LMFDB - Embedded newform 525.2.bb.a.41.4

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			41.4
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51682 + 2.08772i) q^{2} +(0.356101 + 1.69505i) q^{3} +(-1.43980 - 4.43126i) q^{4} +(1.66426 - 1.49340i) q^{5} +(-4.07893 - 1.82764i) q^{6} +(-2.38379 + 1.14785i) q^{7} +(6.52662 + 2.12063i) q^{8} +(-2.74638 + 1.20722i) q^{9} +O(q^{10})$	\(q+(-1.51682 + 2.08772i) q^{2} +(0.356101 + 1.69505i) q^{3} +(-1.43980 - 4.43126i) q^{4} +(1.66426 - 1.49340i) q^{5} +(-4.07893 - 1.82764i) q^{6} +(-2.38379 + 1.14785i) q^{7} +(6.52662 + 2.12063i) q^{8} +(-2.74638 + 1.20722i) q^{9} +(0.593408 + 5.73972i) q^{10} +(-2.79937 + 3.85300i) q^{11} +(6.99849 - 4.01851i) q^{12} +(0.0489901 + 0.0674291i) q^{13} +(1.21937 - 6.71776i) q^{14} +(3.12402 + 2.28921i) q^{15} +(-6.78806 + 4.93181i) q^{16} +(-0.980587 + 3.01794i) q^{17} +(1.64543 - 7.56481i) q^{18} +(-4.44996 - 1.44588i) q^{19} +(-9.01384 - 5.22459i) q^{20} +(-2.79454 - 3.63188i) q^{21} +(-3.79785 - 11.6886i) q^{22} +(3.47912 - 4.78859i) q^{23} +(-1.27043 + 11.8181i) q^{24} +(0.539541 - 4.97080i) q^{25} -0.215082 q^{26} +(-3.02428 - 4.22537i) q^{27} +(8.51862 + 8.91049i) q^{28} +(-1.55280 + 0.504535i) q^{29} +(-9.51779 + 3.04978i) q^{30} +(-8.62654 - 2.80293i) q^{31} -7.92721i q^{32} +(-7.52787 - 3.37301i) q^{33} +(-4.81323 - 6.62485i) q^{34} +(-2.25305 + 5.47026i) q^{35} +(9.30375 + 10.4318i) q^{36} +(5.65143 - 4.10601i) q^{37} +(9.76836 - 7.09713i) q^{38} +(-0.0968503 + 0.107052i) q^{39} +(14.0290 - 6.21755i) q^{40} +(-6.30543 + 4.58116i) q^{41} +(11.8211 - 0.325305i) q^{42} -4.37935 q^{43} +(21.1042 + 6.85716i) q^{44} +(-2.76785 + 6.11056i) q^{45} +(4.72005 + 14.5268i) q^{46} +(1.40749 + 4.33180i) q^{47} +(-10.7769 - 9.74987i) q^{48} +(4.36487 - 5.47247i) q^{49} +(9.55926 + 8.66621i) q^{50} +(-5.46474 - 0.587453i) q^{51} +(0.228260 - 0.314173i) q^{52} +(-0.176583 + 0.0573752i) q^{53} +(13.4087 + 0.0952533i) q^{54} +(1.09517 + 10.5930i) q^{55} +(-17.9922 + 2.43648i) q^{56} +(0.866202 - 8.05778i) q^{57} +(1.30198 - 4.00709i) q^{58} +(0.335313 - 0.243619i) q^{59} +(5.64610 - 17.1394i) q^{60} +(5.88303 - 8.09729i) q^{61} +(18.9366 - 13.7583i) q^{62} +(5.16108 - 6.03019i) q^{63} +(2.97368 + 2.16050i) q^{64} +(0.182231 + 0.0390582i) q^{65} +(18.4603 - 10.5999i) q^{66} +(-4.72186 + 14.5324i) q^{67} +14.7851 q^{68} +(9.35582 + 4.19205i) q^{69} +(-8.00291 - 13.0011i) q^{70} +(-4.99917 + 1.62433i) q^{71} +(-20.4847 + 2.05499i) q^{72} +(-6.40258 + 8.81240i) q^{73} +18.0267i q^{74} +(8.61789 - 0.855559i) q^{75} +21.8007i q^{76} +(2.25041 - 12.3980i) q^{77} +(-0.0765909 - 0.364575i) q^{78} +(0.838302 + 2.58003i) q^{79} +(-3.93197 + 18.3451i) q^{80} +(6.08525 - 6.63096i) q^{81} -20.1127i q^{82} +(-2.20517 + 6.78682i) q^{83} +(-12.0702 + 17.6125i) q^{84} +(2.87502 + 6.48704i) q^{85} +(6.64267 - 9.14286i) q^{86} +(-1.40816 - 2.45240i) q^{87} +(-26.4412 + 19.2106i) q^{88} +(0.654200 + 0.475304i) q^{89} +(-8.55881 - 15.0471i) q^{90} +(-0.194181 - 0.104503i) q^{91} +(-26.2287 - 8.52224i) q^{92} +(1.67919 - 15.6205i) q^{93} +(-11.1785 - 3.63211i) q^{94} +(-9.56517 + 4.23922i) q^{95} +(13.4370 - 2.82289i) q^{96} +(-0.796311 + 0.258737i) q^{97} +(4.80428 + 17.4133i) q^{98} +(3.03673 - 13.9612i) 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 $

$2$	−1.51682	+	2.08772i	−1.07255	+	1.47624i	−0.205085	+	0.978744i	$0.565747\pi$
$2$	−1.51682	+	2.08772i	−1.07255	+	1.47624i	−0.867466	+	0.497496i	$0.834253\pi$
$3$	0.356101	+	1.69505i	0.205595	+	0.978637i
$3$	0.356101	+	1.69505i	0.205595	+	0.978637i
$4$	−1.43980	−	4.43126i	−0.719902	−	2.21563i
$5$	1.66426	−	1.49340i	0.744281	−	0.667867i
$5$	1.66426	−	1.49340i	0.744281	−	0.667867i
$6$	−4.07893	−	1.82764i	−1.66521	−	0.746131i
$7$	−2.38379	+	1.14785i	−0.900986	+	0.433848i
$7$	−2.38379	+	1.14785i	−0.900986	+	0.433848i
$8$	6.52662	+	2.12063i	2.30751	+	0.749755i
$9$	−2.74638	+	1.20722i	−0.915461	+	0.402406i
$10$	0.593408	+	5.73972i	0.187652	+	1.81506i
$11$	−2.79937	+	3.85300i	−0.844040	+	1.16172i	0.141104	+	0.989995i	$0.454935\pi$
$11$	−2.79937	+	3.85300i	−0.844040	+	1.16172i	−0.985145	+	0.171727i	$0.945065\pi$
$12$	6.99849	−	4.01851i	2.02029	−	1.16005i
$13$	0.0489901	+	0.0674291i	0.0135874	+	0.0187015i	0.815757	−	0.578395i	$-0.196321\pi$
$13$	0.0489901	+	0.0674291i	0.0135874	+	0.0187015i	−0.802169	+	0.597097i	$0.796321\pi$
$14$	1.21937	−	6.71776i	0.325891	−	1.79540i
$15$	3.12402	+	2.28921i	0.806620	+	0.591071i
$16$	−6.78806	+	4.93181i	−1.69701	+	1.23295i
$17$	−0.980587	+	3.01794i	−0.237827	+	0.731957i	0.758907	+	0.651200i	$0.225734\pi$
$17$	−0.980587	+	3.01794i	−0.237827	+	0.731957i	−0.996734	+	0.0807574i	$0.974266\pi$
$18$	1.64543	−	7.56481i	0.387832	−	1.78304i
$19$	−4.44996	−	1.44588i	−1.02089	−	0.331707i	−0.249708	−	0.968321i	$-0.580334\pi$
$19$	−4.44996	−	1.44588i	−1.02089	−	0.331707i	−0.771183	+	0.636614i	$0.780334\pi$
$20$	−9.01384	−	5.22459i	−2.01555	−	1.16825i
$21$	−2.79454	−	3.63188i	−0.609818	−	0.792542i
$22$	−3.79785	−	11.6886i	−0.809704	−	2.49201i
$23$	3.47912	−	4.78859i	0.725446	−	0.998490i	−0.273880	−	0.961764i	$-0.588307\pi$
$23$	3.47912	−	4.78859i	0.725446	−	0.998490i	0.999325	−	0.0367264i	$-0.0116930\pi$
$24$	−1.27043	+	11.8181i	−0.259326	+	2.41236i
$25$	0.539541	−	4.97080i	0.107908	−	0.994161i
$26$	−0.215082			−0.0421811
$27$	−3.02428	−	4.22537i	−0.582023	−	0.813172i
$28$	8.51862	+	8.91049i	1.60987	+	1.68392i
$29$	−1.55280	+	0.504535i	−0.288347	+	0.0936897i	−0.449619	−	0.893220i	$-0.648440\pi$
$29$	−1.55280	+	0.504535i	−0.288347	+	0.0936897i	0.161272	+	0.986910i	$0.448440\pi$
$30$	−9.51779	+	3.04978i	−1.73770	+	0.556810i
$31$	−8.62654	−	2.80293i	−1.54937	−	0.503421i	−0.595428	−	0.803408i	$-0.703018\pi$
$31$	−8.62654	−	2.80293i	−1.54937	−	0.503421i	−0.953943	+	0.299987i	$0.903018\pi$
$32$		−	7.92721i		−	1.40135i
$33$	−7.52787	−	3.37301i	−1.31043	−	0.587165i
$34$	−4.81323	−	6.62485i	−0.825462	−	1.13615i
$35$	−2.25305	+	5.47026i	−0.380834	+	0.924643i
$36$	9.30375	+	10.4318i	1.55062	+	1.73863i
$37$	5.65143	−	4.10601i	0.929090	−	0.675023i	−0.0166798	−	0.999861i	$-0.505310\pi$
$37$	5.65143	−	4.10601i	0.929090	−	0.675023i	0.945770	+	0.324837i	$0.105310\pi$
$38$	9.76836	−	7.09713i	1.58464	−	1.15131i
$39$	−0.0968503	+	0.107052i	−0.0155085	+	0.0171421i
$40$	14.0290	−	6.21755i	2.21817	−	0.983080i
$41$	−6.30543	+	4.58116i	−0.984742	+	0.715457i	−0.958763	−	0.284206i	$-0.908270\pi$
$41$	−6.30543	+	4.58116i	−0.984742	+	0.715457i	−0.0259786	+	0.999662i	$0.508270\pi$
$42$	11.8211	−	0.325305i	1.82404	−	0.0501957i
$43$	−4.37935			−0.667845			−0.333923	−	0.942601i	$-0.608372\pi$
$43$	−4.37935			−0.667845			−0.333923	+	0.942601i	$0.608372\pi$
$44$	21.1042	+	6.85716i	3.18157	+	1.03376i
$45$	−2.76785	+	6.11056i	−0.412607	+	0.910909i
$46$	4.72005	+	14.5268i	0.695934	+	2.14186i
$47$	1.40749	+	4.33180i	0.205303	+	0.631858i	0.999701	+	0.0244601i	$0.00778667\pi$
$47$	1.40749	+	4.33180i	0.205303	+	0.631858i	−0.794398	+	0.607398i	$0.792213\pi$
$48$	−10.7769	−	9.74987i	−1.55551	−	1.40727i
$49$	4.36487	−	5.47247i	0.623552	−	0.781782i
$50$	9.55926	+	8.66621i	1.35188	+	1.22559i
$51$	−5.46474	−	0.587453i	−0.765216	−	0.0822599i
$52$	0.228260	−	0.314173i	0.0316540	−	0.0435679i
$53$	−0.176583	+	0.0573752i	−0.0242555	+	0.00788109i	−0.321120	−	0.947039i	$-0.604059\pi$
$53$	−0.176583	+	0.0573752i	−0.0242555	+	0.00788109i	0.296864	+	0.954920i	$0.404059\pi$
$54$	13.4087	+	0.0952533i	1.82469	+	0.0129623i
$55$	1.09517	+	10.5930i	0.147672	+	1.42835i
$56$	−17.9922	+	2.43648i	−2.40431	+	0.325589i
$57$	0.866202	−	8.05778i	0.114731	−	1.06728i
$58$	1.30198	−	4.00709i	0.170959	−	0.526157i
$59$	0.335313	−	0.243619i	0.0436541	−	0.0317165i	−0.565744	−	0.824581i	$-0.691411\pi$
$59$	0.335313	−	0.243619i	0.0436541	−	0.0317165i	0.609398	+	0.792864i	$0.291411\pi$
$60$	5.64610	−	17.1394i	0.728908	−	2.21268i
$61$	5.88303	−	8.09729i	0.753244	−	1.03675i	−0.244502	−	0.969649i	$-0.578624\pi$
$61$	5.88303	−	8.09729i	0.753244	−	1.03675i	0.997746	−	0.0671031i	$-0.0213756\pi$
$62$	18.9366	−	13.7583i	2.40495	−	1.74730i
$63$	5.16108	−	6.03019i	0.650235	−	0.759733i
$64$	2.97368	+	2.16050i	0.371710	+	0.270063i
$65$	0.182231	+	0.0390582i	0.0226030	+	0.00484457i
$66$	18.4603	−	10.5999i	2.27231	−	1.30475i
$67$	−4.72186	+	14.5324i	−0.576867	+	1.77541i	0.0528663	+	0.998602i	$0.483164\pi$
$67$	−4.72186	+	14.5324i	−0.576867	+	1.77541i	−0.629733	+	0.776812i	$0.716836\pi$
$68$	14.7851			1.79296
$69$	9.35582	+	4.19205i	1.12631	+	0.504664i
$70$	−8.00291	−	13.0011i	−0.956531	−	1.55393i
$71$	−4.99917	+	1.62433i	−0.593292	+	0.192772i	−0.590247	−	0.807223i	$-0.700969\pi$
$71$	−4.99917	+	1.62433i	−0.593292	+	0.192772i	−0.00304569	+	0.999995i	$0.500969\pi$
$72$	−20.4847	+	2.05499i	−2.41414	+	0.242183i
$73$	−6.40258	+	8.81240i	−0.749365	+	1.03141i	0.248659	+	0.968591i	$0.420010\pi$
$73$	−6.40258	+	8.81240i	−0.749365	+	1.03141i	−0.998025	+	0.0628219i	$0.979990\pi$
$74$			18.0267i			2.09556i
$75$	8.61789	−	0.855559i	0.995108	−	0.0987914i
$76$			21.8007i			2.50071i
$77$	2.25041	−	12.3980i	0.256458	−	1.41288i
$78$	−0.0765909	−	0.364575i	−0.00867222	−	0.0412800i
