LMFDB - Embedded newform 585.2.i.h.391.13

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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.13
Character	$\chi$	$=$	585.391
Dual form			585.2.i.h.196.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17680 + 2.03828i) q^{2} +(0.988775 + 1.42208i) q^{3} +(-1.76973 + 3.06526i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.73501 + 3.68891i) q^{6} +(0.0389983 + 0.0675470i) q^{7} -3.62327 q^{8} +(-1.04465 + 2.81224i) q^{9} +O(q^{10})$	\(q+(1.17680 + 2.03828i) q^{2} +(0.988775 + 1.42208i) q^{3} +(-1.76973 + 3.06526i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.73501 + 3.68891i) q^{6} +(0.0389983 + 0.0675470i) q^{7} -3.62327 q^{8} +(-1.04465 + 2.81224i) q^{9} +2.35360 q^{10} +(0.518744 + 0.898492i) q^{11} +(-6.10892 + 0.514150i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.0917866 + 0.158979i) q^{14} +(1.72595 - 0.145263i) q^{15} +(-0.724419 - 1.25473i) q^{16} -3.01674 q^{17} +(-6.96149 + 1.18017i) q^{18} -1.33883 q^{19} +(1.76973 + 3.06526i) q^{20} +(-0.0574970 + 0.122248i) q^{21} +(-1.22092 + 2.11469i) q^{22} +(3.66011 - 6.33950i) q^{23} +(-3.58260 - 5.15260i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.35360 q^{26} +(-5.03217 + 1.29510i) q^{27} -0.276066 q^{28} +(2.04671 + 3.54501i) q^{29} +(2.32719 + 3.34702i) q^{30} +(3.49130 - 6.04711i) q^{31} +(-1.91828 + 3.32255i) q^{32} +(-0.764809 + 1.62610i) q^{33} +(-3.55011 - 6.14897i) q^{34} +0.0779966 q^{35} +(-6.77151 - 8.17902i) q^{36} +5.18283 q^{37} +(-1.57554 - 2.72891i) q^{38} +(-1.72595 + 0.145263i) q^{39} +(-1.81164 + 3.13785i) q^{40} +(1.65670 - 2.86949i) q^{41} +(-0.316838 + 0.0266663i) q^{42} +(-2.67701 - 4.63672i) q^{43} -3.67215 q^{44} +(1.91315 + 2.31081i) q^{45} +17.2289 q^{46} +(4.80910 + 8.32961i) q^{47} +(1.06805 - 2.27083i) q^{48} +(3.49696 - 6.05691i) q^{49} +(1.17680 - 2.03828i) q^{50} +(-2.98288 - 4.29006i) q^{51} +(-1.76973 - 3.06526i) q^{52} +10.9978 q^{53} +(-8.56165 - 8.73290i) q^{54} +1.03749 q^{55} +(-0.141301 - 0.244741i) q^{56} +(-1.32380 - 1.90393i) q^{57} +(-4.81715 + 8.34355i) q^{58} +(0.0239283 - 0.0414450i) q^{59} +(-2.60919 + 5.54756i) q^{60} +(-2.28587 - 3.95924i) q^{61} +16.4343 q^{62} +(-0.230698 + 0.0391099i) q^{63} -11.9274 q^{64} +(0.500000 + 0.866025i) q^{65} +(-4.21449 + 0.354708i) q^{66} +(-4.19018 + 7.25760i) q^{67} +(5.33881 - 9.24710i) q^{68} +(12.6343 - 1.06335i) q^{69} +(0.0917866 + 0.158979i) q^{70} +2.31094 q^{71} +(3.78504 - 10.1895i) q^{72} -2.28031 q^{73} +(6.09917 + 10.5641i) q^{74} +(0.737173 - 1.56735i) q^{75} +(2.36937 - 4.10386i) q^{76} +(-0.0404603 + 0.0700793i) q^{77} +(-2.32719 - 3.34702i) q^{78} +(-1.22456 - 2.12100i) q^{79} -1.44884 q^{80} +(-6.81743 - 5.87560i) q^{81} +7.79844 q^{82} +(0.908528 + 1.57362i) q^{83} +(-0.272967 - 0.392588i) q^{84} +(-1.50837 + 2.61258i) q^{85} +(6.30062 - 10.9130i) q^{86} +(-3.01756 + 6.41581i) q^{87} +(-1.87955 - 3.25548i) q^{88} -9.90169 q^{89} +(-2.45869 + 6.61891i) q^{90} -0.0779966 q^{91} +(12.9548 + 22.4384i) q^{92} +(12.0516 - 1.01431i) q^{93} +(-11.3187 + 19.6046i) q^{94} +(-0.669415 + 1.15946i) q^{95} +(-6.62169 + 0.557307i) q^{96} +(-4.63238 - 8.02353i) q^{97} +16.4609 q^{98} +(-3.06868 + 0.520229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.17680	+	2.03828i	0.832125	+	1.44128i	0.896350	+	0.443347i	$0.146209\pi$
$2$	1.17680	+	2.03828i	0.832125	+	1.44128i	−0.0642249	+	0.997935i	$0.520457\pi$
$3$	0.988775	+	1.42208i	0.570870	+	0.821041i
$3$	0.988775	+	1.42208i	0.570870	+	0.821041i
$4$	−1.76973	+	3.06526i	−0.884864	+	1.53263i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.73501	+	3.68891i	−0.708317	+	1.50599i
$7$	0.0389983	+	0.0675470i	0.0147400	+	0.0255304i	0.873301	−	0.487180i	$-0.161975\pi$
$7$	0.0389983	+	0.0675470i	0.0147400	+	0.0255304i	−0.858561	+	0.512711i	$0.828641\pi$
$8$	−3.62327			−1.28102
$9$	−1.04465	+	2.81224i	−0.348216	+	0.937415i
$10$	2.35360			0.744275
$11$	0.518744	+	0.898492i	0.156407	+	0.270905i	0.933571	−	0.358394i	$-0.116675\pi$
$11$	0.518744	+	0.898492i	0.156407	+	0.270905i	−0.777163	+	0.629299i	$0.783342\pi$
$12$	−6.10892	+	0.514150i	−1.76349	+	0.148422i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.0917866	+	0.158979i	−0.0245310	+	0.0424889i
$15$	1.72595	−	0.145263i	0.445638	−	0.0375066i
$16$	−0.724419	−	1.25473i	−0.181105	−	0.313683i
$17$	−3.01674			−0.731667			−0.365834	−	0.930680i	$-0.619216\pi$
$17$	−3.01674			−0.731667			−0.365834	+	0.930680i	$0.619216\pi$
$18$	−6.96149	+	1.18017i	−1.64084	+	0.278169i
$19$	−1.33883			−0.307149			−0.153574	−	0.988137i	$-0.549078\pi$
$19$	−1.33883			−0.307149			−0.153574	+	0.988137i	$0.549078\pi$
$20$	1.76973	+	3.06526i	0.395723	+	0.685413i
$21$	−0.0574970	+	0.122248i	−0.0125469	+	0.0266766i
$22$	−1.22092	+	2.11469i	−0.260301	+	0.450854i
$23$	3.66011	−	6.33950i	0.763186	−	1.32188i	−0.178014	−	0.984028i	$-0.556967\pi$
$23$	3.66011	−	6.33950i	0.763186	−	1.32188i	0.941200	−	0.337850i	$-0.109700\pi$
$24$	−3.58260	−	5.15260i	−0.731296	−	1.05177i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.35360			−0.461580
$27$	−5.03217	+	1.29510i	−0.968441	+	0.249242i
$28$	−0.276066			−0.0521715
$29$	2.04671	+	3.54501i	0.380065	+	0.658291i	0.991071	−	0.133334i	$-0.0425684\pi$
$29$	2.04671	+	3.54501i	0.380065	+	0.658291i	−0.611006	+	0.791626i	$0.709235\pi$
$30$	2.32719	+	3.34702i	0.424884	+	0.611080i
$31$	3.49130	−	6.04711i	0.627056	−	1.08609i	−0.361083	−	0.932534i	$-0.617593\pi$
$31$	3.49130	−	6.04711i	0.627056	−	1.08609i	0.988139	−	0.153560i	$-0.0490737\pi$
$32$	−1.91828	+	3.32255i	−0.339106	+	0.587349i
$33$	−0.764809	+	1.62610i	−0.133136	+	0.283069i
$34$	−3.55011	−	6.14897i	−0.608839	−	1.05454i
$35$	0.0779966			0.0131838
$36$	−6.77151	−	8.17902i	−1.12859	−	1.36317i
$37$	5.18283			0.852052			0.426026	−	0.904711i	$-0.359913\pi$
$37$	5.18283			0.852052			0.426026	+	0.904711i	$0.359913\pi$
$38$	−1.57554	−	2.72891i	−0.255586	−	0.442688i
$39$	−1.72595	+	0.145263i	−0.276373	+	0.0232606i
$40$	−1.81164	+	3.13785i	−0.286445	+	0.496137i
$41$	1.65670	−	2.86949i	0.258733	−	0.448139i	−0.707170	−	0.707044i	$-0.750028\pi$
$41$	1.65670	−	2.86949i	0.258733	−	0.448139i	0.965903	+	0.258905i	$0.0833616\pi$
$42$	−0.316838	+	0.0266663i	−0.0488891	+	0.00411470i
$43$	−2.67701	−	4.63672i	−0.408240	−	0.707093i	0.586453	−	0.809984i	$-0.300524\pi$
$43$	−2.67701	−	4.63672i	−0.408240	−	0.707093i	−0.994693	+	0.102891i	$0.967191\pi$
$44$	−3.67215			−0.553597
$45$	1.91315	+	2.31081i	0.285196	+	0.344476i
$46$	17.2289			2.54027
$47$	4.80910	+	8.32961i	0.701480	+	1.21500i	0.967947	+	0.251155i	$0.0808103\pi$
$47$	4.80910	+	8.32961i	0.701480	+	1.21500i	−0.266467	+	0.963844i	$0.585856\pi$
$48$	1.06805	−	2.27083i	0.154159	−	0.327766i
$49$	3.49696	−	6.05691i	0.499565	−	0.865273i
$50$	1.17680	−	2.03828i	0.166425	−	0.288257i
$51$	−2.98288	−	4.29006i	−0.417687	−	0.600729i
$52$	−1.76973	−	3.06526i	−0.245417	−	0.425075i
$53$	10.9978			1.51067			0.755333	−	0.655342i	$-0.227475\pi$
$53$	10.9978			1.51067			0.755333	+	0.655342i	$0.227475\pi$
$54$	−8.56165	−	8.73290i	−1.16509	−	1.18840i
$55$	1.03749			0.139895
$56$	−0.141301	−	0.244741i	−0.0188822	−	0.0327049i
$57$	−1.32380	−	1.90393i	−0.175342	−	0.252182i
$58$	−4.81715	+	8.34355i	−0.632523	+	1.09556i
$59$	0.0239283	−	0.0414450i	0.00311520	−	0.00539568i	−0.864464	−	0.502695i	$-0.832342\pi$
$59$	0.0239283	−	0.0414450i	0.00311520	−	0.00539568i	0.867579	+	0.497300i	$0.165675\pi$
$60$	−2.60919	+	5.54756i	−0.336845	+	0.716186i
$61$	−2.28587	−	3.95924i	−0.292675	−	0.506929i	0.681766	−	0.731570i	$-0.261212\pi$
$61$	−2.28587	−	3.95924i	−0.292675	−	0.506929i	−0.974441	+	0.224642i	$0.927879\pi$
$62$	16.4343			2.08716
$63$	−0.230698	+	0.0391099i	−0.0290652	+	0.00492739i
$64$	−11.9274			−1.49093
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	−4.21449	+	0.354708i	−0.518768	+	0.0436615i
$67$	−4.19018	+	7.25760i	−0.511912	+	0.886657i	0.487993	+	0.872848i	$0.337729\pi$
$67$	−4.19018	+	7.25760i	−0.511912	+	0.886657i	−0.999905	+	0.0138094i	$0.995604\pi$
$68$	5.33881	−	9.24710i	0.647426	−	1.12138i
$69$	12.6343	−	1.06335i	1.52100	−	0.128013i
$70$	0.0917866	+	0.158979i	0.0109706	+	0.0190016i
$71$	2.31094			0.274259			0.137129	−	0.990553i	$-0.456212\pi$
$71$	2.31094			0.274259			0.137129	+	0.990553i	$0.456212\pi$
$72$	3.78504	−	10.1895i	0.446071	−	1.20085i
$73$	−2.28031			−0.266890			−0.133445	−	0.991056i	$-0.542604\pi$
$73$	−2.28031			−0.266890			−0.133445	+	0.991056i	$0.542604\pi$
$74$	6.09917	+	10.5641i	0.709014	+	1.22805i
$75$	0.737173	−	1.56735i	0.0851214	−	0.180982i
$76$	2.36937	−	4.10386i	0.271785	−	0.470745i
$77$	−0.0404603	+	0.0700793i	−0.00461088	+	0.00798628i
