	0.0894337i
$349$		−	0.733921i		−	0.0392859i	−0.999807	−	0.0196429i	$-0.993747\pi$
$349$		−	0.733921i		−	0.0392859i	0.999807	−	0.0196429i	$-0.00625294\pi$
$350$	0.139487	−	23.8023i	0.00745587	−	1.27229i
$351$	−30.3398	+	14.6642i	−1.61942	+	0.782717i
$352$	19.0766	+	13.8600i	1.01679	+	0.738738i
$353$	2.10697	+	6.48460i	0.112143	+	0.345140i	0.991340	−	0.131317i	$-0.0419206\pi$
$353$	2.10697	+	6.48460i	0.112143	+	0.345140i	−0.879197	+	0.476458i	$0.841921\pi$
$354$	−0.265048	−	0.529320i	−0.0140871	−	0.0281330i
$355$	0.308959	−	0.116774i	0.0163979	−	0.00619770i
$356$	−0.440352	+	1.35526i	−0.0233386	+	0.0718289i
$357$	−7.81037	−	9.69545i	−0.413369	−	0.513138i
$358$	11.2436	−	34.6043i	0.594243	−	1.82889i
$359$	0.692905	+	0.953702i	0.0365701	+	0.0503345i	0.826911	−	0.562334i	$-0.190096\pi$
$359$	0.692905	+	0.953702i	0.0365701	+	0.0503345i	−0.790340	+	0.612668i	$0.790096\pi$
$360$	7.26181	−	5.65352i	0.382731	−	0.297967i
$361$	−8.49399	−	6.17124i	−0.447052	−	0.324802i
$362$	7.62008	−	5.53631i	0.400502	−	0.290982i
$363$	−4.49328	−	4.55668i	−0.235836	−	0.239164i
$364$	2.12543	−	21.1272i	0.111403	−	1.10736i
$365$	5.95683	−	9.06996i	0.311795	−	0.474743i
$366$	−0.107209	−	0.108721i	−0.00560388	−	0.00568294i
$367$	6.58674	+	2.14016i	0.343825	+	0.111716i	0.475839	−	0.879532i	$-0.342144\pi$
$367$	6.58674	+	2.14016i	0.343825	+	0.111716i	−0.132014	+	0.991248i	$0.542144\pi$
$368$		−	42.8941i		−	2.23601i
$369$	−0.0927427	+	6.61937i	−0.00482799	+	0.344591i
$370$	1.00201	+	21.2123i	0.0520922	+	1.10278i
$371$	−11.2187	+	12.5718i	−0.582444	+	0.652694i
$372$	6.91411	+	13.8080i	0.358480	+	0.715911i
$373$	−16.8940	−	12.2742i	−0.874740	−	0.635536i	0.0571145	−	0.998368i	$-0.481810\pi$
$373$	−16.8940	−	12.2742i	−0.874740	−	0.635536i	−0.931855	+	0.362832i	$0.881810\pi$
$374$	−18.7391			−0.968977
$375$	−15.9184	+	11.0274i	−0.822024	+	0.569453i
$376$			12.9669i			0.668716i
$377$	8.87325	+	6.44680i	0.456996	+	0.332027i
$378$	−23.7843	−	6.79705i	−1.22333	−	0.349603i
$379$	7.95667	+	24.4881i	0.408706	+	1.25787i	0.917760	+	0.397135i	$0.129995\pi$
$379$	7.95667	+	24.4881i	0.408706	+	1.25787i	−0.509054	+	0.860735i	$0.670005\pi$
$380$	0.380694	+	8.05918i	0.0195292	+	0.413427i
$381$	10.5204	+	1.74190i	0.538979	+	0.0892404i
$382$	−42.8142			−2.19057
$383$	1.70316	−	5.24179i	0.0870275	−	0.267843i	−0.898067	−	0.439860i	$-0.855028\pi$
$383$	1.70316	−	5.24179i	0.0870275	−	0.267843i	0.985094	+	0.172016i	$0.0550282\pi$
$384$	−12.5521	+	12.3775i	−0.640548	+	0.631636i
$385$	1.20281	−	22.6466i	0.0613010	−	1.15418i
$386$	−3.11043	+	4.28114i	−0.158317	+	0.217904i
$387$	−15.3484	+	20.5146i	−0.780204	+	1.04282i
$388$	−0.278586	−	0.383441i	−0.0141431	−	0.0194663i
$389$	5.07057	−	6.97904i	0.257088	−	0.353851i	−0.660890	−	0.750483i	$-0.729821\pi$
$389$	5.07057	−	6.97904i	0.257088	−	0.353851i	0.917978	+	0.396632i	$0.129821\pi$
$390$	−39.4104	+	22.1189i	−1.99562	+	1.12003i
$391$	13.8560	+	19.0711i	0.700726	+	0.964466i
$392$	−7.07916	+	6.48924i	−0.357551	+	0.327756i
$393$	−1.14767	−	7.58985i	−0.0578925	−	0.382857i
$394$	5.69819	−	17.5372i	0.287071	−	0.883513i
$395$	−1.17979	−	3.12149i	−0.0593617	−	0.157059i
$396$	−11.6298	+	8.20313i	−0.584422	+	0.412223i
$397$	22.4199	−	7.28468i	1.12522	−	0.365608i	0.313465	−	0.949600i	$-0.398510\pi$
$397$	22.4199	−	7.28468i	1.12522	−	0.365608i	0.811759	+	0.583992i	$0.198510\pi$
$398$	−30.4924	−	22.1540i	−1.52845	−	1.11048i
$399$	−10.4049	+	8.38188i	−0.520896	+	0.419619i
$400$	18.5386	−	16.3491i	0.926930	−	0.817457i
$401$		−	22.4582i		−	1.12151i	−0.827982	−	0.560755i	$-0.810511\pi$
$401$		−	22.4582i		−	1.12151i	0.827982	−	0.560755i	$-0.189489\pi$
$402$	8.58416	+	4.44986i	0.428139	+	0.221939i
$403$	14.4376	+	44.4344i	0.719189	+	2.21344i
$404$	2.53111	+	7.78997i	0.125928	+	0.387565i
$405$	6.58483	+	19.0168i	0.327203	+	0.944954i
$406$	1.70901	+	7.86775i	0.0848168	+	0.390470i
$407$			20.2330i			1.00291i
$408$	1.05454	−	6.36905i	0.0522077	−	0.315315i
$409$	−3.68781	−	5.07583i	−0.182350	−	0.250984i	0.708050	−	0.706163i	$-0.249575\pi$
$409$	−3.68781	−	5.07583i	−0.182350	−	0.250984i	−0.890400	+	0.455179i	$0.849575\pi$
$410$	0.418921	+	8.86842i	0.0206890	+	0.437980i
$411$	−6.92358	−	3.58905i	−0.341515	−	0.177035i
$412$	5.15010	+	7.08850i	0.253727	+	0.349225i
$413$	0.202359	−	0.460011i	0.00995745	−	0.0226357i
$414$	44.3371	+	15.0959i	2.17905	+	0.741924i
$415$	7.26425	−	26.5618i	0.356588	−	1.30387i
$416$	32.2730	−	23.4477i	1.58232	−	1.14962i
$417$	5.34401	−	32.2758i	0.261697	−	1.58055i
$418$			20.1103i			0.983629i
$419$	−2.24873	+	6.92087i	−0.109857	+	0.338106i	−0.990840	−	0.135043i	$-0.956883\pi$
$419$	−2.24873	+	6.92087i	−0.109857	+	0.338106i	0.880982	+	0.473149i	$0.156883\pi$
$420$	−12.3832	−	2.73205i	−0.604238	−	0.133310i
$421$	−0.320699	−	0.987010i	−0.0156299	−	0.0481039i	0.942937	−	0.332970i	$-0.108051\pi$
$421$	−0.320699	−	0.987010i	−0.0156299	−	0.0481039i	−0.958567	+	0.284866i	$0.908051\pi$
$422$	44.5964	−	14.4903i	2.17092	−	0.705374i
$423$	−26.8419	−	9.13915i	−1.30510	−	0.444361i
$424$	−8.73706			−0.424309
$425$	−2.96121	+	13.2574i	−0.143640	+	0.643080i
$426$	−0.0688264	−	0.455166i	−0.00333465	−	0.0220529i
$427$	0.0129750	−	0.128974i	0.000627906	−	0.00624149i
$428$	−11.5612	+	3.75646i	−0.558831	+	0.181575i
$429$	−38.5016	+	19.2790i	−1.85888	+	0.930800i
$430$	−18.8626	+	28.7205i	−0.909637	+	1.38503i
$431$	−25.9978	−	8.44719i	−1.25227	−	0.406887i	−0.393535	−	0.919310i	$-0.628748\pi$
$431$	−25.9978	−	8.44719i	−1.25227	−	0.406887i	−0.858733	+	0.512423i	$0.828748\pi$
$432$	−11.1784	−	23.1278i	−0.537821	−	1.11274i
$433$	−24.0497	−	7.81421i	−1.15575	−	0.375527i	−0.332445	−	0.943123i	$-0.607874\pi$
$433$	−24.0497	−	7.81421i	−1.15575	−	0.375527i	−0.823307	+	0.567596i	$0.807874\pi$
