LMFDB - Embedded newform 525.2.bb.a.41.17

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			41.17
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.17

$q$-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} +(4.35756 - 1.91689i) 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} +(4.57325 + 0.292261i) 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} +(-0.695010 + 3.19960i) 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} +(-5.24520 - 2.73639i) 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} +(-5.26216 + 6.34807i) 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} +(2.41672 + 2.70821i) 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} +(-7.30941 + 3.09394i) 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} +(9.53069 - 4.74129i) 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} +(-9.28359 + 4.08386i) 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} +(-1.40492 - 5.49433i) 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} +(-1.71747 - 17.0719i) 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} +(-12.5140 - 1.42812i) 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	$0.155944\pi$
$13$	3.81188	+	5.24660i	1.05722	+	1.45514i	0.174850	+	0.984595i	$0.444056\pi$
$14$	4.35756	−	1.91689i	1.16461	−	0.512311i
$15$	−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	$-0.793132\pi$
$17$	0.839544	−	2.58385i	0.203619	−	0.626676i	0.999767	−	0.0215740i	$-0.00686774\pi$
$18$	1.59597	+	5.15662i	0.376174	+	1.21543i
$19$	−2.77292	−	0.900977i	−0.636152	−	0.206698i	−0.0268535	−	0.999639i	$-0.508549\pi$
$19$	−2.77292	−	0.900977i	−0.636152	−	0.206698i	−0.609298	+	0.792941i	$0.708549\pi$
$20$	−0.978345	−	2.58850i	−0.218765	−	0.578807i
$21$	4.57325	+	0.292261i	0.997964	+	0.0637766i
$22$	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
$28$	−0.695010	+	3.19960i	−0.131344	+	0.604668i
$29$	−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	0.850934	−	0.525273i	$-0.176037\pi$
$31$	6.85172	+	2.22626i	1.23061	+	0.399848i	0.379672	+	0.925121i	$0.376037\pi$
$32$			6.15123i			1.08739i
$33$	−1.08457	+	6.55041i	−0.188800	+	1.14028i
$34$	2.87334	+	3.95482i	0.492774	+	0.678245i
$35$	−5.24520	−	2.73639i	−0.886601	−	0.462534i
$36$	−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	−0.439590	−	0.898199i	$-0.644876\pi$
$41$	1.78524	−	1.29705i	0.278807	−	0.202565i	0.718397	+	0.695633i	$0.244876\pi$
$42$	−5.26216	+	6.34807i	−0.811968	+	0.979529i
$43$	−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	$0.142098\pi$
$47$	2.92074	+	8.98910i	0.426033	+	1.31120i	−0.475968	+	0.879462i	$0.657902\pi$
$48$	−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
$56$	2.41672	+	2.70821i	0.322948	+	0.361900i
$57$	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	−0.577737	−	0.816223i	$-0.696064\pi$
$59$	0.153670	−	0.111648i	0.0200062	−	0.0145353i	0.597743	+	0.801687i	$0.296064\pi$
$60$	3.52260	+	3.25020i	0.454765	+	0.419599i
$61$	0.0287978	−	0.0396367i	0.00368717	−	0.00507496i	−0.807169	−	0.590320i	$-0.799002\pi$
$61$	0.0287978	−	0.0396367i	0.00368717	−	0.00507496i	0.810857	+	0.585245i	$0.199002\pi$
$62$	−10.4872	+	7.61938i	−1.33187	+	0.967662i
$63$	−7.30941	+	3.09394i	−0.920900	+	0.389800i
$64$	−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
$70$	9.53069	−	4.74129i	1.13914	−	0.566692i
$71$	−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	−0.608784	−	0.793336i	$-0.708342\pi$
$73$	2.85240	−	3.92599i	0.333848	−	0.459502i	0.942632	+	0.333834i	$0.108342\pi$
$74$		−	9.49701i		−	1.10400i
$75$	−7.34370	+	4.59021i	−0.847978	+	0.530032i
$76$			3.60819i			0.413888i
$77$	−9.28359	+	4.08386i	−1.05796	+	0.465399i
$78$	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	$-0.663766\pi$
