LMFDB - Embedded newform 403.2.k.d.66.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.8
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247442 + 0.761548i) q^{2} +(-0.990504 + 3.04846i) q^{3} +(1.09931 - 0.798693i) q^{4} -0.800250 q^{5} -2.56664 q^{6} +(-0.623500 + 0.452999i) q^{7} +(2.17588 + 1.58087i) q^{8} +(-5.88494 - 4.27566i) q^{9} +O(q^{10})$	\(q+(0.247442 + 0.761548i) q^{2} +(-0.990504 + 3.04846i) q^{3} +(1.09931 - 0.798693i) q^{4} -0.800250 q^{5} -2.56664 q^{6} +(-0.623500 + 0.452999i) q^{7} +(2.17588 + 1.58087i) q^{8} +(-5.88494 - 4.27566i) q^{9} +(-0.198015 - 0.609429i) q^{10} +(-4.71624 + 3.42655i) q^{11} +(1.34591 + 4.14229i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.499260 - 0.362734i) q^{14} +(0.792650 - 2.43953i) q^{15} +(0.174291 - 0.536412i) q^{16} +(-2.89769 - 2.10530i) q^{17} +(1.79994 - 5.53964i) q^{18} +(0.887777 + 2.73230i) q^{19} +(-0.879719 + 0.639154i) q^{20} +(-0.763369 - 2.34941i) q^{21} +(-3.77648 - 2.74377i) q^{22} +(7.36818 + 5.35329i) q^{23} +(-6.97443 + 5.06722i) q^{24} -4.35960 q^{25} -0.800739 q^{26} +(11.0837 - 8.05278i) q^{27} +(-0.323610 + 0.995969i) q^{28} +(1.06340 + 3.27280i) q^{29} +2.05395 q^{30} +(-1.38176 - 5.39358i) q^{31} +5.83070 q^{32} +(-5.77423 - 17.7713i) q^{33} +(0.886274 - 2.72767i) q^{34} +(0.498955 - 0.362512i) q^{35} -9.88428 q^{36} +8.07381 q^{37} +(-1.86110 + 1.35217i) q^{38} +(-2.59317 - 1.88405i) q^{39} +(-1.74125 - 1.26509i) q^{40} +(-1.32029 - 4.06343i) q^{41} +(1.60030 - 1.16268i) q^{42} +(-1.60569 - 4.94180i) q^{43} +(-2.44783 + 7.53365i) q^{44} +(4.70942 + 3.42160i) q^{45} +(-2.25359 + 6.93585i) q^{46} +(-3.42136 + 10.5299i) q^{47} +(1.46259 + 1.06264i) q^{48} +(-1.97958 + 6.09251i) q^{49} +(-1.07875 - 3.32005i) q^{50} +(9.28808 - 6.74819i) q^{51} +(0.419897 + 1.29231i) q^{52} +(2.56683 + 1.86491i) q^{53} +(8.87515 + 6.44817i) q^{54} +(3.77417 - 2.74209i) q^{55} -2.07279 q^{56} -9.20864 q^{57} +(-2.22927 + 1.61966i) q^{58} +(-0.775572 + 2.38696i) q^{59} +(-1.07707 - 3.31487i) q^{60} +8.84084 q^{61} +(3.76557 - 2.38687i) q^{62} +5.60612 q^{63} +(1.09418 + 3.36754i) q^{64} +(0.247291 - 0.761083i) q^{65} +(12.1049 - 8.79471i) q^{66} +4.14962 q^{67} -4.86694 q^{68} +(-23.6175 + 17.1591i) q^{69} +(0.399533 + 0.290278i) q^{70} +(4.17647 + 3.03438i) q^{71} +(-6.04566 - 18.6066i) q^{72} +(-2.56290 + 1.86206i) q^{73} +(1.99780 + 6.14859i) q^{74} +(4.31820 - 13.2901i) q^{75} +(3.15820 + 2.29457i) q^{76} +(1.38835 - 4.27290i) q^{77} +(0.793135 - 2.44102i) q^{78} +(10.6476 + 7.73591i) q^{79} +(-0.139476 + 0.429264i) q^{80} +(6.82656 + 21.0100i) q^{81} +(2.76780 - 2.01093i) q^{82} +(4.81704 + 14.8253i) q^{83} +(-2.71563 - 1.97302i) q^{84} +(2.31888 + 1.68476i) q^{85} +(3.36610 - 2.44562i) q^{86} -11.0303 q^{87} -15.6789 q^{88} +(-7.48785 + 5.44024i) q^{89} +(-1.44040 + 4.43310i) q^{90} +(-0.238156 - 0.732968i) q^{91} +12.3755 q^{92} +(17.8107 + 1.13014i) q^{93} -8.86560 q^{94} +(-0.710444 - 2.18652i) q^{95} +(-5.77533 + 17.7746i) q^{96} +(-4.93918 + 3.58852i) q^{97} -5.12957 q^{98} +42.4055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.247442	+	0.761548i	0.174968	+	0.538496i	0.999632	−	0.0271269i	$-0.00863583\pi$
$2$	0.247442	+	0.761548i	0.174968	+	0.538496i	−0.824664	+	0.565623i	$0.808636\pi$
$3$	−0.990504	+	3.04846i	−0.571867	+	1.76003i	0.0747387	+	0.997203i	$0.476188\pi$
$3$	−0.990504	+	3.04846i	−0.571867	+	1.76003i	−0.646606	+	0.762824i	$0.723812\pi$
$4$	1.09931	−	0.798693i	0.549653	−	0.399346i
$5$	−0.800250			−0.357883			−0.178941	−	0.983860i	$-0.557267\pi$
$5$	−0.800250			−0.357883			−0.178941	+	0.983860i	$0.557267\pi$
$6$	−2.56664			−1.04783
$7$	−0.623500	+	0.452999i	−0.235661	+	0.171217i	−0.699348	−	0.714781i	$-0.746526\pi$
$7$	−0.623500	+	0.452999i	−0.235661	+	0.171217i	0.463687	+	0.885999i	$0.346526\pi$
$8$	2.17588	+	1.58087i	0.769290	+	0.558922i
$9$	−5.88494	−	4.27566i	−1.96165	−	1.42522i
$10$	−0.198015	−	0.609429i	−0.0626180	−	0.192718i
$11$	−4.71624	+	3.42655i	−1.42200	+	1.03314i	−0.430562	+	0.902561i	$0.641685\pi$
$11$	−4.71624	+	3.42655i	−1.42200	+	1.03314i	−0.991437	+	0.130582i	$0.958315\pi$
$12$	1.34591	+	4.14229i	0.388532	+	1.19578i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−0.499260	−	0.362734i	−0.133433	−	0.0969447i
$15$	0.792650	−	2.43953i	0.204661	−	0.629883i
$16$	0.174291	−	0.536412i	0.0435727	−	0.134103i
$17$	−2.89769	−	2.10530i	−0.702794	−	0.510610i	0.178047	−	0.984022i	$-0.443022\pi$
$17$	−2.89769	−	2.10530i	−0.702794	−	0.510610i	−0.880841	+	0.473412i	$0.843022\pi$
$18$	1.79994	−	5.53964i	0.424250	−	1.30571i
$19$	0.887777	+	2.73230i	0.203670	+	0.626832i	0.999765	+	0.0216608i	$0.00689538\pi$
$19$	0.887777	+	2.73230i	0.203670	+	0.626832i	−0.796095	+	0.605171i	$0.793105\pi$
$20$	−0.879719	+	0.639154i	−0.196711	+	0.142919i
$21$	−0.763369	−	2.34941i	−0.166581	−	0.512683i
$22$	−3.77648	−	2.74377i	−0.805148	−	0.584974i
$23$	7.36818	+	5.35329i	1.53637	+	1.11624i	0.952561	+	0.304349i	$0.0984388\pi$
$23$	7.36818	+	5.35329i	1.53637	+	1.11624i	0.583810	+	0.811890i	$0.301561\pi$
$24$	−6.97443	+	5.06722i	−1.42365	+	1.03434i
$25$	−4.35960			−0.871920
$26$	−0.800739			−0.157038
$27$	11.0837	−	8.05278i	2.13306	−	1.54976i
$28$	−0.323610	+	0.995969i	−0.0611565	+	0.188220i
$29$	1.06340	+	3.27280i	0.197468	+	0.607744i	0.999939	+	0.0110526i	$0.00351821\pi$
$29$	1.06340	+	3.27280i	0.197468	+	0.607744i	−0.802471	+	0.596691i	$0.796482\pi$
$30$	2.05395			0.374999
$31$	−1.38176	−	5.39358i	−0.248171	−	0.968716i
$31$	−1.38176	−	5.39358i	−0.248171	−	0.968716i
$32$	5.83070			1.03073
$33$	−5.77423	−	17.7713i	−1.00516	−	3.09358i
$34$	0.886274	−	2.72767i	0.151995	−	0.467792i
$35$	0.498955	−	0.362512i	0.0843389	−	0.0612758i
$36$	−9.88428			−1.64738
$37$	8.07381			1.32733			0.663663	−	0.748032i	$-0.269001\pi$
$37$	8.07381			1.32733			0.663663	+	0.748032i	$0.269001\pi$
$38$	−1.86110	+	1.35217i	−0.301911	+	0.219351i
$39$	−2.59317	−	1.88405i	−0.415240	−	0.301689i
$40$	−1.74125	−	1.26509i	−0.275315	−	0.200028i
$41$	−1.32029	−	4.06343i	−0.206194	−	0.634601i	−0.999662	−	0.0259887i	$-0.991727\pi$
$41$	−1.32029	−	4.06343i	−0.206194	−	0.634601i	0.793468	−	0.608612i	$-0.208273\pi$
$42$	1.60030	−	1.16268i	0.246931	−	0.179406i
$43$	−1.60569	−	4.94180i	−0.244865	−	0.753617i	−0.995659	−	0.0930803i	$-0.970329\pi$
$43$	−1.60569	−	4.94180i	−0.244865	−	0.753617i	0.750793	−	0.660537i	$-0.229671\pi$
$44$	−2.44783	+	7.53365i	−0.369024	+	1.13574i
$45$	4.70942	+	3.42160i	0.702039	+	0.510061i
$46$	−2.25359	+	6.93585i	−0.332274	+	1.02264i
$47$	−3.42136	+	10.5299i	−0.499057	+	1.53594i	0.311480	+	0.950253i	$0.399175\pi$
$47$	−3.42136	+	10.5299i	−0.499057	+	1.53594i	−0.810537	+	0.585688i	$0.800825\pi$
$48$	1.46259	+	1.06264i	0.211107	+	0.153378i