$78$	−2.32719	−	3.34702i	−0.263502	−	0.378976i
$79$	−1.22456	−	2.12100i	−0.137773	−	0.238631i	0.788880	−	0.614547i	$-0.210661\pi$
$79$	−1.22456	−	2.12100i	−0.137773	−	0.238631i	−0.926654	+	0.375917i	$0.877328\pi$
$80$	−1.44884			−0.161985
$81$	−6.81743	−	5.87560i	−0.757492	−	0.652845i
$82$	7.79844			0.861194
$83$	0.908528	+	1.57362i	0.0997239	+	0.172727i	0.911570	−	0.411144i	$-0.134871\pi$
$83$	0.908528	+	1.57362i	0.0997239	+	0.172727i	−0.811846	+	0.583871i	$0.801537\pi$
$84$	−0.272967	−	0.392588i	−0.0297831	−	0.0428349i
$85$	−1.50837	+	2.61258i	−0.163606	+	0.283374i
$86$	6.30062	−	10.9130i	0.679414	−	1.17678i
$87$	−3.01756	+	6.41581i	−0.323516	+	0.687847i
$88$	−1.87955	−	3.25548i	−0.200361	−	0.347035i
$89$	−9.90169			−1.04958			−0.524789	−	0.851233i	$-0.675856\pi$
$89$	−9.90169			−1.04958			−0.524789	+	0.851233i	$0.675856\pi$
$90$	−2.45869	+	6.61891i	−0.259168	+	0.697694i
$91$	−0.0779966			−0.00817626
$92$	12.9548	+	22.4384i	1.35063	+	2.33936i
$93$	12.0516	−	1.01431i	1.24969	−	0.105179i
$94$	−11.3187	+	19.6046i	−1.16744	+	2.02206i
$95$	−0.669415	+	1.15946i	−0.0686805	+	0.118958i
$96$	−6.62169	+	0.557307i	−0.675823	+	0.0568799i
$97$	−4.63238	−	8.02353i	−0.470347	−	0.814666i	0.529078	−	0.848573i	$-0.322538\pi$
$97$	−4.63238	−	8.02353i	−0.470347	−	0.814666i	−0.999425	+	0.0339079i	$0.989205\pi$
$98$	16.4609			1.66280
$99$	−3.06868	+	0.520229i	−0.308414	+	0.0522850i
$100$	3.53946			0.353946
$101$	−2.71516	−	4.70279i	−0.270168	−	0.467945i	0.698737	−	0.715379i	$-0.253746\pi$
$101$	−2.71516	−	4.70279i	−0.270168	−	0.467945i	−0.968905	+	0.247434i	$0.920413\pi$
$102$	5.23409	−	11.1285i	0.518252	−	1.10189i
$103$	−6.53557	+	11.3199i	−0.643969	+	1.11539i	0.340570	+	0.940219i	$0.389380\pi$
$103$	−6.53557	+	11.3199i	−0.643969	+	1.11539i	−0.984539	+	0.175167i	$0.943953\pi$
$104$	1.81164	−	3.13785i	0.177646	−	0.307691i
$105$	0.0771211	+	0.110918i	0.00752625	+	0.0108245i
$106$	12.9422	+	22.4166i	1.25706	+	2.17730i
$107$	16.5067			1.59576			0.797882	−	0.602814i	$-0.205954\pi$
$107$	16.5067			1.59576			0.797882	+	0.602814i	$0.205954\pi$
$108$	4.93575	−	17.7169i	0.474942	−	1.70481i
$109$	−15.2455			−1.46025			−0.730126	−	0.683312i	$-0.760539\pi$
$109$	−15.2455			−1.46025			−0.730126	+	0.683312i	$0.760539\pi$
$110$	1.22092	+	2.11469i	0.116410	+	0.201628i
$111$	5.12465	+	7.37042i	0.486411	+	0.699569i
$112$	0.0565022	−	0.0978647i	0.00533896	−	0.00924735i
$113$	5.21241	−	9.02815i	0.490342	−	0.849297i	−0.509596	−	0.860414i	$-0.670205\pi$
$113$	5.21241	−	9.02815i	0.490342	−	0.849297i	0.999938	+	0.0111164i	$0.00353854\pi$
$114$	2.32289	−	4.93883i	0.217559	−	0.462564i
$115$	−3.66011	−	6.33950i	−0.341307	−	0.591162i
$116$	−14.4885			−1.34522
$117$	−1.91315	−	2.31081i	−0.176871	−	0.213635i
$118$	0.112635			0.0103689
$119$	−0.117648	−	0.203772i	−0.0107848	−	0.0186797i
$120$	−6.25358	+	0.526326i	−0.570871	+	0.0480467i
$121$	4.96181	−	8.59410i	0.451073	−	0.781282i
$122$	5.38003	−	9.31848i	0.487085	−	0.843656i
$123$	5.71876	−	0.481313i	0.515643	−	0.0433985i
$124$	12.3573	+	21.4035i	1.10972	+	1.92209i
$125$	−1.00000			−0.0894427
$126$	−0.351203	−	0.424203i	−0.0312877	−	0.0377910i
$127$	−14.9255			−1.32442			−0.662211	−	0.749317i	$-0.730382\pi$
$127$	−14.9255			−1.32442			−0.662211	+	0.749317i	$0.730382\pi$
$128$	−10.1996	−	17.6663i	−0.901530	−	1.56150i
$129$	3.94684	−	8.39160i	0.347500	−	0.738839i
$130$	−1.17680	+	2.03828i	−0.103212	+	0.178769i
$131$	−6.40678	+	11.0969i	−0.559763	+	0.969537i	0.437753	+	0.899095i	$0.355774\pi$
$131$	−6.40678	+	11.0969i	−0.559763	+	0.969537i	−0.997516	+	0.0704422i	$0.977559\pi$
$132$	−3.63093	−	5.22210i	−0.316032	−	0.454526i
$133$	−0.0522121	−	0.0904340i	−0.00452736	−	0.00784162i
$134$	−19.7240			−1.70390
$135$	−1.39449	+	5.00554i	−0.120019	+	0.430808i
$136$	10.9305			0.937281
$137$	6.65026	+	11.5186i	0.568170	+	0.984099i	0.996747	+	0.0805941i	$0.0256817\pi$
$137$	6.65026	+	11.5186i	0.568170	+	0.984099i	−0.428577	+	0.903505i	$0.640985\pi$
$138$	17.0355	+	24.5010i	1.45016	+	2.08566i
$139$	−2.24902	+	3.89542i	−0.190760	+	0.330405i	−0.945502	−	0.325616i	$-0.894428\pi$
$139$	−2.24902	+	3.89542i	−0.190760	+	0.330405i	0.754743	+	0.656021i	$0.227762\pi$
$140$	−0.138033	+	0.239080i	−0.0116659	+	0.0202059i
$141$	−7.09029	+	15.0751i	−0.597110	+	1.26955i
$142$	2.71952	+	4.71035i	0.228217	+	0.395284i
$143$	−1.03749			−0.0867592
$144$	4.28537	−	0.726493i	0.357114	−	0.0605411i
$145$	4.09342			0.339940
$146$	−2.68347	−	4.64791i	−0.222086	−	0.384664i
$147$	12.0711	−	1.01595i	0.995611	−	0.0837945i
$148$	−9.17220	+	15.8867i	−0.753950	+	1.30588i
$149$	−0.830835	+	1.43905i	−0.0680647	+	0.117891i	−0.898049	−	0.439895i	$-0.855016\pi$
$149$	−0.830835	+	1.43905i	−0.0680647	+	0.117891i	0.829985	+	0.557786i	$0.188349\pi$
$150$	4.06220	−	0.341891i	0.331677	−	0.0279152i
$151$	−9.27202	−	16.0596i	−0.754546	−	1.30691i	−0.945600	−	0.325333i	$-0.894524\pi$
$151$	−9.27202	−	16.0596i	−0.754546	−	1.30691i	0.191054	−	0.981580i	$-0.438810\pi$
$152$	4.85095			0.393464
$153$	3.15143	−	8.48381i	0.254778	−	0.685876i
$154$	−0.190455			−0.0153473
$155$	−3.49130	−	6.04711i	−0.280428	−	0.485716i
$156$	2.60919	−	5.54756i	0.208903	−	0.444160i
$157$	−5.30231	+	9.18387i	−0.423170	+	0.732953i	−0.996248	−	0.0865487i	$-0.972416\pi$
$157$	−5.30231	+	9.18387i	−0.423170	+	0.732953i	0.573077	+	0.819501i	$0.305750\pi$
$158$	2.88212	−	4.99199i	0.229290	−	0.397141i
$159$	10.8744	+	15.6398i	0.862393	+	1.24032i
$160$	1.91828	+	3.32255i	0.151653	+	0.262671i
$161$	0.570953			0.0449974
$162$	3.95337	−	20.8103i	0.310606	−	1.63501i
$163$	2.10755			0.165076			0.0825379	−	0.996588i	$-0.473697\pi$
$163$	2.10755			0.165076			0.0825379	+	0.996588i	$0.473697\pi$
$164$	5.86382	+	10.1564i	0.457888	+	0.793085i
$165$	1.02584	+	1.47540i	0.0798618	+	0.114859i
$166$	−2.13832	+	3.70367i	−0.165965	+	0.287461i
$167$	−3.20410	+	5.54967i	−0.247941	+	0.429446i	−0.962954	−	0.269664i	$-0.913087\pi$
$167$	−3.20410	+	5.54967i	−0.247941	+	0.429446i	0.715013	+	0.699111i	$0.246421\pi$
$168$	0.208327	−	0.442937i	0.0160728	−	0.0341733i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−7.10022			−0.544562
$171$	1.39860	−	3.76512i	0.106954	−	0.287926i
$172$	18.9503			1.44495
$173$	−4.92009	−	8.52184i	−0.374067	−	0.647904i	0.616120	−	0.787653i	$-0.288704\pi$
$173$	−4.92009	−	8.52184i	−0.374067	−	0.647904i	−0.990187	+	0.139749i	$0.955370\pi$
$174$	−16.6283	+	1.39950i	−1.26059	+	0.106096i
$175$	0.0389983	−	0.0675470i	0.00294799	−	0.00510607i
$176$	0.751577	−	1.30177i	0.0566523	−	0.0981246i
$177$	0.0825980	−	0.00695176i	0.00620844	−	0.000522527i
$178$	−11.6523	−	20.1824i	−0.873380	−	1.51274i
$179$	13.5026			1.00923			0.504614	−	0.863345i	$-0.331635\pi$
$179$	13.5026			1.00923			0.504614	+	0.863345i	$0.331635\pi$
$180$	−10.4690	+	1.77479i	−0.780313	+	0.132285i
$181$	−2.07776			−0.154439			−0.0772194	−	0.997014i	$-0.524604\pi$
$181$	−2.07776			−0.154439			−0.0772194	+	0.997014i	$0.524604\pi$
$182$	−0.0917866	−	0.158979i	−0.00680367	−	0.0117843i
$183$	3.37016	−	7.16549i	0.249129	−	0.529689i
$184$	−13.2616	+	22.9697i	−0.977657	+	1.69335i
$185$	2.59141	−	4.48846i	0.190525	−	0.329998i
$186$	16.2498	+	23.3709i	1.19149	+	1.71364i
$187$	−1.56492	−	2.71052i	−0.114438	−	0.198213i
$188$	−34.0432			−2.48286
$189$	−0.283726	−	0.289401i	−0.0206380	−	0.0210508i
$190$	−3.15108			−0.228603
$191$	−5.25502	−	9.10197i	−0.380240	−	0.658595i	0.610856	−	0.791742i	$-0.290825\pi$
$191$	−5.25502	−	9.10197i	−0.380240	−	0.658595i	−0.991096	+	0.133146i	$0.957492\pi$
$192$	−11.7935	−	16.9618i	−0.851124	−	1.22411i
$193$	9.16311	−	15.8710i	0.659575	−	1.14242i	−0.321151	−	0.947028i	$-0.604070\pi$
$193$	9.16311	−	15.8710i	0.659575	−	1.14242i	0.980726	−	0.195389i	$-0.0625970\pi$
$194$	10.9028	−	18.8842i	0.782776	−	1.35581i
$195$	−0.737173	+	1.56735i	−0.0527901	+	0.112240i
$196$	12.3773	+	21.4382i	0.884095	+	1.53130i
$197$	−7.66870			−0.546372			−0.273186	−	0.961961i	$-0.588077\pi$
$197$	−7.66870			−0.546372			−0.273186	+	0.961961i	$0.588077\pi$
$198$	−4.67161	−	5.64263i	−0.331997	−	0.401004i
$199$	16.8297			1.19302			0.596512	−	0.802604i	$-0.296553\pi$
$199$	16.8297			1.19302			0.596512	+	0.802604i	$0.296553\pi$
$200$	1.81164	+	3.13785i	0.128102	+	0.221879i
$201$	−14.4641	+	1.21735i	−1.02022	+	0.0858653i
$202$	6.39040	−	11.0685i	0.449627	−	0.778777i
$203$	−0.159636	+	0.276498i	−0.0112043	+	0.0194064i
$204$	18.4290	−	1.55106i	1.29029	−	0.108596i
$205$	−1.65670	−	2.86949i	−0.115709	−	0.200414i
$206$	−30.7643			−2.14345
$207$	14.0047	+	16.9157i	0.973394	+	1.17572i
$208$	1.44884			0.100459
$209$	−0.694511	−	1.20293i	−0.0480403	−	0.0832083i
$210$	−0.135325	+	0.287723i	−0.00933833	+	0.0198548i
$211$	0.816583	−	1.41436i	0.0562159	−	0.0973688i	−0.836548	−	0.547894i	$-0.815430\pi$