$83$	3.80555	−	11.7123i	0.417714	−	1.28559i	0.909801	−	0.415045i	$-0.136234\pi$
$84$	−1.40492	−	5.49433i	−0.153289	−	0.599481i
$85$	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	0.636063	−	0.771637i	$-0.280562\pi$
$89$	0.931573	+	0.676828i	0.0987466	+	0.0717436i	−0.537316	+	0.843381i	$0.680562\pi$
$90$	4.10879	+	11.3493i	0.433105	+	1.19632i
$91$	−1.71747	−	17.0719i	−0.180040	−	1.78962i
$92$	−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	−0.327450	−	0.944868i	$-0.606189\pi$
$97$	−0.364241	+	0.118349i	−0.0369831	+	0.0120165i	0.290467	+	0.956885i	$0.406189\pi$
$98$	−12.5140	−	1.42812i	−1.26410	−	0.144262i
$99$	−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	$-0.393190\pi$
$101$	6.61867			0.658583			0.329291	+	0.944228i	$0.393190\pi$
$102$	−7.51704	−	3.89669i	−0.744298	−	0.385830i
$103$	6.73355	−	2.18786i	0.663477	−	0.215577i	0.0421297	−	0.999112i	$-0.486586\pi$
$103$	6.73355	−	2.18786i	0.663477	−	0.215577i	0.621347	+	0.783535i	$0.286586\pi$
$104$	−2.74934	−	8.46159i	−0.269595	−	0.829727i
$105$	10.2455	+	0.170273i	0.999862	+	0.0166169i
$106$	−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
$112$	−13.0138	+	1.30921i	−1.22969	+	0.123709i
$113$	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
$119$	−5.36313	+	4.78589i	−0.491637	+	0.438722i
$120$	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
$126$	3.22674	−	13.9123i	0.287461	−	1.23941i
$127$	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	−0.992889	−	0.119041i	$-0.962018\pi$
$131$	−1.36951	+	4.21491i	−0.119654	+	0.368258i	0.873235	+	0.487299i	$0.162018\pi$
$132$	8.12439	−	1.22850i	0.707137	−	0.106927i
$133$	5.13609	+	5.75557i	0.445355	+	0.499071i
$134$	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	$0.495717\pi$
$139$	−11.1022	+	15.2808i	−0.941674	+	1.29610i	−0.955128	+	0.296193i	$0.904283\pi$
$140$	−1.21477	+	7.21989i	−0.102667	+	0.610192i
$141$	−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
$147$	−10.0620	−	6.76439i	−0.829897	−	0.557917i
$148$	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
$154$	3.87365	−	17.8331i	0.312148	−	1.43703i
$155$	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	$0.0181246\pi$
$157$			1.42614i			0.113818i	−0.998379	+	0.0569092i	$0.981875\pi$
$158$	−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
$161$	−21.0132	+	9.24372i	−1.65607	+	0.728507i
$162$	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	$-0.776139\pi$
$167$	3.02999	−	9.32534i	0.234467	−	0.721616i	0.997192	−	0.0748926i	$-0.0238614\pi$
$168$	−5.84310	−	2.32013i	−0.450805	−	0.179002i
$169$	−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	0.483152	−	0.875536i	$-0.339492\pi$
$173$	−2.63362	−	1.91344i	−0.200230	−	0.145476i	−0.683382	+	0.730061i	$0.739492\pi$
$174$	0.788042	+	5.21152i	0.0597413	+	0.395084i
$175$	−12.0043	−	5.55853i	−0.907438	−	0.420185i
$176$		−	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	0.488138	−	0.872766i	$-0.337676\pi$
$181$	4.97852	+	1.61762i	0.370051	+	0.120237i	−0.118087	+	0.993003i	$0.537676\pi$
$182$	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
$189$	8.92101	−	10.4602i	0.648908	−	0.760867i
$190$	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
$196$	5.85365	−	6.38579i	0.418118	−	0.456128i
$197$	−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	$-0.733661\pi$
$199$		−	20.9472i		−	1.48491i	0.669896	−	0.742455i	$-0.266339\pi$
$200$	−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
$203$	4.37263	+	0.949812i	0.306899	+	0.0666637i
$204$	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
$210$	−11.0837	+	14.7341i	−0.764845	+	1.01675i
$211$	−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
$217$	−12.6910	−	14.2217i	−0.861519	−	0.965429i
$218$			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	−0.989822	−	0.142313i	$-0.954546\pi$