$79$	0.838302	+	2.58003i	0.0943164	+	0.290276i	0.987075	−	0.160260i	$-0.0512331\pi$
$79$	0.838302	+	2.58003i	0.0943164	+	0.290276i	−0.892759	+	0.450535i	$0.851233\pi$
$80$	−3.93197	+	18.3451i	−0.439607	+	2.05104i
$81$	6.08525	−	6.63096i	0.676139	−	0.736774i
$82$		−	20.1127i		−	2.22108i
$83$	−2.20517	+	6.78682i	−0.242049	+	0.744951i	0.754059	+	0.656807i	$0.228093\pi$
$83$	−2.20517	+	6.78682i	−0.242049	+	0.744951i	−0.996108	+	0.0881436i	$0.971907\pi$
$84$	−12.0702	+	17.6125i	−1.31697	+	1.92168i
$85$	2.87502	+	6.48704i	0.311839	+	0.703619i
$86$	6.64267	−	9.14286i	0.716298	−	0.985900i
$87$	−1.40816	−	2.45240i	−0.150971	−	0.262925i
$88$	−26.4412	+	19.2106i	−2.81864	+	2.04786i
$89$	0.654200	+	0.475304i	0.0693451	+	0.0503821i	0.621918	−	0.783083i	$-0.286354\pi$
$89$	0.654200	+	0.475304i	0.0693451	+	0.0503821i	−0.552573	+	0.833465i	$0.686354\pi$
$90$	−8.55881	−	15.0471i	−0.902178	−	1.58610i
$91$	−0.194181	−	0.104503i	−0.0203557	−	0.0109549i
$92$	−26.2287	−	8.52224i	−2.73454	−	0.888504i
$93$	1.67919	−	15.6205i	0.174124	−	1.61977i
$94$	−11.1785	−	3.63211i	−1.15297	−	0.374624i
$95$	−9.56517	+	4.23922i	−0.981365	+	0.434935i
$96$	13.4370	−	2.82289i	1.37141	−	0.288110i
$97$	−0.796311	+	0.258737i	−0.0808531	+	0.0262708i	−0.349164	−	0.937062i	$-0.613534\pi$
$97$	−0.796311	+	0.258737i	−0.0808531	+	0.0262708i	0.268311	+	0.963332i	$0.413534\pi$
$98$	4.80428	+	17.4133i	0.485305	+	1.75901i
$99$	3.03673	−	13.9612i	0.305203	−	1.40316i
$100$	−22.8038	+	4.76613i	−2.28038	+	0.476613i
$101$	−15.8210			−1.57424			−0.787122	−	0.616797i	$-0.788430\pi$
$101$	−15.8210			−1.57424			−0.787122	+	0.616797i	$0.788430\pi$
$102$	9.51544	−	10.5178i	0.942169	−	1.04142i
$103$	0.412980	−	0.134185i	0.0406921	−	0.0132217i	−0.288600	−	0.957450i	$-0.593190\pi$
$103$	0.412980	−	0.134185i	0.0406921	−	0.0132217i	0.329292	+	0.944228i	$0.393190\pi$
$104$	0.176748	+	0.543974i	0.0173316	+	0.0533411i
$105$	−10.0747	−	1.87106i	−0.983188	−	0.182597i
$106$	0.148060	−	0.455683i	0.0143809	−	0.0442598i
$107$			11.9000i			1.15042i	0.818006	+	0.575209i	$0.195079\pi$
$107$			11.9000i			1.15042i	−0.818006	+	0.575209i	$0.804921\pi$
$108$	−14.3693	+	19.4851i	−1.38269	+	1.87495i
$109$	8.66105	−	6.29262i	0.829578	−	0.602724i	−0.0898617	−	0.995954i	$-0.528643\pi$
$109$	8.66105	−	6.29262i	0.829578	−	0.602724i	0.919440	+	0.393230i	$0.128643\pi$
$110$	−23.7763	−	13.7812i	−2.26698	−	1.31398i
$111$	8.97237	+	8.11731i	0.851619	+	0.770461i
$112$	10.5203	−	19.5481i	0.994073	−	1.84712i
$113$	2.52143	+	3.47046i	0.237197	+	0.326473i	0.910976	−	0.412460i	$-0.135330\pi$
$113$	2.52143	+	3.47046i	0.237197	+	0.326473i	−0.673779	+	0.738933i	$0.735330\pi$
$114$	15.5085	+	14.0306i	1.45250	+	1.31408i
$115$	−1.36110	−	13.1652i	−0.126923	−	1.22766i
$116$	4.47145	+	6.15442i	0.415164	+	0.571424i
$117$	−0.215947	−	0.126045i	−0.0199643	−	0.0116528i
$118$			1.06957i			0.0984615i
$119$	−1.12664	−	8.31968i	−0.103279	−	0.762664i
$120$	15.5348	+	21.5657i	1.41812	+	1.96867i
$121$	−3.60994	−	11.1103i	−0.328177	−	1.01002i
$122$	7.98140	+	24.5642i	0.722602	+	2.22394i
$123$	−10.0107	−	9.05665i	−0.902631	−	0.816611i
$124$			42.2621i			3.79525i
$125$	−6.52544	−	9.07847i	−0.583653	−	0.812003i
$126$	4.76093	+	19.9216i	0.424137	+	1.77476i
$127$	8.07707	+	5.86833i	0.716724	+	0.520730i	0.885336	−	0.464952i	$-0.153928\pi$
$127$	8.07707	+	5.86833i	0.716724	+	0.520730i	−0.168612	+	0.985683i	$0.553928\pi$
$128$	6.05740	−	1.96817i	0.535404	−	0.173963i
$129$	−1.55949	−	7.42322i	−0.137306	−	0.653578i
$130$	−0.357953	+	0.321203i	−0.0313946	+	0.0281713i
$131$	−1.81865	+	5.59724i	−0.158896	+	0.489033i	−0.998535	−	0.0541129i	$-0.982767\pi$
$131$	−1.81865	+	5.59724i	−0.158896	+	0.489033i	0.839638	+	0.543146i	$0.182767\pi$
$132$	−4.10801	+	38.2144i	−0.357556	+	3.32614i
$133$	12.2674	−	1.66123i	1.06372	−	0.144047i
$134$	−23.1773	−	31.9009i	−2.00222	−	2.75582i
$135$	−11.3433	−	2.51567i	−0.976279	−	0.216514i
$136$	−12.7998	+	17.6175i	−1.09758	+	1.51069i
$137$	4.18837	+	5.76479i	0.357836	+	0.492519i	0.949544	−	0.313633i	$-0.101546\pi$
$137$	4.18837	+	5.76479i	0.357836	+	0.492519i	−0.591708	+	0.806152i	$0.701546\pi$
$138$	−22.9429	+	13.1737i	−1.95303	+	1.12142i
$139$	−0.343247	+	0.472439i	−0.0291138	+	0.0400717i	−0.823326	−	0.567569i	$-0.807884\pi$
$139$	−0.343247	+	0.472439i	−0.0291138	+	0.0400717i	0.794212	+	0.607641i	$0.207884\pi$
$140$	27.4841	+	2.10773i	2.32283	+	0.178136i
$141$	−6.84141	+	3.92832i	−0.576151	+	0.330824i
$142$	4.19168	−	12.9007i	0.351758	−	1.08260i
$143$	−0.396945			−0.0331942
$144$	12.6888	−	21.7393i	1.05740	−	1.81161i
$145$	−1.83079	+	3.15862i	−0.152039	+	0.262309i
$146$	−8.68626	−	26.7336i	−0.718880	−	2.21249i
$147$	10.8304	+	5.44991i	0.893280	+	0.449501i
$148$	−26.3317	−	19.1311i	−2.16446	−	1.57257i
$149$			0.454465i			0.0372312i	0.999827	+	0.0186156i	$0.00592588\pi$
$149$			0.454465i			0.0372312i	−0.999827	+	0.0186156i	$0.994074\pi$
$150$	−11.2856	+	19.2895i	−0.921465	+	1.57498i
$151$	15.5805			1.26792			0.633961	−	0.773365i	$-0.281428\pi$
$151$	15.5805			1.26792			0.633961	+	0.773365i	$0.281428\pi$
$152$	−25.9770	−	18.8734i	−2.10701	−	1.53084i
$153$	−0.950236	−	9.47219i	−0.0768220	−	0.765781i
$154$	22.4700	+	23.5037i	1.81069	+	1.89398i
$155$	−18.5427	+	8.21801i	−1.48939	+	0.660087i
$156$	0.613822	+	0.275035i	0.0491451	+	0.0220204i
$157$			24.2329i			1.93400i	0.254784	+	0.966998i	$0.417996\pi$
$157$			24.2329i			1.93400i	−0.254784	+	0.966998i	$0.582004\pi$
$158$	−6.65793	−	2.16329i	−0.529676	−	0.172102i
$159$	−0.160135	−	0.278885i	−0.0126995	−	0.0221170i
$160$	−11.8385	−	13.1930i	−0.935913	−	1.04300i
$161$	−2.79687	+	15.4085i	−0.220424	+	1.21436i
$162$	4.61338	+	22.7623i	0.362461	+	1.78837i
$163$	−5.66203	+	4.11371i	−0.443484	+	0.322210i	−0.787018	−	0.616930i	$-0.788376\pi$
$163$	−5.66203	+	4.11371i	−0.443484	+	0.322210i	0.343534	+	0.939140i	$0.388376\pi$
$164$	29.3789	+	21.3450i	2.29411	+	1.66677i
$165$	−17.5656	+	5.62852i	−1.36748	+	0.438180i
$166$	−10.8241	−	14.8981i	−0.840116	−	1.15632i
$167$	−4.15632	+	12.7918i	−0.321626	+	0.989862i	0.651315	+	0.758807i	$0.274218\pi$
$167$	−4.15632	+	12.7918i	−0.321626	+	0.989862i	−0.972941	+	0.231055i	$0.925782\pi$
$168$	−10.5370	−	29.6301i	−0.812948	−	2.28601i
$169$	4.01507	−	12.3571i	0.308852	−	0.950548i
$170$	−17.9040	−	3.83743i	−1.37317	−	0.294317i
$171$	13.9668	−	1.40113i	1.06807	−	0.107147i
$172$	6.30541	+	19.4061i	0.480783	+	1.47970i
$173$	−1.00040	−	0.726833i	−0.0760590	−	0.0552601i	0.549106	−	0.835753i	$-0.314968\pi$
$173$	−1.00040	−	0.726833i	−0.0760590	−	0.0552601i	−0.625165	+	0.780493i	$0.714968\pi$
$174$	7.25586	+	0.779997i	0.550065	+	0.0591314i
$175$	4.41960	+	12.4686i	0.334091	+	0.942541i
$176$		−	39.9603i		−	3.01212i
$177$	0.532352	+	0.481620i	0.0400140	+	0.0362007i
$178$	−1.98460	+	0.644837i	−0.148752	+	0.0483326i
$179$	4.12850	−	1.34143i	0.308578	−	0.100263i	−0.150634	−	0.988590i	$-0.548132\pi$
$179$	4.12850	−	1.34143i	0.308578	−	0.100263i	0.459213	+	0.888326i	$0.348132\pi$
$180$	31.0627	+	3.46706i	2.31527	+	0.258420i
$181$	4.46804	+	1.45175i	0.332107	+	0.107908i	0.470324	−	0.882494i	$-0.344137\pi$
$181$	4.46804	+	1.45175i	0.332107	+	0.107908i	−0.138217	+	0.990402i	$0.544137\pi$
$182$	0.512710	−	0.246883i	0.0380046	−	0.0183002i
$183$	15.8203	+	7.08857i	1.16947	+	0.524002i
$184$	32.8617	−	23.8754i	2.42260	−	1.76012i
$185$	3.27358	−	15.2733i	0.240678	−	1.12292i
$186$	30.0643	+	27.1992i	2.20442	+	1.99434i
$187$	−8.88307	−	12.2265i	−0.649595	−	0.894090i
$188$	17.1688	−	12.4739i	1.25217	−	0.909752i
$189$	12.0593	+	6.60093i	0.877188	+	0.480147i
$190$	5.65830	−	26.3995i	0.410496	−	1.91522i
$191$	4.72837	+	6.50804i	0.342133	+	0.470905i	0.945063	−	0.326889i	$-0.106000\pi$
$191$	4.72837	+	6.50804i	0.342133	+	0.470905i	−0.602930	+	0.797794i	$0.706000\pi$
$192$	−2.60323	+	5.80989i	−0.187872	+	0.419293i
$193$	−16.6377			−1.19761			−0.598803	−	0.800896i	$-0.704357\pi$
$193$	−16.6377			−1.19761			−0.598803	+	0.800896i	$0.704357\pi$
$194$	0.667687	−	2.05493i	0.0479371	−	0.147535i
$195$	−0.00131297	+	0.322799i	−9.40237e−5	+	0.0231161i
$196$	−30.5345	−	11.4626i	−2.18104	−	0.818756i
$197$	10.7368	−	3.48860i	0.764965	−	0.248552i	0.0995568	−	0.995032i	$-0.468257\pi$
$197$	10.7368	−	3.48860i	0.764965	−	0.248552i	0.665408	+	0.746480i	$0.268257\pi$
$198$	24.5410	+	27.5165i	1.74405	+	1.95551i
$199$			0.663905i			0.0470630i	0.999723	+	0.0235315i	$0.00749100\pi$
$199$			0.663905i			0.0470630i	−0.999723	+	0.0235315i	$0.992509\pi$
$200$	14.0626	−	31.2984i	0.994377	−	2.21313i
$201$	−26.3146	−	2.82879i	−1.85609	−	0.199527i
$202$	23.9975	−	33.0297i	1.68846	−	2.32396i
$203$	3.12241	−	2.98509i	0.219150	−	0.209512i
$204$	5.26499	+	25.0615i	0.368623	+	1.75466i
$205$	−3.65240	+	17.0407i	−0.255095	+	1.19018i
$206$	−0.346273	+	1.06572i	−0.0241260	+	0.0742522i
$207$	−3.77412	+	17.3514i	−0.262319	+	1.20600i
$208$	−0.665096	−	0.216103i	−0.0461161	−	0.0149840i
$209$	18.0280	−	13.0981i	1.24702	−	0.906016i
$210$	19.1877	−	18.1950i	1.32408	−	1.25558i
$211$	−10.6468	−	7.73538i	−0.732958	−	0.532525i	0.157540	−	0.987513i	$-0.449644\pi$
$211$	−10.6468	−	7.73538i	−0.732958	−	0.532525i	−0.890498	+	0.454987i	$0.849644\pi$