$211$	0.816583	−	1.41436i	0.0562159	−	0.0973688i	0.892764	+	0.450525i	$0.148763\pi$
$212$	−19.4631	+	33.7111i	−1.33673	+	2.31529i
$213$	2.28500	+	3.28636i	0.156566	+	0.225177i
$214$	19.4251	+	33.6453i	1.32787	+	2.29995i
$215$	−5.35402			−0.365141
$216$	18.2329	−	4.69251i	1.24059	−	0.319285i
$217$	0.544619			0.0369712
$218$	−17.9409	−	31.0746i	−1.21511	−	2.10464i
$219$	−2.25471	−	3.24279i	−0.152359	−	0.219127i
$220$	−1.83607	+	3.18017i	−0.123788	+	0.214407i
$221$	1.50837	−	2.61258i	0.101464	−	0.175741i
$222$	−8.99228	+	19.1190i	−0.603523	+	1.28318i
$223$	6.10112	+	10.5675i	0.408561	+	0.707649i	0.994729	−	0.102541i	$-0.0326972\pi$
$223$	6.10112	+	10.5675i	0.408561	+	0.707649i	−0.586167	+	0.810190i	$0.699364\pi$
$224$	−0.299238			−0.0199937
$225$	2.95780	−	0.501431i	0.197187	−	0.0334288i
$226$	24.5359			1.63210
$227$	−4.50193	−	7.79757i	−0.298803	−	0.517543i	0.677059	−	0.735929i	$-0.263254\pi$
$227$	−4.50193	−	7.79757i	−0.298803	−	0.517543i	−0.975862	+	0.218386i	$0.929921\pi$
$228$	8.17881	−	0.688360i	0.541655	−	0.0455878i
$229$	11.8467	−	20.5191i	0.782852	−	1.35594i	−0.147422	−	0.989074i	$-0.547098\pi$
$229$	11.8467	−	20.5191i	0.782852	−	1.35594i	0.930274	−	0.366865i	$-0.119569\pi$
$230$	8.61446	−	14.9207i	0.568021	−	0.983841i
$231$	−0.139665	+	0.0117547i	−0.00918927	+	0.000773404i
$232$	−7.41579	−	12.8445i	−0.486870	−	0.843284i
$233$	25.4172			1.66514			0.832569	−	0.553921i	$-0.186869\pi$
$233$	25.4172			1.66514			0.832569	+	0.553921i	$0.186869\pi$
$234$	2.45869	−	6.61891i	0.160729	−	0.432692i
$235$	9.61821			0.627423
$236$	0.0846931	+	0.146693i	0.00551305	+	0.00954888i
$237$	1.80542	−	3.83861i	0.117275	−	0.249345i
$238$	0.276896	−	0.479599i	0.0179485	−	0.0310878i
$239$	0.142609	−	0.247006i	0.00922462	−	0.0159775i	−0.861376	−	0.507967i	$-0.830397\pi$
$239$	0.142609	−	0.247006i	0.00922462	−	0.0159775i	0.870601	+	0.491990i	$0.163730\pi$
$240$	−1.43258	−	2.06037i	−0.0924724	−	0.132996i
$241$	5.80005	+	10.0460i	0.373614	+	0.647118i	0.990119	−	0.140233i	$-0.0447852\pi$
$241$	5.80005	+	10.0460i	0.373614	+	0.647118i	−0.616505	+	0.787351i	$0.711452\pi$
$242$	23.3563			1.50140
$243$	1.61470	−	15.5046i	0.103583	−	0.994621i
$244$	16.1815			1.03591
$245$	−3.49696	−	6.05691i	−0.223412	−	0.386962i
$246$	7.71091	+	11.0900i	0.491629	+	0.707075i
$247$	0.669415	−	1.15946i	0.0425939	−	0.0737747i
$248$	−12.6499	+	21.9103i	−0.803272	+	1.39131i
$249$	−1.33948	+	2.84796i	−0.0848864	+	0.180482i
$250$	−1.17680	−	2.03828i	−0.0744275	−	0.128912i
$251$	−22.4343			−1.41604			−0.708019	−	0.706193i	$-0.750411\pi$
$251$	−22.4343			−1.41604			−0.708019	+	0.706193i	$0.750411\pi$
$252$	0.288391	−	0.776363i	0.0181669	−	0.0489063i
$253$	7.59465			0.477472
$254$	−17.5643	−	30.4223i	−1.10208	−	1.90887i
$255$	−5.20674	+	0.438220i	−0.326059	+	0.0274424i
$256$	12.0785	−	20.9206i	0.754908	−	1.30754i
$257$	−0.959804	+	1.66243i	−0.0598709	+	0.103700i	−0.894407	−	0.447253i	$-0.852402\pi$
$257$	−0.959804	+	1.66243i	−0.0598709	+	0.103700i	0.834536	+	0.550953i	$0.185736\pi$
$258$	21.7491	−	1.83049i	1.35404	−	0.113961i
$259$	0.202121	+	0.350085i	0.0125592	+	0.0217532i
$260$	−3.53946			−0.219508
$261$	−12.1075	+	2.05257i	−0.749436	+	0.127051i
$262$	−30.1580			−1.86317
$263$	12.4110	+	21.4965i	0.765295	+	1.32553i	0.940090	+	0.340925i	$0.110740\pi$
$263$	12.4110	+	21.4965i	0.765295	+	1.32553i	−0.174795	+	0.984605i	$0.555926\pi$
$264$	2.77111	−	5.89182i	0.170550	−	0.362616i
$265$	5.49890	−	9.52438i	0.337795	−	0.585078i
$266$	0.122887	−	0.212846i	0.00753466	−	0.0130504i
$267$	−9.79055	−	14.0810i	−0.599172	−	0.861746i
$268$	−14.8310	−	25.6880i	−0.905944	−	1.56914i
$269$	10.3259			0.629584			0.314792	−	0.949161i	$-0.398065\pi$
$269$	10.3259			0.629584			0.314792	+	0.949161i	$0.398065\pi$
$270$	−11.8437	+	3.04816i	−0.720787	+	0.185505i
$271$	−28.5144			−1.73213			−0.866065	−	0.499932i	$-0.833358\pi$
$271$	−28.5144			−1.73213			−0.866065	+	0.499932i	$0.833358\pi$
$272$	2.18539	+	3.78520i	0.132509	+	0.229511i
$273$	−0.0771211	−	0.110918i	−0.00466758	−	0.00671304i
$274$	−15.6521	+	27.1102i	−0.945577	+	1.63779i
$275$	0.518744	−	0.898492i	0.0312815	−	0.0541811i
$276$	−19.0999	+	40.6094i	−1.14968	+	2.44440i
$277$	−9.57360	−	16.5820i	−0.575222	−	0.996314i	−0.996017	−	0.0891583i	$-0.971582\pi$
$277$	−9.57360	−	16.5820i	−0.575222	−	0.996314i	0.420795	−	0.907156i	$-0.361751\pi$
$278$	−10.5866			−0.634943
$279$	13.3588	+	16.1355i	0.799769	+	0.966006i
$280$	−0.282603			−0.0168888
$281$	−6.20045	−	10.7395i	−0.369888	−	0.640664i	0.619660	−	0.784870i	$-0.287271\pi$
$281$	−6.20045	−	10.7395i	−0.369888	−	0.640664i	−0.989548	+	0.144206i	$0.953937\pi$
$282$	−39.0711	+	3.28837i	−2.32665	+	0.195820i
$283$	−11.5577	+	20.0185i	−0.687032	+	1.18997i	0.285762	+	0.958301i	$0.407753\pi$
$283$	−11.5577	+	20.0185i	−0.687032	+	1.18997i	−0.972794	+	0.231673i	$0.925580\pi$
$284$	−4.08974	+	7.08364i	−0.242682	+	0.420337i
$285$	−2.31075	+	0.194482i	−0.136877	+	0.0115201i
$286$	−1.22092	−	2.11469i	−0.0721945	−	0.125045i
$287$	0.258434			0.0152549
$288$	−7.33990	−	8.86555i	−0.432508	−	0.522407i
$289$	−7.89927			−0.464663
$290$	4.81715	+	8.34355i	0.282873	+	0.489950i
$291$	6.82974	−	14.5211i	0.400366	−	0.851242i
$292$	4.03552	−	6.98973i	0.236161	−	0.409043i
$293$	−9.84737	+	17.0562i	−0.575290	+	0.996431i	0.420720	+	0.907190i	$0.361777\pi$
$293$	−9.84737	+	17.0562i	−0.575290	+	0.996431i	−0.996010	+	0.0892407i	$0.971556\pi$
$294$	16.2761	+	23.4088i	0.949244	+	1.36523i
$295$	−0.0239283	−	0.0414450i	−0.00139316	−	0.00241302i
$296$	−18.7788			−1.09150
$297$	−3.77405	−	3.84953i	−0.218992	−	0.223373i
$298$	−3.91092			−0.226553
$299$	3.66011	+	6.33950i	0.211670	+	0.366623i
$300$	3.49973	+	5.03340i	0.202057	+	0.290604i
$301$	0.208798	−	0.361648i	0.0120349	−	0.0208450i
$302$	21.8227	−	37.7980i	1.25575	−	2.17503i
$303$	4.00308	−	8.51118i	0.229971	−	0.488955i
$304$	0.969875	+	1.67987i	0.0556261	+	0.0963473i
$305$	−4.57173			−0.261777
$306$	21.0010	−	3.56027i	1.20055	−	0.203527i
$307$	−26.9891			−1.54035			−0.770175	−	0.637833i	$-0.779831\pi$
$307$	−26.9891			−1.54035			−0.770175	+	0.637833i	$0.779831\pi$
$308$	−0.143207	−	0.248043i	−0.00816000	−	0.0141335i
$309$	−22.5601	+	1.89875i	−1.28340	+	0.108016i
$310$	8.21714	−	14.2325i	0.466702	−	0.808352i
$311$	10.0010	−	17.3223i	0.567106	−	0.982256i	−0.429745	−	0.902950i	$-0.641396\pi$
$311$	10.0010	−	17.3223i	0.567106	−	0.982256i	0.996850	−	0.0793053i	$-0.0252702\pi$
$312$	6.25358	−	0.526326i	0.354039	−	0.0297973i
$313$	−10.7728	−	18.6590i	−0.608915	−	1.05467i	−0.991420	−	0.130718i	$-0.958272\pi$
$313$	−10.7728	−	18.6590i	−0.608915	−	1.05467i	0.382505	−	0.923954i	$-0.375062\pi$
$314$	−24.9591			−1.40852
$315$	−0.0814789	+	0.219345i	−0.00459081	+	0.0123587i
$316$	8.66854			0.487643
$317$	−8.10937	−	14.0458i	−0.455468	−	0.788893i	0.543247	−	0.839573i	$-0.317195\pi$
$317$	−8.10937	−	14.0458i	−0.455468	−	0.788893i	−0.998715	+	0.0506795i	$0.983861\pi$
$318$	−19.0814	+	40.5700i	−1.07003	+	2.27505i
$319$	−2.12344	+	3.67791i	−0.118890	+	0.205923i
$320$	−5.96370	+	10.3294i	−0.333381	+	0.577433i
$321$	16.3214	+	23.4739i	0.910973	+	1.31019i
$322$	0.671898	+	1.16376i	0.0374434	+	0.0648539i
$323$	4.03891			0.224731
$324$	30.0752	−	10.4990i	1.67085	−	0.583276i
$325$	1.00000			0.0554700
$326$	2.48017	+	4.29577i	0.137364	+	0.237921i
$327$	−15.0744	−	21.6804i	−0.833614	−	1.19893i
$328$	−6.00268	+	10.3969i	−0.331443	+	0.574075i
$329$	−0.375094	+	0.649681i	−0.0206796	+	0.0358181i
$330$	−1.80006	+	3.82721i	−0.0990900	+	0.210681i
$331$	−2.48536	−	4.30476i	−0.136607	−	0.236611i	0.789603	−	0.613618i	$-0.210287\pi$
$331$	−2.48536	−	4.30476i	−0.136607	−	0.236611i	−0.926210	+	0.377007i	$0.876953\pi$
$332$	−6.43139			−0.352968
$333$	−5.41422	+	14.5754i	−0.296698	+	0.798726i
$334$	−15.0824			−0.825272
$335$	4.19018	+	7.25760i	0.228934	+	0.396525i
$336$	0.195040	−	0.0164153i	0.0106403	−	0.000895529i
$337$	12.7558	−	22.0937i	0.694853	−	1.20352i	−0.275378	−	0.961336i	$-0.588803\pi$
$337$	12.7558	−	22.0937i	0.694853	−	1.20352i	0.970230	−	0.242184i	$-0.0778637\pi$
$338$	1.17680	−	2.03828i	0.0640096	−	0.110868i
$339$	17.9927	−	1.51433i	0.977229	−	0.0822474i
$340$	−5.33881	−	9.24710i	−0.289538	−	0.501494i
$341$	7.24437			0.392305
$342$	9.32025	−	1.58005i	0.503981	−	0.0854393i
$343$	1.09148			0.0589343
$344$	9.69953	+	16.8001i	0.522964	+	0.905800i
$345$	5.39628	−	11.4733i	0.290526	−	0.617703i
$346$	11.5799	−	20.0571i	0.622542	−	1.07827i
$347$	−8.09828	+	14.0266i	−0.434738	+	0.752989i	−0.997274	−	0.0737840i	$-0.976492\pi$
$347$	−8.09828	+	14.0266i	−0.434738	+	0.752989i	0.562536	+	0.826773i	$0.309826\pi$
$348$	−14.3259	−	20.6038i	−0.767947	−	1.10448i