$223$	−8.19237	+	11.2758i	−0.548602	+	0.755086i	0.441220	+	0.897399i	$0.354546\pi$
$224$	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	−0.225270	−	0.974296i	$-0.572326\pi$
$227$	−18.4037	−	13.3710i	−1.22149	−	0.887467i	−0.996223	+	0.0868294i	$0.972326\pi$
$228$	−2.79817	−	5.58815i	−0.185313	−	0.370084i
$229$	−2.39404	+	0.777870i	−0.158203	+	0.0514031i	−0.387048	−	0.922060i	$-0.626505\pi$
$229$	−2.39404	+	0.777870i	−0.158203	+	0.0514031i	0.228845	+	0.973463i	$0.426505\pi$
$230$	12.3423	+	32.6553i	0.813830	+	2.15323i
$231$	11.2108	−	13.5243i	0.737617	−	0.889834i
$232$	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
$238$	−1.29461	−	12.8686i	−0.0839168	−	0.834147i
$239$	−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	0.880850	−	0.473396i	$-0.156972\pi$
$241$	2.45943	+	3.38511i	0.158426	+	0.218054i	−0.722424	+	0.691450i	$0.756972\pi$
$242$	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
$245$	8.33944	+	13.2459i	0.532787	+	0.846249i
$246$	−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	$-0.785401\pi$
$251$	−24.7536			−1.56243			−0.781217	+	0.624260i	$0.785401\pi$
$252$	6.43674	+	7.41977i	0.405476	+	0.467401i
$253$	−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	$-0.536953\pi$
$257$	−3.71383			−0.231662			−0.115831	+	0.993269i	$0.536953\pi$
$258$	−4.34767	+	26.2583i	−0.270674	+	1.63477i
$259$	13.8945	−	1.39781i	0.863360	−	0.0868557i
$260$	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
$266$	−13.8102	+	1.38934i	−0.846760	+	0.0851857i
$267$	−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	$0.367439\pi$
$269$	−7.54932	+	23.2344i	−0.460290	+	1.41663i	−0.864810	+	0.502099i	$0.832561\pi$
$270$	−15.1649	−	14.3907i	−0.922907	−	0.875793i
$271$	−11.9066	+	3.86869i	−0.723274	+	0.235006i	−0.647442	−	0.762115i	$-0.724161\pi$
$271$	−11.9066	+	3.86869i	−0.723274	+	0.235006i	−0.0758320	+	0.997121i	$0.524161\pi$
$272$	−4.15035	−	12.7735i	−0.251652	−	0.774505i
$273$	15.8993	+	25.1080i	0.962267	+	1.51961i
$274$	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
$280$	5.68368	+	5.79401i	0.339665	+	0.346259i
$281$	−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	0.108773	−	0.994067i	$-0.465308\pi$
$283$	−6.51920	−	2.11822i	−0.387526	−	0.125915i	−0.496299	+	0.868152i	$0.665308\pi$
$284$	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
$287$	−5.80899	+	0.584395i	−0.342894	+	0.0344958i
$288$	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	$-0.770746\pi$
$293$	−25.7327			−1.50332			−0.751660	+	0.659551i	$0.770746\pi$
$294$	20.4884	−	7.49288i	1.19491	−	0.436994i
$295$	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	$0.0944002\pi$
$307$			10.2409i			0.584478i	−0.956345	+	0.292239i	$0.905600\pi$
$308$	8.35681	+	9.36475i	0.476174	+	0.533606i
$309$	−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	0.740542	−	0.672010i	$-0.234569\pi$
$311$	5.82425	+	4.23156i	0.330263	+	0.239950i	−0.410279	+	0.911960i	$0.634569\pi$
$312$	10.8200	+	10.9727i	0.612562	+	0.621205i
$313$	−5.77397	−	7.94719i	−0.326364	−	0.449202i	0.614033	−	0.789281i	$-0.289546\pi$
$313$	−5.77397	−	7.94719i	−0.326364	−	0.449202i	−0.940397	+	0.340079i	$0.889546\pi$
$314$	−2.07600	−	1.50830i	−0.117155	−	0.0851184i
$315$	−15.9997	+	7.68175i	−0.901481	+	0.432818i
$316$	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
$322$	8.76791	−	40.3647i	0.488617	−	2.24944i
$323$	−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
$329$	5.30814	−	24.4370i	0.292647	−	1.34725i
$330$	−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
$336$	19.1397	−	12.1199i	1.04415	−	0.661194i
$337$	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	$0.00625294\pi$
$349$			0.733921i			0.0392859i	−0.999807	+	0.0196429i	$0.993747\pi$
$350$	20.7873	−	11.5956i	1.11113	−	0.619811i