$212$	0.508489	+	0.699875i	0.0349232	+	0.0480676i
$213$	−4.53353	−	7.89541i	−0.310632	−	0.540985i
$214$	−24.8439	−	18.0501i	−1.69829	−	1.23388i
$215$	−7.28839	+	6.54010i	−0.497064	+	0.446031i
$216$	−10.7779	−	33.9908i	−0.733345	−	2.31278i
$217$	23.7812	−	3.22041i	1.61437	−	0.218616i
$218$			27.6266i			1.87111i
$219$	−17.2174	−	7.71459i	−1.16344	−	0.521303i
$220$	45.3633	−	20.1047i	3.05839	−	1.35546i
$221$	−0.251536	+	0.0817290i	−0.0169201	+	0.00549769i
$222$	−30.5561	+	6.41931i	−2.05079	+	0.430836i
$223$	14.8609	−	20.4542i	0.995157	−	1.36972i	0.0669065	−	0.997759i	$-0.478687\pi$
$223$	14.8609	−	20.4542i	0.995157	−	1.36972i	0.928250	−	0.371956i	$-0.121313\pi$
$224$	9.09928	+	18.8968i	0.607971	+	1.26259i
$225$	4.51905	+	14.3031i	0.301270	+	0.953539i
$226$	−11.0699			−0.736358
$227$	−12.0100	−	8.72575i	−0.797130	−	0.579148i	0.112941	−	0.993602i	$-0.463973\pi$
$227$	−12.0100	−	8.72575i	−0.797130	−	0.579148i	−0.910071	+	0.414453i	$0.863973\pi$
$228$	−36.9533	+	7.76325i	−2.44729	+	0.514134i
$229$	−7.07073	+	2.29742i	−0.467247	+	0.151818i	−0.533172	−	0.846007i	$-0.679000\pi$
$229$	−7.07073	+	2.29742i	−0.467247	+	0.151818i	0.0659253	+	0.997825i	$0.479000\pi$
$230$	29.5497	+	17.1276i	1.94845	+	1.12936i
$231$	21.8166	−	0.600368i	1.43542	−	0.0395013i
$232$	−11.2045			−0.735609
$233$	2.07221	+	0.673303i	0.135755	+	0.0441096i	0.376107	−	0.926576i	$-0.377263\pi$
$233$	2.07221	+	0.673303i	0.135755	+	0.0441096i	−0.240351	+	0.970686i	$0.577263\pi$
$234$	0.590698	−	0.259651i	0.0386152	−	0.0169739i
$235$	8.81152	+	5.10732i	0.574800	+	0.333165i
$236$	−1.56233	−	1.13510i	−0.101699	−	0.0738885i
$237$	−4.07476	+	2.33971i	−0.264684	+	0.151981i
$238$	19.0781	+	10.2673i	1.23665	+	0.665532i
$239$	−4.12976	+	5.68412i	−0.267132	+	0.367675i	−0.921419	−	0.388571i	$-0.872969\pi$
$239$	−4.12976	+	5.68412i	−0.267132	+	0.367675i	0.654287	+	0.756246i	$0.272969\pi$
$240$	−32.4960	−	0.132176i	−2.09761	−	0.00853192i
$241$	13.2037	+	18.1734i	0.850527	+	1.17065i	0.983746	+	0.179564i	$0.0574686\pi$
$241$	13.2037	+	18.1734i	0.850527	+	1.17065i	−0.133219	+	0.991087i	$0.542531\pi$
$242$	28.6707	+	9.31568i	1.84302	+	0.598835i
$243$	13.4068	+	7.95351i	0.860045	+	0.510218i
$244$	−44.3516	−	14.4107i	−2.83932	−	0.922551i
$245$	−0.908277	−	15.6261i	−0.0580277	−	0.998315i
$246$	34.0921	−	7.16216i	2.17363	−	0.456643i
$247$	−0.120510	−	0.370891i	−0.00766785	−	0.0235992i
$248$	−50.3582	−	36.5874i	−3.19775	−	2.32330i
$249$	−12.2893	−	1.32108i	−0.778801	−	0.0837202i
$250$	28.8512	+	0.147101i	1.82471	+	0.00930346i
$251$	4.94665			0.312230			0.156115	−	0.987739i	$-0.450103\pi$
$251$	4.94665			0.312230			0.156115	+	0.987739i	$0.450103\pi$
$252$	−34.1523	−	14.1878i	−2.15139	−	0.893748i
$253$	8.71111	+	26.8100i	0.547663	+	1.68553i
$254$	−24.5029	+	7.96146i	−1.53745	+	0.499547i
$255$	−9.97206	+	7.18334i	−0.624475	+	0.449838i
$256$	−7.35067	+	22.6230i	−0.459417	+	1.41394i
$257$	−20.6968			−1.29103			−0.645517	−	0.763746i	$-0.723358\pi$
$257$	−20.6968			−1.29103			−0.645517	+	0.763746i	$0.723358\pi$
$258$	17.8631	+	8.00388i	1.11211	+	0.498300i
$259$	−8.75871	+	16.2749i	−0.544240	+	1.01127i
$260$	−0.0892997	−	0.863748i	−0.00553813	−	0.0535674i
$261$	3.65550	−	3.26021i	0.226270	−	0.201802i
$262$	−8.92690	−	12.2868i	−0.551506	−	0.759082i
$263$	−15.1530	−	20.8563i	−0.934372	−	1.28605i	−0.958130	−	0.286335i	$-0.907563\pi$
$263$	−15.1530	−	20.8563i	−0.934372	−	1.28605i	0.0237576	−	0.999718i	$-0.492437\pi$
$264$	−41.9787	−	37.9782i	−2.58361	−	2.33739i
$265$	−0.208196	+	0.359195i	−0.0127894	+	0.0220652i
$266$	−15.1392	+	28.1307i	−0.928244	+	1.72480i
$267$	−0.572703	+	1.27816i	−0.0350488	+	0.0782220i
$268$	71.1953			4.34895
$269$	−3.90689	+	12.0242i	−0.238207	+	0.733127i	0.758472	+	0.651705i	$0.225946\pi$
$269$	−3.90689	+	12.0242i	−0.238207	+	0.733127i	−0.996680	+	0.0814217i	$0.974054\pi$
$270$	22.4578	−	19.8659i	1.36674	−	1.20900i
$271$	−18.6140	+	6.04806i	−1.13072	+	0.367393i	−0.813850	−	0.581075i	$-0.802632\pi$
$271$	−18.6140	+	6.04806i	−1.13072	+	0.367393i	−0.316871	+	0.948469i	$0.602632\pi$
$272$	−8.22761	−	25.3220i	−0.498872	−	1.53537i
$273$	0.107990	−	0.366360i	0.00653585	−	0.0221731i
$274$	−18.3882			−1.11087
$275$	17.6421	+	15.9939i	1.06386	+	0.964471i
$276$	5.10553	−	47.4938i	0.307317	−	2.85879i
$277$	−1.57755	−	1.14616i	−0.0947859	−	0.0688660i	0.539383	−	0.842061i	$-0.318658\pi$
$277$	−1.57755	−	1.14616i	−0.0947859	−	0.0688660i	−0.634169	+	0.773195i	$0.718658\pi$
$278$	−0.465677	−	1.43321i	−0.0279295	−	0.0859580i
$279$	27.0755	−	2.71618i	1.62097	−	0.162613i
$280$	−26.3052	+	30.9245i	−1.57204	+	1.84809i
$281$	15.9285	+	5.17548i	0.950213	+	0.308743i	0.742802	−	0.669511i	$-0.233496\pi$
$281$	15.9285	+	5.17548i	0.950213	+	0.308743i	0.207411	+	0.978254i	$0.433496\pi$
$282$	2.17594	−	20.2415i	0.129575	−	1.20536i
$283$	11.3448	+	3.68614i	0.674377	+	0.219118i	0.626132	−	0.779717i	$-0.284637\pi$
$283$	11.3448	+	3.68614i	0.674377	+	0.219118i	0.0482453	+	0.998836i	$0.484637\pi$
$284$	14.3956	+	19.8139i	0.854224	+	1.17574i
$285$	−10.5919	−	14.7038i	−0.627407	−	0.870980i
$286$	0.602093	−	0.828711i	0.0356025	−	0.0490027i
$287$	9.77228	−	18.1582i	0.576840	−	1.07184i
$288$	9.56987	+	21.7712i	0.563910	+	1.28288i
$289$	5.60690	+	4.07365i	0.329818	+	0.239627i
$290$	−3.81733	−	8.61323i	−0.224161	−	0.505786i
$291$	−0.722139	−	1.25765i	−0.0423325	−	0.0737247i
$292$	48.2685	+	15.6834i	2.82470	+	0.917800i
$293$	−8.72896			−0.509951			−0.254976	−	0.966947i	$-0.582067\pi$
$293$	−8.72896			−0.509951			−0.254976	+	0.966947i	$0.582067\pi$
$294$	−27.8057	+	14.3444i	−1.62166	+	0.836582i
$295$	0.194229	−	0.906202i	0.0113085	−	0.0527611i
$296$	45.5921	−	14.8138i	2.64999	−	0.861033i
$297$	24.7464	+	0.175795i	1.43593	+	0.0102007i
$298$	−0.948795	−	0.689340i	−0.0549622	−	0.0399324i
$299$	0.493333			0.0285302
$300$	−16.1993	−	36.9563i	−0.935266	−	2.13367i
$301$	10.4394	−	5.02685i	0.601719	−	0.289743i
$302$	−23.6327	+	32.5277i	−1.35991	+	1.87176i
$303$	−5.63386	−	26.8173i	−0.323657	−	1.54061i
$304$	37.3374	−	12.1316i	2.14144	−	0.695798i
$305$	−2.30155	−	22.2617i	−0.131787	−	1.27470i
$306$	21.2166	+	12.3838i	1.21287	+	0.707932i
$307$			3.80146i			0.216961i	0.994099	+	0.108480i	$0.0345985\pi$
$307$			3.80146i			0.216961i	−0.994099	+	0.108480i	$0.965402\pi$
$308$	−58.1788	+	7.87848i	−3.31505	+	0.448918i
$309$	0.374513	+	0.652237i	0.0213053	+	0.0371045i
$310$	10.9690	−	51.1772i	0.622997	−	2.90667i
$311$	6.39917	+	4.64927i	0.362864	+	0.263636i	0.754245	−	0.656593i	$-0.228003\pi$
$311$	6.39917	+	4.64927i	0.362864	+	0.263636i	−0.391382	+	0.920228i	$0.628003\pi$
$312$	−0.859123	+	0.493306i	−0.0486383	+	0.0279280i
$313$	−16.4691	−	22.6677i	−0.930887	−	1.28126i	−0.959513	−	0.281666i	$-0.909113\pi$
$313$	−16.4691	−	22.6677i	−0.930887	−	1.28126i	0.0286257	−	0.999590i	$-0.490887\pi$
$314$	−50.5915	−	36.7569i	−2.85504	−	2.07431i
$315$	−0.416062	−	17.7434i	−0.0234424	−	0.999725i
$316$	10.2258	−	7.42947i	0.575246	−	0.417940i
$317$	1.17168	+	0.380702i	0.0658081	+	0.0213824i	0.341736	−	0.939796i	$-0.388985\pi$
$317$	1.17168	+	0.380702i	0.0658081	+	0.0213824i	−0.275928	+	0.961178i	$0.588985\pi$
$318$	0.825129	+	0.0887005i	0.0462710	+	0.00497408i
$319$	2.40288	−	7.39530i	0.134535	−	0.414057i
$320$	8.17547	−	0.845231i	0.457023	−	0.0472499i
$321$	−20.1711	+	4.23761i	−1.12584	+	0.236520i
$322$	−27.9263	−	29.2109i	−1.55627	−	1.62786i
$323$	8.72714	−	12.0119i	0.485591	−	0.668359i
$324$	−38.1451	−	17.4181i	−2.11917	−	0.967670i
$325$	0.361609	−	0.207140i	0.0200585	−	0.0114900i
$326$		−	18.0605i		−	1.00028i
$327$	13.7505	+	12.4401i	0.760405	+	0.687939i
$328$	−50.8681	+	16.5280i	−2.80872	+	0.912608i
$329$	−8.32742	−	8.71050i	−0.459106	−	0.480225i
$330$	14.8930	−	45.2095i	0.819833	−	2.48870i
$331$	−5.76438	+	17.7409i	−0.316839	+	0.975130i	0.658152	+	0.752885i	$0.271338\pi$
$331$	−5.76438	+	17.7409i	−0.316839	+	0.975130i	−0.974991	+	0.222245i	$0.928662\pi$
$332$	33.2492			1.82479
$333$	−10.5642	+	18.0992i	−0.578913	+	0.991829i
$334$	−20.4014	−	28.0801i	−1.11631	−	1.53647i
$335$	13.8442	+	31.2373i	0.756388	+	1.70668i
$336$	36.8812	+	10.8713i	2.01204	+	0.593078i
$337$	3.10806	−	2.25814i	0.169307	−	0.123009i	−0.499905	−	0.866080i	$-0.666632\pi$
$337$	3.10806	−	2.25814i	0.169307	−	0.123009i	0.669212	+	0.743072i	$0.266632\pi$
$338$	19.7081	+	27.1258i	1.07198	+	1.47545i
$339$	−4.98471	+	5.50979i	−0.270732	+	0.299251i
$340$	24.6063	−	22.0800i	1.33446	−	1.19746i
$341$	34.9485	−	25.3916i	1.89257	−	1.37503i
$342$	−18.2599	+	31.2840i	−0.987382	+	1.69164i
$343$	−4.12331	+	18.0554i	−0.222638	+	0.974901i
$344$	−28.5824	−	9.28698i	−1.54106	−	0.500720i
$345$	21.8309	−	6.99526i	1.17534	−	0.376612i
$346$	3.03485	−	0.986082i	0.163154	−	0.0530121i
$347$	24.7047	−	8.02703i	1.32622	−	0.430914i	0.441591	−	0.897217i	$-0.354414\pi$
$347$	24.7047	−	8.02703i	1.32622	−	0.430914i	0.884625	+	0.466303i	$0.154414\pi$
$348$	−8.83976	+	9.77092i	−0.473861	+	0.523776i
$349$			18.8248i			1.00767i	0.863800	+	0.503835i	$0.168078\pi$
$349$			18.8248i			1.00767i	−0.863800	+	0.503835i	$0.831922\pi$
$350$	−32.7348	−	9.68576i	−1.74975	−	0.517726i
$351$	0.136753	−	0.410926i	0.00729932	−	0.0219336i
