LMFDB - Embedded newform 585.2.i.g.196.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.13
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35654 - 2.34960i) q^{2} +(1.35813 - 1.07494i) q^{3} +(-2.68041 - 4.64261i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.683325 - 4.64925i) q^{6} +(-1.23495 + 2.13900i) q^{7} -9.11822 q^{8} +(0.689008 - 2.91981i) q^{9} +O(q^{10})$	\(q+(1.35654 - 2.34960i) q^{2} +(1.35813 - 1.07494i) q^{3} +(-2.68041 - 4.64261i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.683325 - 4.64925i) q^{6} +(-1.23495 + 2.13900i) q^{7} -9.11822 q^{8} +(0.689008 - 2.91981i) q^{9} -2.71308 q^{10} +(-0.122432 + 0.212059i) q^{11} +(-8.63087 - 3.42397i) q^{12} +(0.500000 + 0.866025i) q^{13} +(3.35052 + 5.80328i) q^{14} +(-1.60999 - 0.638701i) q^{15} +(-7.00842 + 12.1389i) q^{16} +3.50397 q^{17} +(-5.92571 - 5.57973i) q^{18} +7.96546 q^{19} +(-2.68041 + 4.64261i) q^{20} +(0.622076 + 4.23252i) q^{21} +(0.332169 + 0.575334i) q^{22} +(-2.77910 - 4.81355i) q^{23} +(-12.3837 + 9.80154i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.71308 q^{26} +(-2.20286 - 4.70610i) q^{27} +13.2407 q^{28} +(-0.993004 + 1.71993i) q^{29} +(-3.68471 + 2.91640i) q^{30} +(-3.34974 - 5.80192i) q^{31} +(9.89622 + 17.1408i) q^{32} +(0.0616723 + 0.419610i) q^{33} +(4.75329 - 8.23293i) q^{34} +2.46990 q^{35} +(-15.4024 + 4.62749i) q^{36} +8.76248 q^{37} +(10.8055 - 18.7156i) q^{38} +(1.60999 + 0.638701i) q^{39} +(4.55911 + 7.89661i) q^{40} +(-2.93288 - 5.07990i) q^{41} +(10.7886 + 4.27996i) q^{42} +(-2.96172 + 5.12985i) q^{43} +1.31268 q^{44} +(-2.87313 + 0.863205i) q^{45} -15.0799 q^{46} +(2.29931 - 3.98251i) q^{47} +(3.53032 + 24.0198i) q^{48} +(0.449799 + 0.779075i) q^{49} +(1.35654 + 2.34960i) q^{50} +(4.75883 - 3.76656i) q^{51} +(2.68041 - 4.64261i) q^{52} -7.83420 q^{53} +(-14.0457 - 1.20820i) q^{54} +0.244865 q^{55} +(11.2605 - 19.5038i) q^{56} +(10.8181 - 8.56239i) q^{57} +(2.69410 + 4.66632i) q^{58} +(4.26863 + 7.39348i) q^{59} +(1.35019 + 9.18654i) q^{60} +(-5.27110 + 9.12981i) q^{61} -18.1762 q^{62} +(5.39456 + 5.07960i) q^{63} +25.6649 q^{64} +(0.500000 - 0.866025i) q^{65} +(1.06958 + 0.424314i) q^{66} +(7.37676 + 12.7769i) q^{67} +(-9.39210 - 16.2676i) q^{68} +(-8.94865 - 3.55003i) q^{69} +(3.35052 - 5.80328i) q^{70} +7.58645 q^{71} +(-6.28252 + 26.6234i) q^{72} -5.64578 q^{73} +(11.8867 - 20.5883i) q^{74} +(0.251863 + 1.71364i) q^{75} +(-21.3507 - 36.9805i) q^{76} +(-0.302396 - 0.523764i) q^{77} +(3.68471 - 2.91640i) q^{78} +(2.98574 - 5.17145i) q^{79} +14.0168 q^{80} +(-8.05054 - 4.02354i) q^{81} -15.9143 q^{82} +(0.215206 - 0.372748i) q^{83} +(17.9825 - 14.2330i) q^{84} +(-1.75199 - 3.03453i) q^{85} +(8.03541 + 13.9177i) q^{86} +(0.500201 + 3.40330i) q^{87} +(1.11636 - 1.93360i) q^{88} +14.7091 q^{89} +(-1.86934 + 7.92168i) q^{90} -2.46990 q^{91} +(-14.8983 + 25.8046i) q^{92} +(-10.7861 - 4.27896i) q^{93} +(-6.23821 - 10.8049i) q^{94} +(-3.98273 - 6.89829i) q^{95} +(31.8656 + 12.6414i) q^{96} +(-2.29136 + 3.96875i) q^{97} +2.44069 q^{98} +(0.534814 + 0.503589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.35654	−	2.34960i	0.959220	−	1.66142i	0.234820	−	0.972039i	$-0.424550\pi$
$2$	1.35654	−	2.34960i	0.959220	−	1.66142i	0.724400	−	0.689380i	$-0.242117\pi$
$3$	1.35813	−	1.07494i	0.784114	−	0.620617i
$3$	1.35813	−	1.07494i	0.784114	−	0.620617i
$4$	−2.68041	−	4.64261i	−1.34021	−	2.32131i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.683325	−	4.64925i	−0.278966	−	1.89805i
$7$	−1.23495	+	2.13900i	−0.466767	+	0.808464i	−0.999279	−	0.0379580i	$-0.987915\pi$
$7$	−1.23495	+	2.13900i	−0.466767	+	0.808464i	0.532512	+	0.846422i	$0.321248\pi$
$8$	−9.11822			−3.22378
$9$	0.689008	−	2.91981i	0.229669	−	0.973269i
$10$	−2.71308			−0.857953
$11$	−0.122432	+	0.212059i	−0.0369147	+	0.0639382i	−0.883893	−	0.467690i	$-0.845086\pi$
$11$	−0.122432	+	0.212059i	−0.0369147	+	0.0639382i	0.846978	+	0.531628i	$0.178420\pi$
$12$	−8.63087	−	3.42397i	−2.49152	−	0.988414i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	3.35052	+	5.80328i	0.895465	+	1.55099i
$15$	−1.60999	−	0.638701i	−0.415697	−	0.164912i
$16$	−7.00842	+	12.1389i	−1.75210	+	3.03473i
$17$	3.50397			0.849838			0.424919	−	0.905231i	$-0.360303\pi$
$17$	3.50397			0.849838			0.424919	+	0.905231i	$0.360303\pi$
$18$	−5.92571	−	5.57973i	−1.39670	−	1.31516i
$19$	7.96546			1.82740			0.913700	−	0.406388i	$-0.133212\pi$
$19$	7.96546			1.82740			0.913700	+	0.406388i	$0.133212\pi$
$20$	−2.68041	+	4.64261i	−0.599359	+	1.03812i
$21$	0.622076	+	4.23252i	0.135748	+	0.923612i
$22$	0.332169	+	0.575334i	0.0708187	+	0.122662i
$23$	−2.77910	−	4.81355i	−0.579483	−	1.00369i	−0.995539	−	0.0943552i	$-0.969921\pi$
$23$	−2.77910	−	4.81355i	−0.579483	−	1.00369i	0.416055	−	0.909339i	$-0.363412\pi$
$24$	−12.3837	+	9.80154i	−2.52781	+	2.00073i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.71308			0.532080
$27$	−2.20286	−	4.70610i	−0.423940	−	0.905690i
$28$	13.2407			2.50226
$29$	−0.993004	+	1.71993i	−0.184396	+	0.319384i	−0.943373	−	0.331734i	$-0.892366\pi$
$29$	−0.993004	+	1.71993i	−0.184396	+	0.319384i	0.758977	+	0.651118i	$0.225700\pi$
$30$	−3.68471	+	2.91640i	−0.672733	+	0.532460i
$31$	−3.34974	−	5.80192i	−0.601631	−	1.04205i	−0.992574	−	0.121640i	$-0.961185\pi$
$31$	−3.34974	−	5.80192i	−0.601631	−	1.04205i	0.390944	−	0.920415i	$-0.372149\pi$
$32$	9.89622	+	17.1408i	1.74942	+	3.03009i
$33$	0.0616723	+	0.419610i	0.0107358	+	0.0730447i
$34$	4.75329	−	8.23293i	0.815182	−	1.41194i
$35$	2.46990			0.417489
$36$	−15.4024	+	4.62749i	−2.56706	+	0.771249i
$37$	8.76248			1.44054			0.720271	−	0.693692i	$-0.244017\pi$
$37$	8.76248			1.44054			0.720271	+	0.693692i	$0.244017\pi$
$38$	10.8055	−	18.7156i	1.75288	−	3.03608i
$39$	1.60999	+	0.638701i	0.257804	+	0.102274i
$40$	4.55911	+	7.89661i	0.720858	+	1.24856i
$41$	−2.93288	−	5.07990i	−0.458039	−	0.793347i	0.540818	−	0.841139i	$-0.318115\pi$
$41$	−2.93288	−	5.07990i	−0.458039	−	0.793347i	−0.998857	+	0.0477927i	$0.984781\pi$
$42$	10.7886	+	4.27996i	1.66472	+	0.660413i
$43$	−2.96172	+	5.12985i	−0.451659	+	0.782295i	−0.998489	−	0.0549477i	$-0.982501\pi$
$43$	−2.96172	+	5.12985i	−0.451659	+	0.782295i	0.546831	+	0.837243i	$0.315834\pi$
$44$	1.31268			0.197894
$45$	−2.87313	+	0.863205i	−0.428301	+	0.128679i
$46$	−15.0799			−2.22341
$47$	2.29931	−	3.98251i	0.335388	−	0.580909i	−0.648171	−	0.761495i	$-0.724466\pi$
$47$	2.29931	−	3.98251i	0.335388	−	0.580909i	0.983559	+	0.180585i	$0.0577992\pi$
$48$	3.53032	+	24.0198i	0.509558	+	3.46696i
$49$	0.449799	+	0.779075i	0.0642570	+	0.111296i
$50$	1.35654	+	2.34960i	0.191844	+	0.332284i
$51$	4.75883	−	3.76656i	0.666370	−	0.527424i
$52$	2.68041	−	4.64261i	0.371707	−	0.643815i
$53$	−7.83420			−1.07611			−0.538055	−	0.842910i	$-0.680841\pi$
$53$	−7.83420			−1.07611			−0.538055	+	0.842910i	$0.680841\pi$
$54$	−14.0457	−	1.20820i	−1.91138	−	0.164415i
$55$	0.244865			0.0330175
$56$	11.2605	−	19.5038i	1.50475	−	2.60631i
$57$	10.8181	−	8.56239i	1.43289	−	1.13412i
$58$	2.69410	+	4.66632i	0.353753	+	0.612718i
$59$	4.26863	+	7.39348i	0.555728	+	0.962549i	0.997846	+	0.0655925i	$0.0208938\pi$
$59$	4.26863	+	7.39348i	0.555728	+	0.962549i	−0.442118	+	0.896957i	$0.645773\pi$
$60$	1.35019	+	9.18654i	0.174309	+	1.18598i
$61$	−5.27110	+	9.12981i	−0.674895	+	1.16895i	0.301604	+	0.953433i	$0.402478\pi$
$61$	−5.27110	+	9.12981i	−0.674895	+	1.16895i	−0.976500	+	0.215520i	$0.930855\pi$
$62$	−18.1762			−2.30839
$63$	5.39456	+	5.07960i	0.679651	+	0.639969i
$64$	25.6649			3.20811
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	1.06958	+	0.424314i	0.131656	+	0.0522294i
$67$	7.37676	+	12.7769i	0.901215	+	1.56095i	0.825919	+	0.563789i	$0.190657\pi$
$67$	7.37676	+	12.7769i	0.901215	+	1.56095i	0.0752966	+	0.997161i	$0.476010\pi$
$68$	−9.39210	−	16.2676i	−1.13896	−	1.97274i
$69$	−8.94865	−	3.55003i	−1.07729	−	0.427374i
$70$	3.35052	−	5.80328i	0.400464	−	0.693624i
$71$	7.58645			0.900346			0.450173	−	0.892941i	$-0.351362\pi$
$71$	7.58645			0.900346			0.450173	+	0.892941i	$0.351362\pi$
$72$	−6.28252	+	26.6234i	−0.740403	+	3.13760i
$73$	−5.64578			−0.660788			−0.330394	−	0.943843i	$-0.607182\pi$
$73$	−5.64578			−0.660788			−0.330394	+	0.943843i	$0.607182\pi$
$74$	11.8867	−	20.5883i	1.38180	−	2.39334i
$75$	0.251863	+	1.71364i	0.0290826	+	0.197874i
$76$	−21.3507	−	36.9805i	−2.44910	−	4.24196i
$77$	−0.302396	−	0.523764i	−0.0344612	−	0.0596885i
$78$	3.68471	−	2.91640i	0.417211	−	0.330218i
$79$	2.98574	−	5.17145i	0.335922	−	0.581834i	−0.647740	−	0.761862i	$-0.724286\pi$