$49$	−1.97958	+	6.09251i	−0.282796	+	0.870358i
$50$	−1.07875	−	3.32005i	−0.152558	−	0.469525i
$51$	9.28808	−	6.74819i	1.30059	−	0.944935i
$52$	0.419897	+	1.29231i	0.0582293	+	0.179211i
$53$	2.56683	+	1.86491i	0.352582	+	0.256166i	0.749951	−	0.661493i	$-0.230077\pi$
$53$	2.56683	+	1.86491i	0.352582	+	0.256166i	−0.397370	+	0.917659i	$0.630077\pi$
$54$	8.87515	+	6.44817i	1.20775	+	0.877485i
$55$	3.77417	−	2.74209i	0.508909	−	0.369744i
$56$	−2.07279			−0.276989
$57$	−9.20864			−1.21971
$58$	−2.22927	+	1.61966i	−0.292717	+	0.212671i
$59$	−0.775572	+	2.38696i	−0.100971	+	0.310756i	−0.988764	−	0.149487i	$-0.952238\pi$
$59$	−0.775572	+	2.38696i	−0.100971	+	0.310756i	0.887793	+	0.460243i	$0.152238\pi$
$60$	−1.07707	−	3.31487i	−0.139049	−	0.427948i
$61$	8.84084			1.13195			0.565977	−	0.824421i	$-0.308499\pi$
$61$	8.84084			1.13195			0.565977	+	0.824421i	$0.308499\pi$
$62$	3.76557	−	2.38687i	0.478228	−	0.303133i
$63$	5.60612			0.706305
$64$	1.09418	+	3.36754i	0.136772	+	0.420942i
$65$	0.247291	−	0.761083i	0.0306727	−	0.0944007i
$66$	12.1049	−	8.79471i	1.49001	−	1.08255i
$67$	4.14962			0.506957			0.253478	−	0.967341i	$-0.418425\pi$
$67$	4.14962			0.506957			0.253478	+	0.967341i	$0.418425\pi$
$68$	−4.86694			−0.590203
$69$	−23.6175	+	17.1591i	−2.84321	+	2.06571i
$70$	0.399533	+	0.290278i	0.0477533	+	0.0346948i
$71$	4.17647	+	3.03438i	0.495655	+	0.360115i	0.807355	−	0.590066i	$-0.200898\pi$
$71$	4.17647	+	3.03438i	0.495655	+	0.360115i	−0.311700	+	0.950181i	$0.600898\pi$
$72$	−6.04566	−	18.6066i	−0.712488	−	2.19281i
$73$	−2.56290	+	1.86206i	−0.299965	+	0.217937i	−0.727579	−	0.686024i	$-0.759354\pi$
$73$	−2.56290	+	1.86206i	−0.299965	+	0.217937i	0.427614	+	0.903962i	$0.359354\pi$
$74$	1.99780	+	6.14859i	0.232239	+	0.714759i
$75$	4.31820	−	13.2901i	0.498623	−	1.53460i
$76$	3.15820	+	2.29457i	0.362271	+	0.263205i
$77$	1.38835	−	4.27290i	0.158217	−	0.486942i
$78$	0.793135	−	2.44102i	0.0898048	−	0.276391i
$79$	10.6476	+	7.73591i	1.19794	+	0.870358i	0.994081	−	0.108641i	$-0.0346500\pi$
$79$	10.6476	+	7.73591i	1.19794	+	0.870358i	0.203864	+	0.978999i	$0.434650\pi$
$80$	−0.139476	+	0.429264i	−0.0155939	+	0.0479931i
$81$	6.82656	+	21.0100i	0.758506	+	2.33444i
$82$	2.76780	−	2.01093i	0.305652	−	0.222070i
$83$	4.81704	+	14.8253i	0.528739	+	1.62729i	0.756801	+	0.653645i	$0.226761\pi$
$83$	4.81704	+	14.8253i	0.528739	+	1.62729i	−0.228062	+	0.973647i	$0.573239\pi$
$84$	−2.71563	−	1.97302i	−0.296300	−	0.215274i
$85$	2.31888	+	1.68476i	0.251518	+	0.182738i
$86$	3.36610	−	2.44562i	0.362976	−	0.263718i
$87$	−11.0303			−1.18257
$88$	−15.6789			−1.67138
$89$	−7.48785	+	5.44024i	−0.793710	+	0.576664i	−0.909062	−	0.416661i	$-0.863200\pi$
$89$	−7.48785	+	5.44024i	−0.793710	+	0.576664i	0.115352	+	0.993325i	$0.463200\pi$
$90$	−1.44040	+	4.43310i	−0.151832	+	0.467290i
$91$	−0.238156	−	0.732968i	−0.0249655	−	0.0768359i
$92$	12.3755			1.29024
$93$	17.8107	+	1.13014i	1.84689	+	0.117190i
$94$	−8.86560			−0.914417
$95$	−0.710444	−	2.18652i	−0.0728900	−	0.224332i
$96$	−5.77533	+	17.7746i	−0.589442	+	1.81412i
$97$	−4.93918	+	3.58852i	−0.501498	+	0.364359i	−0.809589	−	0.586998i	$-0.800310\pi$
$97$	−4.93918	+	3.58852i	−0.501498	+	0.364359i	0.308091	+	0.951357i	$0.400310\pi$
$98$	−5.12957			−0.518165
$99$	42.4055			4.26192
$100$	−4.79253	+	3.48198i	−0.479253	+	0.348198i
$101$	−7.18927	−	5.22331i	−0.715360	−	0.519739i	0.169539	−	0.985524i	$-0.445772\pi$
$101$	−7.18927	−	5.22331i	−0.715360	−	0.519739i	−0.884898	+	0.465784i	$0.845772\pi$
$102$	7.43733	+	5.40354i	0.736405	+	0.535030i
$103$	−4.20375	−	12.9378i	−0.414208	−	1.27480i	−0.912957	−	0.408055i	$-0.866207\pi$
$103$	−4.20375	−	12.9378i	−0.414208	−	1.27480i	0.498749	−	0.866746i	$-0.333793\pi$
$104$	−2.17588	+	1.58087i	−0.213363	+	0.155017i
$105$	0.610886	+	1.88011i	0.0596164	+	0.183480i
$106$	−0.785079	+	2.41623i	−0.0762537	+	0.234685i
$107$	−9.58844	−	6.96641i	−0.926950	−	0.673469i	0.0182942	−	0.999833i	$-0.494176\pi$
$107$	−9.58844	−	6.96641i	−0.926950	−	0.673469i	−0.945244	+	0.326364i	$0.894176\pi$
$108$	5.75268	−	17.7049i	0.553552	−	1.70366i
$109$	−2.13041	+	6.55674i	−0.204057	+	0.628022i	0.795694	+	0.605699i	$0.207106\pi$
$109$	−2.13041	+	6.55674i	−0.204057	+	0.628022i	−0.999751	+	0.0223232i	$0.992894\pi$
$110$	3.02213	+	2.19570i	0.288148	+	0.209352i
$111$	−7.99713	+	24.6126i	−0.759054	+	2.33613i
$112$	0.134324	+	0.413406i	0.0126924	+	0.0390632i
$113$	7.81408	−	5.67726i	0.735087	−	0.534072i	−0.156082	−	0.987744i	$-0.549886\pi$
$113$	7.81408	−	5.67726i	0.735087	−	0.534072i	0.891169	+	0.453672i	$0.149886\pi$
$114$	−2.27860	−	7.01282i	−0.213411	−	0.656811i
$115$	−5.89638	−	4.28397i	−0.549841	−	0.399483i
$116$	3.78296	+	2.74848i	0.351239	+	0.255190i
$117$	5.88494	−	4.27566i	0.544063	−	0.395285i
$118$	−2.00970			−0.185008
$119$	2.76041			0.253046
$120$	5.58129	−	4.05504i	0.509499	−	0.370173i
$121$	7.10249	−	21.8592i	0.645681	−	1.98720i
$122$	2.18760	+	6.73273i	0.198056	+	0.609553i
$123$	13.6949			1.23483
$124$	−5.82679	−	4.82560i	−0.523261	−	0.433352i
$125$	7.49002			0.669928
$126$	1.38719	+	4.26933i	0.123581	+	0.380343i
$127$	4.31519	−	13.2808i	0.382911	−	1.17848i	−0.555073	−	0.831801i	$-0.687310\pi$
$127$	4.31519	−	13.2808i	0.382911	−	1.17848i	0.937984	−	0.346678i	$-0.112690\pi$
$128$	7.14048	−	5.18786i	0.631135	−	0.458547i
$129$	16.6553			1.46642
$130$	0.640791			0.0562011
$131$	7.56554	−	5.49669i	0.661004	−	0.480248i	−0.205998	−	0.978552i	$-0.566044\pi$
$131$	7.56554	−	5.49669i	0.661004	−	0.480248i	0.867002	+	0.498305i	$0.166044\pi$
$132$	−20.5414	−	14.9242i	−1.78790	−	1.29899i
$133$	−1.79126	−	1.30142i	−0.155322	−	0.112848i
$134$	1.02679	+	3.16014i	0.0887012	+	0.272994i
$135$	−8.86973	+	6.44423i	−0.763384	+	0.554631i
$136$	−2.97683	−	9.16175i	−0.255261	−	0.785614i
$137$	−2.17418	+	6.69145i	−0.185753	+	0.571689i	−0.999961	−	0.00888485i	$-0.997172\pi$
$137$	−2.17418	+	6.69145i	−0.185753	+	0.571689i	0.814207	+	0.580574i	$0.197172\pi$
$138$	−18.9114	−	13.7400i	−1.60985	−	1.16962i
$139$	−1.49163	+	4.59076i	−0.126518	+	0.389383i	−0.994175	−	0.107781i	$-0.965625\pi$
$139$	−1.49163	+	4.59076i	−0.126518	+	0.389383i	0.867656	+	0.497164i	$0.165625\pi$
$140$	0.258969	−	0.797024i	0.0218869	−	0.0673608i
$141$	−28.7110	−	20.8598i	−2.41790	−	1.75671i
$142$	−1.27739	+	3.93141i	−0.107196	+	0.329917i
$143$	−1.80144	−	5.54427i	−0.150644	−	0.463635i
$144$	−3.31921	+	2.41154i	−0.276600	+	0.200962i
$145$	−0.850983	−	2.61906i	−0.0706703	−	0.217501i
$146$	−2.05222	−	1.49102i	−0.169843	−	0.123398i
$147$	−16.6120	−	12.0693i	−1.37013	−	0.995459i
$148$	8.87558	−	6.44849i	0.729569	−	0.530063i
$149$	7.59053			0.621841			0.310920	−	0.950436i	$-0.399363\pi$
$149$	7.59053			0.621841			0.310920	+	0.950436i	$0.399363\pi$