$349$	−7.82529	−	13.5538i	−0.418878	−	0.725518i	0.576949	−	0.816780i	$-0.304243\pi$
$349$	−7.82529	−	13.5538i	−0.418878	−	0.725518i	−0.995827	+	0.0912622i	$0.970910\pi$
$350$	0.183573			0.00981240
$351$	1.39449	−	5.00554i	0.0744325	−	0.267176i
$352$	−3.98038			−0.212155
$353$	−5.74531	−	9.95118i	−0.305792	−	0.529648i	0.671645	−	0.740873i	$-0.265588\pi$
$353$	−5.74531	−	9.95118i	−0.305792	−	0.529648i	−0.977437	+	0.211225i	$0.932255\pi$
$354$	0.111371	+	0.160177i	0.00591931	+	0.00851331i
$355$	1.15547	−	2.00134i	0.0613261	−	0.106220i
$356$	17.5233	−	30.3513i	0.928733	−	1.60861i
$357$	0.173454	−	0.368790i	0.00918014	−	0.0195184i
$358$	15.8898	+	27.5220i	0.839805	+	1.45458i
$359$	−29.3245			−1.54769			−0.773844	−	0.633376i	$-0.781669\pi$
$359$	−29.3245			−1.54769			−0.773844	+	0.633376i	$0.781669\pi$
$360$	−6.93187	−	8.37270i	−0.365341	−	0.441280i
$361$	−17.2075			−0.905660
$362$	−2.44512	−	4.23506i	−0.128512	−	0.222590i
$363$	17.1277	−	1.44153i	0.898969	−	0.0756607i
$364$	0.138033	−	0.239080i	0.00723488	−	0.0125312i
$365$	−1.14015	+	1.97480i	−0.0596784	+	0.103366i
$366$	18.5713	−	1.56303i	0.970738	−	0.0817010i
$367$	−1.68166	−	2.91272i	−0.0877820	−	0.152043i	0.818791	−	0.574091i	$-0.194645\pi$
$367$	−1.68166	−	2.91272i	−0.0877820	−	0.152043i	−0.906573	+	0.422048i	$0.861311\pi$
$368$	−10.6058			−0.552867
$369$	6.33904	+	7.65665i	0.329997	+	0.398589i
$370$	12.1983			0.634161
$371$	0.428896	+	0.742869i	0.0222672	+	0.0385678i
$372$	−18.2190	+	38.7364i	−0.944609	+	2.00839i
$373$	−3.93890	+	6.82238i	−0.203949	+	0.353249i	−0.949797	−	0.312866i	$-0.898711\pi$
$373$	−3.93890	+	6.82238i	−0.203949	+	0.353249i	0.745849	+	0.666115i	$0.232044\pi$
$374$	3.68320	−	6.37949i	0.190454	−	0.329876i
$375$	−0.988775	−	1.42208i	−0.0510601	−	0.0734361i
$376$	−17.4247	−	30.1805i	−0.898610	−	1.55644i
$377$	−4.09342			−0.210822
$378$	0.255991	−	0.918882i	0.0131668	−	0.0472622i
$379$	15.4148			0.791805			0.395903	−	0.918293i	$-0.370432\pi$
$379$	15.4148			0.791805			0.395903	+	0.918293i	$0.370432\pi$
$380$	−2.36937	−	4.10386i	−0.121546	−	0.210524i
$381$	−14.7579	−	21.2253i	−0.756072	−	1.08740i
$382$	12.3683	−	21.4224i	0.632815	−	1.09607i
$383$	−17.1158	+	29.6454i	−0.874575	+	1.51481i	−0.0173604	+	0.999849i	$0.505526\pi$
$383$	−17.1158	+	29.6454i	−0.874575	+	1.51481i	−0.857215	+	0.514959i	$0.827807\pi$
$384$	15.0378	−	31.9728i	0.767395	−	1.63160i
$385$	0.0404603	+	0.0700793i	0.00206205	+	0.00357157i
$386$	43.1327			2.19539
$387$	15.8361	−	2.68467i	0.804994	−	0.136470i
$388$	32.7922			1.66477
$389$	14.1998	+	24.5948i	0.719959	+	1.24701i	0.961016	+	0.276494i	$0.0891727\pi$
$389$	14.1998	+	24.5948i	0.719959	+	1.24701i	−0.241057	+	0.970511i	$0.577494\pi$
$390$	−4.06220	+	0.341891i	−0.205698	+	0.0173123i
$391$	−11.0416	+	19.1246i	−0.558399	+	0.967175i
$392$	−12.6704	+	21.9458i	−0.639953	+	1.10843i
$393$	−22.1155	+	1.86133i	−1.11558	+	0.0938916i
$394$	−9.02455	−	15.6310i	−0.454650	−	0.787477i
$395$	−2.44912			−0.123228
$396$	3.83610	−	10.3270i	0.192771	−	0.518950i
$397$	−29.4099			−1.47604			−0.738021	−	0.674778i	$-0.764239\pi$
$397$	−29.4099			−1.47604			−0.738021	+	0.674778i	$0.764239\pi$
$398$	19.8052	+	34.3036i	0.992745	+	1.71949i
$399$	0.0769787	−	0.163669i	0.00385376	−	0.00819369i
$400$	−0.724419	+	1.25473i	−0.0362210	+	0.0627366i
$401$	−16.4045	+	28.4134i	−0.819201	+	1.41890i	0.0870705	+	0.996202i	$0.472249\pi$
$401$	−16.4045	+	28.4134i	−0.819201	+	1.41890i	−0.906272	+	0.422696i	$0.861084\pi$
$402$	−19.5026	−	28.0493i	−0.972704	−	1.39897i
$403$	3.49130	+	6.04711i	0.173914	+	0.301228i
$404$	19.2204			0.956248
$405$	−8.49713	+	2.96626i	−0.422226	+	0.147395i
$406$	−0.751442			−0.0372935
$407$	2.68856	+	4.65673i	0.133267	+	0.230825i
$408$	10.8078	+	15.5441i	0.535065	+	0.769546i
$409$	−7.24656	+	12.5514i	−0.358320	+	0.620628i	−0.987680	−	0.156486i	$-0.949984\pi$
$409$	−7.24656	+	12.5514i	−0.358320	+	0.620628i	0.629361	+	0.777113i	$0.283317\pi$
$410$	3.89922	−	6.75365i	0.192569	−	0.333539i
$411$	−9.80479	+	20.8465i	−0.483635	+	1.02828i
$412$	−23.1324	−	40.0664i	−1.13965	−	1.97393i
$413$	0.00373265			0.000183672
$414$	−17.9981	+	48.4519i	−0.884560	+	2.38128i
$415$	1.81706			0.0891957
$416$	−1.91828	−	3.32255i	−0.0940512	−	0.162901i
$417$	−7.76339	+	0.653397i	−0.380175	+	0.0319970i
$418$	1.63460	−	2.83122i	0.0799511	−	0.138479i
$419$	6.35956	−	11.0151i	0.310685	−	0.538122i	−0.667826	−	0.744318i	$-0.732775\pi$
$419$	6.35956	−	11.0151i	0.310685	−	0.538122i	0.978511	+	0.206195i	$0.0661083\pi$
$420$	−0.476475	+	0.0401020i	−0.0232496	+	0.00195678i
$421$	5.37790	+	9.31479i	0.262103	+	0.453975i	0.966800	−	0.255532i	$-0.0822507\pi$
$421$	5.37790	+	9.31479i	0.262103	+	0.453975i	−0.704698	+	0.709508i	$0.748917\pi$
$422$	3.84383			0.187115
$423$	−28.4487	+	4.82287i	−1.38322	+	0.234496i
$424$	−39.8481			−1.93519
$425$	1.50837	+	2.61258i	0.0731667	+	0.126729i
$426$	−4.00952	+	8.52488i	−0.194262	+	0.413032i
$427$	0.178290	−	0.308807i	0.00862805	−	0.0149442i
$428$	−29.2124	+	50.5973i	−1.41203	+	2.44571i
$429$	−1.02584	−	1.47540i	−0.0495282	−	0.0712328i
$430$	−6.30062	−	10.9130i	−0.303843	−	0.526271i
$431$	33.6881			1.62270			0.811351	−	0.584560i	$-0.198733\pi$
$431$	33.6881			1.62270			0.811351	+	0.584560i	$0.198733\pi$
$432$	5.27040	+	5.37582i	0.253572	+	0.258644i
$433$	40.2183			1.93277			0.966384	−	0.257104i	$-0.0827683\pi$
$433$	40.2183			1.93277			0.966384	+	0.257104i	$0.0827683\pi$
$434$	0.640909	+	1.11009i	0.0307646	+	0.0532859i
$435$	4.04747	+	5.82119i	0.194062	+	0.279105i
$436$	26.9804	−	46.7314i	1.29213	−	2.23803i
$437$	−4.90027	+	8.48752i	−0.234412	+	0.406013i
$438$	3.95637	−	8.41186i	0.189042	−	0.401934i
$439$	−9.07679	−	15.7215i	−0.433212	−	0.750345i	0.563936	−	0.825818i	$-0.309286\pi$
$439$	−9.07679	−	15.7215i	−0.433212	−	0.750345i	−0.997148	+	0.0754738i	$0.975953\pi$
$440$	−3.75910			−0.179208
$441$	13.3804	+	16.1616i	0.637163	+	0.769601i
$442$	7.10022			0.337723
$443$	−4.30495	−	7.45640i	−0.204534	−	0.354264i	0.745450	−	0.666562i	$-0.232235\pi$
$443$	−4.30495	−	7.45640i	−0.204534	−	0.354264i	−0.949984	+	0.312298i	$0.898901\pi$
$444$	−31.6615	+	2.66475i	−1.50259	+	0.126464i
$445$	−4.95085	+	8.57512i	−0.234693	+	0.406500i
$446$	−14.3596	+	24.8716i	−0.679948	+	1.17771i
$447$	−2.86796	+	0.241378i	−0.135650	+	0.0114168i
$448$	−0.465148	−	0.805660i	−0.0219762	−	0.0380639i
$449$	−38.0939			−1.79776			−0.898881	−	0.438192i	$-0.855619\pi$
$449$	−38.0939			−1.79776			−0.898881	+	0.438192i	$0.855619\pi$
$450$	4.50280	+	5.43874i	0.212264	+	0.256385i
$451$	3.43762			0.161871
$452$	18.4491	+	31.9548i	0.867772	+	1.50303i
$453$	13.6702	−	29.0649i	0.642281	−	1.36559i
$454$	10.5958	−	18.3524i	0.497284	−	0.861320i
$455$	−0.0389983	+	0.0675470i	−0.00182827	+	0.00316665i
$456$	4.79650	+	6.89845i	0.224617	+	0.323050i
$457$	14.7544	+	25.5554i	0.690182	+	1.19543i	0.971778	+	0.235898i	$0.0758030\pi$
$457$	14.7544	+	25.5554i	0.690182	+	1.19543i	−0.281596	+	0.959533i	$0.590864\pi$
$458$	55.7649			2.60572
$459$	15.1808	−	3.90699i	0.708577	−	0.182363i
$460$	25.9096			1.20804
$461$	−16.7495	−	29.0111i	−0.780104	−	1.35118i	−0.931881	−	0.362765i	$-0.881833\pi$
$461$	−16.7495	−	29.0111i	−0.780104	−	1.35118i	0.151777	−	0.988415i	$-0.451501\pi$
$462$	−0.188317	−	0.270843i	−0.00876131	−	0.0126008i
$463$	−5.51218	+	9.54738i	−0.256173	+	0.443704i	−0.965213	−	0.261463i	$-0.915795\pi$
$463$	−5.51218	+	9.54738i	−0.256173	+	0.443704i	0.709041	+	0.705168i	$0.249128\pi$
$464$	2.96535	−	5.13614i	0.137663	−	0.238439i
$465$	5.14739	−	10.9442i	0.238704	−	0.507523i
$466$	29.9111	+	51.8075i	1.38560	+	2.39994i
$467$	23.9869			1.10998			0.554990	−	0.831857i	$-0.312722\pi$
$467$	23.9869			1.10998			0.554990	+	0.831857i	$0.312722\pi$
$468$	10.4690	−	1.77479i	0.483929	−	0.0820399i
$469$	−0.653639			−0.0301822
$470$	11.3187	+	19.6046i	0.522094	+	0.904294i
$471$	−18.3030	+	1.54045i	−0.843359	+	0.0709804i
$472$	−0.0866987	+	0.150166i	−0.00399063	+	0.00691197i
$473$	2.77737	−	4.81054i	0.127703	−	0.221189i
$474$	9.94880	−	0.837329i	0.456963	−	0.0384598i
$475$	0.669415	+	1.15946i	0.0307149	+	0.0531997i
$476$	0.832818			0.0381722
$477$	−11.4888	+	30.9285i	−0.526037	+	1.41612i
$478$	0.671291			0.0307041
$479$	14.7875	+	25.6128i	0.675660	+	1.17028i	0.976275	+	0.216532i	$0.0694747\pi$
$479$	14.7875	+	25.6128i	0.675660	+	1.17028i	−0.300615	+	0.953746i	$0.597192\pi$
$480$	−2.82820	+	6.01320i	−0.129089	+	0.274464i
$481$	−2.59141	+	4.48846i	−0.118158	+	0.204656i
$482$	−13.6510	+	23.6443i	−0.621787	+	1.07697i
$483$	0.564544	+	0.811943i	0.0256876	+	0.0369447i
$484$	17.5621	+	30.4185i	0.798277	+	1.38266i
$485$	−9.26477			−0.420692
$486$	33.5029	−	14.9547i	1.51972	−	0.678357i