$79$	2.98574	−	5.17145i	0.335922	−	0.581834i	0.983661	+	0.180028i	$0.0576189\pi$
$80$	14.0168			1.56713
$81$	−8.05054	−	4.02354i	−0.894504	−	0.447060i
$82$	−15.9143			−1.75744
$83$	0.215206	−	0.372748i	0.0236220	−	0.0409145i	−0.853973	−	0.520318i	$-0.825814\pi$
$83$	0.215206	−	0.372748i	0.0236220	−	0.0409145i	0.877595	+	0.479403i	$0.159147\pi$
$84$	17.9825	−	14.2330i	1.96206	−	1.55294i
$85$	−1.75199	−	3.03453i	−0.190030	−	0.329141i
$86$	8.03541	+	13.9177i	0.866480	+	1.50079i
$87$	0.500201	+	3.40330i	0.0536272	+	0.364872i
$88$	1.11636	−	1.93360i	0.119005	−	0.206122i
$89$	14.7091			1.55916			0.779580	−	0.626303i	$-0.215433\pi$
$89$	14.7091			1.55916			0.779580	+	0.626303i	$0.215433\pi$
$90$	−1.86934	+	7.92168i	−0.197045	+	0.835019i
$91$	−2.46990			−0.258916
$92$	−14.8983	+	25.8046i	−1.55326	+	2.69032i
$93$	−10.7861	−	4.27896i	−1.11846	−	0.443708i
$94$	−6.23821	−	10.8049i	−0.643422	−	1.11444i
$95$	−3.98273	−	6.89829i	−0.408619	−	0.707749i
$96$	31.8656	+	12.6414i	3.25227	+	1.29021i
$97$	−2.29136	+	3.96875i	−0.232652	+	0.402966i	−0.958588	−	0.284797i	$-0.908074\pi$
$97$	−2.29136	+	3.96875i	−0.232652	+	0.402966i	0.725935	+	0.687763i	$0.241407\pi$
$98$	2.44069			0.246547
$99$	0.534814	+	0.503589i	0.0537509	+	0.0506126i
$100$	5.36083			0.536083
$101$	1.62080	−	2.80731i	0.161276	−	0.279338i	−0.774051	−	0.633124i	$-0.781772\pi$
$101$	1.62080	−	2.80731i	0.161276	−	0.279338i	0.935327	+	0.353786i	$0.115106\pi$
$102$	−2.39435	−	16.2909i	−0.237076	−	1.61303i
$103$	2.08597	+	3.61301i	0.205537	+	0.356000i	0.950304	−	0.311325i	$-0.100773\pi$
$103$	2.08597	+	3.61301i	0.205537	+	0.356000i	−0.744767	+	0.667325i	$0.767439\pi$
$104$	−4.55911	−	7.89661i	−0.447057	−	0.774326i
$105$	3.35443	−	2.65499i	0.327359	−	0.259101i
$106$	−10.6274	+	18.4072i	−1.03223	+	1.78787i
$107$	8.81572			0.852247			0.426124	−	0.904665i	$-0.359879\pi$
$107$	8.81572			0.852247			0.426124	+	0.904665i	$0.359879\pi$
$108$	−15.9441	+	22.8413i	−1.53422	+	2.19791i
$109$	−7.87252			−0.754051			−0.377025	−	0.926203i	$-0.623053\pi$
$109$	−7.87252			−0.754051			−0.377025	+	0.926203i	$0.623053\pi$
$110$	0.332169	−	0.575334i	0.0316711	−	0.0548560i
$111$	11.9005	−	9.41914i	1.12955	−	0.894025i
$112$	−17.3101	−	29.9819i	−1.63565	−	2.83303i
$113$	9.33480	+	16.1684i	0.878144	+	1.52099i	0.853375	+	0.521297i	$0.174552\pi$
$113$	9.33480	+	16.1684i	0.878144	+	1.52099i	0.0247691	+	0.999693i	$0.492115\pi$
$114$	−5.44300	−	37.0334i	−0.509783	−	3.46850i
$115$	−2.77910	+	4.81355i	−0.259153	+	0.448866i
$116$	10.6466			0.988517
$117$	2.87313	−	0.863205i	0.265621	−	0.0798033i
$118$	23.1623			2.13226
$119$	−4.32723	+	7.49498i	−0.396676	+	0.687064i
$120$	14.6802	+	5.82381i	1.34011	+	0.531639i
$121$	5.47002	+	9.47435i	0.497275	+	0.861305i
$122$	14.3009	+	24.7700i	1.29475	+	2.24257i
$123$	−9.44380	−	3.74647i	−0.851519	−	0.337807i
$124$	−17.9574	+	31.1031i	−1.61262	+	2.79314i
$125$	1.00000			0.0894427
$126$	19.2530	−	5.78437i	1.71519	−	0.515313i
$127$	−20.4899			−1.81818			−0.909092	−	0.416595i	$-0.863223\pi$
$127$	−20.4899			−1.81818			−0.909092	+	0.416595i	$0.863223\pi$
$128$	15.0231	−	26.0207i	1.32786	−	2.29993i
$129$	1.49190	+	10.1507i	0.131354	+	0.893716i
$130$	−1.35654	−	2.34960i	−0.118977	−	0.206074i
$131$	−3.66054	−	6.34024i	−0.319823	−	0.553950i	0.660628	−	0.750714i	$-0.270290\pi$
$131$	−3.66054	−	6.34024i	−0.319823	−	0.553950i	−0.980451	+	0.196764i	$0.936957\pi$
$132$	1.78278	−	1.41105i	0.155171	−	0.122816i
$133$	−9.83694	+	17.0381i	−0.852971	+	1.47739i
$134$	40.0276			3.45786
$135$	−2.97418	+	4.26078i	−0.255976	+	0.366710i
$136$	−31.9500			−2.73969
$137$	−1.01932	+	1.76552i	−0.0870867	+	0.150839i	−0.906278	−	0.422681i	$-0.861089\pi$
$137$	−1.01932	+	1.76552i	−0.0870867	+	0.150839i	0.819192	+	0.573520i	$0.194422\pi$
$138$	−20.4804	+	16.2100i	−1.74341	+	1.37988i
$139$	−5.13383	−	8.89205i	−0.435445	−	0.754214i	0.561886	−	0.827214i	$-0.310076\pi$
$139$	−5.13383	−	8.89205i	−0.435445	−	0.754214i	−0.997332	+	0.0730008i	$0.976742\pi$
$140$	−6.62035	−	11.4668i	−0.559522	−	0.969121i
$141$	−1.15822	−	7.88037i	−0.0975396	−	0.663647i
$142$	10.2913	−	17.8251i	0.863630	−	1.49585i
$143$	−0.244865			−0.0204766
$144$	30.6145	+	28.8270i	2.55121	+	2.40225i
$145$	1.98601			0.164929
$146$	−7.65874	+	13.2653i	−0.633842	+	1.09785i
$147$	1.44834	+	0.574574i	0.119457	+	0.0473901i
$148$	−23.4871	−	40.6808i	−1.93063	−	3.34394i
$149$	−6.67476	−	11.5610i	−0.546818	−	0.947116i	−0.998490	−	0.0549324i	$-0.982506\pi$
$149$	−6.67476	−	11.5610i	−0.546818	−	0.947116i	0.451672	−	0.892184i	$-0.350828\pi$
$150$	4.36803	+	1.73285i	0.356648	+	0.141487i
$151$	4.93522	−	8.54806i	0.401623	−	0.695631i	−0.592299	−	0.805718i	$-0.701780\pi$
$151$	4.93522	−	8.54806i	0.401623	−	0.695631i	0.993922	+	0.110087i	$0.0351129\pi$
$152$	−72.6308			−5.89113
$153$	2.41426	−	10.2309i	0.195182	−	0.827121i
$154$	−1.64085			−0.132223
$155$	−3.34974	+	5.80192i	−0.269057	+	0.466021i
$156$	−1.35019	−	9.18654i	−0.108102	−	0.735512i
$157$	2.86062	+	4.95475i	0.228303	+	0.395432i	0.957305	−	0.289079i	$-0.0933491\pi$
$157$	2.86062	+	4.95475i	0.228303	+	0.395432i	−0.729003	+	0.684511i	$0.760016\pi$
$158$	−8.10056	−	14.0306i	−0.644446	−	1.11621i
$159$	−10.6398	+	8.42129i	−0.843793	+	0.667852i
$160$	9.89622	−	17.1408i	0.782365	−	1.35510i
$161$	13.7282			1.08193
$162$	−20.3746	+	13.4574i	−1.60078	+	1.05732i
$163$	11.2651			0.882351			0.441176	−	0.897421i	$-0.354562\pi$
$163$	11.2651			0.882351			0.441176	+	0.897421i	$0.354562\pi$
$164$	−15.7227	+	27.2325i	−1.22773	+	2.12650i
$165$	0.332557	−	0.263215i	0.0258895	−	0.0204912i
$166$	−0.583873	−	1.01130i	−0.0453174	−	0.0784920i
$167$	1.79775	+	3.11379i	0.139114	+	0.240952i	0.927161	−	0.374662i	$-0.122241\pi$
$167$	1.79775	+	3.11379i	0.139114	+	0.240952i	−0.788048	+	0.615614i	$0.788908\pi$
$168$	−5.67222	−	38.5930i	−0.437621	−	2.97752i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−9.50657			−0.729121
$171$	5.48826	−	23.2576i	0.419698	−	1.77855i
$172$	31.7546			2.42126
$173$	1.92088	−	3.32706i	0.146042	−	0.252952i	−0.783719	−	0.621115i	$-0.786680\pi$
$173$	1.92088	−	3.32706i	0.146042	−	0.252952i	0.929761	+	0.368163i	$0.120013\pi$
$174$	8.67495	+	3.44145i	0.657646	+	0.260896i
$175$	−1.23495	−	2.13900i	−0.0933534	−	0.161693i
$176$	−1.71611	−	2.97240i	−0.129357	−	0.224053i
$177$	13.7449	+	5.45275i	1.03313	+	0.409854i
$178$	19.9535	−	34.5605i	1.49558	−	2.59042i
$179$	−0.0659855			−0.00493199			−0.00246599	−	0.999997i	$-0.500785\pi$
$179$	−0.0659855			−0.00493199			−0.00246599	+	0.999997i	$0.500785\pi$
$180$	11.7087	+	11.0251i	0.872716	+	0.821762i
$181$	10.5050			0.780827			0.390414	−	0.920640i	$-0.372332\pi$
$181$	10.5050			0.780827			0.390414	+	0.920640i	$0.372332\pi$
$182$	−3.35052	+	5.80328i	−0.248357	+	0.430167i
$183$	2.65519	+	18.0655i	0.196277	+	1.33544i
$184$	25.3405	+	43.8910i	1.86812	+	3.23569i
$185$	−4.38124	−	7.58853i	−0.322115	−	0.557920i
$186$	−24.6856	+	19.5384i	−1.81004	+	1.43262i
$187$	−0.428999	+	0.743049i	−0.0313715	+	0.0543371i
$188$	−24.6524			−1.79796
$189$	12.7868	+	1.09990i	0.930099	+	0.0800059i
$190$	−21.6110			−1.56782
$191$	2.66055	−	4.60821i	0.192511	−	0.333439i	−0.753571	−	0.657367i	$-0.771670\pi$
$191$	2.66055	−	4.60821i	0.192511	−	0.333439i	0.946082	+	0.323928i	$0.105004\pi$
$192$	34.8561	−	27.5882i	2.51552	−	1.99101i
$193$	−5.60828	−	9.71382i	−0.403693	−	0.699216i	0.590476	−	0.807055i	$-0.298940\pi$
$193$	−5.60828	−	9.71382i	−0.403693	−	0.699216i	−0.994168	+	0.107839i	$0.965607\pi$
$194$	6.21665	+	10.7676i	0.446330	+	0.773066i
$195$	−0.251863	−	1.71364i	−0.0180363	−	0.122716i
$196$	2.41130	−	4.17649i	0.172236	−	0.298321i
$197$	−1.62738			−0.115946			−0.0579731	−	0.998318i	$-0.518464\pi$
$197$	−1.62738			−0.115946			−0.0579731	+	0.998318i	$0.518464\pi$
$198$	1.90873	−	0.573460i	0.135648	−	0.0407540i
$199$	−9.54597			−0.676696			−0.338348	−	0.941021i	$-0.609868\pi$
$199$	−9.54597			−0.676696			−0.338348	+	0.941021i	$0.609868\pi$
$200$	4.55911	−	7.89661i	0.322378	−	0.558374i
$201$	23.7530	+	9.42309i	1.67541	+	0.664654i
$202$	−4.39738	−	7.61648i	−0.309398	−	0.535893i
$203$	−2.45262	−	4.24806i	−0.172140	−	0.298155i
$204$	−30.2423	−	11.9975i	−2.11739	−	0.839992i
$205$	−2.93288	+	5.07990i	−0.204841	+	0.354795i
$206$	11.3188			0.788620
$207$	−15.9695	+	4.79787i	−1.10995	+	0.333475i
$208$	−14.0168			−0.971893
$209$	−0.975229	+	1.68915i	−0.0674580	+	0.116841i
$210$	−1.68774	−	11.4832i	−0.116465	−	0.792415i
$211$	4.68338	+	8.11186i	0.322417	+	0.558443i	0.980986	−	0.194077i	$-0.0621712\pi$
$211$	4.68338	+	8.11186i	0.322417	+	0.558443i	−0.658569	+	0.752520i	$0.728838\pi$