$351$	−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	0.879197	−	0.476458i	$-0.158079\pi$
$353$	−2.10697	−	6.48460i	−0.112143	−	0.345140i	−0.991340	+	0.131317i	$0.958079\pi$
$354$	−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
$357$	4.59460	−	11.5712i	0.243172	−	0.612414i
$358$	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
$364$	−19.4363	+	8.55006i	−1.01874	+	0.448145i
$365$	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	0.132014	−	0.991248i	$-0.457856\pi$
$367$	−6.58674	−	2.14016i	−0.343825	−	0.111716i	−0.475839	+	0.879532i	$0.657856\pi$
$368$		−	42.8941i		−	2.23601i
$369$	0.0927427	−	6.61937i	0.00482799	−	0.344591i
$370$	−1.00201	−	21.2123i	−0.0520922	−	1.10278i
$371$	−16.4656	−	3.57661i	−0.854851	−	0.185688i
$372$	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
$378$	5.79170	+	24.0489i	0.297893	+	1.23694i
$379$	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	−0.985094	−	0.172016i	$-0.944972\pi$
$383$	−1.70316	+	5.24179i	−0.0870275	+	0.267843i	0.898067	+	0.439860i	$0.144972\pi$
$384$	12.5521	−	12.3775i	0.640548	−	0.631636i
$385$	−20.3047	+	10.1011i	−1.03483	+	0.514801i
$386$	−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
$392$	−1.91288	−	9.41093i	−0.0966148	−	0.475324i
$393$	−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	−0.811759	−	0.583992i	$-0.801490\pi$
$397$	−22.4199	+	7.28468i	−1.12522	+	0.365608i	−0.313465	+	0.949600i	$0.601490\pi$
$398$	30.4924	+	22.1540i	1.52845	+	1.11048i
$399$	−12.4179	−	4.93081i	−0.621674	−	0.246849i
$400$	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
$406$	−6.00716	+	5.36061i	−0.298131	+	0.266043i
$407$			20.2330i			1.00291i
$408$	1.05454	−	6.36905i	0.0522077	−	0.315315i
$409$	3.68781	+	5.07583i	0.182350	+	0.250984i	0.890400	−	0.455179i	$-0.150425\pi$
$409$	3.68781	+	5.07583i	0.182350	+	0.250984i	−0.708050	+	0.706163i	$0.750425\pi$
$410$	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
$413$	−0.500029	+	0.0503039i	−0.0246048	+	0.00247529i
$414$	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	−0.880982	−	0.473149i	$-0.843117\pi$
$419$	2.24873	−	6.92087i	0.109857	−	0.338106i	0.990840	+	0.135043i	$0.0431172\pi$
$420$	−3.71769	−	12.1238i	−0.181405	−	0.591580i
$421$	−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
$427$	−0.118652	+	0.0521952i	−0.00574198	+	0.00252590i
$428$	−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	0.823307	−	0.567596i	$-0.192126\pi$
$433$	24.0497	+	7.81421i	1.15575	+	0.375527i	0.332445	+	0.943123i	$0.392126\pi$
$434$	34.1243	−	3.43297i	1.63802	−	0.164788i
$435$	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	−0.971003	−	0.239067i	$-0.923158\pi$
$439$	−9.29403	+	12.7921i	−0.443580	+	0.610535i	0.527423	+	0.849603i	$0.323158\pi$
$440$	−9.17695	+	7.35330i	−0.437494	+	0.350555i
$441$	20.8292	+	2.67317i	0.991865	+	0.127294i
$442$	−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
$448$	1.25803	+	2.85980i	0.0594362	+	0.135113i
$449$		−	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
$455$	−5.63733	−	37.9502i	−0.264282	−	1.77914i
$456$	−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	0.653205	−	0.757181i	$-0.273424\pi$
$461$	2.89719	+	2.10493i	0.134935	+	0.0980363i	−0.518270	+	0.855217i	$0.673424\pi$
$462$	7.83035	+	30.6228i	0.364301	+	1.42470i
$463$	−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	−0.975483	−	0.220074i	$-0.929370\pi$
$467$	−1.23058	+	3.78733i	−0.0569444	+	0.175257i	0.918539	+	0.395331i	$0.129370\pi$
$468$	−7.11863	−	23.0004i	−0.329059	−	1.06320i
$469$	−6.12448	+	5.46530i	−0.282802	+	0.252364i
$470$	−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	0.926274	−	0.376851i	$-0.122993\pi$
$479$	−0.976231	−	3.00453i	−0.0446051	−	0.137280i	−0.970879	+	0.239571i	$0.922993\pi$