$352$	30.5435	+	22.1912i	1.62797	+	1.18279i
$353$	5.48068	+	16.8678i	0.291707	+	0.897782i	0.984308	+	0.176461i	$0.0564648\pi$
$353$	5.48068	+	16.8678i	0.291707	+	0.897782i	−0.692601	+	0.721321i	$0.743535\pi$
$354$	−1.81297	+	0.380873i	−0.0963581	+	0.0202432i
$355$	−5.89417	+	10.1690i	−0.312830	+	0.539717i
$356$	1.16428	−	3.58328i	0.0617066	−	0.189913i
$357$	13.7011	−	4.87235i	0.725138	−	0.257872i
$358$	−3.46165	+	10.6538i	−0.182954	+	0.563073i
$359$	−18.7208	−	25.7669i	−0.988044	−	1.35993i	−0.932382	−	0.361476i	$-0.882273\pi$
$359$	−18.7208	−	25.7669i	−0.988044	−	1.35993i	−0.0556620	−	0.998450i	$-0.517727\pi$
$360$	−31.0230	+	34.0118i	−1.63505	+	1.79258i
$361$	2.34023	+	1.70028i	0.123170	+	0.0894882i
$362$	−9.80805	+	7.12597i	−0.515500	+	0.374533i
$363$	17.5469	−	10.0754i	0.920975	−	0.528822i
$364$	−0.183498	+	1.01093i	−0.00961793	+	0.0529871i
$365$	2.50481	+	24.2277i	0.131108	+	1.26814i
$366$	−38.7954	+	22.2762i	−2.02787	+	1.16440i
$367$	−23.8146	−	7.73782i	−1.24311	−	0.403911i	−0.387663	−	0.921801i	$-0.626718\pi$
$367$	−23.8146	−	7.73782i	−1.24311	−	0.403911i	−0.855447	+	0.517890i	$0.826718\pi$
$368$			49.6636i			2.58889i
$369$	11.7867	−	20.1936i	0.613589	−	1.05124i
$370$	26.9209	+	30.0011i	1.39955	+	1.55968i
$371$	0.355077	−	0.339461i	0.0184347	−	0.0176240i
$372$	−71.6364	+	15.0496i	−3.71417	+	0.780284i
$373$	10.0556	+	7.30580i	0.520658	+	0.378280i	0.816852	−	0.576848i	$-0.195717\pi$
$373$	10.0556	+	7.30580i	0.520658	+	0.378280i	−0.296194	+	0.955128i	$0.595717\pi$
$374$	38.9995			2.01662
$375$	13.0647	−	14.2938i	0.674661	−	0.738128i
$376$			31.2568i			1.61195i
$377$	−0.110092	−	0.0799866i	−0.00567003	−	0.00411952i
$378$	−32.0727	+	15.1641i	−1.64964	+	0.779957i
$379$	−0.0596553	−	0.183600i	−0.00306429	−	0.00943090i	0.949513	−	0.313729i	$-0.101578\pi$
$379$	−0.0596553	−	0.183600i	−0.00306429	−	0.00943090i	−0.952577	+	0.304298i	$0.901578\pi$
$380$	32.5571	+	36.2821i	1.67014	+	1.86123i
$381$	−7.07086	+	15.7808i	−0.362251	+	0.808472i
$382$	−20.7590			−1.06212
$383$	6.73467	−	20.7272i	0.344126	−	1.05911i	−0.617924	−	0.786237i	$-0.712026\pi$
$383$	6.73467	−	20.7272i	0.344126	−	1.05911i	0.962050	−	0.272873i	$-0.0879737\pi$
$384$	5.49319	+	9.56673i	0.280323	+	0.488200i
$385$	−14.7698	−	23.9942i	−0.752739	−	1.22286i
$386$	25.2363	−	34.7348i	1.28449	−	1.76796i
$387$	12.0274	−	5.28683i	0.611386	−	0.268745i
$388$	2.29306	+	3.15613i	0.116413	+	0.160228i
$389$	7.24529	−	9.97229i	0.367351	−	0.505615i	−0.584828	−	0.811158i	$-0.698838\pi$
$389$	7.24529	−	9.97229i	0.367351	−	0.505615i	0.952178	+	0.305543i	$0.0988379\pi$
$390$	−0.671922	−	0.492368i	−0.0340241	−	0.0249320i
$391$	11.0401	+	15.1954i	0.558321	+	0.768463i
$392$	40.0929	−	26.4605i	2.02500	−	1.33646i
$393$	−10.1352	−	1.08952i	−0.511254	−	0.0549593i
$394$	−9.00254	+	27.7070i	−0.453542	+	1.39586i
$395$	5.24816	+	3.04193i	0.264063	+	0.153056i
$396$	−66.2382	+	6.64492i	−3.32860	+	0.333920i
$397$	−26.8106	+	8.71128i	−1.34558	+	0.437206i	−0.891204	−	0.453602i	$-0.850139\pi$
$397$	−26.8106	+	8.71128i	−1.34558	+	0.437206i	−0.454379	+	0.890809i	$0.650139\pi$
$398$	−1.38605	−	1.00702i	−0.0694763	−	0.0504775i
$399$	7.18430	+	20.2023i	0.359665	+	1.01138i
$400$	20.8526	+	36.4030i	1.04263	+	1.82015i
$401$			36.3581i			1.81563i	0.419366	+	0.907817i	$0.362253\pi$
$401$			36.3581i			1.81563i	−0.419366	+	0.907817i	$0.637747\pi$
$402$	45.8201	−	50.6467i	2.28530	−	2.52603i
$403$	−0.233616	−	0.718996i	−0.0116372	−	0.0358157i
$404$	22.7791	+	70.1068i	1.13330	+	3.48794i
$405$	0.224811	−	20.1234i	0.0111709	−	0.999938i
$406$	1.49590	+	11.0465i	0.0742405	+	0.548230i
$407$			33.2692i			1.64909i
$408$	−34.4205	−	15.4228i	−1.70407	−	0.763541i
$409$	−18.6420	−	25.6585i	−0.921788	−	1.26873i	−0.962978	−	0.269581i	$-0.913115\pi$
$409$	−18.6420	−	25.6585i	−0.921788	−	1.26873i	0.0411894	−	0.999151i	$-0.486885\pi$
$410$	−30.0363	−	33.4729i	−1.48339	−	1.65311i
$411$	−8.28013	+	9.15233i	−0.408428	+	0.451451i
$412$	−1.18922	−	1.63682i	−0.0585886	−	0.0806403i
$413$	−0.519676	+	0.965627i	−0.0255716	+	0.0475154i
$414$	−30.5001	−	34.1981i	−1.49900	−	1.68075i
$415$	6.46542	+	14.5883i	0.317375	+	0.716109i
$416$	0.534525	−	0.388355i	0.0262073	−	0.0190407i
$417$	−0.923038	−	0.413585i	−0.0452014	−	0.0202533i
$418$			57.5049i			2.81266i
$419$	−0.595295	+	1.83213i	−0.0290821	+	0.0895054i	−0.964544	−	0.263922i	$-0.914984\pi$
$419$	−0.595295	+	1.83213i	−0.0290821	+	0.0895054i	0.935462	+	0.353427i	$0.114984\pi$
$420$	6.21440	+	47.3375i	0.303232	+	2.30983i
$421$	0.698106	+	2.14855i	0.0340236	+	0.104714i	0.966626	−	0.256191i	$-0.0824678\pi$
$421$	0.698106	+	2.14855i	0.0340236	+	0.104714i	−0.932602	+	0.360905i	$0.882468\pi$
$422$	32.2986	−	10.4944i	1.57227	−	0.510862i
$423$	−9.09493	−	10.1976i	−0.442210	−	0.495827i
$424$	−1.27416			−0.0618787
$425$	14.4725	+	6.50261i	0.702019	+	0.315423i
$426$	23.3599	+	2.51117i	1.13179	+	0.121666i
$427$	−4.72937	+	26.0551i	−0.228870	+	1.26089i
$428$	52.7321	−	17.1337i	2.54890	−	0.828188i
$429$	−0.141353	−	0.672842i	−0.00682457	−	0.0324851i
$430$	−2.59874	−	25.1363i	−0.125323	−	1.21218i
$431$	14.0436	+	4.56306i	0.676458	+	0.219795i	0.627044	−	0.778984i	$-0.284265\pi$
$431$	14.0436	+	4.56306i	0.676458	+	0.219795i	0.0494143	+	0.998778i	$0.484265\pi$
$432$	41.3677	+	13.7668i	1.99030	+	0.662357i
$433$	31.3582	+	10.1889i	1.50698	+	0.489648i	0.942045	−	0.335487i	$-0.108901\pi$
$433$	31.3582	+	10.1889i	1.50698	+	0.489648i	0.564936	+	0.825135i	$0.308901\pi$
$434$	−29.3484	+	54.5332i	−1.40877	+	2.61768i
$435$	−6.00596	−	1.97850i	−0.287964	−	0.0948618i
$436$	−40.3545	−	29.3192i	−1.93263	−	1.40414i
$437$	−22.4056	+	16.2786i	−1.07181	+	0.778713i
$438$	42.2215	−	24.2435i	2.01742	−	1.15840i
$439$	−9.23582	+	12.7120i	−0.440802	+	0.606711i	−0.970390	−	0.241543i	$-0.922346\pi$
$439$	−9.23582	+	12.7120i	−0.440802	+	0.606711i	0.529588	+	0.848255i	$0.322346\pi$
$440$	−15.3160	+	71.4587i	−0.730161	+	3.40666i
$441$	−5.38114	+	20.2989i	−0.256245	+	0.966612i
$442$	0.210907	−	0.649104i	0.0100318	−	0.0308747i
$443$			25.0802i			1.19160i	0.803135	+	0.595798i	$0.203164\pi$
$443$			25.0802i			1.19160i	−0.803135	+	0.595798i	$0.796836\pi$
$444$	23.0515	−	51.4462i	1.09397	−	2.44153i
$445$	1.79858	−	0.185948i	0.0852608	−	0.00881479i
$446$	20.1615	+	62.0506i	0.954673	+	2.93818i
$447$	−0.770341	+	0.161835i	−0.0364359	+	0.00765455i
$448$	−9.56855	−	1.73683i	−0.452072	−	0.0820576i
$449$		−	9.02137i		−	0.425745i	−0.977080	−	0.212872i	$-0.931718\pi$
$449$		−	9.02137i		−	0.425745i	0.977080	−	0.212872i	$-0.0682819\pi$
$450$	−36.7154	−	12.2606i	−1.73078	−	0.577972i
$451$		−	37.1191i		−	1.74787i
$452$	11.7481	−	16.1699i	0.552585	−	0.760569i
$453$	5.54822	+	26.4097i	0.260678	+	1.24084i
$454$	36.4338	−	11.8381i	1.70992	−	0.555588i
$455$	−0.479232	+	0.116068i	−0.0224668	+	0.00544135i
$456$	22.7409	−	50.7532i	1.06494	−	2.37674i
$457$	15.2177			0.711856			0.355928	−	0.934513i	$-0.384165\pi$
$457$	15.2177			0.711856			0.355928	+	0.934513i	$0.384165\pi$
$458$	5.92863	−	18.2464i	0.277027	−	0.852601i
$459$	15.7175	−	4.98375i	0.733628	−	0.232622i
$460$	−56.3786	+	24.9866i	−2.62867	+	1.16501i
$461$	−27.4281	−	19.9277i	−1.27746	−	0.928126i	−0.277983	−	0.960586i	$-0.589666\pi$
$461$	−27.4281	−	19.9277i	−1.27746	−	0.928126i	−0.999473	+	0.0324596i	$0.989666\pi$
$462$	−31.8383	+	46.4575i	−1.48125	+	2.16140i
$463$	18.6230	−	13.5304i	0.865483	−	0.628810i	−0.0638880	−	0.997957i	$-0.520350\pi$
$463$	18.6230	−	13.5304i	0.865483	−	0.628810i	0.929371	+	0.369147i	$0.120350\pi$
$464$	8.05221	−	11.0829i	0.373814	−	0.514511i
$465$	−20.5330	−	28.5044i	−0.952196	−	1.32186i
$466$	−4.54884	+	3.30492i	−0.210721	+	0.153098i
$467$	2.02020	−	6.21753i	0.0934837	−	0.287713i	−0.893372	−	0.449318i	$-0.851667\pi$
$467$	2.02020	−	6.21753i	0.0934837	−	0.287713i	0.986856	+	0.161605i	$0.0516670\pi$
$468$	−0.247615	+	1.13840i	−0.0114460	+	0.0526225i
$469$	−5.42515	−	40.0621i	−0.250510	−	1.84990i
$470$	−24.0281	+	10.6491i	−1.10833	+	0.491207i
$471$	−41.0760	+	8.62936i	−1.89268	+	0.397620i
$472$	2.70509	−	0.878937i	0.124512	−	0.0404564i
$473$	12.2594	−	16.8736i	0.563688	−	0.775850i
$474$	1.29599	−	12.0559i	0.0595269	−	0.553744i
$475$	−9.58812	+	21.3398i	−0.439933	+	0.979135i
$476$	−35.2445	+	16.9711i	−1.61543	+	0.777871i
$477$	0.415700	−	0.370748i	0.0190336	−	0.0169754i
$478$	−5.60277	−	17.2435i	−0.256265	−	0.788701i
$479$	0.169270	+	0.520959i	0.00773413	+	0.0238032i	0.954849	−	0.297091i	$-0.0960165\pi$
$479$	0.169270	+	0.520959i	0.00773413	+	0.0238032i	−0.947115	+	0.320894i	$0.896017\pi$
$480$	18.1470	−	24.7648i	0.828295	−	1.13035i
$481$	0.553729	+	0.179917i	0.0252479	+	0.00820353i
$482$	−57.9686			−2.64040
$483$	−27.1141	+	0.746152i	−1.23373	+	0.0339511i
$484$	−44.0349	+	31.9932i	−2.00158	+	1.45424i
$485$	−0.938874	+	1.61981i	−0.0426321	+	0.0735519i
$486$	−36.9403	+	15.9256i	−1.67565	+	0.722398i
$487$	6.37177	−	4.62936i	0.288732	−	0.209776i	−0.433985	−	0.900920i	$-0.642893\pi$
$487$	6.37177	−	4.62936i	0.288732	−	0.209776i	0.722717	+	0.691144i	$0.242893\pi$
$488$	55.5676	−	40.3723i	2.51543	−	1.82757i
$489$	−8.98919	−	8.13253i	−0.406505	−	0.367766i
$490$	34.0006	+	21.8057i	1.53599	+	0.985081i