$212$	20.9989	+	36.3712i	1.44221	+	2.49798i
$213$	10.3033	−	8.15497i	0.705973	−	0.558770i
$214$	11.9589	−	20.7134i	0.817493	−	1.41594i
$215$	5.92345			0.403976
$216$	20.0861	+	42.9113i	1.36669	+	2.91974i
$217$	16.5470			1.12329
$218$	−10.6794	+	18.4973i	−0.723301	+	1.25279i
$219$	−7.66767	+	6.06887i	−0.518133	+	0.410096i
$220$	−0.656339	−	1.13681i	−0.0442504	−	0.0766439i
$221$	1.75199	+	3.03453i	0.117851	+	0.204124i
$222$	−5.98762	−	40.7390i	−0.401863	−	2.73422i
$223$	−4.34600	+	7.52750i	−0.291030	+	0.504079i	−0.974054	−	0.226318i	$-0.927331\pi$
$223$	−4.34600	+	7.52750i	−0.291030	+	0.504079i	0.683024	+	0.730396i	$0.260665\pi$
$224$	−48.8853			−3.26629
$225$	2.18412	+	2.05660i	0.145608	+	0.137107i
$226$	50.6522			3.36934
$227$	13.2003	−	22.8635i	0.876132	−	1.51750i	0.0205798	−	0.999788i	$-0.493449\pi$
$227$	13.2003	−	22.8635i	0.876132	−	1.51750i	0.855552	−	0.517717i	$-0.173218\pi$
$228$	−68.7488	−	27.2735i	−4.55300	−	1.80623i
$229$	2.04166	+	3.53625i	0.134917	+	0.233682i	0.925566	−	0.378587i	$-0.123590\pi$
$229$	2.04166	+	3.53625i	0.134917	+	0.233682i	−0.790649	+	0.612270i	$0.790257\pi$
$230$	7.53995	+	13.0596i	0.497169	+	0.861122i
$231$	−0.973706	−	0.386281i	−0.0640652	−	0.0254154i
$232$	9.05442	−	15.6827i	0.594452	−	1.02962i
$233$	−22.2833			−1.45983			−0.729914	−	0.683539i	$-0.760440\pi$
$233$	−22.2833			−1.45983			−0.729914	+	0.683539i	$0.760440\pi$
$234$	1.86934	−	7.92168i	0.122202	−	0.517857i
$235$	−4.59861			−0.299980
$236$	22.8834	−	39.6352i	1.48958	−	2.58003i
$237$	−1.50399	−	10.2330i	−0.0976948	−	0.664703i
$238$	11.7401	+	20.3345i	0.761000	+	1.31809i
$239$	−9.37033	−	16.2299i	−0.606116	−	1.04982i	−0.991874	−	0.127224i	$-0.959393\pi$
$239$	−9.37033	−	16.2299i	−0.606116	−	1.04982i	0.385758	−	0.922600i	$-0.373940\pi$
$240$	19.0366	−	15.0673i	1.22881	−	0.972587i
$241$	0.638263	−	1.10550i	0.0411142	−	0.0712118i	−0.844736	−	0.535183i	$-0.820243\pi$
$241$	0.638263	−	1.10550i	0.0411142	−	0.0712118i	0.885850	+	0.463971i	$0.153576\pi$
$242$	29.6813			1.90798
$243$	−15.2587	+	3.18937i	−0.978846	+	0.204598i
$244$	56.5149			3.61800
$245$	0.449799	−	0.779075i	0.0287366	−	0.0497733i
$246$	−21.6136	+	17.1069i	−1.37803	+	1.09070i
$247$	3.98273	+	6.89829i	0.253415	+	0.438928i
$248$	30.5436	+	52.9031i	1.93952	+	3.35935i
$249$	−0.108405	−	0.737573i	−0.00686989	−	0.0467418i
$250$	1.35654	−	2.34960i	0.0857953	−	0.148602i
$251$	−7.61693			−0.480776			−0.240388	−	0.970677i	$-0.577275\pi$
$251$	−7.61693			−0.480776			−0.240388	+	0.970677i	$0.577275\pi$
$252$	9.12295	−	38.6603i	0.574692	−	2.43537i
$253$	1.36101			0.0855659
$254$	−27.7954	+	48.1431i	−1.74404	+	3.02076i
$255$	−5.64135	−	2.23799i	−0.353275	−	0.140148i
$256$	−15.0940	−	26.1435i	−0.943374	−	1.63397i
$257$	5.94485	+	10.2968i	0.370829	+	0.642295i	0.989693	−	0.143203i	$-0.0457401\pi$
$257$	5.94485	+	10.2968i	0.370829	+	0.642295i	−0.618864	+	0.785498i	$0.712407\pi$
$258$	25.8738	+	10.2644i	1.61083	+	0.639036i
$259$	−10.8212	+	18.7429i	−0.672398	+	1.16463i
$260$	−5.36083			−0.332465
$261$	4.33768	+	4.08443i	0.268496	+	0.252820i
$262$	−19.8627			−1.22712
$263$	−3.56872	+	6.18121i	−0.220057	+	0.381150i	−0.954825	−	0.297169i	$-0.903958\pi$
$263$	−3.56872	+	6.18121i	−0.220057	+	0.381150i	0.734768	+	0.678318i	$0.237291\pi$
$264$	−0.562341	−	3.82610i	−0.0346097	−	0.235480i
$265$	3.91710	+	6.78461i	0.240625	+	0.416775i
$266$	26.6884	+	46.2257i	1.63637	+	2.83428i
$267$	19.9768	−	15.8114i	1.22256	−	0.967641i
$268$	39.5456	−	68.4950i	2.41563	−	4.18400i
$269$	−11.8164			−0.720460			−0.360230	−	0.932863i	$-0.617302\pi$
$269$	−11.8164			−0.720460			−0.360230	+	0.932863i	$0.617302\pi$
$270$	5.97654	+	12.7681i	0.363721	+	0.777039i
$271$	−30.4847			−1.85181			−0.925905	−	0.377755i	$-0.876696\pi$
$271$	−30.4847			−1.85181			−0.925905	+	0.377755i	$0.876696\pi$
$272$	−24.5573	+	42.5345i	−1.48901	+	2.57903i
$273$	−3.35443	+	2.65499i	−0.203019	+	0.160688i
$274$	2.76551	+	4.79000i	0.167071	+	0.289375i
$275$	−0.122432	−	0.212059i	−0.00738295	−	0.0127876i
$276$	7.50466	+	51.0607i	0.451727	+	3.07349i
$277$	0.195103	−	0.337928i	0.0117226	−	0.0203041i	−0.860105	−	0.510118i	$-0.829602\pi$
$277$	0.195103	−	0.337928i	0.0117226	−	0.0203041i	0.871827	+	0.489814i	$0.162935\pi$
$278$	−27.8570			−1.67075
$279$	−19.2485	+	5.78302i	−1.15238	+	0.346220i
$280$	−22.5211			−1.34589
$281$	−4.75909	+	8.24298i	−0.283903	+	0.491735i	−0.972343	−	0.233559i	$-0.924963\pi$
$281$	−4.75909	+	8.24298i	−0.283903	+	0.491735i	0.688439	+	0.725294i	$0.258296\pi$
$282$	−20.0869	−	7.96870i	−1.19616	−	0.474529i
$283$	12.1701	+	21.0792i	0.723435	+	1.25303i	0.959615	+	0.281317i	$0.0907714\pi$
$283$	12.1701	+	21.0792i	0.723435	+	1.25303i	−0.236179	+	0.971709i	$0.575895\pi$
$284$	−20.3348	−	35.2209i	−1.20665	−	2.08998i
$285$	−12.8243	−	5.08754i	−0.759645	−	0.301360i
$286$	−0.332169	+	0.575334i	−0.0196416	+	0.0340202i
$287$	14.4878			0.855190
$288$	56.8662	−	17.0849i	3.35088	−	1.00674i
$289$	−4.72218			−0.277775
$290$	2.69410	−	4.66632i	0.158203	−	0.274016i
$291$	1.15422	+	7.85314i	0.0676614	+	0.460359i
$292$	15.1330	+	26.2112i	0.885593	+	1.53389i
$293$	8.37193	+	14.5006i	0.489093	+	0.847135i	0.999921	−	0.0125484i	$-0.00399438\pi$
$293$	8.37193	+	14.5006i	0.489093	+	0.847135i	−0.510828	+	0.859683i	$0.670661\pi$
$294$	3.31476	−	2.62359i	0.193321	−	0.153011i
$295$	4.26863	−	7.39348i	0.248529	−	0.430465i
$296$	−79.8982			−4.64399
$297$	1.26767	+	0.109044i	0.0735578	+	0.00632735i
$298$	−36.2184			−2.09808
$299$	2.77910	−	4.81355i	0.160720	−	0.278375i
$300$	7.28068	−	5.76257i	0.420350	−	0.332702i
$301$	−7.31516	−	12.6702i	−0.421639	−	0.730299i
$302$	−13.3897	−	23.1916i	−0.770490	−	1.33453i
$303$	−0.816440	−	5.55495i	−0.0469032	−	0.319123i
$304$	−55.8252	+	96.6922i	−3.20180	+	5.54568i
$305$	10.5422			0.603645
$306$	−20.7635	−	19.5512i	−1.18697	−	1.11767i
$307$	−19.2365			−1.09789			−0.548944	−	0.835859i	$-0.684970\pi$
$307$	−19.2365			−1.09789			−0.548944	+	0.835859i	$0.684970\pi$
$308$	−1.62109	+	2.80781i	−0.0923702	+	0.159990i
$309$	6.71678	+	2.66462i	0.382104	+	0.151585i
$310$	9.08812	+	15.7411i	0.516171	+	0.894034i
$311$	2.57294	+	4.45646i	0.145898	+	0.252703i	0.929708	−	0.368299i	$-0.120060\pi$
$311$	2.57294	+	4.45646i	0.145898	+	0.252703i	−0.783810	+	0.621001i	$0.786726\pi$
$312$	−14.6802	−	5.82381i	−0.831104	−	0.329708i
$313$	−16.7043	+	28.9328i	−0.944185	+	1.63538i	−0.186811	+	0.982396i	$0.559815\pi$
$313$	−16.7043	+	28.9328i	−0.944185	+	1.63538i	−0.757374	+	0.652981i	$0.773518\pi$
$314$	15.5222			0.875970
$315$	1.70178	−	7.21163i	0.0958844	−	0.406329i
$316$	−32.0121			−1.80082
$317$	−17.4855	+	30.2858i	−0.982085	+	1.70102i	−0.327852	+	0.944729i	$0.606325\pi$
$317$	−17.4855	+	30.2858i	−0.982085	+	1.70102i	−0.654233	+	0.756293i	$0.727009\pi$
$318$	5.35330	+	36.4232i	0.300198	+	2.04251i
$319$	−0.243152	−	0.421151i	−0.0136139	−	0.0235799i
$320$	−12.8324	−	22.2264i	−0.717355	−	1.24250i
$321$	11.9728	−	9.47637i	0.668259	−	0.528919i
$322$	18.6229	−	32.2558i	1.03781	−	1.79755i
$323$	27.9107			1.55299
$324$	2.89903	+	48.1603i	0.161057	+	2.67557i
$325$	−1.00000			−0.0554700
$326$	15.2816	−	26.4685i	0.846369	−	1.46595i
$327$	−10.6919	+	8.46249i	−0.591262	+	0.467977i
$328$	26.7426	+	46.3196i	1.47662	+	2.55757i
$329$	5.67905	+	9.83641i	0.313096	+	0.542299i
$330$	−0.167322	−	1.13844i	−0.00921078	−	0.0626689i
$331$	−7.36091	+	12.7495i	−0.404592	+	0.700774i	−0.994274	−	0.106862i	$-0.965920\pi$
$331$	−7.36091	+	12.7495i	−0.404592	+	0.700774i	0.589682	+	0.807636i	$0.299253\pi$
$332$	−2.30737			−0.126633
$333$	6.03742	−	25.5847i	0.330848	−	1.40204i
$334$	9.75489			0.533764
$335$	7.37676	−	12.7769i	0.403036	−	0.698078i
$336$	−55.7381	−	22.1119i	−3.04076	−	1.20630i
$337$	0.497439	+	0.861589i	0.0270972	+	0.0469338i	0.879256	−	0.476350i	$-0.158040\pi$
$337$	0.497439	+	0.861589i	0.0270972	+	0.0469338i	−0.852159	+	0.523283i	$0.824707\pi$
$338$	1.35654	+	2.34960i	0.0737862	+	0.127801i
$339$	30.0578	+	11.9243i	1.63252	+	0.647639i
$340$	−9.39210	+	16.2676i	−0.509358	+	0.882234i
$341$	1.64046			0.0888362
$342$	−47.2010	−	44.4451i	−2.55234	−	2.40332i
$343$	−19.5112			−1.05351
$344$	27.0056	−	46.7751i	1.45605	−	2.52195i
$345$	1.39991	+	9.52477i	0.0753684	+	0.512797i
$346$	−5.21151	−	9.02659i	−0.280172	−	0.485273i
$347$	−10.7406	−	18.6032i	−0.576584	−	0.998673i	−0.995868	−	0.0908174i	$-0.971052\pi$
$347$	−10.7406	−	18.6032i	−0.576584	−	0.998673i	0.419284	−	0.907855i	$-0.362281\pi$
$348$	14.4595	−	11.4445i	0.775110	−	0.613490i
$349$	9.73844	−	16.8675i	0.521287	−	0.902895i	−0.478407	−	0.878138i	$-0.658786\pi$