$480$	−11.6600	−	20.7752i	−0.532204	−	0.948255i
$481$	−32.5541	−	10.5775i	−1.48434	−	0.482291i
$482$	−7.52875			−0.342925
$483$	25.3754	−	30.6119i	1.15462	−	1.39289i
$484$	−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
$490$	−28.1016	−	1.86948i	−1.26950	−	0.0844545i
$491$	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
$497$	0.381899	+	0.0829552i	0.0171305	+	0.00372105i
$498$	−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	$0.305226\pi$
$503$	13.2512	+	40.7830i	0.590841	+	1.81842i	0.0164166	+	0.999865i	$0.494774\pi$
$504$	10.8487	−	0.938081i	0.483240	−	0.0417854i
$505$	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	−0.894475	−	0.447117i	$-0.852451\pi$
$509$	−16.8226	+	12.2224i	−0.745650	+	0.541746i	0.148826	+	0.988863i	$0.452451\pi$
$510$	−17.2010	−	7.91044i	−0.761674	−	0.350280i
$511$	−11.7524	+	5.16990i	−0.519896	+	0.228703i
$512$	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	$0.0166873\pi$
$521$	5.05631	+	15.5617i	0.221521	+	0.681772i	−0.777105	+	0.629371i	$0.783313\pi$
$522$	−5.26203	−	7.46015i	−0.230313	−	0.326522i
$523$	−14.0872	+	19.3894i	−0.615990	+	0.847837i	−0.997053	−	0.0767117i	$-0.975558\pi$
$523$	−14.0872	+	19.3894i	−0.615990	+	0.847837i	0.381064	+	0.924549i	$0.375558\pi$
$524$	5.48454			0.239593
$525$	22.9022	−	0.700670i	0.999532	−	0.0305798i
$526$	−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
$539$	26.6605	+	3.04254i	1.14835	+	0.131052i
$540$	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
$546$	−53.3645	−	3.41035i	−2.28379	−	0.145949i
$547$	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
$553$	0.838115	−	3.85842i	0.0356403	−	0.164077i
$554$	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
$560$	−28.9292	+	4.29729i	−1.22248	+	0.181594i
$561$	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	−0.942166	−	0.335148i	$-0.891214\pi$
$563$	−21.7005	+	15.7663i	−0.914566	+	0.664471i	0.0275994	+	0.999619i	$0.491214\pi$
$564$	−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
$567$	−5.70439	+	23.1184i	−0.239562	+	0.970881i
$568$	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	−0.999214	−	0.0396392i	$-0.987379\pi$
$577$	−15.6794	+	21.5808i	−0.652741	+	0.898421i	0.346473	+	0.938060i	$0.387379\pi$
$578$	−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
$581$	−24.3104	+	21.6939i	−1.00857	+	0.900013i
$582$	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	−0.859358	−	0.511375i	$-0.829136\pi$
$587$	−15.4713	+	11.2405i	−0.638567	+	0.463946i	0.220790	+	0.975321i	$0.429136\pi$
$588$	−4.11357	+	14.4295i	−0.169641	+	0.595061i
$589$	−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	$-0.350132\pi$
$593$	22.0927			0.907240			0.453620	+	0.891195i	$0.350132\pi$
$594$	−35.5089	+	4.86155i	−1.45695	+	0.199472i
$595$	−11.4740	+	11.2555i	−0.470389	+	0.461431i
$596$	−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	$-0.961820\pi$
$601$		−	5.86687i		−	0.239315i	0.992815	−	0.119657i	$-0.0381796\pi$
$602$	−37.2147	+	16.3708i	−1.51676	+	0.667223i
$603$	−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	$-0.960117\pi$
$607$		−	6.15776i		−	0.249936i	0.992161	−	0.124968i	$-0.0398828\pi$
$608$	5.54212	−	17.0569i	0.224763	−	0.691748i
$609$	−7.50865	+	1.91999i	−0.304266	+	0.0778018i
$610$	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
$616$	13.8442	−	1.39276i	0.557800	−	0.0561158i
$617$	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	0.607861	−	0.794043i	$-0.292028\pi$
$619$	15.7465	+	5.11634i	0.632904	+	0.205643i	0.0250429	+	0.999686i	$0.492028\pi$
$620$	−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
$623$	−1.22673	−	2.78866i	−0.0491480	−	0.111725i
$624$	−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
$630$	5.73932	−	31.4147i	0.228660	−	1.25159i