$434$	−13.8099	+	31.3933i	−0.662898	+	1.50692i
$435$	4.44178	−	4.81404i	0.212967	−	0.230816i
$436$	−7.45683	−	5.41770i	−0.357117	−	0.259461i
$437$	20.4666	−	14.8698i	0.979049	−	0.711321i
$438$	−10.6189	−	10.7688i	−0.507392	−	0.514551i
$439$	9.29403	−	12.7921i	0.443580	−	0.610535i	−0.527423	−	0.849603i	$-0.676842\pi$
$439$	9.29403	−	12.7921i	0.443580	−	0.610535i	0.971003	+	0.239067i	$0.0768417\pi$
$440$	9.17695	−	7.35330i	0.437494	−	0.350555i
$441$	−8.44353	−	19.2278i	−0.402073	−	0.915608i
$442$	−9.79650	+	30.1505i	−0.465972	+	1.43411i
$443$		−	16.5256i		−	0.785153i	−0.919719	−	0.392576i	$-0.871584\pi$
$443$		−	16.5256i		−	0.785153i	0.919719	−	0.392576i	$-0.128416\pi$
$444$	11.1616	+	1.84806i	0.529705	+	0.0877050i
$445$	2.15215	+	1.41346i	0.102022	+	0.0670043i
$446$	7.74963	+	23.8509i	0.366956	+	1.12937i
$447$	−12.9462	−	25.8546i	−0.612336	−	1.22288i
$448$	3.10858	+	0.312729i	0.146867	+	0.0147751i
$449$		−	21.7580i		−	1.02682i	−0.858143	−	0.513411i	$-0.828382\pi$
$449$		−	21.7580i		−	1.02682i	0.858143	−	0.513411i	$-0.171618\pi$
$450$	10.3748	+	24.9161i	0.489071	+	1.17455i
$451$			8.45899i			0.398318i
$452$	6.32162	−	8.70097i	0.297344	−	0.409259i
$453$	27.2080	−	13.6239i	1.27834	−	0.640109i
$454$	−38.9278	+	12.6484i	−1.82697	+	0.593620i
$455$	−35.8087	−	13.7745i	−1.67874	−	0.645760i
$456$	−6.83510	−	1.13171i	−0.320083	−	0.0529971i
$457$	7.85790			0.367577			0.183788	−	0.982966i	$-0.441164\pi$
$457$	7.85790			0.367577			0.183788	+	0.982966i	$0.441164\pi$
$458$	−1.39963	+	4.30763i	−0.0654006	+	0.201282i
$459$	12.4409	+	6.67189i	0.580692	+	0.311417i
$460$	23.1599	+	6.33389i	1.07984	+	0.295319i
$461$	−2.89719	−	2.10493i	−0.134935	−	0.0980363i	0.518270	−	0.855217i	$-0.326576\pi$
$461$	−2.89719	−	2.10493i	−0.134935	−	0.0980363i	−0.653205	+	0.757181i	$0.726576\pi$
$462$	−30.5101	−	8.25859i	−1.41946	−	0.384224i
$463$	−27.6849	+	20.1142i	−1.28662	+	0.934788i	−0.999731	−	0.0231750i	$-0.992623\pi$
$463$	−27.6849	+	20.1142i	−1.28662	+	0.934788i	−0.286893	+	0.957963i	$0.592623\pi$
$464$	−4.91434	+	6.76401i	−0.228142	+	0.314011i
$465$	27.3610	−	5.46883i	1.26884	−	0.253611i
$466$	−0.222470	+	0.161634i	−0.0103057	+	0.00748755i
$467$	1.23058	−	3.78733i	0.0569444	−	0.175257i	−0.918539	−	0.395331i	$-0.870630\pi$
$467$	1.23058	−	3.78733i	0.0569444	−	0.175257i	0.975483	+	0.220074i	$0.0706299\pi$
$468$	7.11863	+	23.0004i	0.329059	+	1.06320i
$469$	1.74239	+	8.02140i	0.0804560	+	0.370394i
$470$	−36.6809	−	10.0317i	−1.69196	−	0.462726i
$471$	−1.10598	−	2.20872i	−0.0509608	−	0.101772i
$472$	0.247836	−	0.0805268i	0.0114076	−	0.00370655i
$473$	−19.2429	+	26.4856i	−0.884790	+	1.21781i
$474$	−4.59865	+	0.695369i	−0.211223	+	0.0319394i
$475$	14.2275	+	3.17789i	0.652803	+	0.145811i
$476$	−7.68381	+	4.48201i	−0.352187	+	0.205433i
$477$	6.15794	−	18.0860i	0.281953	−	0.828102i
$478$	−4.79722	−	14.7643i	−0.219420	−	0.675305i
$479$	0.976231	+	3.00453i	0.0446051	+	0.137280i	0.970879	−	0.239571i	$-0.0770068\pi$
$479$	0.976231	+	3.00453i	0.0446051	+	0.137280i	−0.926274	+	0.376851i	$0.877007\pi$
$480$	−11.6600	−	20.7752i	−0.532204	−	0.948255i
$481$	32.5541	+	10.5775i	1.48434	+	0.482291i
$482$	7.52875			0.342925
$483$	14.1547	+	37.1571i	0.644059	+	1.69070i
$484$	−3.69912	+	2.68757i	−0.168142	+	0.122162i
$485$	−0.801074	+	0.302772i	−0.0363749	+	0.0137482i
$486$	27.8399	−	3.41497i	1.26284	−	0.154906i
$487$	11.8744	−	8.62728i	0.538082	−	0.390939i	−0.285290	−	0.958441i	$-0.592090\pi$
$487$	11.8744	−	8.62728i	0.538082	−	0.390939i	0.823372	+	0.567502i	$0.192090\pi$
$488$	0.0543780	−	0.0395079i	0.00246158	−	0.00178844i
$489$	12.0425	−	23.2309i	0.544579	−	1.05054i
$490$	−12.8802	−	25.0459i	−0.581866	−	1.13146i
$491$	16.9919	+	23.3874i	0.766834	+	1.05546i	0.996615	+	0.0822144i	$0.0261992\pi$
$491$	16.9919	+	23.3874i	0.766834	+	1.05546i	−0.229780	+	0.973243i	$0.573801\pi$
$492$	4.66643	+	0.772635i	0.210379	+	0.0348331i
$493$		−	4.59480i		−	0.206939i
$494$	32.3568	+	10.5133i	1.45580	+	0.473018i
$495$	8.75362	+	24.1793i	0.393446	+	1.08678i
$496$	−33.8720	+	11.0057i	−1.52090	+	0.494170i
$497$	0.260203	−	0.291587i	0.0116717	−	0.0130795i
$498$	−34.0738	−	17.6632i	−1.52688	−	0.791507i
$499$	−8.13877			−0.364342			−0.182171	−	0.983267i	$-0.558312\pi$
$499$	−8.13877			−0.364342			−0.182171	+	0.983267i	$0.558312\pi$
$500$	6.08996	+	12.4238i	0.272351	+	0.555608i
$501$	2.53919	+	16.7923i	0.113443	+	0.750224i
$502$	−26.1797	+	36.0332i	−1.16846	+	1.60824i
$503$	−13.2512	−	40.7830i	−0.590841	−	1.81842i	−0.574425	−	0.818557i	$-0.694774\pi$
$503$	−13.2512	−	40.7830i	−0.590841	−	1.81842i	−0.0164166	−	0.999865i	$-0.505226\pi$
$504$	4.52388	−	9.90501i	0.201510	−	0.441204i
$505$	14.7833	−	0.698324i	0.657849	−	0.0310750i
$506$	56.9182	+	18.4938i	2.53032	+	0.822151i
$507$	7.52471	+	49.7628i	0.334184	+	2.21004i
$508$	2.35444	−	7.24621i	0.104461	−	0.321499i
$509$	16.8226	−	12.2224i	0.745650	−	0.541746i	−0.148826	−	0.988863i	$-0.547549\pi$
$509$	16.8226	−	12.2224i	0.745650	−	0.541746i	0.894475	+	0.447117i	$0.147549\pi$
$510$	17.2010	+	7.91044i	0.761674	+	0.350280i
$511$	1.28517	−	12.7748i	0.0568526	−	0.565124i
$512$	9.90113	+	13.6277i	0.437572	+	0.602267i
$513$	7.16010	−	13.3513i	0.316126	−	0.589472i
$514$	−3.92779	+	5.40614i	−0.173247	+	0.238454i
$515$	14.8091	−	5.59721i	0.652566	−	0.246643i
$516$	12.8532	+	13.0346i	0.565831	+	0.573815i
$517$	−34.4586	−	11.1963i	−1.51549	−	0.492411i
$518$	12.6602	+	21.7042i	0.556257	+	0.953628i
$519$	5.56267	+	0.921029i	0.244174	+	0.0404287i
$520$	−7.03362	−	18.6095i	−0.308445	−	0.816082i
$521$	−5.05631	−	15.5617i	−0.221521	−	0.681772i	−0.998626	−	0.0524008i	$-0.983313\pi$
$521$	−5.05631	−	15.5617i	−0.221521	−	0.681772i	0.777105	−	0.629371i	$-0.216687\pi$