$349$	9.73844	−	16.8675i	0.521287	−	0.902895i	0.999694	−	0.0247568i	$-0.00788113\pi$
$350$	−6.70105			−0.358186
$351$	2.97418	−	4.26078i	0.158750	−	0.227424i
$352$	−4.84647			−0.258318
$353$	−17.5257	+	30.3555i	−0.932801	+	1.61566i	−0.154291	+	0.988025i	$0.549309\pi$
$353$	−17.5257	+	30.3555i	−0.932801	+	1.61566i	−0.778509	+	0.627633i	$0.784024\pi$
$354$	31.4573	−	24.8981i	1.67194	−	1.32332i
$355$	−3.79322	−	6.57006i	−0.201323	−	0.348702i
$356$	−39.4264	−	68.2886i	−2.08960	−	3.61929i
$357$	2.17974	+	14.8306i	0.115364	+	0.784920i
$358$	−0.0895121	+	0.155039i	−0.00473086	+	0.00819409i
$359$	31.1901			1.64615			0.823074	−	0.567933i	$-0.192257\pi$
$359$	31.1901			1.64615			0.823074	+	0.567933i	$0.192257\pi$
$360$	26.1978	−	7.87089i	1.38075	−	0.414832i
$361$	44.4485			2.33939
$362$	14.2504	−	24.6825i	0.748986	−	1.29728i
$363$	17.6133	+	6.98741i	0.924460	+	0.366744i
$364$	6.62035	+	11.4668i	0.347001	+	0.601023i
$365$	2.82289	+	4.88939i	0.147757	+	0.255922i
$366$	46.0487	+	18.2681i	2.40700	+	0.954886i
$367$	−1.86146	+	3.22414i	−0.0971674	+	0.168299i	−0.910511	−	0.413485i	$-0.864312\pi$
$367$	−1.86146	+	3.22414i	−0.0971674	+	0.168299i	0.813344	+	0.581783i	$0.197645\pi$
$368$	77.9085			4.06126
$369$	−16.8531	+	5.06335i	−0.877337	+	0.263588i
$370$	−23.7734			−1.23592
$371$	9.67484	−	16.7573i	0.502293	−	0.869996i
$372$	9.04559	+	61.5450i	0.468992	+	3.19096i
$373$	11.9753	+	20.7418i	0.620057	+	1.07397i	0.989475	+	0.144706i	$0.0462237\pi$
$373$	11.9753	+	20.7418i	0.620057	+	1.07397i	−0.369418	+	0.929263i	$0.620443\pi$
$374$	1.16391	+	2.01595i	0.0601845	+	0.104243i
$375$	1.35813	−	1.07494i	0.0701333	−	0.0555097i
$376$	−20.9656	+	36.3134i	−1.08122	+	1.87272i
$377$	−1.98601			−0.102285
$378$	19.9301	−	28.5517i	1.02509	−	1.46854i
$379$	−11.9070			−0.611624			−0.305812	−	0.952092i	$-0.598928\pi$
$379$	−11.9070			−0.611624			−0.305812	+	0.952092i	$0.598928\pi$
$380$	−21.3507	+	36.9805i	−1.09527	+	1.89706i
$381$	−27.8278	+	22.0254i	−1.42566	+	1.12840i
$382$	−7.21831	−	12.5025i	−0.369321	−	0.639682i
$383$	−2.40300	−	4.16212i	−0.122787	−	0.212674i	0.798078	−	0.602554i	$-0.205850\pi$
$383$	−2.40300	−	4.16212i	−0.122787	−	0.212674i	−0.920866	+	0.389879i	$0.872517\pi$
$384$	−7.56750	−	51.4883i	−0.386178	−	2.62750i
$385$	−0.302396	+	0.523764i	−0.0154115	+	0.0266935i
$386$	−30.4315			−1.54892
$387$	12.9375	+	12.1822i	0.657652	+	0.619254i
$388$	24.5672			1.24721
$389$	−3.18853	+	5.52269i	−0.161665	+	0.280012i	−0.935466	−	0.353417i	$-0.885020\pi$
$389$	−3.18853	+	5.52269i	−0.161665	+	0.280012i	0.773801	+	0.633429i	$0.218353\pi$
$390$	−4.36803	−	1.73285i	−0.221184	−	0.0877463i
$391$	−9.73790	−	16.8665i	−0.492467	−	0.852978i
$392$	−4.10137	−	7.10378i	−0.207150	−	0.358795i
$393$	−11.7869	−	4.67598i	−0.594568	−	0.235872i
$394$	−2.20761	+	3.82370i	−0.111218	+	0.192635i
$395$	−5.97148			−0.300458
$396$	0.904445	−	3.83277i	0.0454501	−	0.192604i
$397$	14.8929			0.747455			0.373728	−	0.927538i	$-0.378079\pi$
$397$	14.8929			0.747455			0.373728	+	0.927538i	$0.378079\pi$
$398$	−12.9495	+	22.4292i	−0.649101	+	1.12428i
$399$	4.95512	+	33.7140i	0.248066	+	1.68781i
$400$	−7.00842	−	12.1389i	−0.350421	−	0.606947i
$401$	−6.83732	−	11.8426i	−0.341439	−	0.591390i	0.643261	−	0.765647i	$-0.277581\pi$
$401$	−6.83732	−	11.8426i	−0.341439	−	0.591390i	−0.984700	+	0.174257i	$0.944248\pi$
$402$	54.3625	−	43.0272i	2.71135	−	2.14600i
$403$	3.34974	−	5.80192i	0.166862	−	0.289014i
$404$	−17.3777			−0.864573
$405$	0.540781	+	8.98374i	0.0268716	+	0.446406i
$406$	−13.3083			−0.660481
$407$	−1.07281	+	1.85816i	−0.0531773	+	0.0921057i
$408$	−43.3921	+	34.3443i	−2.14823	+	1.70030i
$409$	10.9527	+	18.9706i	0.541575	+	0.938036i	0.998814	+	0.0486919i	$0.0155053\pi$
$409$	10.9527	+	18.9706i	0.541575	+	0.938036i	−0.457238	+	0.889344i	$0.651161\pi$
$410$	7.95715	+	13.7822i	0.392976	+	0.680654i
$411$	0.513459	+	3.49351i	0.0253271	+	0.172322i
$412$	11.1825	−	19.3687i	0.550924	−	0.954228i
$413$	−21.0862			−1.03758
$414$	−10.3902	+	44.0304i	−0.510649	+	2.16397i
$415$	−0.430413			−0.0211281
$416$	−9.89622	+	17.1408i	−0.485202	+	0.840394i
$417$	−16.5308	−	6.55796i	−0.809517	−	0.321145i
$418$	2.64588	+	4.58280i	0.129414	+	0.224152i
$419$	−0.196081	−	0.339622i	−0.00957918	−	0.0165916i	0.861196	−	0.508273i	$-0.169716\pi$
$419$	−0.196081	−	0.339622i	−0.00957918	−	0.0165916i	−0.870775	+	0.491681i	$0.836383\pi$
$420$	−21.3174	−	8.45685i	−1.04018	−	0.412652i
$421$	9.39690	−	16.2759i	0.457977	−	0.793239i	−0.540877	−	0.841102i	$-0.681908\pi$
$421$	9.39690	−	16.2759i	0.457977	−	0.793239i	0.998854	+	0.0478624i	$0.0152409\pi$
$422$	25.4128			1.23708
$423$	−10.0439	−	9.45751i	−0.488353	−	0.459840i
$424$	71.4339			3.46914
$425$	−1.75199	+	3.03453i	−0.0849838	+	0.147196i
$426$	−5.18401	−	35.2713i	−0.251166	−	1.70890i
$427$	−13.0191	−	22.5497i	−0.630038	−	1.09126i
$428$	−23.6298	−	40.9280i	−1.14219	−	1.97833i
$429$	−0.332557	+	0.263215i	−0.0160560	+	0.0127081i
$430$	8.03541	−	13.9177i	0.387502	−	0.671173i
$431$	−8.09398			−0.389873			−0.194937	−	0.980816i	$-0.562450\pi$
$431$	−8.09398			−0.389873			−0.194937	+	0.980816i	$0.562450\pi$
$432$	72.5657	+	6.24200i	3.49132	+	0.300318i
$433$	−32.5259			−1.56309			−0.781546	−	0.623847i	$-0.785569\pi$
$433$	−32.5259			−1.56309			−0.781546	+	0.623847i	$0.785569\pi$
$434$	22.4467	−	38.8789i	1.07748	−	1.86625i
$435$	2.69725	−	2.13484i	0.129323	−	0.102358i
$436$	21.1016	+	36.5491i	1.01058	+	1.75038i
$437$	−22.1368	−	38.3421i	−1.05895	−	1.83415i
$438$	3.85790	+	26.2487i	0.184338	+	1.25421i
$439$	1.17370	−	2.03291i	0.0560176	−	0.0970253i	−0.836657	−	0.547728i	$-0.815493\pi$
$439$	1.17370	−	2.03291i	0.0560176	−	0.0970253i	0.892674	+	0.450702i	$0.148826\pi$
$440$	−2.23273			−0.106441
$441$	2.58466	−	0.776538i	0.123079	−	0.0369780i
$442$	9.50657			0.452182
$443$	17.4149	−	30.1634i	0.827405	−	1.43311i	−0.0726617	−	0.997357i	$-0.523149\pi$
$443$	17.4149	−	30.1634i	0.827405	−	1.43311i	0.900067	−	0.435751i	$-0.143517\pi$
$444$	−75.6278	−	30.0024i	−3.58914	−	1.42385i
$445$	−7.35454	−	12.7384i	−0.348639	−	0.603860i
$446$	11.7911	+	20.4227i	0.558324	+	0.967045i
$447$	−21.4926	−	8.52635i	−1.01656	−	0.403283i
$448$	−31.6948	+	54.8971i	−1.49744	+	2.59364i
$449$	11.1016			0.523918			0.261959	−	0.965079i	$-0.415631\pi$
$449$	11.1016			0.523918			0.261959	+	0.965079i	$0.415631\pi$
$450$	7.79505	−	2.34195i	0.367462	−	0.110400i
$451$	1.43632			0.0676335
$452$	50.0423	−	86.6758i	2.35379	−	4.07689i
$453$	−2.48600	−	16.9144i	−0.116802	−	0.794708i
$454$	−35.8134	−	62.0307i	−1.68081	−	2.91124i
$455$	1.23495	+	2.13900i	0.0578953	+	0.100278i
$456$	−98.6417	+	78.0737i	−4.61932	+	3.65614i
$457$	−9.86535	+	17.0873i	−0.461482	+	0.799310i	−0.999035	−	0.0439200i	$-0.986015\pi$
$457$	−9.86535	+	17.0873i	−0.461482	+	0.799310i	0.537553	+	0.843230i	$0.319349\pi$
$458$	11.0784			0.517659
$459$	−7.71875	−	16.4901i	−0.360280	−	0.769690i
$460$	29.7966			1.38927
$461$	1.54073	−	2.66862i	0.0717588	−	0.124290i	−0.827913	−	0.560856i	$-0.810472\pi$
$461$	1.54073	−	2.66862i	0.0717588	−	0.124290i	0.899672	+	0.436566i	$0.143805\pi$
$462$	−2.22848	+	1.76381i	−0.103678	+	0.0820601i
$463$	−4.34843	−	7.53170i	−0.202089	−	0.350028i	0.747113	−	0.664697i	$-0.231440\pi$
$463$	−4.34843	−	7.53170i	−0.202089	−	0.350028i	−0.949201	+	0.314670i	$0.898106\pi$
$464$	−13.9188	−	24.1080i	−0.646163	−	1.11919i
$465$	1.68735	+	11.4805i	0.0782489	+	0.532395i
$466$	−30.2283	+	52.3569i	−1.40030	+	2.42538i
$467$	−33.7102			−1.55992			−0.779961	−	0.625829i	$-0.784761\pi$
$467$	−33.7102			−1.55992			−0.779961	+	0.625829i	$0.784761\pi$
$468$	−11.7087	−	11.0251i	−0.541235	−	0.509635i
$469$	−36.4397			−1.68263
$470$	−6.23821	+	10.8049i	−0.287747	+	0.498393i
$471$	9.21114	+	3.65417i	0.424427	+	0.168375i
$472$	−38.9223	−	67.4154i	−1.79154	−	3.10304i
$473$	−0.725221	−	1.25612i	−0.0333457	−	0.0577565i
$474$	−26.0836	−	10.3477i	−1.19806	−	0.475284i
$475$	−3.98273	+	6.89829i	−0.182740	+	0.316515i
$476$	46.3951			2.12651
$477$	−5.39782	+	22.8743i	−0.247149	+	1.04734i
$478$	−50.8450			−2.32560
$479$	10.7045	−	18.5407i	0.489100	−	0.847146i	−0.510822	−	0.859687i	$-0.670659\pi$
$479$	10.7045	−	18.5407i	0.489100	−	0.847146i	0.999921	+	0.0125412i	$0.00399209\pi$
$480$	−4.98498	−	33.9171i	−0.227532	−	1.54810i
$481$	4.38124	+	7.58853i	0.199767	+	0.346007i
$482$	−1.73166	−	2.99933i	−0.0788751	−	0.136616i
$483$	18.6446	−	14.7570i	0.848360	−	0.671467i
$484$	29.3238	−	50.7904i	1.33290	−	2.30865i
$485$	4.58272			0.208091
$486$	−13.2053	+	40.1784i	−0.599005	+	1.82253i
$487$	36.6853			1.66237			0.831184	−	0.555997i	$-0.187664\pi$