$631$	−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
$637$	−18.8330	+	41.3052i	−0.746191	+	1.63657i
$638$	−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	$-0.893055\pi$
$643$		−	16.7204i		−	0.659386i	0.944088	−	0.329693i	$-0.106945\pi$
$644$	18.9154	+	21.1969i	0.745373	+	0.835274i
$645$	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	$-0.871504\pi$
$647$	−10.3403	−	31.8241i	−0.406519	−	1.25114i	0.513102	−	0.858328i	$-0.328496\pi$
$648$	−0.345920	+	12.3423i	−0.0135890	+	0.484853i
$649$		−	0.728137i		−	0.0285819i
$650$	−58.0844	+	5.49977i	−2.27826	+	0.215719i
$651$	30.6840	+	12.1837i	1.20260	+	0.477518i
$652$	−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
$658$	29.9584	+	33.5718i	1.16790	+	1.30876i
$659$	−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	−0.797591	−	0.603199i	$-0.793892\pi$
$661$	0.579881	−	0.798137i	0.0225547	−	0.0310439i	0.820145	+	0.572155i	$0.193892\pi$
$662$	−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
$665$	12.0791	+	12.3136i	0.468408	+	0.477501i
$666$	−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
$672$	−1.79777	+	28.1311i	−0.0693504	+	1.08518i
$673$	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	0.338229	−	0.941064i	$-0.390172\pi$
$677$	−11.7674	−	8.54952i	−0.452258	−	0.328585i	−0.790487	+	0.612479i	$0.790172\pi$
$678$	24.2179	−	12.1267i	0.930084	−	0.465724i
$679$	0.990194	+	0.215087i	0.0380001	+	0.00825429i
$680$	−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
$686$	26.6953	+	19.9458i	1.01923	+	0.761534i
$687$	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	0.927268	−	0.374399i	$-0.122151\pi$
$691$	7.48259	+	10.2989i	0.284651	+	0.391789i	−0.642616	+	0.766188i	$0.722151\pi$
$692$	−1.24491	+	3.83143i	−0.0473242	+	0.145649i
$693$	−6.87445	+	29.6397i	−0.261139	+	1.12592i
$694$	−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
$700$	−1.95153	+	16.2544i	−0.0737610	+	0.614357i
$701$			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
$714$	11.9847	+	18.9261i	0.448515	+	0.708292i
$715$	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	$-0.663129\pi$
$719$	11.2251	−	34.5472i	0.418625	−	1.28839i	0.908968	−	0.416865i	$-0.136871\pi$
$720$	−1.10054	−	33.1442i	−0.0410147	−	1.23521i
$721$	−18.3053	−	3.97622i	−0.681723	−	0.148082i
$722$	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	$-0.531883\pi$
$727$	23.6517	−	32.5538i	0.877195	−	1.20736i	0.977190	−	0.212367i	$-0.0681173\pi$
$728$	−4.99664	+	23.0029i	−0.185188	+	0.852546i
$729$	−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	−0.0364323	−	0.999336i	$-0.511599\pi$
$733$	−17.6875	−	5.74701i	−0.653302	−	0.212271i	−0.616869	+	0.787066i	$0.711599\pi$
$734$	10.0816	−	7.32471i	0.372119	−	0.270360i
$735$	−23.1879	−	14.0472i	−0.855297	−	0.518137i
$736$	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
$742$	22.6206	−	20.1859i	0.830428	−	0.741048i
$743$			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
$756$	−15.7229	−	6.49956i	−0.571836	−	0.236387i
$757$	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	0.701270	−	0.712896i	$-0.252617\pi$
$761$	6.61985	+	4.80960i	0.239969	+	0.174348i	−0.461300	+	0.887244i	$0.652617\pi$
$762$	13.6622	−	13.4721i	0.494929	−	0.488043i
$763$	−19.6065	+	1.97245i	−0.709803	+	0.0714076i
$764$	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	0.0789366	−	0.996880i	$-0.474848\pi$
$769$	−12.2890	−	3.99295i	−0.443153	−	0.143989i	−0.522090	+	0.852890i	$0.674848\pi$
$770$	6.77056	−	40.2402i	0.243994	−	1.45016i
$771$	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	−0.289360	−	0.957220i	$-0.593442\pi$
$773$	−35.8420	−	26.0407i	−1.28915	−	0.936621i	−0.999788	+	0.0205997i	$0.993442\pi$
$774$	−13.6300	−	44.0389i	−0.489921	−	1.58294i
$775$	35.1554	+	7.85237i	1.26282	+	0.282065i