$150$	11.1895			0.913620
$151$	−7.64698	+	5.55586i	−0.622303	+	0.452129i	−0.853725	−	0.520724i	$-0.825662\pi$
$151$	−7.64698	+	5.55586i	−0.622303	+	0.452129i	0.231422	+	0.972853i	$0.425662\pi$
$152$	−2.38771	+	7.34861i	−0.193669	+	0.596051i
$153$	8.05121	+	24.7791i	0.650902	+	2.00327i
$154$	3.59756			0.289899
$155$	1.10575	+	4.31622i	0.0888160	+	0.346687i
$156$	−4.35547			−0.348716
$157$	−4.98678	−	15.3477i	−0.397988	−	1.22488i	−0.926610	−	0.376024i	$-0.877291\pi$
$157$	−4.98678	−	15.3477i	−0.397988	−	1.22488i	0.528622	−	0.848857i	$-0.322709\pi$
$158$	−3.25661	+	10.0228i	−0.259082	+	0.797373i
$159$	−8.22757	+	5.97768i	−0.652489	+	0.474061i
$160$	−4.66602			−0.368881
$161$	−7.01909			−0.553182
$162$	−14.3109	+	10.3975i	−1.12437	+	0.816905i
$163$	−1.22951	−	0.893289i	−0.0963024	−	0.0699678i	0.538592	−	0.842567i	$-0.318956\pi$
$163$	−1.22951	−	0.893289i	−0.0963024	−	0.0699678i	−0.634894	+	0.772599i	$0.718956\pi$
$164$	−4.69683	−	3.41245i	−0.366761	−	0.266467i
$165$	4.62083	+	14.2214i	0.359731	+	1.10714i
$166$	−10.0983	+	7.33682i	−0.783777	+	0.569448i
$167$	2.05062	+	6.31114i	0.158681	+	0.488371i	0.998515	−	0.0544724i	$-0.0173477\pi$
$167$	2.05062	+	6.31114i	0.158681	+	0.488371i	−0.839834	+	0.542843i	$0.817348\pi$
$168$	2.05311	−	6.31882i	0.158401	−	0.487507i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−0.709241	+	2.18282i	−0.0543963	+	0.167415i
$171$	6.45786	−	19.8752i	0.493845	−	1.51990i
$172$	−5.71212	−	4.15010i	−0.435545	−	0.316442i
$173$	0.950510	−	2.92537i	0.0722659	−	0.222412i	−0.908400	−	0.418103i	$-0.862695\pi$
$173$	0.950510	−	2.92537i	0.0722659	−	0.222412i	0.980666	+	0.195691i	$0.0626951\pi$
$174$	−2.72936	−	8.40009i	−0.206912	−	0.636809i
$175$	2.71821	−	1.97489i	0.205477	−	0.149288i
$176$	1.01604	+	3.12706i	0.0765872	+	0.235711i
$177$	−6.50835	−	4.72859i	−0.489197	−	0.355423i
$178$	−5.99581	−	4.35621i	−0.449405	−	0.326512i
$179$	12.5696	−	9.13234i	0.939495	−	0.682583i	−0.00880382	−	0.999961i	$-0.502802\pi$
$179$	12.5696	−	9.13234i	0.939495	−	0.682583i	0.948299	+	0.317378i	$0.102802\pi$
$180$	7.90990			0.589569
$181$	0.118758			0.00882725			0.00441362	−	0.999990i	$-0.498595\pi$
$181$	0.118758			0.00882725			0.00441362	+	0.999990i	$0.498595\pi$
$182$	0.499260	−	0.362734i	0.0370076	−	0.0268876i
$183$	−8.75689	+	26.9509i	−0.647328	+	1.99227i
$184$	7.56941	+	23.2963i	0.558024	+	1.71742i
$185$	−6.46106			−0.475027
$186$	3.54647	+	13.8434i	0.260040	+	1.01505i
$187$	20.8801			1.52691
$188$	4.64901	+	14.3082i	0.339064	+	1.04353i
$189$	−3.26278	+	10.0418i	−0.237332	+	0.730434i
$190$	1.48935	−	1.08207i	0.108049	−	0.0785019i
$191$	−4.12275			−0.298312			−0.149156	−	0.988814i	$-0.547656\pi$
$191$	−4.12275			−0.298312			−0.149156	+	0.988814i	$0.547656\pi$
$192$	−11.3496			−0.819085
$193$	3.78447	−	2.74958i	0.272412	−	0.197919i	−0.443189	−	0.896428i	$-0.646153\pi$
$193$	3.78447	−	2.74958i	0.272412	−	0.197919i	0.715601	+	0.698509i	$0.246153\pi$
$194$	−3.95499	−	2.87347i	−0.283952	−	0.206303i
$195$	2.07519	+	1.50771i	0.148607	+	0.107969i
$196$	2.68988	+	8.27860i	0.192134	+	0.591329i
$197$	5.69855	−	4.14024i	0.406005	−	0.294980i	−0.365978	−	0.930624i	$-0.619265\pi$
$197$	5.69855	−	4.14024i	0.406005	−	0.294980i	0.771982	+	0.635644i	$0.219265\pi$
$198$	10.4929	+	32.2938i	0.745698	+	2.29502i
$199$	1.17694	−	3.62225i	0.0834311	−	0.256775i	−0.900635	−	0.434576i	$-0.856898\pi$
$199$	1.17694	−	3.62225i	0.0834311	−	0.256775i	0.984066	+	0.177801i	$0.0568984\pi$
$200$	−9.48597	−	6.89196i	−0.670759	−	0.487335i
$201$	−4.11021	+	12.6499i	−0.289912	+	0.892258i
$202$	2.19888	−	6.76745i	0.154712	−	0.476156i
$203$	−2.14560	−	1.55887i	−0.150592	−	0.109411i
$204$	4.82072	−	14.8366i	0.337518	−	1.03877i
$205$	1.05656	+	3.25176i	0.0737934	+	0.227113i
$206$	8.81259	−	6.40272i	0.614002	−	0.446099i
$207$	−20.4724	−	63.0076i	−1.42293	−	4.37933i
$208$	0.456299	+	0.331521i	0.0316387	+	0.0229868i
$209$	−13.5493	−	9.84416i	−0.937226	−	0.680935i
$210$	−1.28064	+	0.930438i	−0.0883724	+	0.0642063i
$211$	18.2532			1.25660			0.628301	−	0.777970i	$-0.283750\pi$
$211$	18.2532			1.25660			0.628301	+	0.777970i	$0.283750\pi$
$212$	4.31123			0.296096
$213$	−13.3870	+	9.72621i	−0.917261	+	0.666429i
$214$	2.93267	−	9.02585i	0.200474	−	0.616994i
$215$	1.28495	+	3.95467i	0.0876330	+	0.269707i
$216$	36.8472			2.50713
$217$	3.30481	+	2.73696i	0.224345	+	0.185797i
$218$	−5.52043			−0.373891
$219$	−3.13784	−	9.65727i	−0.212035	−	0.652578i
$220$	1.95888	−	6.02880i	0.132067	−	0.406462i
$221$	2.89769	−	2.10530i	0.194920	−	0.141618i
$222$	−20.7225			−1.39081
$223$	8.89098			0.595384			0.297692	−	0.954662i	$-0.403783\pi$
$223$	8.89098			0.595384			0.297692	+	0.954662i	$0.403783\pi$
$224$	−3.63544	+	2.64130i	−0.242903	+	0.176479i
$225$	25.6560	+	18.6402i	1.71040	+	1.24268i
$226$	6.25704	+	4.54600i	0.416212	+	0.302396i
$227$	−6.01604	−	18.5155i	−0.399299	−	1.22892i	−0.925563	−	0.378594i	$-0.876408\pi$
$227$	−6.01604	−	18.5155i	−0.399299	−	1.22892i	0.526264	−	0.850321i	$-0.323592\pi$
$228$	−10.1231	+	7.35487i	−0.670419	+	0.487088i
$229$	0.824081	+	2.53626i	0.0544568	+	0.167601i	0.974586	−	0.224015i	$-0.0719164\pi$
$229$	0.824081	+	2.53626i	0.0544568	+	0.167601i	−0.920129	+	0.391615i	$0.871916\pi$
$230$	1.80344	−	5.55041i	0.118915	−	0.365983i
$231$	11.6506	+	8.46465i	0.766553	+	0.556933i
$232$	−2.86004	+	8.80231i	−0.187771	+	0.577900i
$233$	−7.76411	+	23.8955i	−0.508644	+	1.56545i	0.285913	+	0.958256i	$0.407703\pi$
$233$	−7.76411	+	23.8955i	−0.508644	+	1.56545i	−0.794557	+	0.607190i	$0.792297\pi$
$234$	4.71230	+	3.42369i	0.308053	+	0.223813i
$235$	2.73795	−	8.42653i	0.178604	−	0.549686i
$236$	1.05386	+	3.24345i	0.0686004	+	0.211130i
$237$	−34.1290	+	24.7962i	−2.21692	+	1.61069i
$238$	0.683041	+	2.10218i	0.0442750	+	0.136264i
$239$	−6.19428	−	4.50041i	−0.400675	−	0.291107i	0.369141	−	0.929373i	$-0.379652\pi$
$239$	−6.19428	−	4.50041i	−0.400675	−	0.291107i	−0.769816	+	0.638266i	$0.779652\pi$
$240$	−1.17044	−	0.850374i	−0.0755516	−	0.0548914i
$241$	2.34574	−	1.70428i	0.151103	−	0.109782i	−0.509665	−	0.860373i	$-0.670231\pi$
$241$	2.34574	−	1.70428i	0.151103	−	0.109782i	0.660768	+	0.750590i	$0.270231\pi$
$242$	18.4043			1.18307
$243$	−29.7091			−1.90584
$244$	9.71879	−	7.06112i	0.622182	−	0.452042i
$245$	1.58415	−	4.87553i	0.101208	−	0.311486i
$246$	3.38870	+	10.4293i	0.216056	+	0.664951i
$247$	−2.87291			−0.182799
$248$	5.52002	−	13.9202i	0.350522	−	0.883932i
$249$	−49.9657			−3.16645
$250$	1.85335	+	5.70401i	0.117216	+	0.360753i
$251$	−7.38114	+	22.7168i	−0.465893	+	1.43387i	0.391962	+	0.919981i	$0.371796\pi$
$251$	−7.38114	+	22.7168i	−0.465893	+	1.43387i	−0.857856	+	0.513891i	$0.828204\pi$
$252$	6.16285	−	4.47757i	0.388223	−	0.282060i