$487$	36.6853			1.66237			0.831184	+	0.555997i	$0.187664\pi$
$488$	48.0630	−	83.2476i	2.17571	−	3.76844i
$489$	15.2994	−	12.1093i	0.691864	−	0.547602i
$490$	−1.22034	−	2.11370i	−0.0551295	−	0.0954871i
$491$	−18.8695	−	32.6830i	−0.851570	−	1.47496i	−0.879791	−	0.475360i	$-0.842318\pi$
$491$	−18.8695	−	32.6830i	−0.851570	−	1.47496i	0.0282217	−	0.999602i	$-0.491016\pi$
$492$	7.91991	+	53.8860i	0.357057	+	2.42937i
$493$	−3.47946	+	6.02660i	−0.156707	+	0.271424i
$494$	21.6110			0.972323
$495$	0.168714	−	0.714957i	0.00758312	−	0.0321349i
$496$	93.9055			4.21648
$497$	−9.36888	+	16.2274i	−0.420252	+	0.727897i
$498$	−1.88006	−	0.745841i	−0.0842474	−	0.0334219i
$499$	−1.91292	−	3.31328i	−0.0856341	−	0.148323i	0.820027	−	0.572325i	$-0.193958\pi$
$499$	−1.91292	−	3.31328i	−0.0856341	−	0.148323i	−0.905661	+	0.424002i	$0.860625\pi$
$500$	−2.68041	−	4.64261i	−0.119872	−	0.207624i
$501$	5.78871	+	2.29645i	0.258620	+	0.102598i
$502$	−10.3327	+	17.8967i	−0.461170	+	0.798770i
$503$	−11.3840			−0.507589			−0.253794	−	0.967258i	$-0.581679\pi$
$503$	−11.3840			−0.507589			−0.253794	+	0.967258i	$0.581679\pi$
$504$	−49.1888	−	46.3169i	−2.19104	−	2.06312i
$505$	−3.24161			−0.144250
$506$	1.84627	−	3.19783i	0.0820766	−	0.142161i
$507$	0.251863	+	1.71364i	0.0111856	+	0.0761055i
$508$	54.9214	+	95.1267i	2.43674	+	4.22056i
$509$	8.05279	+	13.9478i	0.356934	+	0.618227i	0.987447	−	0.157951i	$-0.0504889\pi$
$509$	8.05279	+	13.9478i	0.356934	+	0.618227i	−0.630513	+	0.776178i	$0.717156\pi$
$510$	−12.9111	+	10.2190i	−0.571714	+	0.452505i
$511$	6.97225	−	12.0763i	0.308434	−	0.534224i
$512$	−21.8102			−0.963885
$513$	−17.5468	−	37.4863i	−0.774709	−	1.65506i
$514$	32.2578			1.42283
$515$	2.08597	−	3.61301i	0.0919189	−	0.159208i
$516$	43.1267	−	34.1343i	1.89855	−	1.50268i
$517$	0.563019	+	0.975177i	0.0247615	+	0.0428882i
$518$	29.3589	+	50.8511i	1.28996	+	2.23427i
$519$	−0.967596	−	6.58339i	−0.0424727	−	0.288979i
$520$	−4.55911	+	7.89661i	−0.199930	+	0.346289i
$521$	−3.24808			−0.142301			−0.0711504	−	0.997466i	$-0.522667\pi$
$521$	−3.24808			−0.142301			−0.0711504	+	0.997466i	$0.522667\pi$
$522$	15.4810	−	4.65113i	0.677586	−	0.203574i
$523$	−17.2610			−0.754769			−0.377385	−	0.926057i	$-0.623177\pi$
$523$	−17.2610			−0.754769			−0.377385	+	0.926057i	$0.623177\pi$
$524$	−19.6235	+	33.9890i	−0.857258	+	1.48482i
$525$	−3.97651	−	1.57753i	−0.173549	−	0.0688489i
$526$	9.68225	+	16.7701i	0.422166	+	0.731213i
$527$	−11.7374	−	20.3297i	−0.511289	−	0.885578i
$528$	−5.52585	−	2.19217i	−0.240482	−	0.0954018i
$529$	−3.94684	+	6.83613i	−0.171602	+	0.297223i
$530$	21.2548			0.923251
$531$	24.5286	−	7.36940i	1.06445	−	0.319805i
$532$	105.468			4.57263
$533$	2.93288	−	5.07990i	0.127037	−	0.220035i
$534$	−10.0511	−	68.3862i	−0.434953	−	2.95936i
$535$	−4.40786	−	7.63463i	−0.190568	−	0.330074i
$536$	−67.2629	−	116.503i	−2.90532	−	5.03216i
$537$	−0.0896165	+	0.0709304i	−0.00386724	+	0.00306087i
$538$	−16.0295	+	27.7639i	−0.691080	+	1.19699i
$539$	−0.220280			−0.00948813
$540$	27.7532	+	2.38729i	1.19431	+	0.102733i
$541$	40.8951			1.75822			0.879109	−	0.476621i	$-0.158139\pi$
$541$	40.8951			1.75822			0.879109	+	0.476621i	$0.158139\pi$
$542$	−41.3537	+	71.6268i	−1.77629	+	3.07663i
$543$	14.2670	−	11.2922i	0.612258	−	0.484595i
$544$	34.6761	+	60.0607i	1.48672	+	2.57508i
$545$	3.93626	+	6.81780i	0.168611	+	0.292043i
$546$	1.68774	+	11.4832i	0.0722288	+	0.491435i
$547$	7.37317	−	12.7707i	0.315254	−	0.546036i	−0.664238	−	0.747521i	$-0.731244\pi$
$547$	7.37317	−	12.7707i	0.315254	−	0.546036i	0.979491	+	0.201486i	$0.0645770\pi$
$548$	10.9288			0.466857
$549$	23.0255	+	21.6811i	0.982703	+	0.925327i
$550$	−0.664339			−0.0283275
$551$	−7.90973	+	13.7001i	−0.336966	+	0.583642i
$552$	81.5957	+	32.3700i	3.47294	+	1.37776i
$553$	7.37447	+	12.7730i	0.313594	+	0.543162i
$554$	−0.529330	−	0.916827i	−0.0224891	−	0.0389523i
$555$	−14.1075	−	5.59660i	−0.598829	−	0.237563i
$556$	−27.5216	+	47.6688i	−1.16717	+	2.02161i
$557$	−13.8053			−0.584948			−0.292474	−	0.956273i	$-0.594479\pi$
$557$	−13.8053			−0.584948			−0.292474	+	0.956273i	$0.594479\pi$
$558$	−12.5236	+	53.0711i	−0.530165	+	2.24668i
$559$	−5.92345			−0.250535
$560$	−17.3101	+	29.9819i	−0.731485	+	1.26697i
$561$	0.216098	+	1.47030i	0.00912366	+	0.0620762i
$562$	12.9118	+	22.3639i	0.544652	+	0.943364i
$563$	−20.5634	−	35.6169i	−0.866644	−	1.50107i	−0.865406	−	0.501072i	$-0.832939\pi$
$563$	−20.5634	−	35.6169i	−0.866644	−	1.50107i	−0.00123837	−	0.999999i	$-0.500394\pi$
$564$	−33.4810	+	26.4998i	−1.40980	+	1.11584i
$565$	9.33480	−	16.1684i	0.392718	−	0.680208i
$566$	66.0369			2.77574
$567$	18.5483	−	12.2512i	0.778957	−	0.514502i
$568$	−69.1749			−2.90251
$569$	−3.90021	+	6.75536i	−0.163505	+	0.283200i	−0.936124	−	0.351671i	$-0.885613\pi$
$569$	−3.90021	+	6.75536i	−0.163505	+	0.283200i	0.772618	+	0.634871i	$0.218947\pi$
$570$	−29.3504	+	23.2305i	−1.22935	+	0.973018i
$571$	−8.07196	−	13.9810i	−0.337801	−	0.585088i	0.646218	−	0.763153i	$-0.276350\pi$
$571$	−8.07196	−	13.9810i	−0.337801	−	0.585088i	−0.984019	+	0.178065i	$0.943016\pi$
$572$	0.656339	+	1.13681i	0.0274429	+	0.0475325i
$573$	−1.34019	−	9.11847i	−0.0559872	−	0.380929i
$574$	19.6534	−	34.0406i	0.820316	−	1.42083i
$575$	5.55821			0.231793
$576$	17.6833	−	74.9365i	0.736805	−	3.12235i
$577$	33.1813			1.38135			0.690677	−	0.723164i	$-0.257313\pi$
$577$	33.1813			1.38135			0.690677	+	0.723164i	$0.257313\pi$
$578$	−6.40584	+	11.0952i	−0.266448	+	0.461501i
$579$	−18.0585	−	7.16403i	−0.750487	−	0.297727i
$580$	−5.32332	−	9.22027i	−0.221039	−	0.382851i
$581$	0.531538	+	0.920651i	0.0220519	+	0.0381950i
$582$	20.0175	+	7.94116i	0.829751	+	0.329172i
$583$	0.959159	−	1.66131i	0.0397243	−	0.0688045i
$584$	51.4794			2.13023
$585$	−2.18412	−	2.05660i	−0.0903023	−	0.0850300i
$586$	45.4275			1.87659
$587$	−18.9439	+	32.8119i	−0.781900	+	1.35429i	0.148933	+	0.988847i	$0.452416\pi$
$587$	−18.9439	+	32.8119i	−0.781900	+	1.35429i	−0.930834	+	0.365444i	$0.880917\pi$
$588$	−1.21463	−	8.26420i	−0.0500906	−	0.340810i
$589$	−26.6822	−	46.2149i	−1.09942	−	1.90425i
$590$	−11.5812	−	20.0591i	−0.476788	−	0.825822i
$591$	−2.21019	+	1.74934i	−0.0909150	+	0.0719582i
$592$	−61.4111	+	106.367i	−2.52398	+	4.37166i
$593$	−26.1993			−1.07588			−0.537939	−	0.842984i	$-0.680797\pi$
$593$	−26.1993			−1.07588			−0.537939	+	0.842984i	$0.680797\pi$
$594$	1.97586	−	2.83060i	0.0810706	−	0.116141i
$595$	8.65446			0.354798
$596$	−35.7823	+	61.9767i	−1.46570	+	2.53866i
$597$	−12.9646	+	10.2613i	−0.530607	+	0.419969i
$598$	−7.53995	−	13.0596i	−0.308331	−	0.534045i
$599$	3.25395	+	5.63600i	0.132953	+	0.230281i	0.924813	−	0.380421i	$-0.124221\pi$
$599$	3.25395	+	5.63600i	0.132953	+	0.230281i	−0.791861	+	0.610702i	$0.790888\pi$
$600$	−2.29654	−	15.6253i	−0.0937558	−	0.637902i
$601$	1.44693	−	2.50615i	0.0590214	−	0.102228i	−0.835005	−	0.550242i	$-0.814535\pi$
$601$	1.44693	−	2.50615i	0.0590214	−	0.102228i	0.894026	+	0.448014i	$0.147869\pi$
$602$	−39.6933			−1.61778
$603$	42.3888	−	12.7353i	1.72621	−	0.518622i
$604$	−52.9138			−2.15303
$605$	5.47002	−	9.47435i	0.222388	−	0.385187i
$606$	−14.1594	−	5.61721i	−0.575188	−	0.228184i
$607$	0.373941	+	0.647684i	0.0151778	+	0.0262887i	0.873515	−	0.486798i	$-0.161835\pi$
$607$	0.373941	+	0.647684i	0.0151778	+	0.0262887i	−0.858337	+	0.513087i	$0.828502\pi$
$608$	78.8279	+	136.534i	3.19689	+	5.53718i
$609$	−7.89737	−	3.13298i	−0.320018	−	0.126955i
$610$	14.3009	−	24.7700i	0.579028	−	1.00291i
$611$	4.59861			0.186040
$612$	−53.9694	+	16.2146i	−2.18159	+	0.655437i
$613$	−42.8520			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$613$	−42.8520			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$614$	−26.0952	+	45.1982i	−1.05312	+	1.82405i
$615$	1.47737	+	10.0518i	0.0595732	+	0.405328i
$616$	2.75731	+	4.77580i	0.111095	+	0.192422i
$617$	0.516415	+	0.894458i	0.0207901	+	0.0360095i	0.876233	−	0.481887i	$-0.160048\pi$
$617$	0.516415	+	0.894458i	0.0207901	+	0.0360095i	−0.855443	+	0.517897i	$0.826715\pi$
$618$	15.3724	−	12.1671i	0.618368	−	0.489431i
$619$	12.5957	−	21.8164i	0.506265	−	0.876877i	−0.493709	−	0.869627i	$-0.664359\pi$
$619$	12.5957	−	21.8164i	0.506265	−	0.876877i	0.999974	−	0.00724946i	$-0.00230760\pi$
$620$	35.9147			1.44237
$621$	−16.5311	+	23.6823i	−0.663370	+	0.950339i
$622$	13.9612			0.559793
$623$	−18.1650	+	31.4626i	−0.727764	+	1.26052i
$624$	−19.0366	+	15.0673i	−0.762075	+	0.603173i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	45.3203	+	78.4971i	1.81136	+	3.13737i
$627$	0.491248	+	3.34239i	0.0196186	+	0.133482i
$628$	15.3353	−	26.5616i	0.611946	−	1.05992i