$776$	0.525422			0.0188615
$777$	−20.4349	+	12.9401i	−0.733098	+	0.464222i
$778$	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
$784$	31.4866	+	14.3563i	1.12452	+	0.512723i
$785$	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	$0.178827\pi$
$787$	30.6181	+	42.1422i	1.09142	+	1.50221i	0.245120	+	0.969493i	$0.421173\pi$
$788$	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
$791$	−2.30155	−	22.8778i	−0.0818337	−	0.813440i
$792$	−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	0.993499	−	0.113841i	$-0.0363153\pi$
$797$	3.46757	+	10.6721i	0.122828	+	0.378025i	−0.870671	+	0.491865i	$0.836315\pi$
$798$	20.3110	−	12.8616i	0.719002	−	0.455297i
$799$	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
$805$	−45.9593	+	22.8636i	−1.61985	+	0.805837i
$806$	−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	$-0.522303\pi$
$811$	25.6402	−	35.2906i	0.900347	−	1.23922i	0.970357	−	0.241676i	$-0.0776970\pi$
$812$	−0.554284	−	5.50968i	−0.0194516	−	0.193352i
$813$	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
$819$	−44.0952	−	26.5558i	−1.54081	−	0.927936i
$820$	−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	−0.640525	−	0.767937i	$-0.721283\pi$
$829$	−20.3660	+	6.61730i	−0.707339	+	0.229828i	−0.0668137	+	0.997765i	$0.521283\pi$
$830$	30.9827	+	38.6665i	1.07542	+	1.34213i
$831$	19.4002	+	3.21215i	0.672985	+	0.111428i
$832$		−	7.65808i		−	0.265496i
$833$	18.6367	−	3.78811i	0.645722	−	0.131250i
$834$	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	0.00223397	−	0.999998i	$-0.499289\pi$
$839$	−27.4631	−	19.9531i	−0.948130	−	0.688857i	−0.950364	+	0.311141i	$0.899289\pi$
$840$	−13.2958	−	4.56569i	−0.458749	−	0.157531i
$841$	−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
$847$	−2.07498	+	9.55255i	−0.0712972	+	0.328230i
$848$	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	−0.0851663	−	0.996367i	$-0.527142\pi$
$853$	12.6049	−	4.09557i	0.431582	−	0.140230i	0.516749	+	0.856137i	$0.327142\pi$
$854$	0.0495085	−	0.227921i	0.00169415	−	0.00779931i
$855$	−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	$-0.246284\pi$
$857$	41.8810			1.43063			0.715314	+	0.698804i	$0.246284\pi$
$858$	12.6557	−	76.4356i	0.432058	−	2.60947i
$859$	29.3994	+	40.4649i	1.00310	+	1.38064i	0.923406	+	0.383824i	$0.125393\pi$
$859$	29.3994	+	40.4649i	1.00310	+	1.38064i	0.0796896	+	0.996820i	$0.474607\pi$
$860$	8.35533	+	22.1065i	0.284914	+	0.753825i
$861$	8.54340	−	5.40997i	0.291158	−	0.184371i
$862$	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
$875$	−27.3990	−	11.1489i	−0.926254	−	0.376900i
$876$	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	$-0.754052\pi$
$881$	8.11937	−	24.9888i	0.273548	−	0.841895i	0.989600	−	0.143848i	$-0.0459476\pi$
$882$	−25.9204	+	27.4934i	−0.872786	+	0.925750i
$883$	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	−0.994637	−	0.103424i	$-0.967020\pi$
$887$	−35.8473	+	26.0446i	−1.20363	+	0.874492i	−0.208997	+	0.977916i	$0.567020\pi$
$888$	−8.93042	+	8.80617i	−0.299685	+	0.295516i
$889$	−6.55898	−	14.9101i	−0.219981	−	0.500070i
$890$	−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
$896$	26.3141	+	5.71588i	0.879092	+	0.190954i
$897$	−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
$903$	−39.0567	−	2.49599i	−1.29973	−	0.0830613i
$904$	−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
$910$	61.2054	+	31.9305i	2.02894	+	1.05849i
$911$	−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
$917$	8.74860	−	7.80698i	0.288904	−	0.257809i
$918$	−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
$924$	−20.2049	−	8.02280i	−0.664693	−	0.263931i
$925$	−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	$0.0560867\pi$
$929$	8.87135	+	27.3032i	0.291060	+	0.895789i	−0.693457	+	0.720498i	$0.743913\pi$