$487$	8.53551			0.386781			0.193390	−	0.981122i	$-0.438052\pi$
$487$	8.53551			0.386781			0.193390	+	0.981122i	$0.438052\pi$
$488$	8.28232	+	14.3454i	0.374923	+	0.649386i
$489$	2.08389	+	2.99711i	0.0942367	+	0.135534i
$490$	8.23046	−	14.2556i	0.371814	−	0.644001i
$491$	−3.15511	+	5.46481i	−0.142388	+	0.246623i	−0.928395	−	0.371594i	$-0.878811\pi$
$491$	−3.15511	+	5.46481i	−0.142388	+	0.246623i	0.786007	+	0.618217i	$0.212145\pi$
$492$	−8.64531	+	18.3813i	−0.389761	+	0.828692i
$493$	−6.17440	−	10.6944i	−0.278081	−	0.481650i
$494$	3.15108			0.141774
$495$	−1.08381	+	2.91767i	−0.0487136	+	0.131140i
$496$	−10.1167			−0.454252
$497$	0.0901229	+	0.156097i	0.00404256	+	0.00700192i
$498$	−7.38124	+	0.621234i	−0.330761	+	0.0278382i
$499$	−0.925459	+	1.60294i	−0.0414293	+	0.0717576i	−0.885996	−	0.463692i	$-0.846524\pi$
$499$	−0.925459	+	1.60294i	−0.0414293	+	0.0717576i	0.844567	+	0.535450i	$0.179858\pi$
$500$	1.76973	−	3.06526i	0.0791447	−	0.137083i
$501$	−11.0602	+	0.930872i	−0.494135	+	0.0415883i
$502$	−26.4007	−	45.7273i	−1.17832	−	2.04091i
$503$	43.5312			1.94096			0.970480	−	0.241181i	$-0.0775346\pi$
$503$	43.5312			1.94096			0.970480	+	0.241181i	$0.0775346\pi$
$504$	0.835882	−	0.141706i	0.0372331	−	0.00631208i
$505$	−5.43031			−0.241646
$506$	8.93741	+	15.4800i	0.397316	+	0.688172i
$507$	0.737173	−	1.56735i	0.0327390	−	0.0696083i
$508$	26.4140	−	45.7505i	1.17193	−	2.02985i
$509$	−13.7438	+	23.8049i	−0.609181	+	1.05513i	0.382194	+	0.924082i	$0.375169\pi$
$509$	−13.7438	+	23.8049i	−0.609181	+	1.05513i	−0.991376	+	0.131051i	$0.958165\pi$
$510$	−7.02052	−	10.0971i	−0.310874	−	0.447108i
$511$	−0.0889281	−	0.154028i	−0.00393395	−	0.00681379i
$512$	16.0576			0.709653
$513$	6.73722	−	1.73392i	0.297455	−	0.0765545i
$514$	−4.51800			−0.199280
$515$	6.53557	+	11.3199i	0.287992	+	0.498816i
$516$	18.7376	+	26.9489i	0.824877	+	1.18636i
$517$	−4.98939	+	8.64188i	−0.219433	+	0.380069i
$518$	−0.475714	+	0.823961i	−0.0209017	+	0.0362028i
$519$	7.25391	−	15.4230i	0.318412	−	0.676993i
$520$	−1.81164	−	3.13785i	−0.0794455	−	0.137604i
$521$	24.5536			1.07571			0.537857	−	0.843036i	$-0.319234\pi$
$521$	24.5536			1.07571			0.537857	+	0.843036i	$0.319234\pi$
$522$	−18.4319	−	22.2631i	−0.806741	−	0.974427i
$523$	41.0287			1.79406			0.897030	−	0.441970i	$-0.145720\pi$
$523$	41.0287			1.79406			0.897030	+	0.441970i	$0.145720\pi$
$524$	−22.6765	−	39.2769i	−0.990628	−	1.71582i
$525$	0.134618	−	0.0113300i	0.00587522	−	0.000494481i
$526$	−29.2106	+	50.5942i	−1.27364	+	2.20601i
$527$	−10.5324	+	18.2426i	−0.458797	+	0.794659i
$528$	2.59437	−	0.218352i	0.112905	−	0.00950255i
$529$	−15.2929	−	26.4880i	−0.664907	−	1.15165i
$530$	25.8845			1.12435
$531$	0.0915568	+	0.110588i	0.00397323	+	0.00479909i
$532$	0.369605			0.0160244
$533$	1.65670	+	2.86949i	0.0717597	+	0.124291i
$534$	17.1796	−	36.5265i	0.743433	−	1.58066i
$535$	8.25335	−	14.2952i	0.356823	−	0.618036i
$536$	15.1822	−	26.2963i	0.655769	−	1.13583i
$537$	13.3510	+	19.2018i	0.576138	+	0.828618i
$538$	12.1516	+	21.0472i	0.523892	+	0.907408i
$539$	7.25611			0.312543
$540$	−12.8754	−	13.1329i	−0.554069	−	0.565151i
$541$	−14.2877			−0.614278			−0.307139	−	0.951665i	$-0.599372\pi$
$541$	−14.2877			−0.614278			−0.307139	+	0.951665i	$0.599372\pi$
$542$	−33.5559	−	58.1205i	−1.44135	−	2.49649i
$543$	−2.05444	−	2.95475i	−0.0881645	−	0.126801i
$544$	5.78694	−	10.0233i	0.248113	−	0.429744i
$545$	−7.62274	+	13.2030i	−0.326522	+	0.565553i
$546$	0.135325	−	0.287723i	0.00579138	−	0.0123134i
$547$	13.4851	+	23.3568i	0.576580	+	0.998667i	0.995868	+	0.0908132i	$0.0289466\pi$
$547$	13.4851	+	23.3568i	0.576580	+	0.998667i	−0.419287	+	0.907854i	$0.637720\pi$
$548$	−47.0766			−2.01101
$549$	13.5223	−	2.29241i	0.577116	−	0.0978377i
$550$	2.44184			0.104120
$551$	−2.74020	−	4.74616i	−0.116736	−	0.202193i
$552$	−45.7776	+	3.85282i	−1.94843	+	0.163987i
$553$	0.0955113	−	0.165430i	0.00406155	−	0.00703482i
$554$	22.5325	−	39.0274i	0.957313	−	1.65812i
$555$	8.94530	−	0.752871i	0.379707	−	0.0319576i
$556$	−7.96031	−	13.7877i	−0.337592	−	0.584727i
$557$	27.5795			1.16858			0.584290	−	0.811545i	$-0.301373\pi$
$557$	27.5795			1.16858			0.584290	+	0.811545i	$0.301373\pi$
$558$	−17.1680	+	46.2172i	−0.726780	+	1.95653i
$559$	5.35402			0.226451
$560$	−0.0565022	−	0.0978647i	−0.00238766	−	0.00413554i
$561$	2.30723	−	4.90554i	0.0974114	−	0.207112i
$562$	14.5934	−	25.2765i	0.615586	−	1.06623i
$563$	−2.92366	+	5.06393i	−0.123218	+	0.213419i	−0.921035	−	0.389480i	$-0.872655\pi$
$563$	−2.92366	+	5.06393i	−0.123218	+	0.213419i	0.797817	+	0.602899i	$0.205988\pi$
$564$	−33.6611	−	48.4123i	−1.41739	−	2.03853i
$565$	−5.21241	−	9.02815i	−0.219288	−	0.379817i
$566$	−54.4043			−2.28679
$567$	0.131011	−	0.689635i	0.00550196	−	0.0289620i
$568$	−8.37318			−0.351331
$569$	−13.5782	−	23.5181i	−0.569228	−	0.985931i	−0.996643	−	0.0818755i	$-0.973909\pi$
$569$	−13.5782	−	23.5181i	−0.569228	−	0.985931i	0.427415	−	0.904056i	$-0.359424\pi$
$570$	−3.11571	−	4.48110i	−0.130503	−	0.187693i
$571$	7.58773	−	13.1423i	0.317537	−	0.549990i	−0.662437	−	0.749118i	$-0.730478\pi$
$571$	7.58773	−	13.1423i	0.317537	−	0.549990i	0.979973	+	0.199128i	$0.0638110\pi$
$572$	1.83607	−	3.18017i	0.0767701	−	0.132970i
$573$	7.74773	−	16.4729i	0.323666	−	0.688165i
$574$	0.304126	+	0.526761i	0.0126940	+	0.0219866i
$575$	−7.32023			−0.305275
$576$	12.4599	−	33.5428i	0.519163	−	1.39761i
$577$	9.39043			0.390929			0.195464	−	0.980711i	$-0.437379\pi$
$577$	9.39043			0.390929			0.195464	+	0.980711i	$0.437379\pi$
$578$	−9.29588	−	16.1009i	−0.386657	−	0.669710i
$579$	31.6301	−	2.66211i	1.31450	−	0.110634i
$580$	−7.24424	+	12.5474i	−0.300801	+	0.521002i
$581$	−0.0708621	+	0.122737i	−0.00293985	+	0.00509198i
$582$	37.6354	−	3.16754i	1.56004	−	0.131299i
$583$	5.70505	+	9.88144i	0.236279	+	0.409247i
$584$	8.26217			0.341891
$585$	−2.95780	+	0.501431i	−0.122290	+	0.0207316i
$586$	−46.3537			−1.91485
$587$	17.1063	+	29.6290i	0.706054	+	1.22292i	0.966310	+	0.257381i	$0.0828596\pi$
$587$	17.1063	+	29.6290i	0.706054	+	1.22292i	−0.260256	+	0.965540i	$0.583807\pi$
$588$	−18.2485	+	38.7991i	−0.752554	+	1.60005i
$589$	−4.67426	+	8.09606i	−0.192600	+	0.333592i
$590$	0.0563177	−	0.0975451i	0.00231856	−	0.00401587i
$591$	−7.58262	−	10.9055i	−0.311907	−	0.448594i
$592$	−3.75454	−	6.50306i	−0.154311	−	0.267274i
$593$	−34.8084			−1.42941			−0.714704	−	0.699427i	$-0.753439\pi$
$593$	−34.8084			−1.42941			−0.714704	+	0.699427i	$0.753439\pi$
$594$	3.40513	−	12.2227i	0.139714	−	0.501504i
$595$	−0.235296			−0.00964618
$596$	−2.94071	−	5.09345i	−0.120456	−	0.208636i
$597$	16.6408	+	23.9332i	0.681061	+	0.979522i
$598$	−8.61446	+	14.9207i	−0.352271	+	0.610152i
$599$	−13.2322	+	22.9189i	−0.540655	+	0.936442i	0.458212	+	0.888843i	$0.348490\pi$
$599$	−13.2322	+	22.9189i	−0.540655	+	0.936442i	−0.998867	+	0.0475987i	$0.984843\pi$
$600$	−2.67098	+	5.67892i	−0.109042	+	0.231841i
$601$	−14.2152	−	24.6215i	−0.579852	−	1.00433i	−0.995496	−	0.0948056i	$-0.969777\pi$
$601$	−14.2152	−	24.6215i	−0.579852	−	1.00433i	0.415644	−	0.909527i	$-0.363556\pi$
$602$	0.982854			0.0400581
$603$	−16.0329	−	19.3654i	−0.652910	−	0.788621i
$604$	65.6358			2.67068
$605$	−4.96181	−	8.59410i	−0.201726	−	0.349400i
$606$	22.0590	−	1.85657i	0.896086	−	0.0754181i
$607$	14.7710	−	25.5842i	0.599537	−	1.03843i	−0.393352	−	0.919388i	$-0.628685\pi$
$607$	14.7710	−	25.5842i	0.599537	−	1.03843i	0.992889	−	0.119041i	$-0.0379819\pi$
$608$	2.56825	−	4.44833i	0.104156	−	0.180404i
$609$	−0.551049	+	0.0463784i	−0.0223296	+	0.00187935i
$610$	−5.38003	−	9.31848i	−0.217831	−	0.377294i
$611$	−9.61821			−0.389111
$612$	20.4279	+	24.6740i	0.825749	+	0.997387i
$613$	34.7033			1.40165			0.700826	−	0.713332i	$-0.252815\pi$
$613$	34.7033			1.40165			0.700826	+	0.713332i	$0.252815\pi$
$614$	−31.7609	−	55.0114i	−1.28176	−	2.22008i
$615$	2.44255	−	5.19325i	0.0984932	−	0.209412i
$616$	0.146599	−	0.253916i	0.00590663	−	0.0102306i
$617$	9.37308	−	16.2346i	0.377346	−	0.653582i	−0.613329	−	0.789827i	$-0.710170\pi$
$617$	9.37308	−	16.2346i	0.377346	−	0.653582i	0.990675	+	0.136245i	$0.0435035\pi$
$618$	−30.4190	−	43.7494i	−1.22363	−	1.75986i
$619$	−15.5917	−	27.0056i	−0.626684	−	1.08545i	−0.988213	−	0.153087i	$-0.951078\pi$
$619$	−15.5917	−	27.0056i	−0.626684	−	1.08545i	0.361529	−	0.932361i	$-0.382255\pi$
$620$	24.7146			0.992563
$621$	−10.2080	+	36.6417i	−0.409633	+	1.47038i
$622$	47.0769			1.88761
$623$	−0.386149	−	0.668830i	−0.0154707	−	0.0267961i
$624$	1.43258	+	2.06037i	0.0573489	+	0.0824808i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	25.3549	−	43.9160i	1.01339	−	1.75524i
$627$	1.02395	−	2.17708i	0.0408926	−	0.0869441i
$628$	−18.7673	−	32.5059i	−0.748897	−	1.29713i