$629$	30.7035			1.22423
$630$	−14.6359	−	13.7814i	−0.583108	−	0.549063i
$631$	26.9115			1.07133			0.535664	−	0.844431i	$-0.320061\pi$
$631$	26.9115			1.07133			0.535664	+	0.844431i	$0.320061\pi$
$632$	−27.2246	+	47.1544i	−1.08294	+	1.87570i
$633$	15.0804	+	5.98256i	0.599391	+	0.237785i
$634$	47.4397	+	82.1680i	1.88407	+	3.26331i
$635$	10.2449	+	17.7448i	0.406558	+	0.704180i
$636$	67.6159	+	26.8240i	2.68115	+	1.06364i
$637$	−0.449799	+	0.779075i	−0.0178217	+	0.0308681i
$638$	−1.31938			−0.0522348
$639$	5.22712	−	22.1510i	0.206782	−	0.876278i
$640$	−30.0461			−1.18768
$641$	13.7947	−	23.8932i	0.544860	−	0.943724i	−0.453756	−	0.891126i	$-0.649916\pi$
$641$	13.7947	−	23.8932i	0.544860	−	0.943724i	0.998616	−	0.0525986i	$-0.0167504\pi$
$642$	−6.02400	−	40.9865i	−0.237748	−	1.61761i
$643$	−2.41222	−	4.17808i	−0.0951286	−	0.164768i	0.814534	−	0.580116i	$-0.196993\pi$
$643$	−2.41222	−	4.17808i	−0.0951286	−	0.164768i	−0.909662	+	0.415349i	$0.863660\pi$
$644$	−36.7973	−	63.7348i	−1.45002	−	2.51150i
$645$	8.04478	−	6.36735i	0.316763	−	0.250714i
$646$	37.8621	−	65.5791i	1.48966	−	2.58017i
$647$	39.9474			1.57049			0.785247	−	0.619182i	$-0.212536\pi$
$647$	39.9474			1.57049			0.785247	+	0.619182i	$0.212536\pi$
$648$	73.4065	+	36.6875i	2.88368	+	1.44122i
$649$	−2.09047			−0.0820582
$650$	−1.35654	+	2.34960i	−0.0532080	+	0.0921589i
$651$	22.4729	−	17.7871i	0.880784	−	0.697130i
$652$	−30.1952	−	52.2996i	−1.18253	−	2.04821i
$653$	−6.38026	−	11.0509i	−0.249679	−	0.432457i	0.713758	−	0.700393i	$-0.246992\pi$
$653$	−6.38026	−	11.0509i	−0.249679	−	0.432457i	−0.963437	+	0.267936i	$0.913658\pi$
$654$	5.37949	+	36.6013i	0.210355	+	1.43123i
$655$	−3.66054	+	6.34024i	−0.143029	+	0.247734i
$656$	82.2194			3.21013
$657$	−3.88999	+	16.4846i	−0.151763	+	0.643125i
$658$	30.8155			1.20131
$659$	11.6266	−	20.1379i	0.452908	−	0.784459i	−0.545657	−	0.838008i	$-0.683720\pi$
$659$	11.6266	−	20.1379i	0.452908	−	0.784459i	0.998565	+	0.0535491i	$0.0170533\pi$
$660$	−2.11340	−	0.838409i	−0.0822638	−	0.0326350i
$661$	−5.78136	−	10.0136i	−0.224869	−	0.389485i	0.731411	−	0.681937i	$-0.238862\pi$
$661$	−5.78136	−	10.0136i	−0.224869	−	0.389485i	−0.956280	+	0.292452i	$0.905529\pi$
$662$	19.9708	+	34.5904i	0.776186	+	1.34439i
$663$	5.64135	+	2.23799i	0.219092	+	0.0869163i
$664$	−1.96230	+	3.39880i	−0.0761520	+	0.131899i
$665$	19.6739			0.762920
$666$	−51.9239	−	48.8923i	−2.01201	−	1.89454i
$667$	11.0386			0.427418
$668$	9.63743	−	16.6925i	0.372883	−	0.645853i
$669$	2.18919	+	14.8950i	0.0846391	+	0.575873i
$670$	−20.0138	−	34.6649i	−0.773200	−	1.33922i
$671$	−1.29071	−	2.23557i	−0.0498272	−	0.0863032i
$672$	−66.3924	+	52.5488i	−2.56114	+	2.02711i
$673$	17.0249	−	29.4880i	0.656261	−	1.13668i	−0.325315	−	0.945606i	$-0.605470\pi$
$673$	17.0249	−	29.4880i	0.656261	−	1.13668i	0.981576	−	0.191072i	$-0.0611962\pi$
$674$	2.69919			0.103969
$675$	5.17703	+	0.445322i	0.199264	+	0.0171404i
$676$	5.36083			0.206186
$677$	−0.325812	+	0.564322i	−0.0125220	+	0.0216887i	−0.872218	−	0.489116i	$-0.837319\pi$
$677$	−0.325812	+	0.564322i	−0.0125220	+	0.0216887i	0.859697	+	0.510805i	$0.170653\pi$
$678$	68.7921	−	54.4481i	2.64194	−	2.09107i
$679$	−5.65943	−	9.80242i	−0.217189	−	0.376182i
$680$	15.9750	+	27.6695i	0.612613	+	1.06108i
$681$	−6.64931	−	45.2410i	−0.254802	−	1.73364i
$682$	2.22536	−	3.85444i	0.0852134	−	0.147594i
$683$	2.91059			0.111370			0.0556852	−	0.998448i	$-0.482266\pi$
$683$	2.91059			0.111370			0.0556852	+	0.998448i	$0.482266\pi$
$684$	−122.687	+	36.8601i	−4.69105	+	1.40938i
$685$	2.03865			0.0778927
$686$	−26.4678	+	45.8436i	−1.01054	+	1.75031i
$687$	6.57409	+	2.60802i	0.250817	+	0.0995020i
$688$	−41.5140	−	71.9043i	−1.58271	−	2.74133i
$689$	−3.91710	−	6.78461i	−0.149230	−	0.258473i
$690$	24.2784	+	9.63154i	0.924265	+	0.366666i
$691$	0.00528508	−	0.00915402i	0.000201054	−	0.000348235i	−0.865925	−	0.500174i	$-0.833269\pi$
$691$	0.00528508	−	0.00915402i	0.000201054	−	0.000348235i	0.866126	+	0.499826i	$0.166603\pi$
$692$	−20.5950			−0.782905
$693$	−1.73764	+	0.522058i	−0.0660076	+	0.0198314i
$694$	−58.2802			−2.21228
$695$	−5.13383	+	8.89205i	−0.194737	+	0.337295i
$696$	−4.56094	−	31.0321i	−0.172882	−	1.17627i
$697$	−10.2767	−	17.7998i	−0.389259	−	0.674216i
$698$	−26.4212	−	45.7629i	−1.00006	−	1.73215i
$699$	−30.2635	+	23.9532i	−1.14467	+	0.905994i
$700$	−6.62035	+	11.4668i	−0.250226	+	0.433404i
$701$	−47.2327			−1.78395			−0.891977	−	0.452082i	$-0.850682\pi$
$701$	−47.2327			−1.78395			−0.891977	+	0.452082i	$0.850682\pi$
$702$	−5.97654	−	12.7681i	−0.225570	−	0.481899i
$703$	69.7971			2.63245
$704$	−3.14221	+	5.44247i	−0.118427	+	0.205121i
$705$	−6.24549	+	4.94323i	−0.235219	+	0.186173i
$706$	47.5488	+	82.3570i	1.78952	+	3.09954i
$707$	4.00322	+	6.93378i	0.150557	+	0.260772i
$708$	−11.5269	−	78.4278i	−0.433209	−	2.94750i
$709$	17.1040	−	29.6250i	0.642353	−	1.11259i	−0.342553	−	0.939499i	$-0.611291\pi$
$709$	17.1040	−	29.6250i	0.642353	−	1.11259i	0.984906	−	0.173090i	$-0.0553752\pi$
$710$	−20.5827			−0.772454
$711$	−13.0424	−	12.2809i	−0.489130	−	0.460572i
$712$	−134.121			−5.02638
$713$	−18.6185	+	32.2483i	−0.697270	+	1.20771i
$714$	37.8030	+	14.9969i	1.41474	+	0.561244i
$715$	0.122432	+	0.212059i	0.00457871	+	0.00793056i
$716$	0.176868	+	0.306345i	0.00660988	+	0.0114487i
$717$	−30.1722	−	11.9697i	−1.12680	−	0.447016i
$718$	42.3107	−	73.2842i	1.57902	−	2.73494i
$719$	−8.91046			−0.332304			−0.166152	−	0.986100i	$-0.553134\pi$
$719$	−8.91046			−0.332304			−0.166152	+	0.986100i	$0.553134\pi$
$720$	9.65771	−	40.9264i	0.359922	−	1.52524i
$721$	−10.3043			−0.383751
$722$	60.2963	−	104.436i	2.24399	−	3.88671i
$723$	−0.321510	−	2.18751i	−0.0119571	−	0.0813543i
$724$	−28.1576	−	48.7705i	−1.04647	−	1.81254i
$725$	−0.993004	−	1.71993i	−0.0368792	−	0.0638767i
$726$	40.3109	−	31.9056i	1.49608	−	1.18413i
$727$	−5.63472	+	9.75962i	−0.208980	+	0.361964i	−0.951394	−	0.307978i	$-0.900348\pi$
$727$	−5.63472	+	9.75962i	−0.208980	+	0.361964i	0.742413	+	0.669942i	$0.233681\pi$
$728$	22.5211			0.834687
$729$	−17.2948	+	20.7338i	−0.640550	+	0.767917i
$730$	15.3175			0.566925
$731$	−10.3778	+	17.9749i	−0.383837	+	0.664824i
$732$	76.7544	−	60.7502i	2.83692	−	2.24539i
$733$	18.9796	+	32.8737i	0.701028	+	1.21422i	0.968106	+	0.250541i	$0.0806086\pi$
$733$	18.9796	+	32.8737i	0.701028	+	1.21422i	−0.267078	+	0.963675i	$0.586058\pi$
$734$	5.05030	+	8.74737i	0.186410	+	0.322871i
$735$	−0.226575	−	1.54159i	−0.00835736	−	0.0568624i
$736$	55.0052	−	95.2719i	2.02752	−	3.51177i
$737$	−3.61262			−0.133073
$738$	−10.9651	+	46.4667i	−0.403630	+	1.71046i
$739$	8.35367			0.307295			0.153647	−	0.988126i	$-0.450898\pi$
$739$	8.35367			0.307295			0.153647	+	0.988126i	$0.450898\pi$
$740$	−23.4871	+	40.6808i	−0.863402	+	1.49546i
$741$	12.8243	+	5.08754i	0.471112	+	0.186896i
$742$	−26.2487	−	45.4640i	−0.963618	−	1.66904i
$743$	−13.1247	−	22.7327i	−0.481499	−	0.833981i	0.518275	−	0.855214i	$-0.326574\pi$
$743$	−13.1247	−	22.7327i	−0.481499	−	0.833981i	−0.999775	+	0.0212326i	$0.993241\pi$
$744$	98.3498	+	39.0165i	3.60568	+	1.43041i
$745$	−6.67476	+	11.5610i	−0.244544	+	0.423563i
$746$	64.9799			2.37908
$747$	−0.940074	−	0.885188i	−0.0343955	−	0.0323873i
$748$	4.59959			0.168178
$749$	−10.8870	+	18.8568i	−0.397801	+	0.689012i
$750$	−0.683325	−	4.64925i	−0.0249515	−	0.169767i
$751$	−25.7911	−	44.6715i	−0.941132	−	1.63009i	−0.763318	−	0.646023i	$-0.776431\pi$
$751$	−25.7911	−	44.6715i	−0.941132	−	1.63009i	−0.177814	−	0.984064i	$-0.556903\pi$
$752$	32.2290	+	55.8223i	1.17527	+	2.03563i
$753$	−10.3447	+	8.18774i	−0.376983	+	0.298378i
$754$	−2.69410	+	4.66632i	−0.0981135	+	0.169938i
$755$	−9.87045			−0.359222
$756$	−29.1674	−	62.3122i	−1.06081	−	2.26627i
$757$	−21.6474			−0.786787			−0.393393	−	0.919370i	$-0.628699\pi$
$757$	−21.6474			−0.786787			−0.393393	+	0.919370i	$0.628699\pi$
$758$	−16.1524	+	27.9768i	−0.586682	+	1.01616i
$759$	1.84842	−	1.46300i	0.0670934	−	0.0531036i
$760$	36.3154	+	62.9001i	1.31730	+	2.28163i
$761$	−22.3143	−	38.6496i	−0.808894	−	1.40105i	−0.913630	−	0.406546i	$-0.866733\pi$
$761$	−22.3143	−	38.6496i	−0.808894	−	1.40105i	0.104736	−	0.994500i	$-0.466600\pi$
$762$	14.0013	+	95.2627i	0.507212	+	3.45100i
$763$	9.72217	−	16.8393i	0.351966	−	0.609623i
$764$	−28.5256			−1.03202
$765$	−10.0674	+	3.02464i	−0.363986	+	0.109356i
$766$	−13.0391			−0.471121
$767$	−4.26863	+	7.39348i	−0.154131	+	0.266963i
$768$	−48.6023	−	19.2811i	−1.75378	−	0.695746i
$769$	6.36213	+	11.0195i	0.229424	+	0.397375i	0.957638	−	0.287976i	$-0.0929823\pi$