$491$	1.51500	+	2.08521i	0.0683708	+	0.0941043i	0.841833	−	0.539738i	$-0.181477\pi$
$491$	1.51500	+	2.08521i	0.0683708	+	0.0941043i	−0.773462	+	0.633842i	$0.781477\pi$
$492$	−25.7190	+	57.3996i	−1.15950	+	2.58778i
$493$		−	5.18098i		−	0.233340i
$494$	0.957106	+	0.310983i	0.0430622	+	0.0139918i
$495$	−15.7957	−	27.7702i	−0.709966	−	1.24818i
$496$	72.3810	−	23.5180i	3.25000	−	1.05599i
$497$	10.0525	−	9.61036i	0.450914	−	0.431084i
$498$	21.3986	−	23.6527i	0.958895	−	1.05990i
$499$	1.91973			0.0859390			0.0429695	−	0.999076i	$-0.486318\pi$
$499$	1.91973			0.0859390			0.0429695	+	0.999076i	$0.486318\pi$
$500$	−30.8337	+	41.9871i	−1.37893	+	1.87772i
$501$	−23.1629	−	2.48998i	−1.03484	−	0.111244i
$502$	−7.50315	+	10.3272i	−0.334882	+	0.460926i
$503$	4.86346	+	14.9682i	0.216851	+	0.667399i	0.999017	+	0.0443287i	$0.0141149\pi$
$503$	4.86346	+	14.9682i	0.216851	+	0.667399i	−0.782166	+	0.623070i	$0.785885\pi$
$504$	46.4722	−	28.4121i	2.07004	−	1.26557i
$505$	−26.3302	+	23.6269i	−1.17168	+	1.05139i
$506$	−69.1850	−	22.4796i	−3.07565	−	0.999338i
$507$	22.3757	+	2.40536i	0.993740	+	0.106826i
$508$	14.3747	−	44.2409i	0.637775	−	1.96287i
$509$	0.506290	−	0.367841i	0.0224409	−	0.0163043i	−0.576508	−	0.817091i	$-0.695585\pi$
$509$	0.506290	−	0.367841i	0.0224409	−	0.0163043i	0.598949	+	0.800787i	$0.295585\pi$
$510$	0.128998	−	31.7147i	0.00571213	−	1.40435i
$511$	5.14704	−	28.3561i	0.227692	−	1.25440i
$512$	−28.5936	−	39.3557i	−1.26367	−	1.73929i
$513$	7.34856	+	23.1754i	0.324447	+	1.02322i
$514$	31.3933	−	43.2092i	1.38470	−	1.90588i
$515$	0.486915	−	0.840061i	0.0214560	−	0.0370175i
$516$	−30.6489	+	17.5985i	−1.34924	+	0.774730i
$517$	−20.6305	−	6.70325i	−0.907328	−	0.294809i
$518$	−20.6920	−	42.9717i	−0.909153	−	1.88807i
$519$	0.875775	−	1.95455i	0.0384423	−	0.0857954i
$520$	1.10652	+	0.641362i	0.0485243	+	0.0281256i
$521$	−8.70245	−	26.7834i	−0.381261	−	1.17340i	−0.939156	−	0.343490i	$-0.888391\pi$
$521$	−8.70245	−	26.7834i	−0.381261	−	1.17340i	0.557895	−	0.829911i	$-0.311609\pi$
$522$	1.26168	+	12.5768i	0.0552224	+	0.550471i
$523$	24.0772	−	33.1394i	1.05282	−	1.44908i	0.166483	−	0.986044i	$-0.446759\pi$
$523$	24.0772	−	33.1394i	1.05282	−	1.44908i	0.886338	−	0.463039i	$-0.153241\pi$
$524$	27.4213			1.19791
$525$	−19.5611	+	11.9315i	−0.853718	+	0.520735i
$526$	66.5263			2.90068
$527$	16.9181	−	23.2858i	0.736966	−	1.01435i
$528$	67.7347	−	14.2299i	2.94777	−	0.619277i
$529$	−3.71898	−	11.4458i	−0.161695	−	0.497645i
$530$	−0.434103	−	0.979489i	−0.0188562	−	0.0425463i
$531$	−0.626798	+	1.07387i	−0.0272007	+	0.0466019i
$532$	−25.0240	−	51.9682i	−1.08493	−	2.25311i
$533$	−0.617807	−	0.200738i	−0.0267602	−	0.00869492i
$534$	−1.79975	−	3.13437i	−0.0778828	−	0.135638i
$535$	17.7714	+	19.8048i	0.768326	+	0.856234i
$536$	−61.6356	+	84.8341i	−2.66225	+	3.66427i
$537$	3.74395	+	6.52032i	0.161563	+	0.281373i
$538$	−19.1771	−	26.3950i	−0.826782	−	1.13797i
$539$	8.86655	+	32.1373i	0.381909	+	1.38425i
$540$	5.18460	+	53.8874i	0.223110	+	2.31894i
$541$	15.2095	−	11.0503i	0.653907	−	0.475091i	−0.210693	−	0.977552i	$-0.567572\pi$
$541$	15.2095	−	11.0503i	0.653907	−	0.475091i	0.864600	+	0.502461i	$0.167572\pi$
$542$	15.6074	−	48.0346i	0.670395	−	2.06326i
$543$	−0.869722	+	8.09052i	−0.0373233	+	0.347197i
$544$	23.9238	+	7.77332i	1.02573	+	0.333278i
$545$	5.01689	−	23.4069i	0.214900	−	1.00264i
$546$	0.601055	+	0.781153i	0.0257228	+	0.0334303i
$547$	−1.54040	−	4.74086i	−0.0658627	−	0.202705i	0.912709	−	0.408610i	$-0.133986\pi$
$547$	−1.54040	−	4.74086i	−0.0658627	−	0.202705i	−0.978572	+	0.205905i	$0.933986\pi$
$548$	19.5149	−	26.8599i	0.833634	−	1.14740i
$549$	−6.38186	+	29.3404i	−0.272371	+	1.25222i
$550$	−60.1507	+	12.5719i	−2.56484	+	0.536067i
$551$	7.63938			0.325449
$552$	52.1721	+	47.2001i	2.22059	+	2.00897i
$553$	−4.95983	−	5.18799i	−0.210913	−	0.220616i
$554$	4.78571	−	1.55497i	0.203325	−	0.0660644i
$555$	27.0547	+	0.110044i	1.14841	+	0.00467110i
$556$	2.58771	+	0.840797i	0.109743	+	0.0356578i
$557$			13.5250i			0.573071i	0.958070	+	0.286535i	$0.0925036\pi$
$557$			13.5250i			0.573071i	−0.958070	+	0.286535i	$0.907496\pi$
$558$	−35.3980	+	60.6460i	−1.49852	+	2.56735i
$559$	−0.214545	−	0.295296i	−0.00907429	−	0.0124897i
$560$	−11.6845	−	48.2441i	−0.493760	−	2.03868i
$561$	17.5613	−	19.4111i	0.741437	−	0.819538i
$562$	−34.9655	+	25.4039i	−1.47493	+	1.07160i
$563$	−15.0186	+	10.9116i	−0.632958	+	0.459871i	−0.857424	−	0.514611i	$-0.827936\pi$
$563$	−15.0186	+	10.9116i	−0.632958	+	0.459871i	0.224466	+	0.974482i	$0.427936\pi$
$564$	27.2577	+	24.6601i	1.14776	+	1.03838i
$565$	9.37909	+	2.01025i	0.394581	+	0.0845720i
$566$	−24.9036	+	18.0935i	−1.04678	+	0.760527i
$567$	−6.89457	+	22.7918i	−0.289545	+	0.957165i
$568$	−36.0723			−1.51356
$569$	−27.4717	−	8.92610i	−1.15167	−	0.374201i	−0.329900	−	0.944016i	$-0.607015\pi$
$569$	−27.4717	−	8.92610i	−1.15167	−	0.374201i	−0.821773	+	0.569814i	$0.807015\pi$
$570$	46.7634	+	0.190208i	1.95870	+	0.00796693i
$571$	−7.38931	−	22.7420i	−0.309233	−	0.951721i	−0.978064	−	0.208306i	$-0.933205\pi$
$571$	−7.38931	−	22.7420i	−0.309233	−	0.951721i	0.668831	−	0.743415i	$-0.266795\pi$
$572$	0.571524	+	1.75897i	0.0238966	+	0.0735462i
$573$	−9.34767	+	10.3323i	−0.390505	+	0.431639i
$574$	23.0865	+	47.9444i	0.963610	+	2.00116i
$575$	−21.9260	−	19.8776i	−0.914379	−	0.828955i
$576$	−10.7751	−	2.34370i	−0.448961	−	0.0976541i
$577$	−4.78879	+	6.59121i	−0.199360	+	0.274396i	−0.896979	−	0.442074i	$-0.854243\pi$
$577$	−4.78879	+	6.59121i	−0.199360	+	0.274396i	0.697619	+	0.716469i	$0.254243\pi$
$578$	−17.0093	+	5.52665i	−0.707493	+	0.229878i
$579$	−5.92469	−	28.2017i	−0.246222	−	1.17202i
$580$	16.6326	+	3.56493i	0.690633	+	0.148026i
$581$	−2.53362	−	18.7095i	−0.105112	−	0.776203i
$582$	3.72097	+	0.400000i	0.154239	+	0.0165805i
$583$	0.273253	−	0.840987i	0.0113170	−	0.0348301i
$584$	−60.4750	+	43.9377i	−2.50248	+	1.81815i
$585$	−0.547628	+	0.112723i	−0.0226416	+	0.00466054i
$586$	13.2402	−	18.2236i	0.546949	−	0.752810i
$587$	29.9245	−	21.7414i	1.23511	−	0.897364i	0.237852	−	0.971301i	$-0.423557\pi$
$587$	29.9245	−	21.7414i	1.23511	−	0.897364i	0.997263	+	0.0739378i	$0.0235566\pi$
$588$	8.55627	−	55.8393i	0.352855	−	2.30277i
$589$	34.3350	+	24.9459i	1.41475	+	1.02788i
$590$	1.59728	+	1.78004i	0.0657592	+	0.0732830i
$591$	9.73673	+	16.9571i	0.400515	+	0.697522i
$592$	−18.1122	+	55.7436i	−0.744407	+	2.29105i
$593$	8.73132			0.358552			0.179276	−	0.983799i	$-0.442624\pi$
$593$	8.73132			0.358552			0.179276	+	0.983799i	$0.442624\pi$
$594$	−37.9027	+	51.3969i	−1.55517	+	2.10884i
$595$	−14.2996	−	12.1636i	−0.586226	−	0.498660i
$596$	2.01385	−	0.654341i	0.0824906	−	0.0268028i
$597$	−1.12535	+	0.236417i	−0.0460576	+	0.00967591i
$598$	−0.748296	+	1.02994i	−0.0306001	+	0.0421174i
$599$			0.255584i			0.0104429i	0.999986	+	0.00522144i	$0.00166204\pi$
$599$			0.255584i			0.0104429i	−0.999986	+	0.00522144i	$0.998338\pi$
$600$	58.0600	+	12.6914i	2.37029	+	0.518126i
$601$		−	12.6731i		−	0.516948i	−0.966018	−	0.258474i	$-0.916780\pi$
$601$		−	12.6731i		−	0.516948i	0.966018	−	0.258474i	$-0.0832197\pi$
$602$	−5.34005	+	29.4194i	−0.217644	+	1.19905i
$603$	−4.57571	−	45.6118i	−0.186337	−	1.85746i
$604$	−22.4328	−	69.0412i	−0.912779	−	2.80925i
$605$	−22.5999	−	13.0993i	−0.918817	−	0.532563i
$606$	64.5325	+	28.9150i	2.62145	+	1.17459i
$607$		−	17.7920i		−	0.722155i	−0.932536	−	0.361078i	$-0.882409\pi$
$607$		−	17.7920i		−	0.722155i	0.932536	−	0.361078i	$-0.117591\pi$
$608$	−11.4618	+	35.2758i	−0.464837	+	1.43062i
$609$	6.17176	+	4.22964i	0.250092	+	0.171394i
$610$	49.9672	+	28.9619i	2.02311	+	1.17263i
$611$	−0.223137	+	0.307121i	−0.00902714	+	0.0124248i
$612$	−40.6056	+	17.8488i	−1.64138	+	0.721497i
$613$	−23.2381	+	16.8835i	−0.938580	+	0.681918i	−0.948078	−	0.318037i	$-0.896976\pi$
$613$	−23.2381	+	16.8835i	−0.938580	+	0.681918i	0.00949880	+	0.999955i	$0.496976\pi$
$614$	−7.93639	−	5.76612i	−0.320286	−	0.232702i
$615$	−30.1855	−	0.122778i	−1.21720	−	0.00495090i
$616$	40.9791	−	76.1446i	1.65110	−	3.06795i
$617$	−22.5871	−	7.33901i	−0.909324	−	0.295457i	−0.183244	−	0.983067i	$-0.558660\pi$
$617$	−22.5871	−	7.33901i	−0.909324	−	0.295457i	−0.726080	+	0.687610i	$0.758660\pi$
$618$	−1.92976	−	0.207447i	−0.0776262	−	0.00834473i
$619$	−10.6205	−	3.45082i	−0.426875	−	0.138700i	0.0876972	−	0.996147i	$-0.472049\pi$
$619$	−10.6205	−	3.45082i	−0.426875	−	0.138700i	−0.514572	+	0.857447i	$0.672049\pi$
$620$	63.1140	+	70.3352i	2.53472	+	2.82473i
$621$	−30.7554	−	0.218482i	−1.23417	−	0.00876738i
$622$	−19.4127	+	6.30758i	−0.778379	+	0.252911i
$623$	−2.10505	−	0.382098i	−0.0843371	−	0.0153084i
$624$	0.129464	−	1.20432i	0.00518269	−	0.0482116i
$625$	−24.4178	−	5.36391i	−0.976712	−	0.214556i
$626$	72.3044			2.88987
$627$	28.6218	+	25.8941i	1.14304	+	1.03411i
$628$	107.382	−	34.8906i	4.28502	−	1.39229i
$629$	6.84995	+	21.0820i	0.273125	+	0.840593i
$630$	37.6742	+	26.0448i	1.50098	+	1.03765i
$631$	6.51234	−	20.0429i	0.259252	−	0.797896i	−0.733710	−	0.679463i	$-0.762213\pi$
$631$	6.51234	−	20.0429i	0.259252	−	0.797896i	0.992962	−	0.118433i	$-0.0377872\pi$