$522$	−5.26203	−	7.46015i	−0.230313	−	0.326522i
$523$	14.0872	−	19.3894i	0.615990	−	0.847837i	−0.381064	−	0.924549i	$-0.624442\pi$
$523$	14.0872	−	19.3894i	0.615990	−	0.847837i	0.997053	+	0.0767117i	$0.0244421\pi$
$524$	−5.48454			−0.239593
$525$	−10.6640	+	20.2800i	−0.465415	+	0.885092i
$526$	−37.8664			−1.65105
$527$	11.5047	−	15.8348i	0.501150	−	0.689774i
$528$	−14.6962	−	29.3495i	−0.639572	−	1.27727i
$529$	−16.1572	−	49.7267i	−0.702486	−	2.16203i
$530$	6.75931	−	24.7155i	0.293606	−	1.07357i
$531$	−0.00798315	+	0.569785i	−0.000346439	+	0.0247266i
$532$	4.80998	+	8.24606i	0.208539	+	0.357512i
$533$	13.6102	+	4.42222i	0.589523	+	0.191548i
$534$	2.55525	−	2.51970i	0.110576	−	0.109038i
$535$	1.03639	+	21.9401i	0.0448071	+	0.948553i
$536$	−2.50182	+	3.44347i	−0.108062	+	0.148735i
$537$	−24.9392	+	24.5922i	−1.07621	+	1.06123i
$538$	25.8376	+	35.5624i	1.11394	+	1.53320i
$539$	−11.1322	−	24.4155i	−0.479497	−	1.05165i
$540$	14.1381	−	2.62045i	0.608407	−	0.112766i
$541$	7.02143	−	5.10137i	0.301875	−	0.219325i	−0.426527	−	0.904475i	$-0.640263\pi$
$541$	7.02143	−	5.10137i	0.301875	−	0.219325i	0.728402	+	0.685150i	$0.240263\pi$
$542$	−6.96099	+	21.4237i	−0.299000	+	0.920228i
$543$	−8.96490	+	1.35560i	−0.384721	+	0.0581743i
$544$	−15.8939	−	5.16423i	−0.681444	−	0.221415i
$545$	−12.9966	+	10.4139i	−0.556713	+	0.446083i
$546$	−29.2379	+	44.7721i	−1.25127	+	1.91607i
$547$	13.3482	+	41.0816i	0.570729	+	1.75652i	0.650283	+	0.759692i	$0.274650\pi$
$547$	13.3482	+	41.0816i	0.570729	+	1.75652i	−0.0795540	+	0.996831i	$0.525350\pi$
$548$	−3.27514	+	4.50785i	−0.139907	+	0.192566i
$549$	0.0434568	+	0.140410i	0.00185469	+	0.00599254i
$550$	13.7015	+	31.6487i	0.584233	+	1.34950i
$551$	−4.93102			−0.210068
$552$	−9.48875	+	18.3046i	−0.403868	+	0.779095i
$553$	−2.94597	−	2.62889i	−0.125275	−	0.111792i
$554$	19.4282	−	6.31259i	0.825424	−	0.268196i
$555$	8.54106	−	18.5723i	0.362548	−	0.788349i
$556$	−22.2307	−	7.22321i	−0.942794	−	0.306332i
$557$		−	4.05652i		−	0.171880i	−0.996300	−	0.0859400i	$-0.972611\pi$
$557$		−	4.05652i		−	0.171880i	0.996300	−	0.0859400i	$-0.0273893\pi$
$558$	0.544807	−	38.8848i	0.0230635	−	1.64612i
$559$	32.5544	+	44.8073i	1.37691	+	1.89515i
$560$	10.5002	−	27.2967i	0.443715	−	1.15349i
$561$	16.0147	+	8.30173i	0.676143	+	0.350499i
$562$	20.1486	−	14.6388i	0.849918	−	0.617502i
$563$	21.7005	−	15.7663i	0.914566	−	0.664471i	−0.0275994	−	0.999619i	$-0.508786\pi$
$563$	21.7005	−	15.7663i	0.914566	−	0.664471i	0.942166	+	0.335148i	$0.108786\pi$
$564$	−9.32385	+	17.9865i	−0.392605	+	0.757368i
$565$	−12.1514	−	15.1650i	−0.511215	−	0.637998i
$566$	−9.97821	+	7.24960i	−0.419416	+	0.304723i
$567$	17.3152	+	16.3457i	0.727172	+	0.686455i
$568$	0.202645			0.00850282
$569$	−16.6311	−	5.40376i	−0.697211	−	0.226538i	−0.0610959	−	0.998132i	$-0.519460\pi$
$569$	−16.6311	−	5.40376i	−0.697211	−	0.226538i	−0.636115	+	0.771594i	$0.719460\pi$
$570$	8.48928	−	18.4597i	0.355577	−	0.773191i
$571$	9.16822	+	28.2169i	0.383678	+	1.18084i	0.937435	+	0.348161i	$0.113194\pi$
$571$	9.16822	+	28.2169i	0.383678	+	1.18084i	−0.553757	+	0.832679i	$0.686806\pi$
$572$	9.50696	+	29.2594i	0.397506	+	1.22340i
$573$	36.5897	+	18.9674i	1.52856	+	0.792374i
$574$	5.29296	+	9.07407i	0.220924	+	0.378744i
$575$	22.0782	−	37.3456i	0.920726	−	1.55742i
$576$	−3.38421	+	1.04741i	−0.141009	+	0.0436422i
$577$	15.6794	−	21.5808i	0.652741	−	0.898421i	−0.346473	−	0.938060i	$-0.612621\pi$
$577$	15.6794	−	21.5808i	0.652741	−	0.898421i	0.999214	+	0.0396392i	$0.0126209\pi$
$578$	−16.4603	+	5.34828i	−0.684659	+	0.222459i
$579$	4.55483	−	2.28075i	0.189292	−	0.0947849i
$580$	−2.92644	−	3.65221i	−0.121514	−	0.151650i
$581$	−6.91620	−	31.8400i	−0.286932	−	1.32095i
$582$	0.178454	+	1.18016i	0.00739716	+	0.0489193i
$583$	7.54402	−	23.2181i	0.312441	−	0.961595i
$584$	5.38611	−	3.91323i	0.222879	−	0.161931i
$585$	43.4797	−	1.44373i	1.79767	−	0.0596907i
$586$	−27.2152	+	37.4585i	−1.12425	+	1.54740i
$587$	15.4713	−	11.2405i	0.638567	−	0.463946i	−0.220790	−	0.975321i	$-0.570864\pi$
$587$	15.4713	−	11.2405i	0.638567	−	0.463946i	0.859358	+	0.511375i	$0.170864\pi$
$588$	−14.4857	+	3.91102i	−0.597379	+	0.161288i
$589$	−16.9935	−	12.3465i	−0.700204	−	0.508728i
$590$	0.0360601	+	0.763381i	0.00148457	+	0.0314279i
$591$	−12.6390	+	12.4632i	−0.519901	+	0.512667i
$592$	−8.06312	+	24.8157i	−0.331392	+	1.01992i
$593$	−22.0927			−0.907240			−0.453620	−	0.891195i	$-0.649868\pi$
$593$	−22.0927			−0.907240			−0.453620	+	0.891195i	$0.649868\pi$
$594$	35.5089	−	4.86155i	1.45695	−	0.199472i
$595$	4.14908	+	15.5282i	0.170095	+	0.636594i
$596$	−19.6483	+	6.38411i	−0.804824	+	0.261503i
$597$	16.2447	+	32.4418i	0.664851	+	1.32775i
$598$	59.5117	−	81.9109i	2.43362	−	3.34958i
$599$			3.97760i			0.162520i	0.996693	+	0.0812602i	$0.0258945\pi$
$599$			3.97760i			0.162520i	−0.996693	+	0.0812602i	$0.974106\pi$
$600$	−11.5278	+	2.87583i	−0.470620	+	0.117405i
$601$			5.86687i			0.239315i	0.992815	+	0.119657i	$0.0381796\pi$
$601$			5.86687i			0.239315i	−0.992815	+	0.119657i	$0.961820\pi$
$602$	−4.06956	+	40.4521i	−0.165863	+	1.64870i
$603$	−5.36479	−	7.60584i	−0.218471	−	0.309734i
$604$	−6.71830	−	20.6768i	−0.273364	−	0.841327i
$605$	2.92089	+	7.72808i	0.118751	+	0.314191i
$606$	3.36943	−	20.3501i	0.136874	−	0.826666i
$607$			6.15776i			0.249936i	0.992161	+	0.124968i	$0.0398828\pi$
$607$			6.15776i			0.249936i	−0.992161	+	0.124968i	$0.960117\pi$
$608$	−5.54212	+	17.0569i	−0.224763	+	0.691748i
$609$	2.02499	−	7.48101i	0.0820567	−	0.303146i
$610$	0.0696917	+	0.184390i	0.00282173	+	0.00746573i
$611$	−36.0287	+	49.5893i	−1.45757	+	2.00617i
$612$	6.04244	−	8.07630i	0.244251	−	0.326465i
$613$	−13.3613	+	9.70755i	−0.539658	+	0.392084i	−0.823958	−	0.566651i	$-0.808239\pi$