$769$	6.36213	+	11.0195i	0.229424	+	0.397375i	−0.728213	+	0.685351i	$0.759649\pi$
$770$	0.820425	+	1.42102i	0.0295661	+	0.0512099i
$771$	19.1423	+	7.59396i	0.689392	+	0.273490i
$772$	−30.0650	+	52.0742i	−1.08206	+	1.87419i
$773$	−12.5964			−0.453059			−0.226530	−	0.974004i	$-0.572738\pi$
$773$	−12.5964			−0.453059			−0.226530	+	0.974004i	$0.572738\pi$
$774$	46.1735	−	13.8724i	1.65967	−	0.498633i
$775$	6.69948			0.240652
$776$	20.8931	−	36.1879i	0.750019	−	1.29907i
$777$	5.45093	+	37.0874i	0.195551	+	1.33050i
$778$	8.65075	+	14.9835i	0.310144	+	0.537186i
$779$	−23.3617	−	40.4637i	−0.837021	−	1.44976i
$780$	−7.28068	+	5.76257i	−0.260690	+	0.206333i
$781$	−0.928826	+	1.60877i	−0.0332360	+	0.0575665i
$782$	−52.8395			−1.88954
$783$	10.2816	+	0.884412i	0.367435	+	0.0316063i
$784$	−12.6095			−0.450340
$785$	2.86062	−	4.95475i	0.102100	−	0.176842i
$786$	−26.9761	+	21.3512i	−0.962204	+	0.761573i
$787$	−15.7003	−	27.1937i	−0.559654	−	0.969349i	−0.997525	−	0.0703115i	$-0.977601\pi$
$787$	−15.7003	−	27.1937i	−0.559654	−	0.969349i	0.437871	−	0.899038i	$-0.355733\pi$
$788$	4.36206	+	7.55531i	0.155392	+	0.269147i
$789$	1.79766	+	12.2310i	0.0639983	+	0.435436i
$790$	−8.10056	+	14.0306i	−0.288205	+	0.499186i
$791$	−46.1120			−1.63956
$792$	−4.87655	−	4.59183i	−0.173281	−	0.163164i
$793$	−10.5422			−0.374365
$794$	20.2029	−	34.9925i	0.716974	−	1.24184i
$795$	12.6130	+	5.00371i	0.447336	+	0.177463i
$796$	25.5872	+	44.3183i	0.906913	+	1.57082i
$797$	0.810152	+	1.40322i	0.0286971	+	0.0497048i	0.880017	−	0.474942i	$-0.157531\pi$
$797$	0.810152	+	1.40322i	0.0286971	+	0.0497048i	−0.851320	+	0.524646i	$0.824198\pi$
$798$	85.9361	+	34.0919i	3.04211	+	1.20684i
$799$	8.05670	−	13.9546i	0.285026	−	0.493679i
$800$	−19.7924			−0.699768
$801$	10.1347	−	42.9477i	0.358091	−	1.51748i
$802$	−37.1004			−1.31006
$803$	0.691226	−	1.19724i	0.0243928	−	0.0422496i
$804$	−19.9201	−	135.534i	−0.702528	−	4.77991i
$805$	−6.86411	−	11.8890i	−0.241928	−	0.419032i
$806$	−9.08812	−	15.7411i	−0.320115	−	0.554456i
$807$	−16.0482	+	12.7020i	−0.564923	+	0.447130i
$808$	−14.7788	+	25.5977i	−0.519917	+	0.900523i
$809$	−3.48609			−0.122564			−0.0612822	−	0.998120i	$-0.519519\pi$
$809$	−3.48609			−0.122564			−0.0612822	+	0.998120i	$0.519519\pi$
$810$	21.8418	+	10.9162i	0.767442	+	0.383556i
$811$	37.6569			1.32231			0.661156	−	0.750248i	$-0.270066\pi$
$811$	37.6569			1.32231			0.661156	+	0.750248i	$0.270066\pi$
$812$	−13.1481	+	22.7731i	−0.461407	+	0.799180i
$813$	−41.4020	+	32.7692i	−1.45203	+	1.14927i
$814$	2.91063	+	5.04135i	0.102017	+	0.176699i
$815$	−5.63255	−	9.75587i	−0.197300	−	0.341733i
$816$	12.3701	+	84.1648i	0.433041	+	2.94636i
$817$	−23.5915	+	40.8616i	−0.825361	+	1.42957i
$818$	59.4311			2.07796
$819$	−1.70178	+	7.21163i	−0.0594650	+	0.251995i
$820$	31.4453			1.09812
$821$	−16.1413	+	27.9575i	−0.563335	+	0.975725i	0.433867	+	0.900977i	$0.357149\pi$
$821$	−16.1413	+	27.9575i	−0.563335	+	0.975725i	−0.997202	+	0.0747483i	$0.976185\pi$
$822$	8.90488	+	3.53267i	0.310593	+	0.123216i
$823$	9.51906	+	16.4875i	0.331814	+	0.574718i	0.982868	−	0.184314i	$-0.0590062\pi$
$823$	9.51906	+	16.4875i	0.331814	+	0.574718i	−0.651054	+	0.759031i	$0.725673\pi$
$824$	−19.0203	−	32.9442i	−0.662605	−	1.14767i
$825$	−0.394229	−	0.156395i	−0.0137253	−	0.00544499i
$826$	−28.6043	+	49.5441i	−0.995270	+	1.72386i
$827$	39.3702			1.36904			0.684518	−	0.728996i	$-0.260013\pi$
$827$	39.3702			1.36904			0.684518	+	0.728996i	$0.260013\pi$
$828$	65.0794	+	61.2797i	2.26167	+	2.12962i
$829$	34.2187			1.18846			0.594232	−	0.804293i	$-0.297456\pi$
$829$	34.2187			1.18846			0.594232	+	0.804293i	$0.297456\pi$
$830$	−0.583873	+	1.01130i	−0.0202665	+	0.0351027i
$831$	−0.0982783	−	0.668672i	−0.00340923	−	0.0231960i
$832$	12.8324	+	22.2264i	0.444885	+	0.770563i
$833$	1.57608	+	2.72986i	0.0546081	+	0.0945840i
$834$	−37.8333	+	29.9446i	−1.31006	+	1.03690i
$835$	1.79775	−	3.11379i	0.0622137	−	0.107757i
$836$	10.4561			0.361631
$837$	−19.9254	+	28.5450i	−0.688724	+	0.986660i
$838$	−1.06397			−0.0367542
$839$	−22.4655	+	38.9114i	−0.775595	+	1.34337i	0.158865	+	0.987300i	$0.449217\pi$
$839$	−22.4655	+	38.9114i	−0.775595	+	1.34337i	−0.934460	+	0.356069i	$0.884117\pi$
$840$	−30.5864	+	24.2088i	−1.05533	+	0.835283i
$841$	12.5279	+	21.6989i	0.431996	+	0.748239i
$842$	−25.4946	−	44.1579i	−0.878602	−	1.52178i
$843$	2.39727	+	16.3107i	0.0825665	+	0.561771i
$844$	25.1068	−	43.4863i	0.864212	−	1.49686i
$845$	1.00000			0.0344010
$846$	−35.8464	+	10.7697i	−1.23242	+	0.370270i
$847$	−27.0208			−0.928446
$848$	54.9053	−	95.0988i	1.88546	−	3.26571i
$849$	39.1873	+	15.5461i	1.34491	+	0.533540i
$850$	4.75329	+	8.23293i	0.163036	+	0.282387i
$851$	−24.3518	−	42.1786i	−0.834770	−	1.44586i
$852$	−65.4776	−	25.9757i	−2.24323	−	0.889914i
$853$	−8.08176	+	13.9980i	−0.276714	+	0.479283i	−0.970566	−	0.240834i	$-0.922579\pi$
$853$	−8.08176	+	13.9980i	−0.276714	+	0.479283i	0.693852	+	0.720118i	$0.255912\pi$
$854$	−70.6438			−2.41738
$855$	−22.8858	+	6.87582i	−0.782678	+	0.235148i
$856$	−80.3836			−2.74746
$857$	4.24485	−	7.35230i	0.145001	−	0.251150i	−0.784372	−	0.620291i	$-0.787015\pi$
$857$	4.24485	−	7.35230i	0.145001	−	0.251150i	0.929373	+	0.369141i	$0.120348\pi$
$858$	0.167322	+	1.13844i	0.00571229	+	0.0388656i
$859$	−4.91077	−	8.50570i	−0.167553	−	0.290211i	0.770006	−	0.638037i	$-0.220253\pi$
$859$	−4.91077	−	8.50570i	−0.167553	−	0.290211i	−0.937559	+	0.347826i	$0.886920\pi$
$860$	−15.8773	−	27.5003i	−0.541411	−	0.937752i
$861$	19.6763	−	15.5736i	0.670566	−	0.530745i
$862$	−10.9798	+	19.0176i	−0.373974	+	0.647743i
$863$	13.0298			0.443541			0.221770	−	0.975099i	$-0.428816\pi$
$863$	13.0298			0.443541			0.221770	+	0.975099i	$0.428816\pi$
$864$	58.8662	−	84.3313i	2.00267	−	2.86901i
$865$	−3.84176			−0.130624
$866$	−44.1227	+	76.4228i	−1.49935	+	2.59695i
$867$	−6.41331	+	5.07606i	−0.217808	+	0.172392i
$868$	−44.3529	−	76.8215i	−1.50544	−	2.60749i
$869$	0.731102	+	1.26631i	0.0248009	+	0.0429565i
$870$	−1.35709	−	9.23345i	−0.0460096	−	0.313043i
$871$	−7.37676	+	12.7769i	−0.249952	+	0.432930i
$872$	71.7833			2.43089
$873$	10.0092	+	9.42483i	0.338761	+	0.318982i
$874$	−120.118			−4.06306
$875$	−1.23495	+	2.13900i	−0.0417489	+	0.0723112i
$876$	48.7280	+	19.3310i	1.64637	+	0.653132i
$877$	−5.06704	−	8.77638i	−0.171102	−	0.296357i	0.767703	−	0.640805i	$-0.221399\pi$
$877$	−5.06704	−	8.77638i	−0.171102	−	0.296357i	−0.938805	+	0.344448i	$0.888066\pi$
$878$	−3.18435	−	5.51545i	−0.107466	−	0.186137i
$879$	26.9574	+	10.6943i	0.909251	+	0.360710i
$880$	−1.71611	+	2.97240i	−0.0578502	+	0.100199i
$881$	−20.7671			−0.699660			−0.349830	−	0.936813i	$-0.613761\pi$
$881$	−20.7671			−0.699660			−0.349830	+	0.936813i	$0.613761\pi$
$882$	1.68165	−	7.12633i	0.0566242	−	0.239956i
$883$	27.8242			0.936357			0.468179	−	0.883634i	$-0.344910\pi$
$883$	27.8242			0.936357			0.468179	+	0.883634i	$0.344910\pi$
$884$	9.39210	−	16.2676i	0.315890	−	0.547138i
$885$	−2.15022	−	14.6298i	−0.0722788	−	0.491775i
$886$	−47.2480	−	81.8360i	−1.58733	−	2.74933i
$887$	13.0425	+	22.5903i	0.437924	+	0.758507i	0.997529	−	0.0702524i	$-0.0223805\pi$
$887$	13.0425	+	22.5903i	0.437924	+	0.758507i	−0.559605	+	0.828759i	$0.689047\pi$
$888$	−108.512	+	85.8858i	−3.64142	+	2.88214i
$889$	25.3040	−	43.8278i	0.848668	−	1.46994i
$890$	−39.9070			−1.33768
$891$	1.83887	−	1.21458i	0.0616046	−	0.0406899i
$892$	46.5964			1.56016
$893$	18.3150	−	31.7225i	0.612889	−	1.06155i
$894$	−49.1891	+	38.9326i	−1.64513	+	1.30210i
$895$	0.0329927	+	0.0571451i	0.00110283	+	0.00191015i
$896$	37.1055	+	64.2686i	1.23961	+	2.14706i
$897$	−1.39991	−	9.52477i	−0.0467415	−	0.318023i
$898$	15.0598	−	26.0844i	0.502553	−	0.870447i
$899$	13.3052			0.443754
$900$	3.69365	−	15.6526i	0.123122	−	0.521753i
$901$	−27.4508			−0.914519
$902$	1.94843	−	3.37477i	0.0648755	−	0.112368i
$903$	−23.5546	−	9.34439i	−0.783849	−	0.310962i
$904$	−85.1167	−	147.427i	−2.83094	−	4.90333i
$905$	−5.25248	−	9.09756i	−0.174598	−	0.302413i
$906$	−43.1145	−	17.1040i	−1.43238	−	0.568242i
$907$	−6.81736	+	11.8080i	−0.226367	+	0.392079i	−0.956729	−	0.290982i	$-0.906018\pi$
$907$	−6.81736	+	11.8080i	−0.226367	+	0.392079i	0.730362	+	0.683060i	$0.239351\pi$
$908$	−141.529			−4.69679
$909$	−7.08006	−	6.66669i	−0.234831	−	0.221120i
$910$	6.70105			0.222138
$911$	−6.65270	+	11.5228i	−0.220414	+	0.381768i	−0.954934	−	0.296819i	$-0.904074\pi$
$911$	−6.65270	+	11.5228i	−0.220414	+	0.381768i	0.734520	+	0.678587i	$0.237407\pi$
$912$	28.1206	+	191.329i	0.931166	+	6.33553i
$913$	0.0526965	+	0.0912729i	0.00174400	+	0.00302069i
$914$	26.7655	+	46.3593i	0.885325	+	1.53343i