$253$	−53.0934			−3.33795
$254$	11.1817			0.701603
$255$	−7.43279	+	5.40024i	−0.465459	+	0.338176i
$256$	11.4469	+	8.31663i	0.715429	+	0.519789i
$257$	−4.85390	−	3.52656i	−0.302778	−	0.219981i	0.426013	−	0.904717i	$-0.359918\pi$
$257$	−4.85390	−	3.52656i	−0.302778	−	0.219981i	−0.728791	+	0.684736i	$0.759918\pi$
$258$	4.12122	+	12.6838i	0.256576	+	0.789660i
$259$	−5.03401	+	3.65743i	−0.312798	+	0.227261i
$260$	−0.336023	−	1.03417i	−0.0208393	−	0.0641366i
$261$	7.73535	−	23.8069i	0.478806	−	1.47361i
$262$	6.05802	+	4.40141i	0.374266	+	0.271920i
$263$	2.31271	−	7.11780i	0.142608	−	0.438902i	−0.854088	−	0.520129i	$-0.825884\pi$
$263$	2.31271	−	7.11780i	0.142608	−	0.438902i	0.996696	+	0.0812269i	$0.0258838\pi$
$264$	15.5300	−	47.7964i	0.955806	−	2.94167i
$265$	−2.05411	−	1.49240i	−0.126183	−	0.0916772i
$266$	0.547865	−	1.68616i	0.0335918	−	0.103385i
$267$	−9.16759	−	28.2149i	−0.561048	−	1.72673i
$268$	4.56170	−	3.31427i	0.278650	−	0.202451i
$269$	2.54171	+	7.82257i	0.154971	+	0.476950i	0.998158	−	0.0606695i	$-0.0193236\pi$
$269$	2.54171	+	7.82257i	0.154971	+	0.476950i	−0.843187	+	0.537620i	$0.819324\pi$
$270$	−7.10234	−	5.16015i	−0.432234	−	0.314037i
$271$	−2.27503	−	1.65291i	−0.138198	−	0.100407i	0.516538	−	0.856264i	$-0.327220\pi$
$271$	−2.27503	−	1.65291i	−0.138198	−	0.100407i	−0.654737	+	0.755857i	$0.727220\pi$
$272$	−1.63435	+	1.18742i	−0.0990969	+	0.0719981i
$273$	2.47031			0.149510
$274$	−5.63385			−0.340353
$275$	20.5609	−	14.9384i	1.23987	−	0.900818i
$276$	−12.2580	+	37.7262i	−0.737844	+	2.27085i
$277$	−0.0757420	−	0.233110i	−0.00455090	−	0.0140062i	0.948755	−	0.316012i	$-0.102344\pi$
$277$	−0.0757420	−	0.233110i	−0.00455090	−	0.0140062i	−0.953306	+	0.302006i	$0.902344\pi$
$278$	−3.86518			−0.231818
$279$	−14.9296	+	37.6488i	−0.893810	+	2.25398i
$280$	1.65875			0.0991294
$281$	−3.48276	−	10.7188i	−0.207764	−	0.639433i	−0.999589	−	0.0286837i	$-0.990868\pi$
$281$	−3.48276	−	10.7188i	−0.207764	−	0.639433i	0.791824	−	0.610749i	$-0.209132\pi$
$282$	8.78141	−	27.0264i	0.522925	−	1.60940i
$283$	−0.995894	+	0.723559i	−0.0591998	+	0.0430111i	−0.616992	−	0.786970i	$-0.711649\pi$
$283$	−0.995894	+	0.723559i	−0.0591998	+	0.0430111i	0.557792	+	0.829981i	$0.311649\pi$
$284$	7.01475			0.416249
$285$	7.36921			0.436514
$286$	3.77648	−	2.74377i	0.223308	−	0.162243i
$287$	2.66393	+	1.93546i	0.157247	+	0.114246i
$288$	−34.3133	−	24.9301i	−2.02193	−	1.46902i
$289$	−1.28894	−	3.96695i	−0.0758200	−	0.233350i
$290$	1.78397	−	1.29613i	0.104758	−	0.0761114i
$291$	−6.04718	−	18.6113i	−0.354492	−	1.09101i
$292$	−1.33020	+	4.09394i	−0.0778442	+	0.239580i
$293$	5.04524	+	3.66558i	0.294746	+	0.214146i	0.725324	−	0.688408i	$-0.241690\pi$
$293$	5.04524	+	3.66558i	0.294746	+	0.214146i	−0.430577	+	0.902554i	$0.641690\pi$
$294$	5.08085	−	15.6373i	0.296321	−	0.911984i
$295$	0.620651	−	1.91017i	0.0361357	−	0.111214i
$296$	17.5676	+	12.7636i	1.02110	+	0.741871i
$297$	−24.6801	+	75.9576i	−1.43209	+	4.40751i
$298$	1.87822	+	5.78056i	0.108802	+	0.334859i
$299$	−7.36818	+	5.35329i	−0.426113	+	0.309589i
$300$	−5.86764	−	18.0587i	−0.338768	−	1.04262i
$301$	3.23978	+	2.35383i	0.186738	+	0.135673i
$302$	−6.12324	−	4.44879i	−0.352353	−	0.255999i
$303$	23.0440	−	16.7425i	1.32385	−	0.961830i
$304$	1.62037			0.0929345
$305$	−7.07489			−0.405107
$306$	−16.8783	+	12.2628i	−0.964866	+	0.701016i
$307$	−2.94837	+	9.07415i	−0.168272	+	0.517889i	−0.999263	−	0.0383979i	$-0.987775\pi$
$307$	−2.94837	+	9.07415i	−0.168272	+	0.517889i	0.830990	+	0.556287i	$0.187775\pi$
$308$	−1.88651	−	5.80609i	−0.107494	−	0.330833i
$309$	43.6042			2.48056
$310$	−3.01340	+	1.91009i	−0.171149	+	0.108486i
$311$	5.40918			0.306727			0.153363	−	0.988170i	$-0.450990\pi$
$311$	5.40918			0.306727			0.153363	+	0.988170i	$0.450990\pi$
$312$	−2.66400	−	8.19893i	−0.150819	−	0.464173i
$313$	7.85315	−	24.1695i	0.443886	−	1.36614i	−0.439815	−	0.898089i	$-0.644956\pi$
$313$	7.85315	−	24.1695i	0.443886	−	1.36614i	0.883701	−	0.468052i	$-0.155044\pi$
$314$	10.4541	−	7.59534i	0.589958	−	0.428630i
$315$	−4.48630			−0.252774
$316$	17.8835			1.00603
$317$	20.2716	−	14.7282i	1.13857	−	0.827217i	0.151647	−	0.988435i	$-0.451542\pi$
$317$	20.2716	−	14.7282i	1.13857	−	0.827217i	0.986919	+	0.161218i	$0.0515422\pi$
$318$	−6.58814	−	4.78656i	−0.369444	−	0.268417i
$319$	−16.2296	−	11.7915i	−0.908685	−	0.660199i
$320$	−0.875617	−	2.69487i	−0.0489485	−	0.150648i
$321$	30.7342	−	22.3297i	1.71542	−	1.24632i
$322$	−1.73682	−	5.34538i	−0.0967891	−	0.297886i
$323$	3.17979	−	9.78639i	0.176928	−	0.544530i
$324$	24.2850	+	17.6441i	1.34917	+	0.980227i
$325$	1.34719	−	4.14623i	0.0747287	−	0.229991i
$326$	0.376051	−	1.15737i	0.0208275	−	0.0641006i
$327$	−17.8778	−	12.9890i	−0.988642	−	0.718291i
$328$	3.55096	−	10.9287i	0.196069	−	0.603438i
$329$	−2.63680	−	8.11525i	−0.145372	−	0.447408i
$330$	−9.68693	+	7.03797i	−0.533248	+	0.387427i
$331$	2.52626	+	7.77502i	0.138856	+	0.427354i	0.996170	−	0.0874398i	$-0.0278685\pi$
$331$	2.52626	+	7.77502i	0.138856	+	0.427354i	−0.857314	+	0.514794i	$0.827869\pi$
$332$	17.1363	+	12.4502i	0.940476	+	0.683296i
$333$	−47.5139	−	34.5208i	−2.60374	−	1.89173i
$334$	−4.29883	+	3.12328i	−0.235222	+	0.170899i
$335$	−3.32073			−0.181431
$336$	−1.39330			−0.0760107
$337$	−5.16516	+	3.75271i	−0.281364	+	0.204423i	−0.719512	−	0.694480i	$-0.755635\pi$
$337$	−5.16516	+	3.75271i	−0.281364	+	0.204423i	0.438148	+	0.898903i	$0.355635\pi$
$338$	0.247442	−	0.761548i	0.0134591	−	0.0414228i
$339$	9.56701	+	29.4442i	0.519609	+	1.59919i
$340$	3.89477			0.211223
$341$	24.9981	+	20.7028i	1.35372	+	1.12112i
$342$	16.7339			0.904865
$343$	−3.19272	−	9.82619i	−0.172391	−	0.530565i
$344$	4.31856	−	13.2911i	0.232841	−	0.716611i
$345$	18.8999	−	13.7316i	1.01754	−	0.739283i
$346$	2.46301			0.132412
$347$	18.2542			0.979939			0.489970	−	0.871740i	$-0.337008\pi$
$347$	18.2542			0.979939			0.489970	+	0.871740i	$0.337008\pi$
$348$	−12.1257	+	8.80981i	−0.650004	+	0.472255i
$349$	6.67346	+	4.84855i	0.357222	+	0.259537i	0.751893	−	0.659286i	$-0.229141\pi$
$349$	6.67346	+	4.84855i	0.357222	+	0.259537i	−0.394670	+	0.918823i	$0.629141\pi$
$350$	2.17658	+	1.58137i	0.116343	+	0.0845280i
$351$	4.23359	+	13.0297i	0.225973	+	0.695472i
$352$	−27.4990	+	19.9792i	−1.46570	+	1.06489i
$353$	4.95871	+	15.2613i	0.263925	+	0.812278i	0.991939	+	0.126716i	$0.0404437\pi$
$353$	4.95871	+	15.2613i	0.263925	+	0.812278i	−0.728014	+	0.685562i	$0.759556\pi$
$354$	1.99061	−	6.12647i	0.105800	−	0.325618i
$355$	−3.34222	−	2.42826i	−0.177386	−	0.128879i
$356$	−3.88636	+	11.9610i	−0.205976	+	0.633930i
$357$	−2.73419	+	8.41498i	−0.144709	+	0.445368i
$358$	10.0650	+	7.31262i	0.531950	+	0.386484i