$629$	−15.6353			−0.623418
$630$	−0.542972	+	0.0920493i	−0.0216325	+	0.00366733i
$631$	−8.29360			−0.330163			−0.165082	−	0.986280i	$-0.552789\pi$
$631$	−8.29360			−0.330163			−0.165082	+	0.986280i	$0.552789\pi$
$632$	4.43691	+	7.68495i	0.176491	+	0.305691i
$633$	2.81876	−	0.237238i	0.112036	−	0.00942935i
$634$	19.0863	−	33.0584i	0.758012	−	1.31292i
$635$	−7.46274	+	12.9258i	−0.296150	+	0.512946i
$636$	−67.1847	+	5.65453i	−2.66405	+	0.224217i
$637$	3.49696	+	6.05691i	0.138555	+	0.239983i
$638$	−9.99548			−0.395725
$639$	−2.41412	+	6.49894i	−0.0955011	+	0.257094i
$640$	−20.3993			−0.806353
$641$	−5.04487	−	8.73798i	−0.199260	−	0.345129i	0.749028	−	0.662538i	$-0.230521\pi$
$641$	−5.04487	−	8.73798i	−0.199260	−	0.345129i	−0.948289	+	0.317409i	$0.897187\pi$
$642$	−28.6394	+	60.8918i	−1.13031	+	2.40321i
$643$	−18.8065	+	32.5737i	−0.741654	+	1.28458i	0.210088	+	0.977683i	$0.432625\pi$
$643$	−18.8065	+	32.5737i	−0.741654	+	1.28458i	−0.951742	+	0.306900i	$0.900708\pi$
$644$	−1.01043	+	1.75012i	−0.0398166	+	0.0689643i
$645$	−5.29392	−	7.61386i	−0.208448	−	0.299796i
$646$	4.75299	+	8.23243i	0.187004	+	0.323901i
$647$	24.9035			0.979058			0.489529	−	0.871987i	$-0.337169\pi$
$647$	24.9035			0.979058			0.489529	+	0.871987i	$0.337169\pi$
$648$	24.7014	+	21.2889i	0.970362	+	0.836307i
$649$	0.0496506			0.00194896
$650$	1.17680	+	2.03828i	0.0461580	+	0.0799480i
$651$	0.538506	+	0.774494i	0.0211057	+	0.0303548i
$652$	−3.72978	+	6.46017i	−0.146070	+	0.253000i
$653$	−1.31120	+	2.27107i	−0.0513113	+	0.0888737i	−0.890540	−	0.454904i	$-0.849673\pi$
$653$	−1.31120	+	2.27107i	−0.0513113	+	0.0888737i	0.839229	+	0.543778i	$0.183007\pi$
$654$	26.4511	−	56.2393i	1.03432	−	2.19913i
$655$	6.40678	+	11.0969i	0.250333	+	0.433590i
$656$	−4.80059			−0.187431
$657$	2.38211	−	6.41278i	0.0929351	−	0.250186i
$658$	−1.76564			−0.0688320
$659$	−4.79039	−	8.29720i	−0.186607	−	0.323213i	0.757510	−	0.652824i	$-0.226416\pi$
$659$	−4.79039	−	8.29720i	−0.186607	−	0.323213i	−0.944117	+	0.329611i	$0.893082\pi$
$660$	−6.33794	+	0.533425i	−0.246704	+	0.0207636i
$661$	−14.3246	+	24.8109i	−0.557162	+	0.965034i	0.440569	+	0.897719i	$0.354777\pi$
$661$	−14.3246	+	24.8109i	−0.557162	+	0.965034i	−0.997732	+	0.0673151i	$0.978557\pi$
$662$	5.84955	−	10.1317i	0.227349	−	0.393780i
$663$	5.20674	−	0.438220i	0.202213	−	0.0170190i
$664$	−3.29184	−	5.70164i	−0.127748	−	0.221267i
$665$	−0.104424			−0.00404940
$666$	−36.0802	+	6.11662i	−1.39808	+	0.237014i
$667$	29.9648			1.16024
$668$	−11.3408	−	19.6428i	−0.438788	−	0.760003i
$669$	−8.99517	+	19.1251i	−0.347773	+	0.739421i
$670$	−9.86202	+	17.0815i	−0.381003	+	0.659917i
$671$	2.37156	−	4.10767i	0.0915531	−	0.158575i
$672$	−0.295879	−	0.425541i	−0.0114138	−	0.0164156i
$673$	20.9864	+	36.3495i	0.808965	+	1.40117i	0.913581	+	0.406656i	$0.133305\pi$
$673$	20.9864	+	36.3495i	0.808965	+	1.40117i	−0.104616	+	0.994513i	$0.533361\pi$
$674$	60.0442			2.31282
$675$	3.63767	+	3.71043i	0.140014	+	0.142815i
$676$	3.53946			0.136133
$677$	−15.8221	−	27.4046i	−0.608091	−	1.05324i	−0.991555	−	0.129688i	$-0.958602\pi$
$677$	−15.8221	−	27.4046i	−0.608091	−	1.05324i	0.383464	−	0.923556i	$-0.374731\pi$
$678$	24.2605	+	34.8921i	0.931718	+	1.34002i
$679$	0.361310	−	0.625808i	0.0138658	−	0.0240163i
$680$	5.46524	−	9.46607i	0.209582	−	0.363007i
$681$	6.63740	−	14.1122i	0.254346	−	0.540779i
$682$	8.52520	+	14.7661i	0.326447	+	0.565422i
$683$	11.7455			0.449429			0.224714	−	0.974425i	$-0.427855\pi$
$683$	11.7455			0.449429			0.224714	+	0.974425i	$0.427855\pi$
$684$	9.06591	+	10.9503i	0.346644	+	0.418696i
$685$	13.3005			0.508187
$686$	1.28445	+	2.22474i	0.0490407	+	0.0849409i
$687$	40.8936	−	3.44176i	1.56019	−	0.131311i
$688$	−3.87855	+	6.71785i	−0.147869	+	0.256116i
$689$	−5.49890	+	9.52438i	−0.209492	+	0.362850i
$690$	29.7362	−	2.50272i	1.13204	−	0.0952768i
$691$	−3.58458	−	6.20867i	−0.136364	−	0.236189i	0.789754	−	0.613424i	$-0.210208\pi$
$691$	−3.58458	−	6.20867i	−0.136364	−	0.236189i	−0.926118	+	0.377235i	$0.876875\pi$
$692$	34.8289			1.32400
$693$	−0.154813	−	0.186992i	−0.00588087	−	0.00710325i
$694$	−38.1203			−1.44703
$695$	2.24902	+	3.89542i	0.0853102	+	0.147762i
$696$	10.9334	−	23.2462i	0.414431	−	0.881146i
$697$	−4.99784	+	8.65651i	−0.189307	+	0.327889i
$698$	18.4176	−	31.9003i	0.697118	−	1.20744i
$699$	25.1319	+	36.1454i	0.950577	+	1.36715i
$700$	0.138033	+	0.239080i	0.00521715	+	0.00903636i
$701$	15.0370			0.567939			0.283970	−	0.958833i	$-0.408348\pi$
$701$	15.0370			0.567939			0.283970	+	0.958833i	$0.408348\pi$
$702$	11.8437	−	3.04816i	0.447013	−	0.115045i
$703$	−6.93893			−0.261707
$704$	−6.18727	−	10.7167i	−0.233192	−	0.403900i
$705$	9.51025	+	13.6779i	0.358177	+	0.515140i
$706$	13.5222	−	23.4211i	0.508915	−	0.881466i
$707$	0.211773	−	0.366801i	0.00796454	−	0.0137950i
$708$	−0.124867	+	0.265487i	−0.00469279	+	0.00997761i
$709$	19.3143	+	33.4533i	0.725362	+	1.25636i	0.958825	+	0.283999i	$0.0916611\pi$
$709$	19.3143	+	33.4533i	0.725362	+	1.25636i	−0.233462	+	0.972366i	$0.575006\pi$
$710$	5.43905			0.204124
$711$	7.24399	−	1.22806i	0.271671	−	0.0460560i
$712$	35.8765			1.34453
$713$	−25.5571	−	44.2662i	−0.957122	−	1.65778i
$714$	0.955818	−	0.0804453i	0.0357706	−	0.00301059i
$715$	−0.518744	+	0.898492i	−0.0193999	+	0.0336017i
$716$	−23.8959	+	41.3889i	−0.893030	+	1.54677i
$717$	0.492272	−	0.0414315i	0.0183842	−	0.00154729i
$718$	−34.5092	−	59.7716i	−1.28787	−	2.23066i
$719$	−0.942162			−0.0351367			−0.0175683	−	0.999846i	$-0.505592\pi$
$719$	−0.942162			−0.0351367			−0.0175683	+	0.999846i	$0.505592\pi$
$720$	1.51352	−	4.07449i	0.0564057	−	0.151847i
$721$	−1.01950			−0.0379683
$722$	−20.2499	−	35.0738i	−0.753622	−	1.30531i
$723$	−8.55128	+	18.1814i	−0.318025	+	0.676172i
$724$	3.67707	−	6.36888i	0.136657	−	0.236698i
$725$	2.04671	−	3.54501i	0.0760129	−	0.131658i
$726$	23.0941	+	33.2146i	0.857103	+	1.23271i
$727$	16.0418	+	27.7853i	0.594959	+	1.03050i	0.993553	+	0.113372i	$0.0361651\pi$
$727$	16.0418	+	27.7853i	0.594959	+	1.03050i	−0.398594	+	0.917128i	$0.630502\pi$
$728$	0.282603			0.0104740
$729$	23.6454	−	13.0343i	0.875756	−	0.482753i
$730$	−5.36694			−0.198639
$731$	8.07585	+	13.9878i	0.298696	+	0.517357i
$732$	15.9998	+	23.0114i	0.591371	+	0.850526i
$733$	−18.7469	+	32.4706i	−0.692434	+	1.19933i	0.278604	+	0.960406i	$0.410128\pi$
$733$	−18.7469	+	32.4706i	−0.692434	+	1.19933i	−0.971038	+	0.238924i	$0.923205\pi$
$734$	3.95797	−	6.85540i	0.146091	−	0.253037i
$735$	5.15573	−	10.9619i	0.190172	−	0.404335i
$736$	14.0422	+	24.3218i	0.517603	+	0.896514i
$737$	−8.69453			−0.320267
$738$	−8.14661	+	21.9311i	−0.299881	+	0.807295i
$739$	34.3049			1.26193			0.630963	−	0.775813i	$-0.282660\pi$
$739$	34.3049			1.26193			0.630963	+	0.775813i	$0.282660\pi$
$740$	9.17220	+	15.8867i	0.337177	+	0.584007i
$741$	2.31075	−	0.194482i	0.0848876	−	0.00714447i
$742$	−1.00945	+	1.74842i	−0.0370581	+	0.0641865i
$743$	−22.3176	+	38.6552i	−0.818754	+	1.41812i	0.0878471	+	0.996134i	$0.472001\pi$
$743$	−22.3176	+	38.6552i	−0.818754	+	1.41812i	−0.906601	+	0.421989i	$0.861332\pi$
$744$	−43.6663	+	3.67512i	−1.60088	+	0.134737i
$745$	0.830835	+	1.43905i	0.0304394	+	0.0527227i
$746$	−18.5412			−0.678843
$747$	−5.37448	+	0.911128i	−0.196642	+	0.0333364i
$748$	11.0779			0.405049
$749$	0.643733	+	1.11498i	0.0235215	+	0.0407404i
$750$	1.73501	−	3.68891i	0.0633538	−	0.134700i
$751$	−16.1703	+	28.0078i	−0.590063	+	1.02202i	0.404161	+	0.914688i	$0.367564\pi$
$751$	−16.1703	+	28.0078i	−0.590063	+	1.02202i	−0.994223	+	0.107330i	$0.965770\pi$
$752$	6.96762	−	12.0683i	0.254083	−	0.440084i
$753$	−22.1824	−	31.9034i	−0.808373	−	1.16262i
$754$	−4.81715	−	8.34355i	−0.175430	−	0.303854i
$755$	−18.5440			−0.674887
$756$	1.38921	−	0.357533i	0.0505250	−	0.0130033i
$757$	30.7792			1.11869			0.559344	−	0.828936i	$-0.311053\pi$
$757$	30.7792			1.11869			0.559344	+	0.828936i	$0.311053\pi$
$758$	18.1402	+	31.4197i	0.658881	+	1.14122i
$759$	7.50941	+	10.8002i	0.272574	+	0.392024i
$760$	2.42547	−	4.20104i	0.0879812	−	0.152388i
$761$	0.786630	−	1.36248i	0.0285153	−	0.0493900i	−0.851416	−	0.524492i	$-0.824255\pi$
$761$	0.786630	−	1.36248i	0.0285153	−	0.0493900i	0.879931	+	0.475102i	$0.157589\pi$
$762$	25.8959	−	55.0588i	0.938110	−	1.99457i
$763$	−0.594548	−	1.02979i	−0.0215241	−	0.0372808i
$764$	37.1999			1.34584
$765$	−5.77148	−	6.97112i	−0.208668	−	0.252042i
$766$	−80.5675			−2.91102
$767$	0.0239283	+	0.0414450i	0.000864000	+	0.00149649i
$768$	41.6939	−	3.50912i	1.50450	−	0.126624i
$769$	15.3446	−	26.5777i	0.553341	−	0.958415i	−0.444689	−	0.895685i	$-0.646686\pi$
$769$	15.3446	−	26.5777i	0.553341	−	0.958415i	0.998031	−	0.0627303i	$-0.0199808\pi$