$613$	−13.3613	+	9.70755i	−0.539658	+	0.392084i	0.284300	+	0.958735i	$0.408239\pi$
$614$	14.9074	+	10.8309i	0.601614	+	0.437098i
$615$	3.57084	−	7.76468i	0.143990	−	0.313102i
$616$	5.60269	−	12.7363i	0.225739	−	0.513158i
$617$	11.3189	+	3.67772i	0.455680	+	0.148060i	0.527859	−	0.849332i	$-0.322995\pi$
$617$	11.3189	+	3.67772i	0.455680	+	0.148060i	−0.0721783	+	0.997392i	$0.522995\pi$
$618$	−3.29900	−	21.8171i	−0.132705	−	0.877612i
$619$	−15.7465	−	5.11634i	−0.632904	−	0.205643i	−0.0250429	−	0.999686i	$-0.507972\pi$
$619$	−15.7465	−	5.11634i	−0.632904	−	0.205643i	−0.607861	+	0.794043i	$0.707972\pi$
$620$	−0.940672	−	19.9137i	−0.0377783	−	0.799755i
$621$	−31.2034	−	32.5432i	−1.25215	−	1.30592i
$622$	12.3196	−	4.00287i	0.493970	−	0.160501i
$623$	3.03125	+	0.304950i	0.121444	+	0.0122176i
$624$	−54.9051	+	8.30229i	−2.19796	+	0.332358i
$625$	24.5557	−	4.69223i	0.982228	−	0.187689i
$626$	−17.6752			−0.706442
$627$	8.90920	−	17.1866i	0.355799	−	0.686367i
$628$	−1.67852	+	0.545385i	−0.0669803	+	0.0217632i
$629$	−4.43122	−	13.6379i	−0.176684	−	0.543778i
$630$	24.5196	+	20.4601i	0.976883	+	0.815150i
$631$	−3.72799	+	11.4736i	−0.148409	+	0.456756i	−0.997434	−	0.0715975i	$-0.977190\pi$
$631$	−3.72799	+	11.4736i	−0.148409	+	0.456756i	0.849025	+	0.528353i	$0.177190\pi$
$632$		−	2.04737i		−	0.0814401i
$633$	−44.5322	−	7.37333i	−1.76999	−	0.293064i
$634$	11.2295	−	8.15870i	0.445980	−	0.324023i
$635$	−11.5069	−	7.55735i	−0.456639	−	0.299904i
$636$	−12.1193	−	6.28239i	−0.480560	−	0.249113i
$637$	−45.1033	+	5.14726i	−1.78706	+	0.203942i
$638$	−6.85665	−	9.43737i	−0.271457	−	0.373629i
$639$	−0.142826	+	0.419483i	−0.00565010	+	0.0165945i
$640$	21.2883	−	8.04608i	0.841493	−	0.318049i
$641$	−8.06944	−	11.1066i	−0.318724	−	0.438686i	0.619353	−	0.785112i	$-0.287395\pi$
$641$	−8.06944	−	11.1066i	−0.318724	−	0.438686i	−0.938077	+	0.346427i	$0.887395\pi$
$642$	30.2018	+	5.00061i	1.19197	+	0.197358i
$643$			16.7204i			0.659386i	0.944088	+	0.329693i	$0.106945\pi$
$643$			16.7204i			0.659386i	−0.944088	+	0.329693i	$0.893055\pi$
$644$	27.7621	−	6.03042i	1.09398	−	0.237632i
$645$	28.8439	−	16.1885i	1.13573	−	0.637423i
$646$	−4.40435	−	13.5552i	−0.173287	−	0.533323i
$647$	10.3403	+	31.8241i	0.406519	+	1.25114i	0.919621	+	0.392808i	$0.128496\pi$
$647$	10.3403	+	31.8241i	0.406519	+	1.25114i	−0.513102	+	0.858328i	$0.671504\pi$
$648$	−0.345920	+	12.3423i	−0.0135890	+	0.484853i
$649$			0.728137i			0.0285819i
$650$	58.0844	−	5.49977i	2.27826	−	0.215719i
$651$	25.7099	−	20.7111i	1.00765	−	0.811733i
$652$	−15.1253	−	10.9892i	−0.592354	−	0.430370i
$653$	−1.87158	+	0.608112i	−0.0732404	+	0.0237973i	−0.345408	−	0.938453i	$-0.612259\pi$
$653$	−1.87158	+	0.608112i	−0.0732404	+	0.0237973i	0.272168	+	0.962250i	$0.412259\pi$
$654$	10.3927	+	20.7550i	0.406388	+	0.811586i
$655$	−2.61419	+	9.55881i	−0.102145	+	0.373494i
$656$	−3.37102	+	10.3749i	−0.131616	+	0.405073i
$657$	4.30437	+	13.9075i	0.167930	+	0.542583i
$658$	−43.9699	+	9.55102i	−1.71412	+	0.372338i
$659$	−10.8828	−	14.9789i	−0.423935	−	0.583497i	0.542613	−	0.839983i	$-0.317435\pi$
$659$	−10.8828	−	14.9789i	−0.423935	−	0.583497i	−0.966548	+	0.256486i	$0.917435\pi$
$660$	18.0168	−	3.60114i	0.701304	−	0.140174i
$661$	−0.579881	+	0.798137i	−0.0225547	+	0.0310439i	−0.820145	−	0.572155i	$-0.806108\pi$
$661$	−0.579881	+	0.798137i	−0.0225547	+	0.0310439i	0.797591	+	0.603199i	$0.206108\pi$
$662$	−15.8352	−	21.7953i	−0.615454	−	0.847100i
$663$	21.7294	−	21.4271i	0.843900	−	0.832159i
$664$	9.93070	−	13.6684i	0.385386	−	0.530438i
$665$	16.6644	−	4.45268i	0.646219	−	0.172667i
$666$	−22.8129	−	17.0679i	−0.883980	−	0.661367i
$667$	−4.53465	+	13.9562i	−0.175582	+	0.540387i
$668$	12.1344			0.469493
$669$	3.94338	−	23.8166i	0.152460	−	0.920801i
$670$	−7.80542	−	9.74119i	−0.301549	−	0.376335i
$671$	0.0580367	+	0.178619i	0.00224048	+	0.00689550i
$672$	−23.6016	−	15.4128i	−0.910453	−	0.594561i
$673$	17.2555	+	12.5369i	0.665151	+	0.483261i	0.868399	−	0.495867i	$-0.165150\pi$
$673$	17.2555	+	12.5369i	0.665151	+	0.483261i	−0.203247	+	0.979127i	$0.565150\pi$
$674$			53.4521i			2.05890i
$675$	2.17179	−	25.8898i	0.0835923	−	0.996500i
$676$	35.9593			1.38305
$677$	11.7674	+	8.54952i	0.452258	+	0.328585i	0.790487	−	0.612479i	$-0.209828\pi$
$677$	11.7674	+	8.54952i	0.452258	+	0.328585i	−0.338229	+	0.941064i	$0.609828\pi$
$678$	−24.2179	+	12.1267i	−0.930084	+	0.465724i
$679$	−0.674658	+	0.756031i	−0.0258910	+	0.0290138i
$680$	−4.57520	+	6.96627i	−0.175451	+	0.267144i
$681$	38.8718	+	6.43612i	1.48957	+	0.246633i
$682$		−	49.6914i		−	1.90278i
$683$	−47.3796	−	15.3946i	−1.81293	−	0.589057i	−0.999977	−	0.00672854i	$-0.997858\pi$
$683$	−47.3796	−	15.3946i	−1.81293	−	0.589057i	−0.812954	−	0.582328i	$-0.802142\pi$
$684$	−8.66727	−	6.48459i	−0.331401	−	0.247944i
$685$	6.29548	+	7.85679i	0.240538	+	0.300192i
$686$	−27.2189	−	19.2252i	−1.03922	−	0.734021i
$687$	3.10450	−	3.06131i	0.118444	−	0.116796i
$688$	−34.1562	+	24.8160i	−1.30219	+	0.946100i
$689$	−33.4131	−	24.2761i	−1.27294	−	0.924844i
$690$	−44.4394	−	41.0030i	−1.69178	−	1.56096i
$691$	−7.48259	−	10.2989i	−0.284651	−	0.391789i	0.642616	−	0.766188i	$-0.277849\pi$
$691$	−7.48259	−	10.2989i	−0.284651	−	0.391789i	−0.927268	+	0.374399i	$0.877849\pi$
$692$	1.24491	−	3.83143i	0.0473242	−	0.145649i
$693$	22.4157	+	20.5744i	0.851501	+	0.781556i
$694$	−13.0977	+	40.3105i	−0.497181	+	1.53017i
$695$	−23.1853	+	35.3023i	−0.879469	+	1.33909i
$696$	3.59343	−	1.79935i	0.136209	−	0.0682041i
$697$	−1.85260	−	5.70172i	−0.0701722	−	0.215968i
$698$	1.06835	+	0.776203i	0.0404377	+	0.0293797i
$699$	0.261733	−	0.0395770i	0.00989965	−	0.00149694i
$700$	13.1879	+	9.70013i	0.498455	+	0.366631i