$359$	7.26665	−	22.3644i	0.383519	−	1.18035i	−0.554030	−	0.832497i	$-0.686911\pi$
$359$	7.26665	−	22.3644i	0.383519	−	1.18035i	0.937549	−	0.347853i	$-0.113089\pi$
$360$	4.83804	+	14.8900i	0.254987	+	0.784770i
$361$	8.69402	−	6.31658i	0.457580	−	0.332451i
$362$	0.0293858	+	0.0904403i	0.00154449	+	0.00475344i
$363$	59.6018	+	43.3033i	3.12828	+	2.27283i
$364$	−0.847222	−	0.615543i	−0.0444065	−	0.0322632i
$365$	2.05096	−	1.49011i	0.107352	−	0.0779960i
$366$	−22.6913			−1.18609
$367$	−19.4578			−1.01569			−0.507845	−	0.861449i	$-0.669558\pi$
$367$	−19.4578			−1.01569			−0.507845	+	0.861449i	$0.669558\pi$
$368$	4.15578	−	3.01935i	0.216635	−	0.157394i
$369$	−9.60401	+	29.5581i	−0.499965	+	1.53873i
$370$	−1.59874	−	4.92041i	−0.0831145	−	0.255800i
$371$	−2.44522			−0.126950
$372$	20.4821	−	12.9829i	1.06195	−	0.673134i
$373$	13.3641			0.691969			0.345985	−	0.938240i	$-0.387545\pi$
$373$	13.3641			0.691969			0.345985	+	0.938240i	$0.387545\pi$
$374$	5.16662	+	15.9012i	0.267159	+	0.822232i
$375$	−7.41889	+	22.8330i	−0.383110	+	1.17909i
$376$	−24.0908	+	17.5030i	−1.24239	+	0.902649i
$377$	−3.44123			−0.177232
$378$	−8.45467			−0.434861
$379$	−19.1846	+	13.9384i	−0.985444	+	0.715967i	−0.958919	−	0.283681i	$-0.908444\pi$
$379$	−19.1846	+	13.9384i	−0.985444	+	0.715967i	−0.0265255	+	0.999648i	$0.508444\pi$
$380$	−2.52735	−	1.83623i	−0.129650	−	0.0941966i
$381$	36.2117	+	26.3093i	1.85518	+	1.34787i
$382$	−1.02014	−	3.13967i	−0.0521949	−	0.160640i
$383$	0.406441	−	0.295297i	0.0207682	−	0.0150890i	−0.577353	−	0.816495i	$-0.695914\pi$
$383$	0.406441	−	0.295297i	0.0207682	−	0.0150890i	0.598121	+	0.801406i	$0.295914\pi$
$384$	8.74230	+	26.9060i	0.446129	+	1.37304i
$385$	−1.11103	+	3.41939i	−0.0566232	+	0.174268i
$386$	3.03038	+	2.20170i	0.154242	+	0.112063i
$387$	−11.6801	+	35.9476i	−0.593731	+	1.82732i
$388$	−2.56354	+	7.88977i	−0.130144	+	0.400542i
$389$	−30.4821	−	22.1465i	−1.54550	−	1.12287i	−0.946764	−	0.321929i	$-0.895669\pi$
$389$	−30.4821	−	22.1465i	−1.54550	−	1.12287i	−0.598739	−	0.800945i	$-0.704331\pi$
$390$	−0.634706	+	1.95342i	−0.0321396	+	0.0989155i
$391$	−10.0804	−	31.0244i	−0.509790	−	1.56897i
$392$	−13.9388	+	10.1271i	−0.704015	+	0.511497i
$393$	9.26272	+	28.5077i	0.467242	+	1.43802i
$394$	4.56305	+	3.31525i	0.229883	+	0.167020i
$395$	−8.52071	−	6.19066i	−0.428724	−	0.311486i
$396$	46.6166	−	33.8690i	2.34257	−	1.70198i
$397$	31.1094			1.56134			0.780668	−	0.624946i	$-0.214879\pi$
$397$	31.1094			1.56134			0.780668	+	0.624946i	$0.214879\pi$
$398$	3.04974			0.152870
$399$	5.74158	−	4.17150i	0.287439	−	0.208836i
$400$	−0.759838	+	2.33854i	−0.0379919	+	0.116927i
$401$	−4.81249	−	14.8113i	−0.240324	−	0.739641i	−0.996370	−	0.0851234i	$-0.972872\pi$
$401$	−4.81249	−	14.8113i	−0.240324	−	0.739641i	0.756046	−	0.654518i	$-0.227128\pi$
$402$	−10.6506			−0.531202
$403$	5.55659	+	0.352581i	0.276793	+	0.0175633i
$404$	−12.0750			−0.600755
$405$	−5.46295	−	16.8132i	−0.271456	−	0.835456i
$406$	0.656243	−	2.01971i	0.0325688	−	0.100237i
$407$	−38.0780	+	27.6653i	−1.88746	+	1.37132i
$408$	30.8778			1.52868
$409$	−29.1719			−1.44246			−0.721230	−	0.692696i	$-0.756423\pi$
$409$	−29.1719			−1.44246			−0.721230	+	0.692696i	$0.756423\pi$
$410$	−2.21493	+	1.60924i	−0.109388	+	0.0794748i
$411$	−18.2451	−	13.2558i	−0.899962	−	0.653861i
$412$	−14.9546	−	10.8651i	−0.736758	−	0.535286i
$413$	−0.597724	−	1.83960i	−0.0294121	−	0.0905210i
$414$	42.9176	−	31.1815i	2.10928	−	1.53248i
$415$	−3.85484	−	11.8640i	−0.189227	−	0.582379i
$416$	−1.80179	+	5.54533i	−0.0883398	+	0.271882i
$417$	−12.5173	−	9.09433i	−0.612974	−	0.445351i
$418$	4.14413	−	12.7543i	0.202696	−	0.623834i
$419$	3.62375	−	11.1527i	0.177032	−	0.544847i	−0.822689	−	0.568492i	$-0.807527\pi$
$419$	3.62375	−	11.1527i	0.177032	−	0.544847i	0.999720	+	0.0236447i	$0.00752704\pi$
$420$	2.17318	+	1.57891i	0.106040	+	0.0770429i
$421$	−9.08755	+	27.9686i	−0.442900	+	1.36311i	0.441871	+	0.897079i	$0.354315\pi$
$421$	−9.08755	+	27.9686i	−0.442900	+	1.36311i	−0.884771	+	0.466027i	$0.845685\pi$
$422$	4.51661	+	13.9007i	0.219865	+	0.676675i
$423$	65.1567	−	47.3391i	3.16803	−	2.30171i
$424$	2.63694	+	8.11566i	0.128061	+	0.394131i
$425$	12.6328	+	9.17825i	0.612780	+	0.445211i
$426$	−10.7195	−	7.78816i	−0.519360	−	0.377337i
$427$	−5.51226	+	4.00489i	−0.266757	+	0.193810i
$428$	−16.1047			−0.778448
$429$	18.6858			0.902159
$430$	−2.69372	+	1.95711i	−0.129903	+	0.0943800i
$431$	−5.78972	+	17.8189i	−0.278881	+	0.858307i	0.709286	+	0.704921i	$0.249018\pi$
$431$	−5.78972	+	17.8189i	−0.278881	+	0.858307i	−0.988166	+	0.153386i	$0.950982\pi$
$432$	−2.38782	−	7.34895i	−0.114884	−	0.353577i
$433$	10.2165			0.490974			0.245487	−	0.969400i	$-0.421052\pi$
$433$	10.2165			0.490974			0.245487	+	0.969400i	$0.421052\pi$
$434$	−1.26658	+	3.19401i	−0.0607978	+	0.153318i
$435$	8.82698			0.423222
$436$	2.89484	+	8.90941i	0.138638	+	0.426683i
$437$	−8.08549	+	24.8846i	−0.386782	+	1.19039i
$438$	6.57804	−	4.77923i	0.314311	−	0.228360i
$439$	−4.58712			−0.218931			−0.109466	−	0.993991i	$-0.534914\pi$
$439$	−4.58712			−0.218931			−0.109466	+	0.993991i	$0.534914\pi$
$440$	12.5470			0.598156
$441$	37.6992	−	27.3900i	1.79520	−	1.30429i
$442$	2.32030	+	1.68579i	0.110365	+	0.0801850i
$443$	25.6963	+	18.6695i	1.22087	+	0.887012i	0.996172	−	0.0874165i	$-0.0278611\pi$
$443$	25.6963	+	18.6695i	1.22087	+	0.887012i	0.224696	+	0.974429i	$0.427861\pi$
$444$	10.8666	+	33.4441i	0.515708	+	1.58719i
$445$	5.99215	−	4.35355i	0.284055	−	0.206378i
$446$	2.20000	+	6.77091i	0.104173	+	0.320612i
$447$	−7.51845	+	23.1394i	−0.355610	+	1.09446i
$448$	−2.20771	−	1.60400i	−0.104305	−	0.0757817i
$449$	8.17179	−	25.1502i	0.385651	−	1.18691i	−0.550356	−	0.834930i	$-0.685508\pi$
$449$	8.17179	−	25.1502i	0.385651	−	1.18691i	0.936007	−	0.351981i	$-0.114492\pi$
$450$	−7.84701	+	24.1506i	−0.369912	+	1.13847i
$451$	20.1503	+	14.6401i	0.948842	+	0.689374i
$452$	4.05568	−	12.4821i	0.190763	−	0.587108i
$453$	−9.36243	−	28.8146i	−0.439885	−	1.35383i
$454$	12.6118	−	9.16301i	0.591901	−	0.430041i
$455$	0.190584	+	0.586557i	0.00893472	+	0.0274982i
$456$	−20.0369	−	14.5577i	−0.938313	−	0.681725i
$457$	10.1547	+	7.37782i	0.475017	+	0.345120i	0.799393	−	0.600808i	$-0.205154\pi$
$457$	10.1547	+	7.37782i	0.475017	+	0.345120i	−0.324376	+	0.945928i	$0.605154\pi$
$458$	−1.72757	+	1.25515i	−0.0807242	+	0.0586495i
$459$	−49.0706			−2.29042
$460$	−9.90351			−0.461753
$461$	−9.08745	+	6.60242i	−0.423245	+	0.307505i	−0.778942	−	0.627096i	$-0.784243\pi$
$461$	−9.08745	+	6.60242i	−0.423245	+	0.307505i	0.355697	+	0.934601i	$0.384243\pi$
$462$	−3.56339	+	10.9670i	−0.165784	+	0.510231i
$463$	−3.06229	−	9.42476i	−0.142317	−	0.438006i	0.854339	−	0.519715i	$-0.173962\pi$