$770$	−0.0952276	+	0.164939i	−0.00343176	+	0.00594399i
$771$	−3.31315	+	0.278847i	−0.119320	+	0.0100424i
$772$	32.4324	+	56.1746i	1.16727	+	2.02177i
$773$	−0.437296			−0.0157284			−0.00786422	−	0.999969i	$-0.502503\pi$
$773$	−0.437296			−0.0157284			−0.00786422	+	0.999969i	$0.502503\pi$
$774$	24.1081	+	29.1191i	0.866547	+	1.04666i
$775$	−6.98260			−0.250823
$776$	16.7844	+	29.0714i	0.602525	+	1.04360i
$777$	−0.297997	+	0.633589i	−0.0106906	+	0.0227299i
$778$	−33.4207	+	57.8864i	−1.19819	+	2.07533i
$779$	−2.21804	+	3.84176i	−0.0794696	+	0.137645i
$780$	−3.49973	−	5.03340i	−0.125310	−	0.180225i
$781$	1.19879	+	2.07636i	0.0428961	+	0.0742981i
$782$	−51.9752			−1.85863
$783$	−14.8905	−	15.1884i	−0.532144	−	0.542788i
$784$	−10.1331			−0.361895
$785$	5.30231	+	9.18387i	0.189248	+	0.327786i
$786$	−29.8195	−	42.8873i	−1.06363	−	1.52974i
$787$	11.7922	−	20.4247i	0.420346	−	0.728061i	−0.575627	−	0.817712i	$-0.695242\pi$
$787$	11.7922	−	20.4247i	0.420346	−	0.728061i	0.995973	+	0.0896515i	$0.0285753\pi$
$788$	13.5715	−	23.5066i	0.483465	−	0.837386i
$789$	−18.2981	+	38.9047i	−0.651430	+	1.38504i
$790$	−2.88212	−	4.99199i	−0.102541	−	0.177607i
$791$	0.813100			0.0289105
$792$	11.1187	−	1.88493i	0.395085	−	0.0669782i
$793$	4.57173			0.162347
$794$	−34.6097	−	59.9457i	−1.22825	−	2.12739i
$795$	18.9817	−	1.59757i	0.673210	−	0.0566599i
$796$	−29.7840	+	51.5873i	−1.05566	+	1.82846i
$797$	2.62625	−	4.54881i	0.0930267	−	0.161127i	−0.815757	−	0.578395i	$-0.803679\pi$
$797$	2.62625	−	4.54881i	0.0930267	−	0.161127i	0.908783	+	0.417268i	$0.137012\pi$
$798$	0.424192	−	0.0357016i	0.0150162	−	0.00126382i
$799$	−14.5078	−	25.1283i	−0.513250	−	0.888975i
$800$	3.83655			0.135643
$801$	10.3438	−	27.8460i	0.365479	−	0.983889i
$802$	−77.2194			−2.72671
$803$	−1.18290	−	2.04884i	−0.0417435	−	0.0723019i
$804$	21.8660	−	46.4905i	0.771153	−	1.63959i
$805$	0.285476	−	0.494459i	0.0100617	−	0.0174274i
$806$	−8.21714	+	14.2325i	−0.289437	+	0.501319i
$807$	10.2100	+	14.6844i	0.359410	+	0.516914i
$808$	9.83775	+	17.0395i	0.346091	+	0.599447i
$809$	−40.3038			−1.41701			−0.708503	−	0.705708i	$-0.750629\pi$
$809$	−40.3038			−1.41701			−0.708503	+	0.705708i	$0.750629\pi$
$810$	−16.0455	−	13.8288i	−0.563782	−	0.485896i
$811$	−13.7105			−0.481441			−0.240721	−	0.970594i	$-0.577384\pi$
$811$	−13.7105			−0.481441			−0.240721	+	0.970594i	$0.577384\pi$
$812$	−0.565026	−	0.978654i	−0.0198285	−	0.0343440i
$813$	−28.1944	−	40.5499i	−0.988820	−	1.42215i
$814$	−6.32782	+	10.9601i	−0.221790	+	0.384151i
$815$	1.05377	−	1.82519i	0.0369121	−	0.0639336i
$816$	−3.22202	+	6.85052i	−0.112793	+	0.239816i
$817$	3.58406	+	6.20778i	0.125390	+	0.217183i
$818$	−34.1111			−1.19267
$819$	0.0814789	−	0.219345i	0.00284710	−	0.00766455i
$820$	11.7276			0.409547
$821$	21.8403	+	37.8285i	0.762232	+	1.32022i	0.941698	+	0.336460i	$0.109230\pi$
$821$	21.8403	+	37.8285i	0.762232	+	1.32022i	−0.179466	+	0.983764i	$0.557437\pi$
$822$	−54.0294	+	4.54732i	−1.88449	+	0.158606i
$823$	−26.0766	+	45.1660i	−0.908974	+	1.57439i	−0.0934819	+	0.995621i	$0.529800\pi$
$823$	−26.0766	+	45.1660i	−0.908974	+	1.57439i	−0.815492	+	0.578768i	$0.803534\pi$
$824$	23.6801	−	41.0152i	0.824937	−	1.42883i
$825$	1.79065	−	0.150708i	0.0623425	−	0.00524699i
$826$	0.00439259	+	0.00760819i	0.000152838	+	0.000264723i
$827$	35.2190			1.22468			0.612342	−	0.790593i	$-0.290228\pi$
$827$	35.2190			1.22468			0.612342	+	0.790593i	$0.290228\pi$
$828$	−76.6354	+	12.9919i	−2.66326	+	0.451500i
$829$	30.9645			1.07544			0.537721	−	0.843123i	$-0.319285\pi$
$829$	30.9645			1.07544			0.537721	+	0.843123i	$0.319285\pi$
$830$	2.13832	+	3.70367i	0.0742220	+	0.128556i
$831$	14.1148	−	30.0103i	0.489637	−	1.04105i
$832$	5.96370	−	10.3294i	0.206754	−	0.358109i
$833$	−10.5494	+	18.2721i	−0.365516	+	0.633092i
$834$	−10.4678	−	15.0551i	−0.362470	−	0.521314i
$835$	3.20410	+	5.54967i	0.110883	+	0.192054i
$836$	4.91638			0.170037
$837$	−9.73719	+	34.9517i	−0.336567	+	1.20811i
$838$	29.9358			1.03411
$839$	−28.1456	−	48.7496i	−0.971694	−	1.68302i	−0.690440	−	0.723390i	$-0.742583\pi$
$839$	−28.1456	−	48.7496i	−0.971694	−	1.68302i	−0.281254	−	0.959633i	$-0.590750\pi$
$840$	−0.279431	−	0.401885i	−0.00964128	−	0.0138664i
$841$	6.12195	−	10.6035i	0.211102	−	0.365639i
$842$	−12.6574	+	21.9233i	−0.436204	+	0.755528i
$843$	9.14161	−	19.4365i	0.314854	−	0.669429i
$844$	2.89026	+	5.00608i	0.0994868	+	0.172316i
$845$	−1.00000			−0.0344010
$846$	−43.3089	−	52.3109i	−1.48899	−	1.79849i
$847$	0.774008			0.0265952
$848$	−7.96702	−	13.7993i	−0.273589	−	0.473870i
$849$	−39.8959	+	3.35779i	−1.36922	+	0.115239i
$850$	−3.55011	+	6.14897i	−0.121768	+	0.210908i
$851$	18.9697	−	32.8566i	0.650274	−	1.12631i
$852$	−14.1174	+	1.18817i	−0.483653	+	0.0407061i
$853$	7.70131	+	13.3391i	0.263688	+	0.456721i	0.967219	−	0.253944i	$-0.0817278\pi$
$853$	7.70131	+	13.3391i	0.263688	+	0.456721i	−0.703531	+	0.710664i	$0.748394\pi$
$854$	0.839248			0.0287185
$855$	−2.56138	−	3.09379i	−0.0875975	−	0.105805i
$856$	−59.8083			−2.04420
$857$	−7.50500	−	12.9990i	−0.256366	−	0.444039i	0.708900	−	0.705309i	$-0.249192\pi$
$857$	−7.50500	−	12.9990i	−0.256366	−	0.444039i	−0.965266	+	0.261270i	$0.915859\pi$
$858$	1.80006	−	3.82721i	0.0614530	−	0.130659i
$859$	−24.6491	+	42.6934i	−0.841015	+	1.45668i	0.0480229	+	0.998846i	$0.484708\pi$
$859$	−24.6491	+	42.6934i	−0.841015	+	1.45668i	−0.889038	+	0.457834i	$0.848625\pi$
$860$	9.47516	−	16.4115i	0.323100	−	0.559626i
$861$	0.255533	+	0.367515i	0.00870855	+	0.0125249i
$862$	39.6443	+	68.6659i	1.35029	+	2.33877i
$863$	−38.8540			−1.32261			−0.661303	−	0.750119i	$-0.729996\pi$
$863$	−38.8540			−1.32261			−0.661303	+	0.750119i	$0.729996\pi$
$864$	5.35004	−	19.2040i	0.182012	−	0.653333i
$865$	−9.84018			−0.334576
$866$	47.3290	+	81.9762i	1.60830	+	2.78566i
$867$	−7.81060	−	11.2334i	−0.265262	−	0.381507i
$868$	−0.963828	+	1.66940i	−0.0327145	+	0.0566631i
$869$	1.27046	−	2.20051i	0.0430976	−	0.0746472i
$870$	−7.10215	+	15.1003i	−0.240785	+	0.511948i
$871$	−4.19018	−	7.25760i	−0.141979	−	0.245914i
$872$	55.2385			1.87061
$873$	27.4033	−	4.64565i	0.927462	−	0.157231i
$874$	−23.0666			−0.780239
$875$	−0.0389983	−	0.0675470i	−0.00131838	−	0.00228351i
$876$	13.9302	−	1.17242i	0.470658	−	0.0396124i
$877$	−12.0357	+	20.8464i	−0.406415	+	0.703932i	−0.994485	−	0.104878i	$-0.966555\pi$
$877$	−12.0357	+	20.8464i	−0.406415	+	0.703932i	0.588070	+	0.808810i	$0.299888\pi$
$878$	21.3632	−	37.0021i	0.720972	−	1.24876i
$879$	−33.9921	+	2.86091i	−1.14653	+	0.0964961i
$880$	−0.751577	−	1.30177i	−0.0253357	−	0.0438826i
$881$	−51.5561			−1.73697			−0.868484	−	0.495716i	$-0.834906\pi$
$881$	−51.5561			−1.73697			−0.868484	+	0.495716i	$0.834906\pi$
$882$	−17.1958	+	46.2921i	−0.579014	+	1.55874i
$883$	−53.3239			−1.79449			−0.897246	−	0.441531i	$-0.854436\pi$
$883$	−53.3239			−1.79449			−0.897246	+	0.441531i	$0.854436\pi$
$884$	5.33881	+	9.24710i	0.179564	+	0.311014i
$885$	0.0352786	−	0.0750078i	0.00118588	−	0.00252136i
$886$	10.1322	−	17.5494i	0.340397	−	0.589584i
$887$	−14.0878	+	24.4008i	−0.473022	+	0.819298i	−0.999523	−	0.0308765i	$-0.990170\pi$
$887$	−14.0878	+	24.4008i	−0.473022	+	0.819298i	0.526501	+	0.850174i	$0.323503\pi$
$888$	−18.5680	−	26.7050i	−0.623102	−	0.896162i
$889$	−0.582068	−	1.00817i	−0.0195219	−	0.0338130i
$890$	−23.3047			−0.781174
$891$	1.74268	−	9.17334i	0.0583819	−	0.307318i
$892$	−43.1893			−1.44609
$893$	−6.43857	−	11.1519i	−0.215459	−	0.373185i
$894$	−3.86702	−	5.56165i	−0.129332	−	0.186009i
$895$	6.75128	−	11.6936i	0.225670	−	0.390873i
$896$	0.795537	−	1.37791i	0.0265770	−	0.0460328i
$897$	−5.39628	+	11.4733i	−0.180176	+	0.383083i
$898$	−44.8290	−	77.6461i	−1.49596	−	2.59108i
$899$	28.5827			0.953288
$900$	−3.69748	+	9.95381i	−0.123249	+	0.331794i
$901$	−33.1776			−1.10530
$902$	4.04540	+	7.00684i	0.134697	+	0.233302i
$903$	0.720748	−	0.0606609i	0.0239850	−	0.00201867i
$904$	−18.8860	+	32.7115i	−0.628138	+	1.08797i
$905$	−1.03888	+	1.79939i	−0.0345336	+	0.0598139i
$906$	75.3296	−	6.34003i	2.50266	−	0.210633i
$907$	7.47688	+	12.9503i	0.248266	+	0.430009i	0.963045	−	0.269341i	$-0.0868060\pi$
$907$	7.47688	+	12.9503i	0.248266	+	0.430009i	−0.714779	+	0.699351i	$0.753473\pi$
$908$	31.8687			1.05760
$909$	16.0618	−	2.72293i	0.532735	−	0.0903138i
$910$	−0.183573			−0.00608539
$911$	14.6748	+	25.4175i	0.486197	+	0.842119i	0.999874	−	0.0158651i	$-0.00505024\pi$
$911$	14.6748	+	25.4175i	0.486197	+	0.842119i	−0.513677	+	0.857984i	$0.671717\pi$
$912$	−1.42993	+	3.04026i	−0.0473498	+	0.100673i
$913$	−0.942587	+	1.63261i	−0.0311951	+	0.0540315i
$914$	−34.7261	+	60.1473i	−1.14864	+	1.98950i
$915$	−4.52042	−	6.50139i	−0.149440	−	0.214929i