$930$	20.9765	−	45.6128i	0.687847	−	1.49570i
$931$	−4.06530	−	20.0004i	−0.133235	−	0.655486i
$932$		−	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	0.994060	−	0.108833i	$-0.0347115\pi$
$937$	17.8573	+	24.5784i	0.583372	+	0.802943i	−0.410688	+	0.911776i	$0.634711\pi$
$938$	−1.47839	−	14.6954i	−0.0482711	−	0.479823i
$939$	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	0.0229760	−	0.999736i	$-0.492686\pi$
$941$	30.0892	−	21.8611i	0.980881	−	0.712652i	0.957905	+	0.287084i	$0.0926859\pi$
$942$	4.38488	+	0.726018i	0.142867	+	0.0236550i
$943$		−	19.1467i		−	0.623503i
$944$	0.290172	−	0.893059i	0.00944431	−	0.0290666i
$945$	18.8221	−	24.3049i	0.612284	−	0.790638i
$946$	−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
$952$	9.02656	−	3.97079i	0.292553	−	0.128694i
$953$	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
$959$	1.19240	+	11.8526i	0.0385046	+	0.382742i
$960$	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
$966$	17.7238	+	69.3139i	0.570254	+	2.23014i
$967$	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	$0.0365360\pi$
$971$	8.00975	+	24.6515i	0.257045	+	0.791103i	−0.736375	+	0.676574i	$0.763464\pi$
$972$	9.35461	−	16.8715i	0.300049	−	0.541152i
$973$	45.7430	−	20.1224i	1.46645	−	0.645094i
$974$			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
$980$	12.4008	−	14.8808i	0.396130	−	0.475348i
$981$	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	$0.357499\pi$
$983$	−14.0206	+	43.1511i	−0.447189	+	1.37631i	−0.880065	+	0.474853i	$0.842501\pi$
$984$	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
$987$	10.7301	+	41.9630i	0.341542	+	1.33570i
$988$	−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
$994$	−0.524657	+	0.468188i	−0.0166411	+	0.0148500i
$995$	−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	−0.252033	−	0.967719i	$-0.581099\pi$
$997$	3.56417	−	1.15807i	0.112878	−	0.0366764i	0.364912	+	0.931042i	$0.381099\pi$
$998$	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.41.17	✓	304
3.2	odd	2	inner	525.2.bb.a.41.59	yes	304
7.6	odd	2	inner	525.2.bb.a.41.18	yes	304
21.20	even	2	inner	525.2.bb.a.41.60	yes	304
25.11	even	5	inner	525.2.bb.a.461.60	yes	304
75.11	odd	10	inner	525.2.bb.a.461.18	yes	304
175.111	odd	10	inner	525.2.bb.a.461.59	yes	304
525.461	even	10	inner	525.2.bb.a.461.17	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.17	✓	304	1.1	even	1	trivial
525.2.bb.a.41.18	yes	304	7.6	odd	2	inner
525.2.bb.a.41.59	yes	304	3.2	odd	2	inner
525.2.bb.a.41.60	yes	304	21.20	even	2	inner
525.2.bb.a.461.17	yes	304	525.461	even	10	inner
525.2.bb.a.461.18	yes	304	75.11	odd	10	inner
525.2.bb.a.461.59	yes	304	175.111	odd	10	inner
525.2.bb.a.461.60	yes	304	25.11	even	5	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} +(4.35756 - 1.91689i) 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} +(4.57325 + 0.292261i) 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} +(-0.695010 + 3.19960i) 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} +(-5.24520 - 2.73639i) 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} +(-5.26216 + 6.34807i) 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} +(2.41672 + 2.70821i) 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} +(-7.30941 + 3.09394i) 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} +(9.53069 - 4.74129i) 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} +(-9.28359 + 4.08386i) 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} +(-1.40492 - 5.49433i) 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} +(-1.71747 - 17.0719i) 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} +(-12.5140 - 1.42812i) 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

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