$463$	−3.06229	−	9.42476i	−0.142317	−	0.438006i	−0.996656	+	0.0817095i	$0.973962\pi$
$464$	1.94091			0.0901044
$465$	−14.2530	−	0.904396i	−0.660969	−	0.0419404i
$466$	−20.1187			−0.931982
$467$	1.24056	+	3.81804i	0.0574061	+	0.176678i	0.975648	−	0.219342i	$-0.0703911\pi$
$467$	1.24056	+	3.81804i	0.0574061	+	0.176678i	−0.918242	+	0.396020i	$0.870391\pi$
$468$	3.05441	−	9.40051i	0.141190	−	0.434539i
$469$	−2.58729	+	1.87977i	−0.119470	+	0.0867999i
$470$	7.09469			0.327254
$471$	51.7263			2.38342
$472$	−5.46103	+	3.96767i	−0.251364	+	0.182627i
$473$	24.5061	+	17.8047i	1.12679	+	0.818663i
$474$	−27.3285	−	19.8553i	−1.25524	−	0.911983i
$475$	−3.87035	−	11.9117i	−0.177584	−	0.546547i
$476$	3.03453	−	2.20472i	0.139088	−	0.101053i
$477$	−7.13193	−	21.9498i	−0.326548	−	1.00501i
$478$	1.89455	−	5.83083i	0.0866548	−	0.266696i
$479$	−20.6201	−	14.9813i	−0.942154	−	0.684515i	0.00678383	−	0.999977i	$-0.497841\pi$
$479$	−20.6201	−	14.9813i	−0.942154	−	0.684515i	−0.948938	+	0.315462i	$0.897841\pi$
$480$	4.62171	−	14.2242i	0.210951	−	0.649241i
$481$	−2.49494	+	7.67865i	−0.113760	+	0.350116i
$482$	1.87833	+	1.36468i	0.0855555	+	0.0621597i
$483$	6.95243	−	21.3974i	0.316347	−	0.973615i
$484$	−9.65098	−	29.7027i	−0.438681	−	1.35012i
$485$	3.95258	−	2.87172i	0.179477	−	0.130398i
$486$	−7.35129	−	22.6249i	−0.333461	−	1.02629i
$487$	25.1352	+	18.2618i	1.13898	+	0.827519i	0.986977	−	0.160860i	$-0.0514269\pi$
$487$	25.1352	+	18.2618i	1.13898	+	0.827519i	0.152005	+	0.988380i	$0.451427\pi$
$488$	19.2366	+	13.9762i	0.870801	+	0.632674i
$489$	3.94098	−	2.86329i	0.178217	−	0.129483i
$490$	4.10494			0.185442
$491$	−29.5380			−1.33303			−0.666517	−	0.745490i	$-0.732215\pi$
$491$	−29.5380			−1.33303			−0.666517	+	0.745490i	$0.732215\pi$
$492$	15.0549	−	10.9380i	0.678728	−	0.493125i
$493$	3.80882	−	11.7223i	0.171541	−	0.527947i
$494$	−0.710878	−	2.18786i	−0.0319839	−	0.0984364i
$495$	−33.9350			−1.52527
$496$	−3.13401	−	0.198862i	−0.140721	−	0.00892916i
$497$	−3.97860			−0.178464
$498$	−12.3636	−	38.0513i	−0.554027	−	1.70512i
$499$	−7.27694	+	22.3961i	−0.325761	+	1.00259i	0.645336	+	0.763899i	$0.276718\pi$
$499$	−7.27694	+	22.3961i	−0.325761	+	1.00259i	−0.971096	+	0.238689i	$0.923282\pi$
$500$	8.23382	−	5.98222i	0.368228	−	0.267533i
$501$	−21.2704			−0.950291
$502$	−19.1263			−0.853650
$503$	−24.3744	+	17.7090i	−1.08680	+	0.789606i	−0.978856	−	0.204551i	$-0.934427\pi$
$503$	−24.3744	+	17.7090i	−1.08680	+	0.789606i	−0.107944	+	0.994157i	$0.534427\pi$
$504$	12.1983	+	8.86255i	0.543354	+	0.394769i
$505$	5.75322	+	4.17996i	0.256015	+	0.186006i
$506$	−13.1375	−	40.4332i	−0.584035	−	1.79747i
$507$	2.59317	−	1.88405i	0.115167	−	0.0836736i
$508$	−5.86355	−	18.0462i	−0.260153	−	0.800669i
$509$	−7.60953	+	23.4197i	−0.337286	+	1.03806i	0.628298	+	0.777972i	$0.283752\pi$
$509$	−7.60953	+	23.4197i	−0.337286	+	1.03806i	−0.965585	+	0.260088i	$0.916248\pi$
$510$	−5.95172	−	4.32418i	−0.263547	−	0.191478i
$511$	0.754458	−	2.32198i	0.0333753	−	0.102718i
$512$	1.95376	−	6.01306i	0.0863448	−	0.265742i
$513$	31.8424	+	23.1349i	1.40588	+	1.02143i
$514$	1.48459	−	4.56910i	0.0654825	−	0.201534i
$515$	3.36405	+	10.3535i	0.148238	+	0.456229i
$516$	18.3093	−	13.3025i	0.806021	−	0.585608i
$517$	−19.9452	−	61.3849i	−0.877187	−	2.69970i
$518$	−4.03093	−	2.92864i	−0.177109	−	0.128677i
$519$	7.97638	+	5.79518i	0.350124	+	0.254380i
$520$	1.74125	−	1.26509i	0.0763588	−	0.0554779i
$521$	−26.1306			−1.14480			−0.572401	−	0.819974i	$-0.693988\pi$
$521$	−26.1306			−1.14480			−0.572401	+	0.819974i	$0.693988\pi$
$522$	20.0442			0.877310
$523$	−6.55661	+	4.76366i	−0.286701	+	0.208300i	−0.721835	−	0.692065i	$-0.756701\pi$
$523$	−6.55661	+	4.76366i	−0.286701	+	0.208300i	0.435134	+	0.900366i	$0.356701\pi$
$524$	3.92668	−	12.0851i	0.171538	−	0.527939i
$525$	3.32798	+	10.2425i	0.145245	+	0.447018i
$526$	5.99281			0.261299
$527$	−7.35119	+	18.5380i	−0.320223	+	0.807526i
$528$	−10.5391			−0.458656
$529$	18.5249	+	57.0137i	0.805430	+	2.47886i
$530$	0.628260	−	1.93358i	0.0272899	−	0.0839895i
$531$	14.7700	−	10.7311i	0.640965	−	0.465688i
$532$	−3.00858			−0.130438
$533$	4.27254			0.185064
$534$	19.2186	−	13.9631i	0.831670	−	0.604244i
$535$	7.67315	+	5.57487i	0.331739	+	0.241023i
$536$	9.02908	+	6.56001i	0.389997	+	0.283349i
$537$	15.3893	+	47.3635i	0.664098	+	2.04388i
$538$	−5.32834	+	3.87126i	−0.229721	+	0.166902i
$539$	−11.5401	−	35.5168i	−0.497068	−	1.52982i
$540$	−4.60358	+	14.1684i	−0.198107	+	0.609709i
$541$	−17.5447	−	12.7470i	−0.754304	−	0.548034i	0.142854	−	0.989744i	$-0.454372\pi$
$541$	−17.5447	−	12.7470i	−0.754304	−	0.548034i	−0.897158	+	0.441710i	$0.854372\pi$
$542$	0.695830	−	2.14155i	0.0298885	−	0.0919873i
$543$	−0.117631	+	0.362030i	−0.00504802	+	0.0155362i
$544$	−16.8956	−	12.2754i	−0.724392	−	0.526302i
$545$	1.70486	−	5.24703i	0.0730283	−	0.224758i
$546$	0.611259	+	1.88126i	0.0261595	+	0.0805106i
$547$	34.2796	−	24.9056i	1.46569	−	1.06489i	0.483857	−	0.875147i	$-0.339236\pi$
$547$	34.2796	−	24.9056i	1.46569	−	1.06489i	0.981834	−	0.189740i	$-0.0607644\pi$
$548$	2.95432	+	9.09246i	0.126202	+	0.388410i
$549$	−52.0278	−	37.8004i	−2.22049	−	1.61328i
$550$	16.4639	+	11.9617i	0.702024	+	0.510051i
$551$	−7.99820	+	5.81103i	−0.340735	+	0.247558i
$552$	−78.5151			−3.34183
$553$	−10.1431			−0.431329
$554$	0.158783	−	0.115362i	0.00674603	−	0.00490128i
$555$	6.39971	−	19.6963i	0.271652	−	0.836060i
$556$	2.02685	+	6.23800i	0.0859576	+	0.264550i
$557$	−12.0417			−0.510224			−0.255112	−	0.966912i	$-0.582112\pi$
$557$	−12.0417			−0.510224			−0.255112	+	0.966912i	$0.582112\pi$
$558$	−32.3656	−	2.05369i	−1.37015	−	0.0869396i
$559$	5.19612			0.219772
$560$	−0.107493	−	0.330828i	−0.00454239	−	0.0139800i
$561$	−20.6818	+	63.6521i	−0.873187	+	2.68739i
$562$	7.30113	−	5.30458i	0.307980	−	0.223760i
$563$	24.5237			1.03355			0.516775	−	0.856121i	$-0.327132\pi$
$563$	24.5237			1.03355			0.516775	+	0.856121i	$0.327132\pi$
$564$	−48.2227			−2.03054
$565$	−6.25322	+	4.54323i	−0.263075	+	0.191135i
$566$	−0.797451	−	0.579382i	−0.0335194	−	0.0243533i
$567$	−13.7739	−	10.0073i	−0.578447	−	0.420267i
$568$	4.29053	+	13.2049i	0.180027	+	0.554065i
$569$	−23.6472	+	17.1807i	−0.991342	+	0.720252i	−0.960214	−	0.279264i	$-0.909910\pi$
$569$	−23.6472	+	17.1807i	−0.991342	+	0.720252i	−0.0311271	+	0.999515i	$0.509910\pi$
$570$	1.82345	+	5.61201i	0.0763760	+	0.235061i
$571$	−4.30667	+	13.2546i	−0.180229	+	0.554687i	−0.999834	−	0.0182424i	$-0.994193\pi$
$571$	−4.30667	+	13.2546i	−0.180229	+	0.554687i	0.819605	+	0.572929i	$0.194193\pi$
$572$	−6.40850	−	4.65605i	−0.267953	−	0.194679i
$573$	4.08360	−	12.5680i	0.170595	−	0.525036i
$574$	−0.814776	+	2.50762i	−0.0340081	+	0.104666i
$575$	−32.1223	−	23.3382i	−1.33959	−	0.973271i