$701$			21.1544i			0.798990i	0.916735	+	0.399495i	$0.130814\pi$
$701$			21.1544i			0.798990i	−0.916735	+	0.399495i	$0.869186\pi$
$702$	10.7414	−	59.6740i	0.405409	−	2.25225i
$703$	−14.6358	+	4.75547i	−0.552000	+	0.179356i
$704$	−4.30513	+	1.39882i	−0.162256	+	0.0527201i
$705$	26.9039	+	24.8234i	1.01326	+	0.934905i
$706$	−11.6678	−	3.79111i	−0.439125	−	0.142680i
$707$	15.1261	−	8.82316i	0.568877	−	0.331829i
$708$	0.401679	+	0.0665073i	0.0150960	+	0.00249950i
$709$	17.4131	−	12.6513i	0.653962	−	0.475131i	−0.210657	−	0.977560i	$-0.567560\pi$
$709$	17.4131	−	12.6513i	0.653962	−	0.475131i	0.864618	+	0.502429i	$0.167560\pi$
$710$	−0.156774	+	0.573246i	−0.00588363	+	0.0215135i
$711$	4.23813	+	1.44300i	0.158942	+	0.0541168i
$712$	0.928546	+	1.27803i	0.0347988	+	0.0478964i
$713$	−50.5717	+	36.7425i	−1.89392	+	1.37602i
$714$	22.3738	−	1.11536i	0.837318	−	0.0417414i
$715$	55.5267	−	2.62293i	2.07658	−	0.0980921i
$716$	14.7093	+	20.2457i	0.549714	+	0.756616i
$717$	−2.44106	+	14.7431i	−0.0911629	+	0.550590i
$718$	−2.12111			−0.0791590
$719$	−11.2251	+	34.5472i	−0.418625	+	1.28839i	0.490344	+	0.871529i	$0.336871\pi$
$719$	−11.2251	+	34.5472i	−0.418625	+	1.28839i	−0.908968	+	0.416865i	$0.863129\pi$
$720$	1.10054	+	33.1442i	0.0410147	+	1.23521i
$721$	12.4721	−	13.9764i	0.464485	−	0.520508i
$722$	17.9667	−	5.83773i	0.668651	−	0.217258i
$723$	−6.43418	−	3.33536i	−0.239290	−	0.124043i
$724$			6.47818i			0.240760i
$725$	−7.76019	+	3.35958i	−0.288206	+	0.124772i
$726$	11.3852	−	1.72157i	0.422544	−	0.0638936i
$727$	−23.6517	+	32.5538i	−0.877195	+	1.20736i	0.0999951	+	0.994988i	$0.468117\pi$
$727$	−23.6517	+	32.5538i	−0.877195	+	1.20736i	−0.977190	+	0.212367i	$0.931883\pi$
$728$	−17.5632	−	15.6728i	−0.650934	−	0.580873i
$729$	−25.3053	−	9.41503i	−0.937233	−	0.348705i
$730$	6.90292	+	18.2637i	0.255488	+	0.675970i
$731$	7.16993	−	22.0668i	0.265189	−	0.816169i
$732$	0.103836	−	0.0157013i	0.00383791	−	0.000580336i
$733$	17.6875	+	5.74701i	0.653302	+	0.212271i	0.616869	−	0.787066i	$-0.288401\pi$
$733$	17.6875	+	5.74701i	0.653302	+	0.212271i	0.0364323	+	0.999336i	$0.488401\pi$
$734$	−10.0816	+	7.32471i	−0.372119	+	0.270360i
$735$	−0.0881731	+	27.1107i	−0.00325231	+	0.999995i
$736$	43.1794	+	31.3717i	1.59161	+	1.15637i
$737$	−6.99056	−	9.62168i	−0.257501	−	0.354419i
$738$	−9.53758	−	7.13572i	−0.351083	−	0.262670i
$739$	−11.0684	−	8.04168i	−0.407159	−	0.295818i	0.365292	−	0.930893i	$-0.380969\pi$
$739$	−11.0684	−	8.04168i	−0.407159	−	0.295818i	−0.772450	+	0.635075i	$0.780969\pi$
$740$	−12.2082	−	8.01792i	−0.448782	−	0.294745i
$741$	−22.9950	−	23.3194i	−0.844742	−	0.856660i
$742$	−6.43546	−	29.6268i	−0.236253	−	1.08763i
$743$			13.5293i			0.496341i	0.968716	+	0.248171i	$0.0798294\pi$
$743$			13.5293i			0.496341i	−0.968716	+	0.248171i	$0.920171\pi$
$744$	16.8891	+	2.79638i	0.619185	+	0.102520i
$745$	1.76135	+	37.2872i	0.0645308	+	1.36610i
$746$	35.7347	−	11.6109i	1.30834	−	0.425105i
$747$	21.2949	+	30.1905i	0.779140	+	1.10461i
$748$	7.57564	−	10.4270i	0.276993	−	0.381248i
$749$	13.0946	+	22.4489i	0.478465	+	0.820264i
$750$	0.783144	−	34.8348i	0.0285964	−	1.27199i
$751$	4.06914			0.148485			0.0742425	−	0.997240i	$-0.476346\pi$
$751$	4.06914			0.148485			0.0742425	+	0.997240i	$0.476346\pi$
$752$	−37.8015	−	27.4644i	−1.37848	−	1.00152i
$753$	38.3369	−	19.1965i	1.39707	−	0.699561i
$754$	−18.7689	+	6.09839i	−0.683523	+	0.222090i
$755$	−39.2391	+	1.85355i	−1.42806	+	0.0674576i
$756$	13.3973	−	10.4864i	0.487256	−	0.381388i
$757$	8.07189			0.293378			0.146689	−	0.989183i	$-0.453138\pi$
$757$	8.07189			0.293378			0.146689	+	0.989183i	$0.453138\pi$
$758$	−44.0618	−	14.3166i	−1.60040	−	0.520001i
$759$	−40.4501	−	41.0208i	−1.46824	−	1.48896i
$760$	7.47602	+	4.90999i	0.271184	+	0.178104i
$761$	−6.61985	−	4.80960i	−0.239969	−	0.174348i	0.461300	−	0.887244i	$-0.347383\pi$
$761$	−6.61985	−	4.80960i	−0.239969	−	0.174348i	−0.701270	+	0.712896i	$0.747383\pi$
$762$	−13.6622	+	13.4721i	−0.494929	+	0.488043i
$763$	−7.93466	+	18.0374i	−0.287254	+	0.652997i
$764$	17.3084	−	23.8230i	0.626198	−	0.861887i
$765$	−11.1958	−	14.3807i	−0.404785	−	0.519936i
$766$	5.82907	+	8.02303i	0.210613	+	0.289884i
$767$	1.17154	+	0.380658i	0.0423020	+	0.0137448i
$768$	−5.35396	−	35.4071i	−0.193194	−	1.27764i
$769$	12.2890	+	3.99295i	0.443153	+	0.143989i	0.522090	−	0.852890i	$-0.325152\pi$
$769$	12.2890	+	3.99295i	0.443153	+	0.143989i	−0.0789366	+	0.996880i	$0.525152\pi$
$770$	31.6940	+	25.7022i	1.14217	+	0.926243i
$771$	5.75175	−	2.88009i	0.207144	−	0.103724i
$772$	−1.12470	−	3.46146i	−0.0404787	−	0.124581i
$773$	35.8420	+	26.0407i	1.28915	+	0.936621i	0.999788	−	0.0205997i	$-0.00655756\pi$
$773$	35.8420	+	26.0407i	1.28915	+	0.936621i	0.289360	+	0.957220i	$0.406558\pi$
$774$	−13.6300	−	44.0389i	−0.489921	−	1.58294i
$775$	−35.1554	−	7.85237i	−1.26282	−	0.282065i
$776$	−0.525422			−0.0188615
$777$	−1.20428	−	24.1574i	−0.0432032	−	0.866642i
$778$	4.79654	+	14.7622i	0.171964	+	0.529251i
$779$	−6.11893	+	1.98816i	−0.219233	+	0.0712333i
$780$	3.62480	−	30.8710i	0.129789	−	1.10536i
$781$	−0.174974	+	0.538516i	−0.00626107	+	0.0192696i
$782$	−42.4156			−1.51678
$783$	1.19204	+	8.70672i	0.0426002	+	0.311153i
$784$	−3.92371	−	34.3819i	−0.140133	−	1.22792i
$785$	0.150470	+	3.18540i	0.00537049	+	0.113692i
$786$	12.2622	+	6.35647i	0.437377	+	0.226728i
$787$	−30.6181	−	42.1422i	−1.09142	−	1.50221i	−0.846296	−	0.532713i	$-0.821173\pi$
$787$	−30.6181	−	42.1422i	−1.09142	−	1.50221i	−0.245120	−	0.969493i	$-0.578827\pi$
$788$	7.45461	+	10.2604i	0.265559	+	0.365511i
$789$	32.3612	+	16.7754i	1.15209	+	0.597221i
$790$	5.79164	+	1.58392i	0.206057	+	0.0563535i
$791$	−21.0468	−	9.25853i	−0.748340	−	0.329195i
$792$	−0.221028	+	15.7756i	−0.00785390	+	0.560560i