$916$	41.9309	+	72.6264i	1.38543	+	2.39964i
$917$	−0.999413			−0.0330035
$918$	25.8283	+	26.3449i	0.852461	+	0.869511i
$919$	−4.84694			−0.159886			−0.0799430	−	0.996799i	$-0.525474\pi$
$919$	−4.84694			−0.159886			−0.0799430	+	0.996799i	$0.525474\pi$
$920$	13.2616	+	22.9697i	0.437222	+	0.757290i
$921$	−26.6862	−	38.3808i	−0.879339	−	1.26469i
$922$	39.4218	−	68.2806i	1.29829	−	2.24870i
$923$	−1.15547	+	2.00134i	−0.0380328	+	0.0658748i
$924$	0.211137	−	0.448911i	0.00694591	−	0.0147681i
$925$	−2.59141	−	4.48846i	−0.0852052	−	0.147580i
$926$	−25.9470			−0.852671
$927$	−25.0071	−	30.2049i	−0.821340	−	0.992061i
$928$	−15.7046			−0.515529
$929$	−22.4349	−	38.8585i	−0.736067	−	1.27491i	−0.954254	−	0.298998i	$-0.903348\pi$
$929$	−22.4349	−	38.8585i	−0.736067	−	1.27491i	0.218187	−	0.975907i	$-0.429986\pi$
$930$	28.3647	−	2.38729i	0.930116	−	0.0782822i
$931$	−4.68183	+	8.10917i	−0.153441	+	0.265767i
$932$	−44.9816	+	77.9104i	−1.47342	+	2.55204i
$933$	34.5225	−	2.90555i	1.13022	−	0.0951233i
$934$	28.2278	+	48.8920i	0.923643	+	1.59980i
$935$	−3.12984			−0.102357
$936$	6.93187	+	8.37270i	0.226575	+	0.273670i
$937$	1.39738			0.0456504			0.0228252	−	0.999739i	$-0.492734\pi$
$937$	1.39738			0.0456504			0.0228252	+	0.999739i	$0.492734\pi$
$938$	−0.769204	−	1.33230i	−0.0251154	−	0.0435012i
$939$	15.8828	−	33.7694i	0.518317	−	1.10202i
$940$	−17.0216	+	29.4823i	−0.555184	+	0.961607i
$941$	−1.66782	+	2.88874i	−0.0543692	+	0.0941703i	−0.891929	−	0.452175i	$-0.850648\pi$
$941$	−1.66782	+	2.88874i	−0.0543692	+	0.0941703i	0.837560	+	0.546346i	$0.183981\pi$
$942$	−24.6789	−	35.4939i	−0.804083	−	1.15645i
$943$	−12.1274	−	21.0053i	−0.394923	−	0.684027i
$944$	−0.0693364			−0.00225671
$945$	−0.392492	+	0.101014i	−0.0127678	+	0.00328597i
$946$	13.0737			0.425061
$947$	−5.81706	−	10.0754i	−0.189029	−	0.327408i	0.755898	−	0.654690i	$-0.227201\pi$
$947$	−5.81706	−	10.0754i	−0.189029	−	0.327408i	−0.944927	+	0.327282i	$0.893867\pi$
$948$	8.57123	+	12.3274i	0.278381	+	0.400375i
$949$	1.14015	−	1.97480i	0.0370109	−	0.0641048i
$950$	−1.57554	+	2.72891i	−0.0511172	+	0.0885376i
$951$	11.9560	−	25.4204i	0.387701	−	0.824313i
$952$	0.426270	+	0.738321i	0.0138155	+	0.0239291i
$953$	26.6894			0.864554			0.432277	−	0.901741i	$-0.357710\pi$
$953$	26.6894			0.864554			0.432277	+	0.901741i	$0.357710\pi$
$954$	−76.5611	+	12.9793i	−2.47876	+	0.420220i
$955$	−10.5100			−0.340097
$956$	0.504759	+	0.874268i	0.0163251	+	0.0282758i
$957$	−7.32990	+	0.616912i	−0.236942	+	0.0199419i
$958$	−34.8040	+	60.2824i	−1.12447	+	1.94763i
$959$	−0.518698	+	0.898410i	−0.0167496	+	0.0290112i
$960$	−20.5861	+	1.73260i	−0.664413	+	0.0559196i
$961$	−8.87837	−	15.3778i	−0.286399	−	0.496058i
$962$	−12.1983			−0.393290
$963$	−17.2437	+	46.4209i	−0.555669	+	1.49589i
$964$	−41.0580			−1.32239
$965$	−9.16311	−	15.8710i	−0.294971	−	0.510904i
$966$	−0.990611	+	2.10620i	−0.0318724	+	0.0677657i
$967$	−16.3454	+	28.3111i	−0.525634	+	0.910425i	0.473920	+	0.880568i	$0.342839\pi$
$967$	−16.3454	+	28.3111i	−0.525634	+	0.910425i	−0.999554	+	0.0298572i	$0.990495\pi$
$968$	−17.9780	+	31.1388i	−0.577834	+	1.00084i
$969$	3.99357	+	5.74366i	0.128292	+	0.184513i
$970$	−10.9028	−	18.8842i	−0.350068	−	0.606335i
$971$	23.4851			0.753673			0.376836	−	0.926280i	$-0.377012\pi$
$971$	23.4851			0.753673			0.376836	+	0.926280i	$0.377012\pi$
$972$	44.6681	+	32.3884i	1.43273	+	1.03886i
$973$	−0.350832			−0.0112472
$974$	10.0446	+	17.3978i	0.321850	+	0.557461i
$975$	0.988775	+	1.42208i	0.0316662	+	0.0455431i
$976$	−3.31185	+	5.73630i	−0.106010	+	0.183614i
$977$	12.0208	−	20.8207i	0.384581	−	0.666114i	−0.607130	−	0.794603i	$-0.707679\pi$
$977$	12.0208	−	20.8207i	0.384581	−	0.666114i	0.991711	+	0.128489i	$0.0410126\pi$
$978$	−3.65662	+	7.77456i	−0.116926	+	0.248603i
$979$	−5.13645	−	8.89659i	−0.164162	−	0.284336i
$980$	24.7547			0.790759
$981$	15.9261	−	42.8740i	0.508483	−	1.36886i
$982$	−14.8518			−0.473939
$983$	−1.71242	−	2.96600i	−0.0546178	−	0.0946008i	0.837424	−	0.546554i	$-0.184061\pi$
$983$	−1.71242	−	2.96600i	−0.0546178	−	0.0946008i	−0.892042	+	0.451953i	$0.850727\pi$
$984$	−20.7206	+	1.74393i	−0.660550	+	0.0555944i
$985$	−3.83435	+	6.64129i	−0.122173	+	0.211609i
$986$	14.5321	−	25.1703i	0.462796	−	0.801586i
$987$	−1.29478	+	0.108974i	−0.0412135	+	0.00346868i
$988$	2.36937	+	4.10386i	0.0753796	+	0.130561i
$989$	−39.1926			−1.24625
$990$	−7.22247	+	1.22441i	−0.229545	+	0.0389144i
$991$	19.2845			0.612593			0.306297	−	0.951936i	$-0.400910\pi$
$991$	19.2845			0.612593			0.306297	+	0.951936i	$0.400910\pi$
$992$	13.3946	+	23.2000i	0.425278	+	0.736602i
$993$	3.66428	−	7.79083i	0.116282	−	0.247234i
$994$	−0.212114	+	0.367392i	−0.00672784	+	0.0116530i
$995$	8.41484	−	14.5749i	0.266768	−	0.462056i
$996$	−6.35920	−	9.14598i	−0.201499	−	0.289801i
$997$	−7.43347	−	12.8751i	−0.235420	−	0.407760i	0.723974	−	0.689827i	$-0.242313\pi$
$997$	−7.43347	−	12.8751i	−0.235420	−	0.407760i	−0.959395	+	0.282067i	$0.908980\pi$
$998$	−4.35633			−0.137897
$999$	−26.0809	+	6.71229i	−0.825162	+	0.212367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.391.13	yes	30
3.2	odd	2		1755.2.i.h.1171.3		30
9.2	odd	6		1755.2.i.h.586.3		30
9.4	even	3		5265.2.a.bk.1.3		15
9.5	odd	6		5265.2.a.bl.1.13		15
9.7	even	3	inner	585.2.i.h.196.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.13	✓	30	9.7	even	3	inner
585.2.i.h.391.13	yes	30	1.1	even	1	trivial
1755.2.i.h.586.3		30	9.2	odd	6
1755.2.i.h.1171.3		30	3.2	odd	2
5265.2.a.bk.1.3		15	9.4	even	3
5265.2.a.bl.1.13		15	9.5	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)

\(f(q)\)	\(=\)	\(q+(1.17680 + 2.03828i) q^{2} +(0.988775 + 1.42208i) q^{3} +(-1.76973 + 3.06526i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.73501 + 3.68891i) q^{6} +(0.0389983 + 0.0675470i) q^{7} -3.62327 q^{8} +(-1.04465 + 2.81224i) q^{9} +O(q^{10})\)	\(q+(1.17680 + 2.03828i) q^{2} +(0.988775 + 1.42208i) q^{3} +(-1.76973 + 3.06526i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.73501 + 3.68891i) q^{6} +(0.0389983 + 0.0675470i) q^{7} -3.62327 q^{8} +(-1.04465 + 2.81224i) q^{9} +2.35360 q^{10} +(0.518744 + 0.898492i) q^{11} +(-6.10892 + 0.514150i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.0917866 + 0.158979i) q^{14} +(1.72595 - 0.145263i) q^{15} +(-0.724419 - 1.25473i) q^{16} -3.01674 q^{17} +(-6.96149 + 1.18017i) q^{18} -1.33883 q^{19} +(1.76973 + 3.06526i) q^{20} +(-0.0574970 + 0.122248i) q^{21} +(-1.22092 + 2.11469i) q^{22} +(3.66011 - 6.33950i) q^{23} +(-3.58260 - 5.15260i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.35360 q^{26} +(-5.03217 + 1.29510i) q^{27} -0.276066 q^{28} +(2.04671 + 3.54501i) q^{29} +(2.32719 + 3.34702i) q^{30} +(3.49130 - 6.04711i) q^{31} +(-1.91828 + 3.32255i) q^{32} +(-0.764809 + 1.62610i) q^{33} +(-3.55011 - 6.14897i) q^{34} +0.0779966 q^{35} +(-6.77151 - 8.17902i) q^{36} +5.18283 q^{37} +(-1.57554 - 2.72891i) q^{38} +(-1.72595 + 0.145263i) q^{39} +(-1.81164 + 3.13785i) q^{40} +(1.65670 - 2.86949i) q^{41} +(-0.316838 + 0.0266663i) q^{42} +(-2.67701 - 4.63672i) q^{43} -3.67215 q^{44} +(1.91315 + 2.31081i) q^{45} +17.2289 q^{46} +(4.80910 + 8.32961i) q^{47} +(1.06805 - 2.27083i) q^{48} +(3.49696 - 6.05691i) q^{49} +(1.17680 - 2.03828i) q^{50} +(-2.98288 - 4.29006i) q^{51} +(-1.76973 - 3.06526i) q^{52} +10.9978 q^{53} +(-8.56165 - 8.73290i) q^{54} +1.03749 q^{55} +(-0.141301 - 0.244741i) q^{56} +(-1.32380 - 1.90393i) q^{57} +(-4.81715 + 8.34355i) q^{58} +(0.0239283 - 0.0414450i) q^{59} +(-2.60919 + 5.54756i) q^{60} +(-2.28587 - 3.95924i) q^{61} +16.4343 q^{62} +(-0.230698 + 0.0391099i) q^{63} -11.9274 q^{64} +(0.500000 + 0.866025i) q^{65} +(-4.21449 + 0.354708i) q^{66} +(-4.19018 + 7.25760i) q^{67} +(5.33881 - 9.24710i) q^{68} +(12.6343 - 1.06335i) q^{69} +(0.0917866 + 0.158979i) q^{70} +2.31094 q^{71} +(3.78504 - 10.1895i) q^{72} -2.28031 q^{73} +(6.09917 + 10.5641i) q^{74} +(0.737173 - 1.56735i) q^{75} +(2.36937 - 4.10386i) q^{76} +(-0.0404603 + 0.0700793i) q^{77} +(-2.32719 - 3.34702i) q^{78} +(-1.22456 - 2.12100i) q^{79} -1.44884 q^{80} +(-6.81743 - 5.87560i) q^{81} +7.79844 q^{82} +(0.908528 + 1.57362i) q^{83} +(-0.272967 - 0.392588i) q^{84} +(-1.50837 + 2.61258i) q^{85} +(6.30062 - 10.9130i) q^{86} +(-3.01756 + 6.41581i) q^{87} +(-1.87955 - 3.25548i) q^{88} -9.90169 q^{89} +(-2.45869 + 6.61891i) q^{90} -0.0779966 q^{91} +(12.9548 + 22.4384i) q^{92} +(12.0516 - 1.01431i) q^{93} +(-11.3187 + 19.6046i) q^{94} +(-0.669415 + 1.15946i) q^{95} +(-6.62169 + 0.557307i) q^{96} +(-4.63238 - 8.02353i) q^{97} +16.4609 q^{98} +(-3.06868 + 0.520229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

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