$915$	14.3176	−	11.3322i	0.473326	−	0.374632i
$916$	10.9450	−	18.9573i	0.361632	−	0.626365i
$917$	18.0823			0.597131
$918$	−49.2159	−	4.23348i	−1.62437	−	0.139726i
$919$	−29.9753			−0.988794			−0.494397	−	0.869236i	$-0.664611\pi$
$919$	−29.9753			−0.988794			−0.494397	+	0.869236i	$0.664611\pi$
$920$	25.3405	−	43.8910i	0.835451	−	1.44704i
$921$	−26.1256	+	20.6781i	−0.860869	+	0.681368i
$922$	−4.18012	−	7.24019i	−0.137665	−	0.238443i
$923$	3.79322	+	6.57006i	0.124855	+	0.216256i
$924$	0.816585	+	5.55594i	0.0268637	+	0.182777i
$925$	−4.38124	+	7.58853i	−0.144054	+	0.249509i
$926$	−23.5953			−0.775390
$927$	11.9865	−	3.60124i	0.393689	−	0.118280i
$928$	−39.3079			−1.29035
$929$	10.3161	−	17.8680i	0.338461	−	0.586232i	−0.645682	−	0.763606i	$-0.723427\pi$
$929$	10.3161	−	17.8680i	0.338461	−	0.586232i	0.984143	+	0.177374i	$0.0567603\pi$
$930$	29.2635	+	11.6092i	0.959589	+	0.380680i
$931$	3.58286	+	6.20569i	0.117423	+	0.203383i
$932$	59.7285	+	103.453i	1.95647	+	3.38871i
$933$	8.28480	+	3.28668i	0.271232	+	0.107601i
$934$	−45.7293	+	79.2055i	−1.49631	+	2.59168i
$935$	0.857999			0.0280596
$936$	−26.1978	+	7.87089i	−0.856303	+	0.257268i
$937$	56.0294			1.83040			0.915200	−	0.403000i	$-0.132033\pi$
$937$	56.0294			1.83040			0.915200	+	0.403000i	$0.132033\pi$
$938$	−49.4320	+	85.6188i	−1.61401	+	2.79555i
$939$	8.41441	+	57.2505i	0.274594	+	1.86830i
$940$	12.3262	+	21.3496i	0.402036	+	0.696347i
$941$	28.4214	+	49.2274i	0.926512	+	1.60477i	0.789111	+	0.614251i	$0.210542\pi$
$941$	28.4214	+	49.2274i	0.926512	+	1.60477i	0.137402	+	0.990515i	$0.456125\pi$
$942$	21.0811	−	16.6855i	0.686860	−	0.543642i
$943$	−16.3016	+	28.2351i	−0.530852	+	0.919462i
$944$	−119.665			−3.89477
$945$	−5.44084	−	11.6236i	−0.176990	−	0.378116i
$946$	−3.93517			−0.127944
$947$	10.8532	−	18.7984i	0.352683	−	0.610864i	−0.634036	−	0.773304i	$-0.718603\pi$
$947$	10.8532	−	18.7984i	0.352683	−	0.610864i	0.986719	+	0.162439i	$0.0519362\pi$
$948$	−43.4764	+	34.4111i	−1.41205	+	1.11762i
$949$	−2.82289	−	4.88939i	−0.0916348	−	0.158716i
$950$	10.8055	+	18.7156i	0.350576	+	0.607216i
$951$	8.80791	+	59.9279i	0.285616	+	1.94329i
$952$	39.4566	−	68.3408i	1.27880	−	2.21494i
$953$	25.5013			0.826068			0.413034	−	0.910716i	$-0.364469\pi$
$953$	25.5013			0.826068			0.413034	+	0.910716i	$0.364469\pi$
$954$	46.4232	+	43.7127i	1.50301	+	1.41525i
$955$	−5.32111			−0.172187
$956$	−50.2328	+	87.0057i	−1.62464	+	2.81397i
$957$	−0.782942	−	0.310602i	−0.0253089	−	0.0100403i
$958$	−29.0421	−	50.3025i	−0.938309	−	1.62520i
$959$	−2.51763	−	4.36066i	−0.0812984	−	0.140813i
$960$	−41.3202	−	16.3922i	−1.33360	−	0.529055i
$961$	−6.94148	+	12.0230i	−0.223919	+	0.387839i
$962$	23.7734			0.766484
$963$	6.07410	−	25.7402i	0.195735	−	0.829466i
$964$	−6.84324			−0.220406
$965$	−5.60828	+	9.71382i	−0.180537	+	0.312699i
$966$	−9.38083	−	63.8259i	−0.301823	−	2.05357i
$967$	3.56222	+	6.16995i	0.114553	+	0.198412i	0.917601	−	0.397502i	$-0.130123\pi$
$967$	3.56222	+	6.16995i	0.114553	+	0.198412i	−0.803048	+	0.595915i	$0.796790\pi$
$968$	−49.8768	−	86.3892i	−1.60310	−	2.77665i
$969$	37.9063	−	30.0024i	1.21772	−	0.963815i
$970$	6.21665	−	10.7676i	0.199605	−	0.345726i
$971$	−17.3440			−0.556596			−0.278298	−	0.960495i	$-0.589770\pi$
$971$	−17.3440			−0.556596			−0.278298	+	0.960495i	$0.589770\pi$
$972$	55.7067	+	62.2914i	1.78679	+	1.99800i
$973$	25.3601			0.813006
$974$	49.7651	−	86.1957i	1.59458	−	2.76189i
$975$	−1.35813	+	1.07494i	−0.0434948	+	0.0344256i
$976$	−73.8842	−	127.971i	−2.36497	−	4.09626i
$977$	9.99158	+	17.3059i	0.319659	+	0.553665i	0.980417	−	0.196934i	$-0.0630984\pi$
$977$	9.99158	+	17.3059i	0.319659	+	0.553665i	−0.660758	+	0.750599i	$0.729765\pi$
$978$	−7.69773	−	52.3743i	−0.246146	−	1.67475i
$979$	−1.80087	+	3.11919i	−0.0575560	+	0.0996898i
$980$	−4.82260			−0.154052
$981$	−5.42423	+	22.9862i	−0.173182	+	0.733894i
$982$	−102.389			−3.26737
$983$	18.0898	−	31.3325i	0.576975	−	0.999350i	−0.418849	−	0.908056i	$-0.637566\pi$
$983$	18.0898	−	31.3325i	0.576975	−	0.999350i	0.995824	−	0.0912942i	$-0.0291004\pi$
$984$	86.1106	+	34.1611i	2.74511	+	1.08902i
$985$	0.813691	+	1.40935i	0.0259264	+	0.0449058i
$986$	9.44006	+	16.3507i	0.300633	+	0.520711i
$987$	18.2864	+	7.25443i	0.582063	+	0.230911i
$988$	21.3507	−	36.9805i	0.679257	−	1.17651i
$989$	32.9237			1.04691
$990$	−1.45100	−	1.36628i	−0.0461157	−	0.0434232i
$991$	−13.7114			−0.435557			−0.217779	−	0.975998i	$-0.569881\pi$
$991$	−13.7114			−0.435557			−0.217779	+	0.975998i	$0.569881\pi$
$992$	66.2995	−	114.834i	2.10501	−	3.64598i
$993$	3.70788	+	25.2279i	0.117666	+	0.800584i
$994$	25.4186	+	44.0262i	0.806228	+	1.39643i
$995$	4.77299	+	8.26706i	0.151314	+	0.262083i
$996$	−3.13370	+	2.48028i	−0.0992950	+	0.0785908i
$997$	−1.87978	+	3.25587i	−0.0595331	+	0.103114i	−0.894256	−	0.447556i	$-0.852295\pi$
$997$	−1.87978	+	3.25587i	−0.0595331	+	0.103114i	0.834723	+	0.550670i	$0.185628\pi$
$998$	−10.3798			−0.328568
$999$	−19.3025	−	41.2371i	−0.610704	−	1.30469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.13	✓	26
3.2	odd	2		1755.2.i.g.586.1		26
9.2	odd	6		5265.2.a.bh.1.13		13
9.4	even	3	inner	585.2.i.g.391.13	yes	26
9.5	odd	6		1755.2.i.g.1171.1		26
9.7	even	3		5265.2.a.bg.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.13	✓	26	1.1	even	1	trivial
585.2.i.g.391.13	yes	26	9.4	even	3	inner
1755.2.i.g.586.1		26	3.2	odd	2
1755.2.i.g.1171.1		26	9.5	odd	6
5265.2.a.bg.1.1		13	9.7	even	3
5265.2.a.bh.1.13		13	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35654 - 2.34960i) q^{2} +(1.35813 - 1.07494i) q^{3} +(-2.68041 - 4.64261i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.683325 - 4.64925i) q^{6} +(-1.23495 + 2.13900i) q^{7} -9.11822 q^{8} +(0.689008 - 2.91981i) q^{9} +O(q^{10})\)	\(q+(1.35654 - 2.34960i) q^{2} +(1.35813 - 1.07494i) q^{3} +(-2.68041 - 4.64261i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.683325 - 4.64925i) q^{6} +(-1.23495 + 2.13900i) q^{7} -9.11822 q^{8} +(0.689008 - 2.91981i) q^{9} -2.71308 q^{10} +(-0.122432 + 0.212059i) q^{11} +(-8.63087 - 3.42397i) q^{12} +(0.500000 + 0.866025i) q^{13} +(3.35052 + 5.80328i) q^{14} +(-1.60999 - 0.638701i) q^{15} +(-7.00842 + 12.1389i) q^{16} +3.50397 q^{17} +(-5.92571 - 5.57973i) q^{18} +7.96546 q^{19} +(-2.68041 + 4.64261i) q^{20} +(0.622076 + 4.23252i) q^{21} +(0.332169 + 0.575334i) q^{22} +(-2.77910 - 4.81355i) q^{23} +(-12.3837 + 9.80154i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.71308 q^{26} +(-2.20286 - 4.70610i) q^{27} +13.2407 q^{28} +(-0.993004 + 1.71993i) q^{29} +(-3.68471 + 2.91640i) q^{30} +(-3.34974 - 5.80192i) q^{31} +(9.89622 + 17.1408i) q^{32} +(0.0616723 + 0.419610i) q^{33} +(4.75329 - 8.23293i) q^{34} +2.46990 q^{35} +(-15.4024 + 4.62749i) q^{36} +8.76248 q^{37} +(10.8055 - 18.7156i) q^{38} +(1.60999 + 0.638701i) q^{39} +(4.55911 + 7.89661i) q^{40} +(-2.93288 - 5.07990i) q^{41} +(10.7886 + 4.27996i) q^{42} +(-2.96172 + 5.12985i) q^{43} +1.31268 q^{44} +(-2.87313 + 0.863205i) q^{45} -15.0799 q^{46} +(2.29931 - 3.98251i) q^{47} +(3.53032 + 24.0198i) q^{48} +(0.449799 + 0.779075i) q^{49} +(1.35654 + 2.34960i) q^{50} +(4.75883 - 3.76656i) q^{51} +(2.68041 - 4.64261i) q^{52} -7.83420 q^{53} +(-14.0457 - 1.20820i) q^{54} +0.244865 q^{55} +(11.2605 - 19.5038i) q^{56} +(10.8181 - 8.56239i) q^{57} +(2.69410 + 4.66632i) q^{58} +(4.26863 + 7.39348i) q^{59} +(1.35019 + 9.18654i) q^{60} +(-5.27110 + 9.12981i) q^{61} -18.1762 q^{62} +(5.39456 + 5.07960i) q^{63} +25.6649 q^{64} +(0.500000 - 0.866025i) q^{65} +(1.06958 + 0.424314i) q^{66} +(7.37676 + 12.7769i) q^{67} +(-9.39210 - 16.2676i) q^{68} +(-8.94865 - 3.55003i) q^{69} +(3.35052 - 5.80328i) q^{70} +7.58645 q^{71} +(-6.28252 + 26.6234i) q^{72} -5.64578 q^{73} +(11.8867 - 20.5883i) q^{74} +(0.251863 + 1.71364i) q^{75} +(-21.3507 - 36.9805i) q^{76} +(-0.302396 - 0.523764i) q^{77} +(3.68471 - 2.91640i) q^{78} +(2.98574 - 5.17145i) q^{79} +14.0168 q^{80} +(-8.05054 - 4.02354i) q^{81} -15.9143 q^{82} +(0.215206 - 0.372748i) q^{83} +(17.9825 - 14.2330i) q^{84} +(-1.75199 - 3.03453i) q^{85} +(8.03541 + 13.9177i) q^{86} +(0.500201 + 3.40330i) q^{87} +(1.11636 - 1.93360i) q^{88} +14.7091 q^{89} +(-1.86934 + 7.92168i) q^{90} -2.46990 q^{91} +(-14.8983 + 25.8046i) q^{92} +(-10.7861 - 4.27896i) q^{93} +(-6.23821 - 10.8049i) q^{94} +(-3.98273 - 6.89829i) q^{95} +(31.8656 + 12.6414i) q^{96} +(-2.29136 + 3.96875i) q^{97} +2.44069 q^{98} +(0.534814 + 0.503589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

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