$576$	7.95926	−	24.4961i	0.331636	−	1.02067i
$577$	6.60517	+	20.3286i	0.274977	+	0.846291i	0.989226	+	0.146399i	$0.0467685\pi$
$577$	6.60517	+	20.3286i	0.274977	+	0.846291i	−0.714249	+	0.699892i	$0.753232\pi$
$578$	2.70209	−	1.96318i	0.112392	−	0.0816575i
$579$	4.63344	+	14.2603i	0.192559	+	0.592637i
$580$	−3.02731	−	2.19947i	−0.125702	−	0.0913281i
$581$	−9.71928	−	7.06147i	−0.403224	−	0.292959i
$582$	12.6771	−	9.21044i	0.525482	−	0.381785i
$583$	−18.4960			−0.766027
$584$	−8.52024			−0.352570
$585$	−4.70942	+	3.42160i	−0.194711	+	0.141466i
$586$	−1.54311	+	4.74922i	−0.0637454	+	0.196188i
$587$	−8.58863	−	26.4331i	−0.354491	−	1.09101i	−0.956304	−	0.292373i	$-0.905555\pi$
$587$	−8.58863	−	26.4331i	−0.354491	−	1.09101i	0.601814	−	0.798637i	$-0.294445\pi$
$588$	−27.9013			−1.15063
$589$	13.5102	−	8.56367i	0.556678	−	0.352860i
$590$	1.60826			0.0662110
$591$	6.97690	+	21.4727i	0.286991	+	0.883269i
$592$	1.40719	−	4.33089i	0.0578352	−	0.177998i
$593$	37.1455	−	26.9878i	1.52538	−	1.10826i	0.566648	−	0.823960i	$-0.308240\pi$
$593$	37.1455	−	26.9878i	1.52538	−	1.10826i	0.958737	−	0.284296i	$-0.0917599\pi$
$594$	−63.9523			−2.62399
$595$	−2.20902			−0.0905608
$596$	8.34432	−	6.06250i	0.341797	−	0.248330i
$597$	9.87651	+	7.17570i	0.404219	+	0.293682i
$598$	−5.89999	−	4.28659i	−0.241268	−	0.175292i
$599$	10.0120	+	30.8138i	0.409079	+	1.25902i	0.917441	+	0.397873i	$0.130251\pi$
$599$	10.0120	+	30.8138i	0.409079	+	1.25902i	−0.508362	+	0.861144i	$0.669749\pi$
$600$	30.4057	−	22.0911i	1.24131	−	0.901863i
$601$	−3.69709	−	11.3785i	−0.150807	−	0.464137i	0.846905	−	0.531745i	$-0.178463\pi$
$601$	−3.69709	−	11.3785i	−0.150807	−	0.464137i	−0.997712	+	0.0676074i	$0.978463\pi$
$602$	−0.990902	+	3.04968i	−0.0403861	+	0.124296i
$603$	−24.4203	−	17.7424i	−0.994470	−	0.722525i
$604$	−3.96895	+	12.2152i	−0.161494	+	0.497028i
$605$	−5.68377	+	17.4928i	−0.231078	+	0.711185i
$606$	18.4523	+	13.4064i	0.749572	+	0.544596i
$607$	1.44766	−	4.45543i	0.0587586	−	0.180840i	−0.917369	−	0.398037i	$-0.869691\pi$
$607$	1.44766	−	4.45543i	0.0587586	−	0.180840i	0.976128	+	0.217197i	$0.0696914\pi$
$608$	5.17637	+	15.9312i	0.209929	+	0.646096i
$609$	6.87738	−	4.99671i	0.278685	−	0.202477i
$610$	−1.75062	−	5.38787i	−0.0708807	−	0.218148i
$611$	−8.95725	−	6.50782i	−0.362371	−	0.263278i
$612$	28.6416	+	20.8094i	1.15777	+	0.841168i
$613$	10.0322	−	7.28883i	0.405197	−	0.294393i	−0.366457	−	0.930435i	$-0.619429\pi$
$613$	10.0322	−	7.28883i	0.405197	−	0.294393i	0.771655	+	0.636042i	$0.219429\pi$
$614$	−7.63995			−0.308323
$615$	−10.9594			−0.441924
$616$	9.77578	−	7.10252i	0.393878	−	0.286169i
$617$	−1.55200	+	4.77656i	−0.0624810	+	0.192297i	−0.977424	−	0.211285i	$-0.932235\pi$
$617$	−1.55200	+	4.77656i	−0.0624810	+	0.192297i	0.914943	+	0.403582i	$0.132235\pi$
$618$	10.7895	+	33.2067i	0.434018	+	1.33577i
$619$	−43.8451			−1.76228			−0.881142	−	0.472851i	$-0.843225\pi$
$619$	−43.8451			−1.76228			−0.881142	+	0.472851i	$0.843225\pi$
$620$	4.66289	+	3.86169i	0.187266	+	0.155089i
$621$	124.775			5.00707
$622$	1.33846	+	4.11935i	0.0536673	+	0.165171i
$623$	2.20425	−	6.78397i	0.0883113	−	0.271794i
$624$	−1.46259	+	1.06264i	−0.0585506	+	0.0425395i
$625$	15.8041			0.632165
$626$	20.3494			0.813327
$627$	43.4301	−	31.5538i	1.73443	−	1.26014i
$628$	−17.7401	−	12.8889i	−0.707907	−	0.514325i
$629$	−23.3954	−	16.9978i	−0.932836	−	0.677745i
$630$	−1.11010	−	3.41653i	−0.0442274	−	0.136118i
$631$	−2.26648	+	1.64670i	−0.0902272	+	0.0655539i	−0.631984	−	0.774981i	$-0.717759\pi$
$631$	−2.26648	+	1.64670i	−0.0902272	+	0.0655539i	0.541757	+	0.840535i	$0.317759\pi$
$632$	10.9384	+	33.6648i	0.435105	+	1.33911i
$633$	−18.0799	+	55.6441i	−0.718610	+	2.21166i
$634$	16.2323	+	11.7934i	0.644665	+	0.468377i
$635$	−3.45323	+	10.6279i	−0.137037	+	0.421757i
$636$	−4.27029	+	13.1426i	−0.169328	+	0.521138i
$637$	−5.18260	−	3.76538i	−0.205342	−	0.149190i
$638$	4.96392	−	15.2774i	0.196523	−	0.604837i
$639$	−11.6043	−	35.7143i	−0.459058	−	1.41284i
$640$	−5.71417	+	4.15159i	−0.225872	+	0.164106i
$641$	−5.21601	−	16.0532i	−0.206020	−	0.634065i	−0.999670	−	0.0256900i	$-0.991822\pi$
$641$	−5.21601	−	16.0532i	−0.206020	−	0.634065i	0.793650	−	0.608375i	$-0.208178\pi$
$642$	24.6101	+	17.8803i	0.971282	+	0.705678i
$643$	30.1516	+	21.9064i	1.18906	+	0.863904i	0.993165	−	0.116720i	$-0.0372380\pi$
$643$	30.1516	+	21.9064i	1.18906	+	0.863904i	0.195897	+	0.980624i	$0.437238\pi$
$644$	−7.71613	+	5.60610i	−0.304058	+	0.220911i
$645$	−13.3284			−0.524805
$646$	8.23963			0.324184
$647$	0.541048	−	0.393094i	0.0212708	−	0.0154541i	−0.577099	−	0.816674i	$-0.695815\pi$
$647$	0.541048	−	0.393094i	0.0212708	−	0.0154541i	0.598370	+	0.801220i	$0.295815\pi$
$648$	−18.3603	+	56.5071i	−0.721260	+	2.21981i
$649$	−4.52127	−	13.9150i	−0.177475	−	0.546213i
$650$	3.49090			0.136924
$651$	−11.6169	+	7.36360i	−0.455304	+	0.288602i
$652$	−2.06507			−0.0808743
$653$	−6.44183	−	19.8259i	−0.252088	−	0.775848i	−0.994389	−	0.105781i	$-0.966266\pi$
$653$	−6.44183	−	19.8259i	−0.252088	−	0.775848i	0.742301	−	0.670066i	$-0.233734\pi$
$654$	5.46800	−	16.8288i	0.213816	−	0.658058i
$655$	−6.05432	+	4.39872i	−0.236562	+	0.171872i
$656$	−2.40979			−0.0940863
$657$	23.0440			0.899034
$658$	5.52770	−	4.01611i	0.215492	−	0.156564i
$659$	−11.9950	−	8.71488i	−0.467259	−	0.339483i	0.329113	−	0.944290i	$-0.393250\pi$
$659$	−11.9950	−	8.71488i	−0.467259	−	0.339483i	−0.796372	+	0.604807i	$0.793250\pi$
$660$	16.4383	+	11.9431i	0.639859	+	0.464885i
$661$	2.81559	+	8.66550i	0.109514	+	0.337049i	0.990763	−	0.135602i	$-0.0432970\pi$
$661$	2.81559	+	8.66550i	0.109514	+	0.337049i	−0.881250	+	0.472651i	$0.843297\pi$
$662$	−5.29595	+	3.84773i	−0.205833	+	0.149546i
$663$	3.54773	+	10.9188i	0.137782	+	0.424051i
$664$	−12.9556	+	39.8733i	−0.502775	+	1.54738i
$665$	1.43345	+	1.04146i	0.0555869	+	0.0403863i
$666$	14.5324	−	44.7260i	0.563117	−	1.73310i
$667$	−9.68496	+	29.8072i	−0.375003	+	1.15414i
$668$	7.29492	+	5.30007i	0.282249	+	0.205066i
$669$	−8.80655	+	27.1038i	−0.340481	+	1.04789i
$670$	−0.821689	−	2.52890i	−0.0317446	−	0.0976999i
$671$	−41.6955	+	30.2936i	−1.60964	+	1.16947i
$672$	−4.45098	−	13.6987i	−0.171700	−	0.528439i
$673$	26.5863	+	19.3161i	1.02483	+	0.744581i	0.967267	−	0.253761i	$-0.0816677\pi$
$673$	26.5863	+	19.3161i	1.02483	+	0.744581i	0.0575609	+	0.998342i	$0.481668\pi$
$674$	−4.13595	−	3.00494i	−0.159311	−	0.115746i
$675$	−48.3205	+	35.1069i	−1.85986	+	1.35126i
$676$	−1.35882			−0.0522622
$677$	26.0045			0.999436			0.499718	−	0.866188i	$-0.333437\pi$
$677$	26.0045			0.999436			0.499718	+	0.866188i	$0.333437\pi$
$678$	−20.0559	+	14.5715i	−0.770243	+	0.559614i
$679$	1.45398	−	4.47488i	0.0557986	−	0.171730i
$680$	2.38221	+	7.33169i	0.0913536	+	0.281157i