$632$			18.6166i			0.740529i
$633$	9.32050	−	20.8015i	0.370456	−	0.826785i
$634$	−2.57202	+	1.86868i	−0.102148	+	0.0742150i
$635$	22.2061	−	2.29581i	0.881223	−	0.0911063i
$636$	−1.00525	+	1.11114i	−0.0398607	+	0.0440596i
$637$	0.582839	+	0.0262221i	0.0230929	+	0.00103896i
$638$	11.7946	+	16.2338i	0.466952	+	0.642704i
$639$	11.7687	−	10.4961i	0.465563	−	0.415220i
$640$	7.14186	−	12.3216i	0.282307	−	0.487056i
$641$	−9.06898	−	12.4824i	−0.358203	−	0.493025i	0.591444	−	0.806346i	$-0.298558\pi$
$641$	−9.06898	−	12.4824i	−0.358203	−	0.493025i	−0.949647	+	0.313322i	$0.898558\pi$
$642$	21.7490	−	48.5393i	0.858363	−	1.91569i
$643$		−	47.9064i		−	1.88924i	−0.328161	−	0.944622i	$-0.606429\pi$
$643$		−	47.9064i		−	1.88924i	0.328161	−	0.944622i	$-0.393571\pi$
$644$	72.3060	−	9.79156i	2.84925	−	0.385842i
$645$	−13.6812	−	10.0252i	−0.538697	−	0.394744i
$646$	11.8400	+	36.4396i	0.465837	+	1.43370i
$647$	2.27569	+	7.00386i	0.0894667	+	0.275350i	0.985772	−	0.168087i	$-0.0537590\pi$
$647$	2.27569	+	7.00386i	0.0894667	+	0.275350i	−0.896305	+	0.443437i	$0.853759\pi$
$648$	53.7780	−	30.3732i	2.11260	−	1.19317i
$649$			1.97394i			0.0774839i
$650$	−0.116046	+	1.06913i	−0.00455169	+	0.0419348i
$651$	13.9272	+	39.1635i	0.545852	+	1.53494i
$652$	26.3811	+	19.1670i	1.03316	+	0.750638i
$653$	−9.40722	+	3.05659i	−0.368133	+	0.119614i	−0.487241	−	0.873268i	$-0.661997\pi$
$653$	−9.40722	+	3.05659i	−0.368133	+	0.119614i	0.119108	+	0.992881i	$0.461997\pi$
$654$	−46.8284	+	9.83785i	−1.83114	+	0.384691i
$655$	5.33217	+	12.0312i	0.208345	+	0.470100i
$656$	20.2082	−	62.1943i	0.788996	−	2.42828i
$657$	6.94547	−	31.9315i	0.270969	−	1.24577i
$658$	30.8162	−	4.17309i	1.20134	−	0.162684i
$659$	17.3882	+	23.9328i	0.677349	+	0.932291i	0.999898	−	0.0142619i	$-0.00453986\pi$
$659$	17.3882	+	23.9328i	0.677349	+	0.932291i	−0.322549	+	0.946553i	$0.604540\pi$
$660$	50.2325	+	69.7338i	1.95530	+	2.71438i
$661$	9.41866	−	12.9637i	0.366343	−	0.504228i	−0.585559	−	0.810630i	$-0.699125\pi$
$661$	9.41866	−	12.9637i	0.366343	−	0.504228i	0.951902	+	0.306401i	$0.0991250\pi$
$662$	−28.2946	−	38.9441i	−1.09970	−	1.51361i
$663$	−0.228107	−	0.397262i	−0.00885893	−	0.0154284i
$664$	−28.7847	+	39.6187i	−1.11706	+	1.53750i
$665$	17.9353	−	21.0848i	0.695501	−	0.817634i
$666$	−21.7621	−	49.5082i	−0.843264	−	1.91840i
$667$	−2.98635	+	9.19105i	−0.115632	+	0.355879i
$668$	62.6683			2.42471
$669$	39.9629	+	17.9061i	1.54505	+	0.692291i
$670$	−86.2138	−	18.4785i	−3.33073	−	0.713887i
$671$	14.7301	+	45.3346i	0.568649	+	1.75012i
$672$	−28.7907	+	22.1529i	−1.11063	+	0.854566i
$673$	−31.0016	−	22.5240i	−1.19503	−	0.868237i	−0.201239	−	0.979542i	$-0.564497\pi$
$673$	−31.0016	−	22.5240i	−1.19503	−	0.868237i	−0.993786	+	0.111305i	$0.964497\pi$
$674$			9.91393i			0.381870i
$675$	−22.6352	+	12.7534i	−0.871229	+	0.490877i
$676$	−60.5386			−2.32841
$677$	35.9724	+	26.1355i	1.38253	+	1.00447i	0.996638	+	0.0819268i	$0.0261074\pi$
$677$	35.9724	+	26.1355i	1.38253	+	1.00447i	0.385895	+	0.922543i	$0.373893\pi$
$678$	−3.94200	−	18.7640i	−0.151392	−	0.720627i
$679$	1.60124	−	1.53082i	0.0614500	−	0.0587475i
$680$	5.00755	+	48.4353i	0.192031	+	1.85741i
$681$	10.5138	−	23.4647i	0.402890	−	0.899171i
$682$			111.477i			4.26868i
$683$	−22.2819	−	7.23983i	−0.852593	−	0.277024i	−0.150061	−	0.988677i	$-0.547947\pi$
$683$	−22.2819	−	7.23983i	−0.852593	−	0.277024i	−0.702532	+	0.711652i	$0.747947\pi$
$684$	−26.3182	−	59.8731i	−1.00630	−	2.28931i
$685$	15.5797	+	3.33924i	0.595268	+	0.127586i
$686$	−31.4403	−	35.9951i	−1.20040	−	1.37430i
$687$	−6.41213	−	11.1671i	−0.244638	−	0.426052i
$688$	29.7273	−	21.5981i	1.13334	−	0.823422i
$689$	−0.0125196	−	0.00909600i	−0.000476958	−	0.000346530i
$690$	−18.5094	+	56.1874i	−0.704640	+	2.13902i
$691$	−12.0591	−	16.5979i	−0.458749	−	0.631413i	0.515500	−	0.856890i	$-0.327606\pi$
$691$	−12.0591	−	16.5979i	−0.458749	−	0.631413i	−0.974249	+	0.225476i	$0.927606\pi$
$692$	−1.78041	+	5.47953i	−0.0676810	+	0.208301i
$693$	8.78655	+	36.7663i	0.333773	+	1.39664i
$694$	−20.7143	+	63.7519i	−0.786303	+	2.41999i
$695$	0.134285	+	1.29887i	0.00509372	+	0.0492688i
$696$	−3.98992	−	18.9921i	−0.151237	−	0.719894i
$697$	−7.64263	−	23.5216i	−0.289485	−	0.890944i
$698$	−39.3009	−	28.5538i	−1.48756	−	1.08078i
$699$	−0.403365	+	3.75227i	−0.0152567	+	0.141924i
$700$	48.8885	−	37.5368i	1.84781	−	1.41876i
$701$		−	47.6533i		−	1.79984i	−0.436054	−	0.899921i	$-0.643624\pi$
$701$		−	47.6533i		−	1.79984i	0.436054	−	0.899921i	$-0.356376\pi$
$702$	0.650469	+	0.908801i	0.0245504	+	0.0343005i
$703$	−31.0854	+	10.1003i	−1.17241	+	0.380939i
$704$	−16.6488	+	5.40953i	−0.627476	+	0.203879i
$705$	−5.51937	+	16.7547i	−0.207871	+	0.631018i
$706$	−43.5284	−	14.1432i	−1.63821	−	0.532287i
$707$	37.7138	−	18.1601i	1.41837	−	0.682982i
$708$	1.36770	−	3.05243i	0.0514013	−	0.114717i
$709$	13.8183	−	10.0396i	0.518958	−	0.377045i	−0.297253	−	0.954799i	$-0.596071\pi$
$709$	13.8183	−	10.0396i	0.518958	−	0.377045i	0.816211	+	0.577754i	$0.196071\pi$
$710$	−12.2897	−	27.7299i	−0.461226	−	1.04069i
$711$	−5.41695	−	6.07374i	−0.203152	−	0.227783i
$712$	3.26177	+	4.48945i	0.122240	+	0.168249i
$713$	−43.4348	+	31.5572i	−1.62665	+	1.18183i
$714$	−10.6099	+	35.9945i	−0.397066	+	1.34706i
$715$	−0.660622	+	0.592796i	−0.0247058	+	0.0221693i
$716$	−11.8885	−	16.3631i	−0.444292	−	0.611516i
$717$	−11.1055	−	4.97602i	−0.414742	−	0.185833i
$718$	82.1900			3.06730
$719$	−14.4248	+	44.3951i	−0.537955	+	1.65566i	0.199220	+	0.979955i	$0.436159\pi$
$719$	−14.4248	+	44.3951i	−0.537955	+	1.65566i	−0.737175	+	0.675701i	$0.763841\pi$
$720$	−11.3478	−	55.1294i	−0.422908	−	2.05455i
$721$	−0.830430	+	0.793909i	−0.0309268	+	0.0295667i
$722$	−7.09940	+	2.30673i	−0.264212	+	0.0858478i
$723$	−26.1029	+	28.8525i	−0.970778	+	1.07304i
$724$		−	21.8893i		−	0.813509i
$725$	1.67014	+	7.99087i	0.0620276	+	0.296774i
$726$	−5.58087	+	51.9156i	−0.207126	+	1.92677i
$727$	−5.77465	+	7.94812i	−0.214170	+	0.294779i	−0.902563	−	0.430559i	$-0.858317\pi$
$727$	−5.77465	+	7.94812i	−0.214170	+	0.294779i	0.688393	+	0.725338i	$0.258317\pi$
$728$	−1.04573	−	1.09384i	−0.0387574	−	0.0405403i
$729$	−8.70743	+	25.5574i	−0.322497	+	0.946570i
$730$	−54.3800	−	31.5197i	−2.01269	−	1.16660i
$731$	4.29434	−	13.2166i	0.158832	−	0.488834i
$732$	8.63322	−	80.3098i	0.319093	−	2.96834i
$733$	−9.96807	−	3.23882i	−0.368179	−	0.119629i	0.119083	−	0.992884i	$-0.462004\pi$
$733$	−9.96807	−	3.23882i	−0.368179	−	0.119629i	−0.487262	+	0.873256i	$0.662004\pi$
$734$	52.2767	−	37.9813i	1.92957	−	1.40191i
$735$	26.1636	−	7.10404i	0.965058	−	0.262037i
$736$	−37.9602	−	27.5797i	−1.39923	−	1.01660i
$737$	−42.7750	−	58.8747i	−1.57564	−	2.16868i
$738$	24.2804	+	55.2373i	0.893775	+	2.03331i
$739$	14.6931	+	10.6751i	0.540493	+	0.392691i	0.824268	−	0.566200i	$-0.191587\pi$
$739$	14.6931	+	10.6751i	0.540493	+	0.392691i	−0.283775	+	0.958891i	$0.591587\pi$
$740$	−72.3933	+	7.48447i	−2.66123	+	0.275135i
$741$	0.585764	−	0.336344i	0.0215186	−	0.0123559i
$742$	0.170113	+	1.25620i	0.00624504	+	0.0461166i
$743$		−	17.7384i		−	0.650760i	−0.945583	−	0.325380i	$-0.894508\pi$
$743$		−	17.7384i		−	0.650760i	0.945583	−	0.325380i	$-0.105492\pi$
$744$	44.0848	−	98.3884i	1.61623	−	3.60709i
$745$	0.678696	+	0.756349i	0.0248655	+	0.0277105i
$746$	−30.5049	+	9.91164i	−1.11686	+	0.362891i
$747$	−2.13692	−	21.3014i	−0.0781858	−	0.779376i
$748$	−41.3889	+	56.9670i	−1.51333	+	2.08292i
$749$	−13.6595	−	28.3671i	−0.499106	−	1.03651i
$750$	10.0246	+	48.9566i	0.366046	+	1.78764i
$751$	16.2956			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$751$	16.2956			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$752$	−30.9177	−	22.4630i	−1.12745	−	0.819143i
$753$	1.76150	+	8.38481i	0.0641928	+	0.305559i
$754$	0.333979	−	0.108516i	0.0121628	−	0.00395193i
$755$	25.9300	−	23.2678i	0.943690	−	0.846802i
$756$	11.8874	−	62.9421i	0.432340	−	2.28918i
$757$	−29.9868			−1.08989			−0.544944	−	0.838473i	$-0.683449\pi$
$757$	−29.9868			−1.08989			−0.544944	+	0.838473i	$0.683449\pi$
$758$	0.473791	+	0.153944i	0.0172089	+	0.00559150i
$759$	−42.3423	+	24.3128i	−1.53693	+	0.882500i
$760$	−71.4181	+	7.38365i	−2.59061	+	0.267833i
$761$	11.5505	+	8.39195i	0.418706	+	0.304208i	0.777117	−	0.629356i	$-0.216681\pi$
$761$	11.5505	+	8.39195i	0.418706	+	0.304208i	−0.358411	+	0.933564i	$0.616681\pi$
$762$	−22.2206	−	38.6985i	−0.804966	−	1.40190i
$763$	−13.4231	+	24.9419i	−0.485948	+	0.902956i
$764$	22.0309	−	30.3229i	0.797050	−	1.09704i
$765$	−15.7272	−	14.3451i	−0.568617	−	0.518650i
$766$	33.0573	+	45.4995i	1.19441	+	1.64396i
$767$	0.0328541	+	0.0106749i	0.00118629	+	0.000385450i
$768$	−40.9648	−	4.40367i	−1.47819	−	0.158904i
$769$	32.8642	+	10.6782i	1.18511	+	0.385066i	0.834264	−	0.551366i	$-0.185893\pi$
$769$	32.8642	+	10.6782i	1.18511	+	0.385066i	0.350849	+	0.936432i	$0.385893\pi$
$770$	72.4963	+	5.55968i	2.61259	+	0.200357i
$771$	−7.37016	−	35.0822i	−0.265430	−	1.26345i
$772$	23.9550	+	73.7259i	0.862159	+	2.65345i
$773$	26.0252	+	18.9084i	0.936062	+	0.680089i	0.947470	−	0.319846i	$-0.103631\pi$
$773$	26.0252	+	18.9084i	0.936062	+	0.680089i	−0.0114075	+	0.999935i	$0.503631\pi$