$793$	0.317731			0.0112830
$794$	−13.1074	+	40.3406i	−0.465166	+	1.43163i
$795$	−16.7260	+	18.1278i	−0.593209	+	0.642925i
$796$	24.6542	−	8.01065i	0.873847	−	0.283930i
$797$	−3.46757	−	10.6721i	−0.122828	−	0.378025i	0.870671	−	0.491865i	$-0.163685\pi$
$797$	−3.46757	−	10.6721i	−0.122828	−	0.378025i	−0.993499	+	0.113841i	$0.963685\pi$
$798$	−1.19698	−	24.0109i	−0.0423725	−	0.849978i
$799$	25.6786			0.908444
$800$	2.89921	+	30.6192i	0.102503	+	1.08255i
$801$	−3.30002	+	1.02136i	−0.116601	+	0.0360879i
$802$	32.6919	+	23.7521i	1.15439	+	0.838715i
$803$	5.74850	+	17.6921i	0.202860	+	0.624340i
$804$	−5.94633	+	2.97753i	−0.209711	+	0.105009i
$805$	2.72253	−	51.2600i	0.0959567	−	1.80668i
$806$	−79.9516	−	25.9779i	−2.81618	−	0.915031i
$807$	−6.32648	−	41.8386i	−0.222703	−	1.47279i
$808$	8.63581	+	2.80594i	0.303807	+	0.0987127i
$809$	−0.0967336	−	0.133142i	−0.00340097	−	0.00468103i	0.807313	−	0.590123i	$-0.200921\pi$
$809$	−0.0967336	−	0.133142i	−0.00340097	−	0.00468103i	−0.810714	+	0.585442i	$0.800921\pi$
$810$	−34.6466	−	10.5270i	−1.21736	−	0.369883i
$811$	−25.6402	+	35.2906i	−0.900347	+	1.23922i	0.0700096	+	0.997546i	$0.477697\pi$
$811$	−25.6402	+	35.2906i	−0.900347	+	1.23922i	−0.970357	+	0.241676i	$0.922303\pi$
$812$	−5.06873	−	2.22974i	−0.177878	−	0.0782485i
$813$	15.4400	−	15.2252i	0.541505	−	0.533971i
$814$	−29.4527	−	21.3986i	−1.03232	−	0.750022i
$815$	−26.3621	+	21.1234i	−0.923425	+	0.739922i
$816$	16.3337	+	16.5641i	0.571794	+	0.579861i
$817$	−23.6815	−	7.69458i	−0.828510	−	0.269199i
$818$	11.2890			0.394712
$819$	44.8219	−	25.3100i	1.56620	−	0.884404i
$820$	−5.10399	−	3.35212i	−0.178239	−	0.117061i
$821$	26.2393	−	8.52566i	0.915758	−	0.297548i	0.187032	−	0.982354i	$-0.440113\pi$
$821$	26.2393	−	8.52566i	0.915758	−	0.297548i	0.728725	+	0.684806i	$0.240113\pi$
$822$	12.5470	−	6.28268i	0.437626	−	0.219134i
$823$	−21.6771	−	15.7494i	−0.755618	−	0.548989i	0.141945	−	0.989875i	$-0.454664\pi$
$823$	−21.6771	−	15.7494i	−0.755618	−	0.548989i	−0.897563	+	0.440886i	$0.854664\pi$
$824$	9.71323			0.338376
$825$	2.31137	−	33.1174i	0.0804714	−	1.15300i
$826$	0.455610	+	0.781082i	0.0158527	+	0.0271773i
$827$	−13.3183	+	18.3310i	−0.463122	+	0.637432i	−0.975152	−	0.221535i	$-0.928893\pi$
$827$	−13.3183	+	18.3310i	−0.463122	+	0.637432i	0.512031	+	0.858967i	$0.328893\pi$
$828$	−26.3239	+	18.5676i	−0.914818	+	0.645268i
$829$	20.3660	−	6.61730i	0.707339	−	0.229828i	0.0668137	−	0.997765i	$-0.478717\pi$
$829$	20.3660	−	6.61730i	0.707339	−	0.229828i	0.640525	+	0.767937i	$0.278717\pi$
$830$	30.9827	+	38.6665i	1.07542	+	1.34213i
$831$	−19.4002	−	3.21215i	−0.672985	−	0.111428i
$832$			7.65808i			0.265496i
$833$	12.8508	+	14.0190i	0.445253	+	0.485730i
$834$	41.3313	+	41.9144i	1.43118	+	1.45138i
$835$	5.78381	−	21.1486i	0.200157	−	0.731876i
$836$	−11.1899	−	8.12997i	−0.387012	−	0.281181i
$837$	−17.6922	+	32.9902i	−0.611531	+	1.14031i
$838$	−7.69627	−	10.5930i	−0.265863	−	0.365929i
$839$	27.4631	+	19.9531i	0.948130	+	0.688857i	0.950364	−	0.311141i	$-0.100711\pi$
$839$	27.4631	+	19.9531i	0.948130	+	0.688857i	−0.00223397	+	0.999998i	$0.500711\pi$
$840$	−10.5192	+	9.32577i	−0.362948	+	0.321770i
$841$	−21.1475	+	15.3645i	−0.729223	+	0.529812i
$842$	1.77594	+	0.577039i	0.0612030	+	0.0198861i
$843$	−23.7046	+	3.58440i	−0.816428	+	0.123453i
$844$	−9.96614	+	30.6726i	−0.343049	+	1.05580i
$845$	17.1399	−	62.6723i	0.589631	−	2.15599i
$846$	41.6920	−	29.4075i	1.43340	−	1.01105i
$847$	7.29354	+	6.50853i	0.250609	+	0.223636i
$848$	18.5054	−	25.4706i	0.635479	−	0.874662i
$849$	11.7392	−	1.77511i	0.402889	−	0.0609215i
$850$	−16.1667	−	18.3318i	−0.554514	−	0.628774i
$851$			45.7969i			1.56990i
$852$	0.281092	+	0.145712i	0.00963004	+	0.00499203i
$853$	−12.6049	+	4.09557i	−0.431582	+	0.140230i	−0.516749	−	0.856137i	$-0.672858\pi$
$853$	−12.6049	+	4.09557i	−0.431582	+	0.140230i	0.0851663	+	0.996367i	$0.472858\pi$
$854$	0.174022	+	0.155292i	0.00595491	+	0.00531398i
$855$	−15.4330	+	12.0150i	−0.527797	+	0.410905i
$856$	−4.16433	+	12.8165i	−0.142334	+	0.438059i
$857$	−41.8810			−1.43063			−0.715314	−	0.698804i	$-0.753716\pi$
$857$	−41.8810			−1.43063			−0.715314	+	0.698804i	$0.753716\pi$
$858$	12.6557	−	76.4356i	0.432058	−	2.60947i
$859$	−29.3994	−	40.4649i	−1.00310	−	1.38064i	−0.923406	−	0.383824i	$-0.874607\pi$
$859$	−29.3994	−	40.4649i	−1.00310	−	1.38064i	−0.0796896	−	0.996820i	$-0.525393\pi$
$860$	−8.35533	−	22.1065i	−0.284914	−	0.753825i
$861$	−0.503483	−	10.0997i	−0.0171587	−	0.344197i
$862$	39.7919	−	28.9105i	1.35532	−	0.984696i
$863$	3.08688	+	4.24872i	0.105078	+	0.144628i	0.858318	−	0.513118i	$-0.171510\pi$
$863$	3.08688	+	4.24872i	0.105078	+	0.144628i	−0.753239	+	0.657747i	$0.771510\pi$
$864$	31.4572	+	5.66235i	1.07020	+	0.192637i
$865$	−6.08428	−	3.99594i	−0.206872	−	0.135866i
$866$	36.8102	−	26.7441i	1.25086	−	0.908803i
$867$	16.4366	+	2.72146i	0.558216	+	0.0924257i
$868$	−11.8852	−	20.3755i	−0.403409	−	0.691590i
$869$	5.44075	+	1.76781i	0.184565	+	0.0599687i
$870$	2.31001	+	11.5572i	0.0783167	+	0.391825i
$871$	−19.1355	+	6.21749i	−0.648380	+	0.210671i
$872$	−9.71784	+	3.15752i	−0.329088	+	0.106927i
$873$	0.370321	−	1.08764i	0.0125335	−	0.0368111i
$874$			45.5192i			1.53971i
$875$	23.1920	−	18.3611i	0.784032	−	0.620720i
$876$	10.2849	−	1.55520i	0.347496	−	0.0525454i
$877$	11.6118	+	8.43649i	0.392104	+	0.284880i	0.766317	−	0.642463i	$-0.222087\pi$
$877$	11.6118	+	8.43649i	0.392104	+	0.284880i	−0.374213	+	0.927343i	$0.622087\pi$
$878$	8.79175	+	27.0582i	0.296707	+	0.913171i
$879$	39.8532	−	19.9558i	1.34422	−	0.673093i
$880$	1.99944	+	42.3275i	0.0674011	+	1.42686i
$881$	−8.11937	+	24.9888i	−0.273548	+	0.841895i	0.716051	+	0.698047i	$0.245948\pi$
$881$	−8.11937	+	24.9888i	−0.273548	+	0.841895i	−0.989600	+	0.143848i	$0.954052\pi$
$882$	36.9194	+	8.04445i	1.24314	+	0.270871i
$883$	9.95899	−	30.6506i	0.335147	−	1.03148i	−0.631503	−	0.775374i	$-0.717562\pi$
$883$	9.95899	−	30.6506i	0.335147	−	1.03148i	0.966650	−	0.256102i	$-0.0824384\pi$
$884$	−12.8162	−	17.6400i	−0.431055	−	0.593296i
$885$	0.307372	−	0.668372i	0.0103322	−	0.0224671i
$886$	24.0559	+	17.4776i	0.808173	+	0.587172i
$887$	35.8473	−	26.0446i	1.20363	−	0.874492i	0.208997	−	0.977916i	$-0.432980\pi$
$887$	35.8473	−	26.0446i	1.20363	−	0.874492i	0.994637	+	0.103424i	$0.0329800\pi$
$888$	8.93042	−	8.80617i	0.299685	−	0.295516i
$889$	−16.2072	−	1.63048i	−0.543573	−	0.0546845i
$890$	−4.33368	+	1.63795i	−0.145265	+	0.0549042i
$891$	−32.5002	−	11.5763i	−1.08880	−	0.387819i
$892$	−16.4042	−	5.33006i	−0.549254	−	0.178464i
$893$		−	27.5576i		−	0.922180i
$894$	51.3280	+	8.49854i	1.71667	+	0.284234i
$895$	42.2966	−	15.9864i	1.41382	−	0.534365i
$896$	17.9288	−	20.0913i	0.598960	−	0.671202i
$897$	−87.1474	+	43.6376i	−2.90977	+	1.45702i
$898$	31.6726	+	23.0115i	1.05693	+	0.767903i
$899$	12.1842			0.406367
$900$	−18.0582	−	4.29998i	−0.601939	−	0.143333i
$901$			17.3022i			0.576419i
$902$	−12.3136	−	8.94633i	−0.409997	−	0.297880i
$903$	21.3988	−	32.7681i	0.712109	−	1.09045i
$904$	−3.68434	−	11.3392i	−0.122539	−	0.377137i
$905$	11.2906	+	3.08780i	0.375312	+	0.102642i
$906$	−8.94342	+	54.0149i	−0.297125	+	1.79452i
$907$	55.4775			1.84210			0.921051	−	0.389443i	$-0.127333\pi$
$907$	55.4775			1.84210			0.921051	+	0.389443i	$0.127333\pi$
$908$	8.69936	−	26.7739i	0.288698	−	0.888522i
$909$	−11.8950	+	15.8988i	−0.394531	+	0.527329i
$910$	57.9230	−	37.5578i	1.92013	−	1.24503i
$911$	−3.22309	+	4.43621i	−0.106786	+	0.146978i	−0.859065	−	0.511866i	$-0.828954\pi$
$911$	−3.22309	+	4.43621i	−0.106786	+	0.146978i	0.752279	+	0.658844i	$0.228954\pi$
$912$	17.7762	−	17.5289i	0.588629	−	0.580440i
$913$	27.7482	+	38.1921i	0.918331	+	1.26397i
$914$	−8.31060	+	11.4386i	−0.274890	+	0.378354i
$915$	0.0221281	−	0.188457i	0.000731534	−	0.00623019i
$916$	−1.83106	−	2.52023i	−0.0604998	−	0.0832709i
$917$	2.48894	+	11.4583i	0.0821919	+	0.378386i
$918$	−22.8698	+	11.0537i	−0.754815	+	0.364826i
$919$	−13.4150	+	41.2872i	−0.442521	+	1.36194i	0.442659	+	0.896690i	$0.354035\pi$
$919$	−13.4150	+	41.2872i	−0.442521	+	1.36194i	−0.885180	+	0.465249i	$0.845965\pi$
$920$	20.7718	−	16.6440i	0.684826	−	0.548737i
$921$	−7.94185	−	15.8604i	−0.261693	−	0.522619i
$922$	6.12820	−	1.99117i	0.201821	−	0.0655757i
$923$	0.774977	+	0.563054i	0.0255087	+	0.0185331i
$924$	16.9296	−	13.6380i	0.556942	−	0.448656i
$925$	−19.7932	+	17.4555i	−0.650795	+	0.573934i
$926$		−	61.5733i		−	2.02342i
$927$	−6.84595	+	20.1067i	−0.224850	+	0.660392i
$928$	−3.21477	−	9.89404i	−0.105530	−	0.324788i
$929$	−8.87135	−	27.3032i	−0.291060	−	0.895789i	−0.984517	−	0.175291i	$-0.943913\pi$
$929$	−8.87135	−	27.3032i	−0.291060	−	0.895789i	0.693457	−	0.720498i	$-0.256087\pi$
$930$	−20.9765	+	45.6128i	−0.687847	+	1.49570i
$931$	15.0448	−	13.7911i	0.493074	−	0.451986i
$932$		−	0.189132i		−	0.00619523i
$933$	−12.3018	−	2.03685i	−0.402744	−	0.0666836i
$934$	4.21166	+	5.79686i	0.137810	+	0.189679i
$935$	−14.5619	−	18.1733i	−0.476225	−	0.594331i
$936$	25.2667	+	8.60283i	0.825869	+	0.281192i
$937$	−17.8573	−	24.5784i	−0.583372	−	0.802943i	0.410688	−	0.911776i	$-0.365289\pi$
$937$	−17.8573	−	24.5784i	−0.583372	−	0.802943i	−0.994060	+	0.108833i	$0.965289\pi$
$938$	−13.5193	−	5.94717i	−0.441422	−	0.194182i
$939$	15.1055	+	7.83038i	0.492948	+	0.255535i
$940$	20.4108	−	16.3548i	0.665728	−	0.533434i
$941$	−30.0892	+	21.8611i	−0.980881	+	0.712652i	−0.957905	−	0.287084i	$-0.907314\pi$
$941$	−30.0892	+	21.8611i	−0.980881	+	0.712652i	−0.0229760	+	0.999736i	$0.507314\pi$
$942$	4.38488	+	0.726018i	0.142867	+	0.0236550i
$943$			19.1467i			0.623503i
$944$	−0.290172	+	0.893059i	−0.00944431	+	0.0290666i
$945$	−11.8906	−	28.3481i	−0.386803	−	0.922163i
$946$	−18.2029	−	56.0229i	−0.591829	−	1.82146i
$947$	19.2792	−	6.26421i	0.626491	−	0.203559i	0.0214711	−	0.999769i	$-0.493165\pi$
$947$	19.2792	−	6.26421i	0.626491	−	0.203559i	0.605020	+	0.796210i	$0.293165\pi$
$948$	1.47217	−	2.83993i	0.0478137	−	0.0922367i
$949$	31.4711			1.02159
$950$	−19.6732	+	17.3497i	−0.638282	+	0.562899i
$951$	−13.2113	+	1.99771i	−0.428407	+	0.0647801i
$952$	−0.987088	+	9.81181i	−0.0319917	+	0.318003i
$953$	15.5043	−	5.03766i	0.502235	−	0.163186i	−0.0469332	−	0.998898i	$-0.514945\pi$
$953$	15.5043	−	5.03766i	0.502235	−	0.163186i	0.549168	+	0.835712i	$0.314945\pi$
$954$	19.8147	+	28.0919i	0.641525	+	0.909510i
$955$	−33.2703	−	41.5215i	−1.07660	−	1.34360i
$956$	10.1546	+	3.29945i	0.328425	+	0.106712i
$957$	1.67889	+	11.1029i	0.0542708	+	0.358907i
$958$	−5.40610	−	1.75655i	−0.174663	−	0.0567515i
$959$	10.9041	+	4.79671i	0.352111	+	0.154894i
$960$	4.54226	+	0.533341i	0.146601	+	0.0172135i
$961$	16.9103	+	12.2861i	0.545495	+	0.396325i
$962$	−49.8270	+	36.2014i	−1.60649	+	1.16718i
$963$	−23.5956	−	17.6535i	−0.760356	−	0.568875i
$964$	−3.04364	+	4.18921i	−0.0980289	+	0.134925i
$965$	−6.56894	+	0.310299i	−0.211462	+	0.00998888i
$966$	−69.0588	−	18.6931i	−2.22193	−	0.601441i
$967$	0.891587	−	2.74402i	0.0286715	−	0.0882418i	−0.935697	−	0.352805i	$-0.885228\pi$
$967$	0.891587	−	2.74402i	0.0286715	−	0.0882418i	0.964368	+	0.264563i	$0.0852278\pi$
$968$			5.06883i			0.162918i
$969$	−2.24115	+	13.5357i	−0.0719960	+	0.434829i
$970$	0.406486	−	1.48632i	0.0130515	−	0.0477229i
$971$	−8.00975	−	24.6515i	−0.257045	−	0.791103i	−0.993420	−	0.114529i	$-0.963464\pi$
$971$	−8.00975	−	24.6515i	−0.257045	−	0.791103i	0.736375	−	0.676574i	$-0.236536\pi$
$972$	−9.35461	+	16.8715i	−0.300049	+	0.541152i