$774$	−7.20592	+	33.1290i	−0.259012	+	1.19080i
$775$	−18.5872	+	41.3685i	−0.667672	+	1.48600i
$776$	−5.74590			−0.206266
$777$	−30.7057	−	9.05096i	−1.10156	−	0.324701i
$778$	9.82955	+	30.2523i	0.352407	+	1.08460i
$779$	34.6827	−	11.2691i	1.24264	−	0.403757i
$780$	1.43230	−	0.458949i	0.0512844	−	0.0164330i
$781$	7.73597	−	23.8089i	0.276815	−	0.851948i
$782$	−48.4695			−1.73326
$783$	6.82794	+	5.03528i	0.244011	+	0.179946i
$784$	−2.63977	+	58.6741i	−0.0942773	+	2.09551i
$785$	36.1893	+	40.3299i	1.29165	+	1.43944i
$786$	17.6479	−	19.5069i	0.629479	−	0.695787i
$787$	27.8145	+	38.2833i	0.991478	+	1.36465i	0.930411	+	0.366519i	$0.119451\pi$
$787$	27.8145	+	38.2833i	0.991478	+	1.36465i	0.0610676	+	0.998134i	$0.480549\pi$
$788$	−30.9178	−	42.5546i	−1.10140	−	1.51595i
$789$	29.9564	−	33.1120i	1.06648	−	1.17882i
$790$	−14.3112	+	6.34263i	−0.509169	+	0.225661i
$791$	−9.99413	−	5.37859i	−0.355350	−	0.191241i
$792$	49.4262	−	84.6800i	1.75628	−	3.00897i
$793$	0.834204			0.0296234
$794$	22.4800	−	69.1863i	0.797785	−	2.45533i
$795$	−0.682993	−	0.224993i	−0.0242233	−	0.00797968i
$796$	2.94194	−	0.955893i	0.104274	−	0.0338807i
$797$	−15.2432	−	46.9137i	−0.539941	−	1.66177i	−0.732724	−	0.680526i	$-0.761751\pi$
$797$	−15.2432	−	46.9137i	−0.539941	−	1.66177i	0.192783	−	0.981241i	$-0.438249\pi$
$798$	−53.0740	−	15.6444i	−1.87880	−	0.553804i
$799$	−14.4533			−0.511320
$800$	−39.4046	−	4.27706i	−1.39316	−	0.151217i
$801$	−2.37048	−	0.515606i	−0.0837568	−	0.0182181i
$802$	−75.9054	−	55.1485i	−2.68031	−	1.94736i
$803$	−16.0310	−	49.3382i	−0.565720	−	1.74111i
$804$	25.3527	+	120.680i	0.894121	+	4.25604i
$805$	18.3562	+	29.8206i	0.646973	+	1.05104i
$806$	1.85541	+	0.602861i	0.0653542	+	0.0212349i
$807$	−21.7728	−	2.34055i	−0.766439	−	0.0823914i
$808$	−103.257	−	33.5504i	−3.63258	−	1.18030i
$809$	19.3091	+	26.5767i	0.678873	+	0.934388i	0.999920	−	0.0126751i	$-0.00403473\pi$
$809$	19.3091	+	26.5767i	0.678873	+	0.934388i	−0.321047	+	0.947063i	$0.604035\pi$
$810$	41.6709	+	30.9928i	1.46417	+	1.08898i
$811$	11.8488	−	16.3085i	0.416069	−	0.572670i	−0.548617	−	0.836074i	$-0.684845\pi$
$811$	11.8488	−	16.3085i	0.416069	−	0.572670i	0.964685	+	0.263404i	$0.0848454\pi$
$812$	−17.7233	−	9.53825i	−0.621968	−	0.334727i
$813$	−16.8802	−	29.3979i	−0.592015	−	1.03103i
$814$	−69.4567	−	50.4632i	−2.43445	−	1.76874i
$815$	−3.27972	+	15.3019i	−0.114883	+	0.536003i
$816$	39.9922	−	22.9634i	1.40001	−	0.803880i
$817$	19.4879	+	6.33201i	0.681796	+	0.221529i
$818$	81.8443			2.86162
$819$	0.659453	+	0.0525875i	0.0230431	+	0.00183755i
$820$	80.7707	−	8.35058i	2.82064	−	0.291615i
$821$	31.1746	−	10.1292i	1.08800	−	0.353513i	0.290527	−	0.956867i	$-0.406169\pi$
$821$	31.1746	−	10.1292i	1.08800	−	0.353513i	0.797473	+	0.603354i	$0.206169\pi$
$822$	−6.54807	−	31.1690i	−0.228390	−	1.08714i
$823$	28.4620	+	20.6788i	0.992122	+	0.720819i	0.960385	−	0.278677i	$-0.0898960\pi$
$823$	28.4620	+	20.6788i	0.992122	+	0.720819i	0.0317374	+	0.999496i	$0.489896\pi$
$824$	2.97992			0.103810
$825$	−20.8282	+	35.5997i	−0.725143	+	1.23942i
$826$	−1.22770	−	2.54962i	−0.0427173	−	0.0887125i
$827$	−17.4299	+	23.9903i	−0.606099	+	0.834223i	−0.996249	−	0.0865278i	$-0.972423\pi$
$827$	−17.4299	+	23.9903i	−0.606099	+	0.834223i	0.390151	+	0.920751i	$0.372423\pi$
$828$	82.3224	−	8.25845i	2.86090	−	0.287001i
$829$	−0.434904	+	0.141309i	−0.0151048	+	0.00490786i	−0.316560	−	0.948573i	$-0.602528\pi$
$829$	−0.434904	+	0.141309i	−0.0151048	+	0.00490786i	0.301455	+	0.953480i	$0.402528\pi$
$830$	−40.2630	−	8.62972i	−1.39755	−	0.299542i
$831$	1.38103	−	3.08218i	0.0479073	−	0.106919i
$832$			0.306356i			0.0106210i
$833$	12.2354	+	18.5391i	0.423933	+	0.642343i
$834$	2.26353	−	1.29971i	0.0783796	−	0.0450053i
$835$	12.1861	+	27.4960i	0.421716	+	0.951539i
$836$	−83.9980	−	61.0281i	−2.90513	−	2.11070i
$837$	14.2457	+	44.9271i	0.492402	+	1.55291i
$838$	−2.92202	−	4.02181i	−0.100939	−	0.138931i
$839$	−21.2041	−	15.4057i	−0.732046	−	0.531863i	0.158164	−	0.987413i	$-0.449443\pi$
$839$	−21.2041	−	15.4057i	−0.732046	−	0.531863i	−0.890210	+	0.455550i	$0.849443\pi$
$840$	−61.7858	−	33.5764i	−2.13181	−	1.15849i
$841$	−21.3049	+	15.4789i	−0.734651	+	0.533755i
$842$	−5.54446	−	1.80151i	−0.191075	−	0.0620840i
$843$	−3.10054	+	28.8425i	−0.106788	+	0.993390i
$844$	−18.9481	+	58.3163i	−0.652221	+	2.00733i
$845$	−11.7719	−	26.5616i	−0.404967	−	0.913747i
$846$	35.0852	−	3.51969i	1.20625	−	0.121009i
$847$	21.3583	+	22.3408i	0.733879	+	0.767639i
$848$	0.915690	−	1.26034i	0.0314449	−	0.0432802i
$849$	−2.20831	+	20.5426i	−0.0757889	+	0.705020i
$850$	−35.5277	+	20.3513i	−1.21859	+	0.698042i
$851$		−	41.3477i		−	1.41738i
$852$	−28.4592	+	31.4571i	−0.974998	+	1.07770i
$853$	−30.0838	+	9.77482i	−1.03005	+	0.334683i	−0.774810	−	0.632194i	$-0.782154\pi$
$853$	−30.0838	+	9.77482i	−1.03005	+	0.334683i	−0.255240	+	0.966878i	$0.582154\pi$
$854$	−47.2220	−	49.3943i	−1.61591	−	1.69024i
$855$	21.1520	−	23.1898i	0.723382	−	0.793073i
$856$	−25.2355	+	77.6669i	−0.862532	+	2.65460i
$857$	−11.6039			−0.396382			−0.198191	−	0.980163i	$-0.563507\pi$
$857$	−11.6039			−0.396382			−0.198191	+	0.980163i	$0.563507\pi$
$858$	1.61911	+	0.725474i	0.0552755	+	0.0247673i
$859$	10.5900	+	14.5759i	0.361327	+	0.497324i	0.950518	−	0.310670i	$-0.100553\pi$
$859$	10.5900	+	14.5759i	0.361327	+	0.497324i	−0.589191	+	0.807994i	$0.700553\pi$
$860$	39.4748	+	22.8803i	1.34608	+	0.780212i
$861$	34.2590	+	10.0983i	1.16754	+	0.344151i
$862$	−30.8280	+	22.3979i	−1.05001	+	0.762874i
$863$	12.0469	+	16.5812i	0.410083	+	0.564431i	0.963239	−	0.268647i	$-0.0865766\pi$
$863$	12.0469	+	16.5812i	0.410083	+	0.564431i	−0.553156	+	0.833078i	$0.686577\pi$
$864$	−33.4954	+	23.9741i	−1.13954	+	0.815616i
$865$	−2.75038	+	0.284351i	−0.0935157	+	0.00966824i
$866$	−68.8363	+	50.0125i	−2.33915	+	1.69949i
$867$	−4.90842	+	10.9546i	−0.166699	+	0.372038i
$868$	−48.5107	−	100.744i	−1.64656	−	3.41947i
$869$	−12.2876	−	3.99247i	−0.416827	−	0.135435i
$870$	13.2405	−	9.53774i	0.448895	−	0.323360i
$871$	−1.21123	+	0.393553i	−0.0410410	+	0.0133350i
$872$	69.8717	−	22.7027i	2.36616	−	0.768811i
$873$	1.87462	−	1.67191i	0.0634464	−	0.0565856i
$874$		−	71.4684i		−	2.41745i
$875$	25.9760	+	14.1509i	0.878149	+	0.478387i
$876$	−9.39565	+	87.4023i	−0.317450	+	2.95305i
$877$	15.2313	+	11.0662i	0.514326	+	0.373680i	0.814462	−	0.580217i	$-0.197032\pi$
$877$	15.2313	+	11.0662i	0.514326	+	0.373680i	−0.300136	+	0.953896i	$0.597032\pi$
$878$	−12.5301	−	38.5636i	−0.422869	−	1.30146i
$879$	−3.10839	−	14.7960i	−0.104843	−	0.499057i
$880$	−59.6765	−	66.5044i	−2.01169	−	2.24186i
$881$	−4.09842	+	12.6136i	−0.138079	+	0.424964i	−0.996056	−	0.0887237i	$-0.971721\pi$
$881$	−4.09842	+	12.6136i	−0.138079	+	0.424964i	0.857977	+	0.513688i	$0.171721\pi$
$882$	−34.2161	−	42.0239i	−1.15212	−	1.41502i
$883$	6.25257	−	19.2434i	0.210416	−	0.647594i	−0.789031	−	0.614353i	$-0.789417\pi$
$883$	6.25257	−	19.2434i	0.210416	−	0.647594i	0.999447	−	0.0332407i	$-0.0105828\pi$
$884$	0.724325	+	0.996948i	0.0243617	+	0.0335310i
$885$	1.60522	+	0.00652917i	0.0539590	+	0.000219476i
$886$	−52.3604	−	38.0420i	−1.75908	−	1.27805i
$887$	−25.0860	+	18.2260i	−0.842305	+	0.611971i	−0.923014	−	0.384767i	$-0.874282\pi$
$887$	−25.0860	+	18.2260i	−0.842305	+	0.611971i	0.0807083	+	0.996738i	$0.474282\pi$
$888$	41.3455	+	72.0057i	1.38746	+	2.41635i
$889$	−25.9900	−	4.71756i	−0.871676	−	0.158222i
$890$	−2.33991	+	4.03698i	−0.0784338	+	0.135320i
$891$	8.51423	+	42.0089i	0.285237	+	1.40735i
$892$	−112.035	−	36.4023i	−3.75120	−	1.21884i
$893$		−	21.3114i		−	0.713158i
$894$	0.830599	−	1.85373i	0.0277794	−	0.0619980i
$895$	4.86762	−	8.39797i	0.162707	−	0.280713i
$896$	−12.1804	+	11.6447i	−0.406918	+	0.389022i
$897$	0.175676	+	0.836224i	0.00586566	+	0.0279207i
$898$	18.8341	+	13.6838i	0.628502	+	0.456633i
$899$	14.8094			0.493923
$900$	56.8741	−	40.6187i	1.89580	−	1.35396i
$901$		−	0.589177i		−	0.0196283i
$902$	77.4943	+	56.3029i	2.58028	+	1.87468i
$903$	12.2383	+	15.9053i	0.407264	+	0.529295i
$904$	9.09690	+	27.9974i	0.302558	+	0.931179i
$905$	9.60404	−	4.25645i	0.319249	−	0.141489i
$906$	−63.5516	−	28.4755i	−2.11136	−	0.946036i
$907$	49.0423			1.62842			0.814212	−	0.580568i	$-0.197169\pi$
$907$	49.0423			1.62842			0.814212	+	0.580568i	$0.197169\pi$
$908$	−21.3741	+	65.7827i	−0.709324	+	2.18307i
$909$	43.4504	−	19.0993i	1.44116	−	0.633485i
$910$	0.484590	−	1.17656i	0.0160640	−	0.0390024i
$911$	−20.6958	+	28.4854i	−0.685683	+	0.943762i	−0.999985	−	0.00556114i	$-0.998230\pi$
$911$	−20.6958	+	28.4854i	−0.685683	+	0.943762i	0.314301	+	0.949323i	$0.398230\pi$
$912$	33.8596	+	58.9686i	1.12120	+	1.95264i
$913$	−19.9765	−	27.4953i	−0.661126	−	0.909962i
$914$	−23.0825	+	31.7704i	−0.763502	+	1.05087i
$915$	36.9151	−	11.8287i	1.22038	−	0.391043i
$916$	20.3609	+	28.0244i	0.672744	+	0.925952i
$917$	−2.08953	−	15.4302i	−0.0690023	−	0.509549i
$918$	−13.4358	+	40.3731i	−0.443448	+	1.33251i
$919$	1.20624	−	3.71242i	0.0397901	−	0.122461i	−0.929188	−	0.369607i	$-0.879492\pi$
$919$	1.20624	−	3.71242i	0.0397901	−	0.122461i	0.968978	+	0.247145i	$0.0794925\pi$
$920$	19.0351	−	88.8105i	0.627567	−	2.92800i
$921$	−6.44367	+	1.35370i	−0.212326	+	0.0446061i
$922$	83.2069	−	27.0356i	2.74027	−	0.890369i
$923$	−0.354437	−	0.257514i	−0.0116664	−	0.00847616i
$924$	−34.0719	−	95.8104i	−1.12088	−	3.15193i
$925$	−17.3610	−	30.3075i	−0.570825	−	0.996506i
$926$			59.4027i			1.95209i
$927$	−0.972210	+	0.867080i	−0.0319316	+	0.0284787i
$928$	3.99955	+	12.3094i	0.131292	+	0.404075i
$929$	11.8943	+	36.6068i	0.390238	+	1.20103i	0.932608	+	0.360890i	$0.117527\pi$
$929$	11.8943	+	36.6068i	0.390238	+	1.20103i	−0.542370	+	0.840140i	$0.682473\pi$
$930$	90.6539	+	0.368731i	2.97266	+	0.0120912i
$931$	−27.3360	+	18.0412i	−0.895901	+	0.591276i
$932$		−	10.1519i		−	0.332538i
$933$	−5.60199	+	12.5025i	−0.183401	+	0.409314i
$934$	9.91619	+	13.6485i	0.324468	+	0.446592i
$935$	−33.0428	−	7.08217i	−1.08061	−	0.231612i
$936$	−1.14211	−	1.28059i	−0.0373311	−	0.0418574i
$937$	7.21332	+	9.92829i	0.235649	+	0.324343i	0.910421	−	0.413683i	$-0.135758\pi$
$937$	7.21332	+	9.92829i	0.235649	+	0.324343i	−0.674772	+	0.738026i	$0.735758\pi$
$938$	91.8673	+	49.4407i	2.99957	+	1.61429i
$939$	32.5583	−	35.9879i	1.06250	−	1.17442i
$940$	9.94501	−	46.3997i	0.324370	−	1.51339i
$941$	−0.00149003	+	0.00108257i	−4.85737e−5	+	3.52909e-5i	−0.587810	−	0.808999i	$-0.700010\pi$
$941$	−0.00149003	+	0.00108257i	−4.85737e−5	+	3.52909e-5i	0.587761	+	0.809035i	$0.300010\pi$
$942$	44.2890	−	98.8442i	1.44301	−	3.22052i
$943$			46.1325i			1.50228i
$944$	−1.07464	+	3.30740i	−0.0349766	+	0.107647i
$945$	29.9277	−	7.02367i	0.973549	−	0.228480i
$946$	16.6321	+	51.1884i	0.540757	+	1.66428i
$947$	−11.2297	+	3.64876i	−0.364917	+	0.118569i	−0.485735	−	0.874106i	$-0.661448\pi$
$947$	−11.2297	+	3.64876i	−0.364917	+	0.118569i	0.120819	+	0.992675i	$0.461448\pi$
$948$	16.2347	+	14.6876i	0.527280	+	0.477030i
$949$	−0.907875			−0.0294709
$950$	−30.0080	−	52.3858i	−0.973588	−	1.69962i
$951$	−0.228072	+	2.12162i	−0.00739575	+	0.0687984i
$952$	10.2898	−	56.6886i	0.333495	−	1.83729i
$953$	−33.6640	+	10.9381i	−1.09048	+	0.354320i	−0.798433	−	0.602083i	$-0.794338\pi$
$953$	−33.6640	+	10.9381i	−1.09048	+	0.354320i	−0.292051	+	0.956403i	$0.594338\pi$
$954$	0.143478	+	1.43022i	0.00464526	+	0.0463051i
$955$	17.5883	+	3.76977i	0.569145	+	0.121987i
$956$	31.1339	+	10.1160i	1.00694	+	0.327175i
$957$	13.3911	+	1.43952i	0.432872	+	0.0465332i
$958$	−1.34437	−	0.436811i	−0.0434345	−	0.0141127i
$959$	−16.6013	−	8.93440i	−0.536084	−	0.288507i
$960$	4.34400	+	13.5568i	0.140202	+	0.437545i
$961$	41.4812	+	30.1378i	1.33810	+	0.972189i
$962$	−1.21552	+	0.883129i	−0.0391900	+	0.0284732i
$963$	−14.3659	−	32.6820i	−0.462935	−	1.05316i
$964$	61.5202	−	84.6753i	1.98143	−	2.72721i
$965$	−27.6895	+	24.8466i	−0.891356	+	0.799842i
$966$	39.5694	−	57.7384i	1.27312	−	1.85770i
$967$	−2.67467	+	8.23180i	−0.0860117	+	0.264717i	−0.984807	−	0.173651i	$-0.944443\pi$
$967$	−2.67467	+	8.23180i	−0.0860117	+	0.264717i	0.898795	+	0.438368i	$0.144443\pi$
$968$		−	80.1679i		−	2.57669i
$969$	23.4685	+	10.5155i	0.753916	+	0.337806i
$970$	−1.95762	−	4.41706i	−0.0628552	−	0.141823i
$971$	−18.1881	−	55.9773i	−0.583685	−	1.79640i	−0.604488	−	0.796614i	$-0.706622\pi$
$971$	−18.1881	−	55.9773i	−0.583685	−	1.79640i	0.0208031	−	0.999784i	$-0.493378\pi$
$972$	15.9410	−	70.8604i	0.511307	−	2.27285i
$973$	0.275937	−	1.52019i	0.00884612	−	0.0487351i
$974$			20.3243i			0.651234i
$975$	0.479881	+	0.539183i	0.0153685	+	0.0172677i
$976$			83.9789i			2.68810i
$977$	−23.0901	+	31.7808i	−0.738719	+	1.01676i	0.259973	+	0.965616i	$0.416286\pi$
$977$	−23.0901	+	31.7808i	−0.738719	+	1.01676i	−0.998691	+	0.0511430i	$0.983714\pi$
$978$	30.6134	−	6.43135i	0.978908	−	0.205652i
$979$	−3.66269	+	1.19008i	−0.117060	+	0.0380351i
$980$	−67.9356	+	26.5233i	−2.17012	+	0.847257i
$981$	−16.1900	+	27.7377i	−0.516907	+	0.885597i
$982$	−6.65131			−0.212252
$983$	−5.42234	+	16.6883i	−0.172946	+	0.532273i	−0.999534	−	0.0305350i	$-0.990279\pi$
$983$	−5.42234	+	16.6883i	−0.172946	+	0.532273i	0.826588	+	0.562808i	$0.190279\pi$
$984$	−46.1300	−	80.3382i	−1.47057	−	2.56109i
$985$	12.6590	−	21.8402i	0.403349	−	0.695887i
$986$	10.8164	+	7.85860i	0.344466	+	0.250269i
$987$	11.7993	−	17.2172i	0.375576	−	0.548030i
$988$	−1.47000	+	1.06802i	−0.0467670	+	0.0339782i
$989$	−15.2363	+	20.9709i	−0.484485	+	0.666837i
$990$	81.9357	+	9.14526i	2.60409	+	0.290656i
$991$	−22.5217	+	16.3630i	−0.715424	+	0.519786i	−0.884919	−	0.465745i	$-0.845786\pi$
$991$	−22.5217	+	16.3630i	−0.715424	+	0.519786i	0.169495	+	0.985531i	$0.445786\pi$
$992$	−22.2194	+	68.3844i	−0.705468	+	2.17121i
$993$	−32.1245	−	3.45334i	−1.01944	−	0.109589i
$994$	4.81600	+	35.5639i	0.152754	+	1.12802i
$995$	0.991472	+	1.10491i	0.0314318	+	0.0350281i
$996$	11.8401	+	56.3590i	0.375167	+	1.78580i
$997$	35.3060	−	11.4716i	1.11815	−	0.363310i	0.309091	−	0.951032i	$-0.399975\pi$
$997$	35.3060	−	11.4716i	1.11815	−	0.363310i	0.809063	+	0.587722i	$0.199975\pi$
$998$	−2.91188	+	4.00786i	−0.0921740	+	0.126867i
$999$	−34.4409	−	11.4617i	−1.08966	−	0.362631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.4	yes	304
3.2	odd	2	inner	525.2.bb.a.41.73	yes	304
7.6	odd	2	inner	525.2.bb.a.41.3	✓	304
21.20	even	2	inner	525.2.bb.a.41.74	yes	304
25.11	even	5	inner	525.2.bb.a.461.74	yes	304
75.11	odd	10	inner	525.2.bb.a.461.3	yes	304
175.111	odd	10	inner	525.2.bb.a.461.73	yes	304
525.461	even	10	inner	525.2.bb.a.461.4	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.3	✓	304	7.6	odd	2	inner
525.2.bb.a.41.4	yes	304	1.1	even	1	trivial
525.2.bb.a.41.73	yes	304	3.2	odd	2	inner
525.2.bb.a.41.74	yes	304	21.20	even	2	inner
525.2.bb.a.461.3	yes	304	75.11	odd	10	inner
525.2.bb.a.461.4	yes	304	525.461	even	10	inner
525.2.bb.a.461.73	yes	304	175.111	odd	10	inner
525.2.bb.a.461.74	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)

\(f(q)\)	\(=\)	\(q+(-1.51682 + 2.08772i) q^{2} +(0.356101 + 1.69505i) q^{3} +(-1.43980 - 4.43126i) q^{4} +(1.66426 - 1.49340i) q^{5} +(-4.07893 - 1.82764i) q^{6} +(-2.38379 + 1.14785i) q^{7} +(6.52662 + 2.12063i) q^{8} +(-2.74638 + 1.20722i) q^{9} +O(q^{10})\)	\(q+(-1.51682 + 2.08772i) q^{2} +(0.356101 + 1.69505i) q^{3} +(-1.43980 - 4.43126i) q^{4} +(1.66426 - 1.49340i) q^{5} +(-4.07893 - 1.82764i) q^{6} +(-2.38379 + 1.14785i) q^{7} +(6.52662 + 2.12063i) q^{8} +(-2.74638 + 1.20722i) q^{9} +(0.593408 + 5.73972i) q^{10} +(-2.79937 + 3.85300i) q^{11} +(6.99849 - 4.01851i) q^{12} +(0.0489901 + 0.0674291i) q^{13} +(1.21937 - 6.71776i) q^{14} +(3.12402 + 2.28921i) q^{15} +(-6.78806 + 4.93181i) q^{16} +(-0.980587 + 3.01794i) q^{17} +(1.64543 - 7.56481i) q^{18} +(-4.44996 - 1.44588i) q^{19} +(-9.01384 - 5.22459i) q^{20} +(-2.79454 - 3.63188i) q^{21} +(-3.79785 - 11.6886i) q^{22} +(3.47912 - 4.78859i) q^{23} +(-1.27043 + 11.8181i) q^{24} +(0.539541 - 4.97080i) q^{25} -0.215082 q^{26} +(-3.02428 - 4.22537i) q^{27} +(8.51862 + 8.91049i) q^{28} +(-1.55280 + 0.504535i) q^{29} +(-9.51779 + 3.04978i) q^{30} +(-8.62654 - 2.80293i) q^{31} -7.92721i q^{32} +(-7.52787 - 3.37301i) q^{33} +(-4.81323 - 6.62485i) q^{34} +(-2.25305 + 5.47026i) q^{35} +(9.30375 + 10.4318i) q^{36} +(5.65143 - 4.10601i) q^{37} +(9.76836 - 7.09713i) q^{38} +(-0.0968503 + 0.107052i) q^{39} +(14.0290 - 6.21755i) q^{40} +(-6.30543 + 4.58116i) q^{41} +(11.8211 - 0.325305i) q^{42} -4.37935 q^{43} +(21.1042 + 6.85716i) q^{44} +(-2.76785 + 6.11056i) q^{45} +(4.72005 + 14.5268i) q^{46} +(1.40749 + 4.33180i) q^{47} +(-10.7769 - 9.74987i) q^{48} +(4.36487 - 5.47247i) q^{49} +(9.55926 + 8.66621i) q^{50} +(-5.46474 - 0.587453i) q^{51} +(0.228260 - 0.314173i) q^{52} +(-0.176583 + 0.0573752i) q^{53} +(13.4087 + 0.0952533i) q^{54} +(1.09517 + 10.5930i) q^{55} +(-17.9922 + 2.43648i) q^{56} +(0.866202 - 8.05778i) q^{57} +(1.30198 - 4.00709i) q^{58} +(0.335313 - 0.243619i) q^{59} +(5.64610 - 17.1394i) q^{60} +(5.88303 - 8.09729i) q^{61} +(18.9366 - 13.7583i) q^{62} +(5.16108 - 6.03019i) q^{63} +(2.97368 + 2.16050i) q^{64} +(0.182231 + 0.0390582i) q^{65} +(18.4603 - 10.5999i) q^{66} +(-4.72186 + 14.5324i) q^{67} +14.7851 q^{68} +(9.35582 + 4.19205i) q^{69} +(-8.00291 - 13.0011i) q^{70} +(-4.99917 + 1.62433i) q^{71} +(-20.4847 + 2.05499i) q^{72} +(-6.40258 + 8.81240i) q^{73} +18.0267i q^{74} +(8.61789 - 0.855559i) q^{75} +21.8007i q^{76} +(2.25041 - 12.3980i) q^{77} +(-0.0765909 - 0.364575i) q^{78} +(0.838302 + 2.58003i) q^{79} +(-3.93197 + 18.3451i) q^{80} +(6.08525 - 6.63096i) q^{81} -20.1127i q^{82} +(-2.20517 + 6.78682i) q^{83} +(-12.0702 + 17.6125i) q^{84} +(2.87502 + 6.48704i) q^{85} +(6.64267 - 9.14286i) q^{86} +(-1.40816 - 2.45240i) q^{87} +(-26.4412 + 19.2106i) q^{88} +(0.654200 + 0.475304i) q^{89} +(-8.55881 - 15.0471i) q^{90} +(-0.194181 - 0.104503i) q^{91} +(-26.2287 - 8.52224i) q^{92} +(1.67919 - 15.6205i) q^{93} +(-11.1785 - 3.63211i) q^{94} +(-9.56517 + 4.23922i) q^{95} +(13.4370 - 2.82289i) q^{96} +(-0.796311 + 0.258737i) q^{97} +(4.80428 + 17.4133i) q^{98} +(3.03673 - 13.9612i) 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

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Representations

Groups

Database

Properties

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