$973$	−5.00216	+	49.7223i	−0.160362	+	1.59402i
$974$			26.4097i			0.846220i
$975$	−52.0763	−	21.0321i	−1.66778	−	0.673567i
$976$			0.242204i			0.00775276i
$977$	−20.4985	+	28.2138i	−0.655805	+	0.902638i	−0.999334	−	0.0365041i	$-0.988378\pi$
$977$	−20.4985	+	28.2138i	−0.655805	+	0.902638i	0.343529	+	0.939142i	$0.388378\pi$
$978$	21.0805	+	42.0992i	0.674080	+	1.34619i
$979$	−4.19804	+	1.36403i	−0.134170	+	0.0435944i
$980$	19.1433	+	2.95840i	0.611510	+	0.0945027i
$981$	0.313025	−	22.3417i	0.00999413	−	0.713316i
$982$	−52.0153			−1.65987
$983$	14.0206	−	43.1511i	0.447189	−	1.37631i	−0.432876	−	0.901454i	$-0.642501\pi$
$983$	14.0206	−	43.1511i	0.447189	−	1.37631i	0.880065	−	0.474853i	$-0.157499\pi$
$984$	3.73362	−	3.68168i	0.119023	−	0.117368i
$985$	21.4357	−	8.10179i	0.682998	−	0.258144i
$986$	6.68854	+	4.85951i	0.213007	+	0.154758i
$987$	41.8086	+	11.3169i	1.33078	+	0.360221i
$988$	−18.9307	+	13.7540i	−0.602267	+	0.437572i
$989$	−43.5558	+	59.9495i	−1.38500	+	1.90628i
$990$	−44.4551	−	12.8298i	−1.41288	−	0.407758i
$991$	−45.7851	+	33.2649i	−1.45441	+	1.05669i	−0.469638	+	0.882859i	$0.655616\pi$
$991$	−45.7851	+	33.2649i	−1.45441	+	1.05669i	−0.984775	+	0.173834i	$0.944384\pi$
$992$	13.6942	−	42.1466i	0.434793	−	1.33815i
$993$	3.87735	+	25.6419i	0.123044	+	0.813721i
$994$	0.149263	+	0.687158i	0.00473432	+	0.0217953i
$995$	−2.21011	−	46.7873i	−0.0700651	−	1.48326i
$996$	23.6033	−	11.8189i	0.747898	−	0.374497i
$997$	−3.56417	+	1.15807i	−0.112878	+	0.0366764i	−0.364912	−	0.931042i	$-0.618901\pi$
$997$	−3.56417	+	1.15807i	−0.112878	+	0.0366764i	0.252033	+	0.967719i	$0.418901\pi$
$998$	8.60766	−	11.8474i	0.272471	−	0.375024i
$999$	11.9349	+	24.6929i	0.377602	+	0.781250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.18	yes	304
3.2	odd	2	inner	525.2.bb.a.41.60	yes	304
7.6	odd	2	inner	525.2.bb.a.41.17	✓	304
21.20	even	2	inner	525.2.bb.a.41.59	yes	304
25.11	even	5	inner	525.2.bb.a.461.59	yes	304
75.11	odd	10	inner	525.2.bb.a.461.17	yes	304
175.111	odd	10	inner	525.2.bb.a.461.60	yes	304
525.461	even	10	inner	525.2.bb.a.461.18	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.17	✓	304	7.6	odd	2	inner
525.2.bb.a.41.18	yes	304	1.1	even	1	trivial
525.2.bb.a.41.59	yes	304	21.20	even	2	inner
525.2.bb.a.41.60	yes	304	3.2	odd	2	inner
525.2.bb.a.461.17	yes	304	75.11	odd	10	inner
525.2.bb.a.461.18	yes	304	525.461	even	10	inner
525.2.bb.a.461.59	yes	304	25.11	even	5	inner
525.2.bb.a.461.60	yes	304	175.111	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05761 + 1.45568i) q^{2} +(1.54874 - 0.775505i) q^{3} +(-0.382420 - 1.17697i) q^{4} +(-2.23358 + 0.105508i) q^{5} +(-0.509079 + 3.07465i) q^{6} +(-2.28537 + 1.33307i) q^{7} +(-1.30476 - 0.423944i) q^{8} +(1.79718 - 2.40211i) q^{9} +O(q^{10})\)	\(q+(-1.05761 + 1.45568i) q^{2} +(1.54874 - 0.775505i) q^{3} +(-0.382420 - 1.17697i) q^{4} +(-2.23358 + 0.105508i) q^{5} +(-0.509079 + 3.07465i) q^{6} +(-2.28537 + 1.33307i) q^{7} +(-1.30476 - 0.423944i) q^{8} +(1.79718 - 2.40211i) q^{9} +(2.20867 - 3.36295i) q^{10} +(2.25320 - 3.10126i) q^{11} +(-1.50501 - 1.52625i) q^{12} +(-3.81188 - 5.24660i) q^{13} +(0.476515 - 4.73663i) q^{14} +(-3.37741 + 1.89555i) q^{15} +(3.99944 - 2.90576i) q^{16} +(-0.839544 + 2.58385i) q^{17} +(1.59597 + 5.15662i) q^{18} +(2.77292 + 0.900977i) q^{19} +(0.978345 + 2.58850i) q^{20} +(-2.50564 + 3.83689i) q^{21} +(2.13143 + 6.55986i) q^{22} +(5.10006 - 7.01963i) q^{23} +(-2.34951 + 0.355273i) q^{24} +(4.97774 - 0.471322i) q^{25} +11.6688 q^{26} +(0.920522 - 5.11397i) q^{27} +(2.44295 + 2.18002i) q^{28} +(-1.60846 + 0.522622i) q^{29} +(0.812667 - 6.92117i) q^{30} +(-6.85172 - 2.22626i) q^{31} +6.15123i q^{32} +(1.08457 - 6.55041i) q^{33} +(-2.87334 - 3.95482i) q^{34} +(4.96390 - 3.21864i) q^{35} +(-3.51449 - 1.19661i) q^{36} +(-4.27009 + 3.10240i) q^{37} +(-4.24420 + 3.08360i) q^{38} +(-9.97236 - 5.16948i) q^{39} +(2.95902 + 0.809247i) q^{40} +(-1.78524 + 1.29705i) q^{41} +(-2.93529 - 7.70535i) q^{42} -8.54026 q^{43} +(-4.51176 - 1.46596i) q^{44} +(-3.76071 + 5.55491i) q^{45} +(4.82443 + 14.8481i) q^{46} +(-2.92074 - 8.98910i) q^{47} +(3.94065 - 7.60185i) q^{48} +(3.44585 - 6.09312i) q^{49} +(-4.57842 + 7.74445i) q^{50} +(0.703555 + 4.65278i) q^{51} +(-4.71734 + 6.49286i) q^{52} +(6.05684 - 1.96799i) q^{53} +(6.47073 + 6.74857i) q^{54} +(-4.70548 + 7.16464i) q^{55} +(3.54702 - 0.770474i) q^{56} +(4.99324 - 0.755036i) q^{57} +(0.940362 - 2.89414i) q^{58} +(-0.153670 + 0.111648i) q^{59} +(3.52260 + 3.25020i) q^{60} +(-0.0287978 + 0.0396367i) q^{61} +(10.4872 - 7.61938i) q^{62} +(-0.905053 + 7.88549i) q^{63} +(-0.955339 - 0.694094i) q^{64} +(9.06768 + 11.3165i) q^{65} +(8.38823 + 8.50658i) q^{66} +(0.958727 - 2.95066i) q^{67} +3.36217 q^{68} +(2.45490 - 14.8267i) q^{69} +(-0.564579 + 10.6299i) q^{70} +(-0.140481 + 0.0456450i) q^{71} +(-3.36326 + 2.37228i) q^{72} +(-2.85240 + 3.92599i) q^{73} -9.49701i q^{74} +(7.34370 - 4.59021i) q^{75} -3.60819i q^{76} +(-1.01520 + 10.0912i) q^{77} +(18.0720 - 9.04924i) q^{78} +(0.461162 + 1.41931i) q^{79} +(-8.62647 + 6.91222i) q^{80} +(-2.54026 - 8.63407i) q^{81} -3.97050i q^{82} +(-3.80555 + 11.7123i) q^{83} +(5.47411 + 1.48175i) q^{84} +(1.60257 - 5.85981i) q^{85} +(9.03228 - 12.4319i) q^{86} +(-2.08580 + 2.05678i) q^{87} +(-4.25465 + 3.09119i) q^{88} +(-0.931573 - 0.676828i) q^{89} +(-4.10879 - 11.3493i) q^{90} +(15.7056 + 6.90892i) q^{91} +(-10.2122 - 3.31816i) q^{92} +(-12.3380 + 1.86565i) q^{93} +(16.1742 + 5.25533i) q^{94} +(-6.28859 - 1.71984i) q^{95} +(4.77031 + 9.52666i) q^{96} +(0.364241 - 0.118349i) q^{97} +(5.22525 + 11.4602i) q^{98} +(-3.40016 - 10.9860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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