$681$	62.4025			2.39127
$682$	−9.58059	+	24.1600i	−0.366860	+	0.925133i
$683$	−45.9466			−1.75810			−0.879048	−	0.476733i	$-0.841821\pi$
$683$	−45.9466			−1.75810			−0.879048	+	0.476733i	$0.841821\pi$
$684$	−8.77504	−	27.0068i	−0.335522	−	1.03263i
$685$	1.73989	−	5.35483i	0.0664778	−	0.204598i
$686$	6.69311	−	4.86283i	0.255544	−	0.185664i
$687$	−8.54794			−0.326124
$688$	−2.93070			−0.111732
$689$	−2.56683	+	1.86491i	−0.0977886	+	0.0710476i
$690$	15.1339	+	10.9954i	0.576137	+	0.418588i
$691$	2.30936	+	1.67785i	0.0878523	+	0.0638284i	0.630844	−	0.775909i	$-0.282709\pi$
$691$	2.30936	+	1.67785i	0.0878523	+	0.0638284i	−0.542992	+	0.839738i	$0.682709\pi$
$692$	−1.29157	−	3.97504i	−0.0490981	−	0.151108i
$693$	−26.4398	+	19.2097i	−1.00437	+	0.729714i
$694$	4.51687	+	13.9015i	0.171458	+	0.527693i
$695$	1.19368	−	3.67376i	0.0452787	−	0.139354i
$696$	−24.0006	−	17.4374i	−0.909740	−	0.660965i
$697$	−4.72893	+	14.5542i	−0.179121	+	0.551278i
$698$	−2.04111	+	6.28190i	−0.0772572	+	0.237773i
$699$	−65.1540	−	47.3371i	−2.46435	−	1.79045i
$700$	1.41081	−	4.34203i	0.0533236	−	0.164113i
$701$	−3.56079	−	10.9590i	−0.134489	−	0.413915i	0.861021	−	0.508569i	$-0.169825\pi$
$701$	−3.56079	−	10.9590i	−0.134489	−	0.413915i	−0.995510	+	0.0946542i	$0.969825\pi$
$702$	−8.87515	+	6.44817i	−0.334971	+	0.243371i
$703$	7.16774	+	22.0600i	0.270337	+	0.832010i
$704$	−16.6994	−	12.1329i	−0.629384	−	0.457274i
$705$	22.9760	+	16.6930i	0.865325	+	0.628696i
$706$	−10.3952	+	7.55259i	−0.391230	+	0.284245i
$707$	6.84866			0.257571
$708$	−10.9314			−0.410826
$709$	−13.6933	+	9.94874i	−0.514262	+	0.373633i	−0.814438	−	0.580251i	$-0.802954\pi$
$709$	−13.6933	+	9.94874i	−0.514262	+	0.373633i	0.300176	+	0.953884i	$0.402954\pi$
$710$	1.02223	−	3.14611i	0.0383638	−	0.118072i
$711$	−29.5842	−	91.0507i	−1.10949	−	3.41467i
$712$	−24.8930			−0.932903
$713$	18.6924	−	47.1378i	0.700037	−	1.76533i
$714$	−7.08497			−0.265148
$715$	1.44160	+	4.43680i	0.0539130	+	0.165927i
$716$	6.52389	−	20.0785i	0.243809	−	0.750368i
$717$	19.8548	−	14.4253i	0.741490	−	0.538724i
$718$	18.8297			0.702717
$719$	−24.8752			−0.927690			−0.463845	−	0.885916i	$-0.653531\pi$
$719$	−24.8752			−0.927690			−0.463845	+	0.885916i	$0.653531\pi$
$720$	2.65619	−	1.92984i	0.0989905	−	0.0719208i
$721$	8.48186	+	6.16243i	0.315881	+	0.229501i
$722$	6.96164	+	5.05793i	0.259086	+	0.188237i
$723$	2.87196	+	8.83899i	0.106809	+	0.328726i
$724$	0.130552	−	0.0948515i	0.00485192	−	0.00352513i
$725$	−4.63599	−	14.2681i	−0.172176	−	0.529904i
$726$	−18.2295	+	56.1047i	−0.676561	+	2.08224i
$727$	9.87190	+	7.17236i	0.366129	+	0.266008i	0.755604	−	0.655029i	$-0.227344\pi$
$727$	9.87190	+	7.17236i	0.366129	+	0.266008i	−0.389475	+	0.921037i	$0.627344\pi$
$728$	0.640528	−	1.97134i	0.0237396	−	0.0730628i
$729$	8.94734	−	27.5371i	0.331383	−	1.01989i
$730$	1.64229	+	1.19319i	0.0607837	+	0.0441620i
$731$	−5.75117	+	17.7003i	−0.212715	+	0.654668i
$732$	11.8990	+	36.6214i	0.439800	+	1.35357i
$733$	4.37260	−	3.17688i	0.161506	−	0.117341i	−0.504097	−	0.863647i	$-0.668175\pi$
$733$	4.37260	−	3.17688i	0.161506	−	0.117341i	0.665603	+	0.746306i	$0.268175\pi$
$734$	−4.81468	−	14.8181i	−0.177713	−	0.546945i
$735$	13.2937	+	9.65846i	0.490346	+	0.356257i
$736$	42.9616	+	31.2135i	1.58359	+	1.15054i
$737$	−19.5706	+	14.2189i	−0.720892	+	0.523759i
$738$	−24.8864			−0.916080
$739$	38.1203			1.40228			0.701139	−	0.713024i	$-0.252675\pi$
$739$	38.1203			1.40228			0.701139	+	0.713024i	$0.252675\pi$
$740$	−7.10269	+	5.16040i	−0.261100	+	0.189700i
$741$	2.84563	−	8.75793i	0.104537	−	0.321731i
$742$	−0.605051	−	1.86216i	−0.0222121	−	0.0683619i
$743$	22.8466			0.838160			0.419080	−	0.907949i	$-0.362353\pi$
$743$	22.8466			0.838160			0.419080	+	0.907949i	$0.362353\pi$
$744$	36.9674	+	30.6155i	1.35529	+	1.12242i
$745$	−6.07432			−0.222546
$746$	3.30685	+	10.1774i	0.121072	+	0.372623i
$747$	35.0401	−	107.842i	1.28205	−	3.94574i
$748$	22.9536	−	16.6768i	0.839268	−	0.609764i
$749$	9.13417			0.333755
$750$	−19.2242			−0.701968
$751$	−18.7030	+	13.5885i	−0.682483	+	0.495853i	−0.874180	−	0.485601i	$-0.838601\pi$
$751$	−18.7030	+	13.5885i	−0.682483	+	0.495853i	0.191698	+	0.981454i	$0.438601\pi$
$752$	5.05204	+	3.67052i	0.184229	+	0.133850i
$753$	−61.9401	−	45.0021i	−2.25722	−	1.63997i
$754$	−0.851504	−	2.62066i	−0.0310099	−	0.0954388i
$755$	6.11950	−	4.44607i	0.222711	−	0.161809i
$756$	4.43352	+	13.6450i	0.161246	+	0.496263i
$757$	−13.4504	+	41.3960i	−0.488863	+	1.50456i	0.337445	+	0.941345i	$0.390437\pi$
$757$	−13.4504	+	41.3960i	−0.488863	+	1.50456i	−0.826307	+	0.563220i	$0.809563\pi$
$758$	−15.3618	−	11.1610i	−0.557966	−	0.405386i
$759$	52.5892	−	161.853i	1.90887	−	5.87489i
$760$	1.91076	−	5.88073i	0.0693107	−	0.213316i
$761$	−23.2448	−	16.8883i	−0.842623	−	0.612201i	0.0804791	−	0.996756i	$-0.474355\pi$
$761$	−23.2448	−	16.8883i	−0.842623	−	0.612201i	−0.923102	+	0.384555i	$0.874355\pi$
$762$	−11.0755	+	34.0870i	−0.401224	+	1.23484i
$763$	−1.64188	−	5.05320i	−0.0594402	−	0.182938i
$764$	−4.53216	+	3.29281i	−0.163968	+	0.119130i
$765$	−6.44298	−	19.8295i	−0.232947	−	0.716936i
$766$	0.325453	+	0.236456i	0.0117591	+	0.00854349i
$767$	−2.03047	−	1.47522i	−0.0733161	−	0.0532673i
$768$	−36.6910	+	26.6576i	−1.32397	+	0.961923i
$769$	19.1473			0.690471			0.345235	−	0.938516i	$-0.387799\pi$
$769$	19.1473			0.690471			0.345235	+	0.938516i	$0.387799\pi$
$770$	−2.87894			−0.103750
$771$	15.5584	−	11.3038i	0.560321	−	0.407097i
$772$	1.96422	−	6.04526i	0.0706940	−	0.217574i
$773$	−6.27679	−	19.3180i	−0.225761	−	0.694819i	−0.998214	−	0.0597475i	$-0.980970\pi$
$773$	−6.27679	−	19.3180i	−0.225761	−	0.694819i	0.772453	−	0.635072i	$-0.219030\pi$
$774$	−30.2659			−1.08789
$775$	6.02390	+	23.5139i	0.216385	+	0.844643i
$776$	−16.4200			−0.589445
$777$	−6.16329	−	18.9687i	−0.221107	−	0.680497i
$778$	9.32310	−	28.6935i	0.334249	−	1.02871i
$779$	9.93037	−	7.21484i	0.355792	−	0.258498i
$780$	3.48546			0.124800
$781$	−30.0947			−1.07687
$782$	21.1323	−	15.3535i	0.755688	−	0.549039i
$783$	38.1415	+	27.7114i	1.36307	+	0.990325i
$784$	2.92307	+	2.12374i	0.104395	+	0.0758477i
$785$	3.99067	+	12.2820i	0.142433	+	0.438364i
$786$	−19.4180	+	14.1080i	−0.692617	+	0.503216i
$787$	7.32237	+	22.5359i	0.261014	+	0.803319i	0.992585	+	0.121553i	$0.0387876\pi$
$787$	7.32237	+	22.5359i	0.261014	+	0.803319i	−0.731571	+	0.681766i	$0.761212\pi$
$788$	2.95767	−	9.10278i	0.105363	−	0.324273i
$789$	19.4075	+	14.1004i	0.690927	+	0.501988i
$790$	2.60610	−	8.02076i	0.0927210	−	0.285366i
$791$	−2.30028	+	7.07954i	−0.0817886	+	0.251719i
$792$	92.2693	+	67.0376i	3.27865	+	2.38208i
$793$	−2.73197	+	8.40814i	−0.0970151	+	0.298582i
$794$	7.69777	+	23.6913i	0.273184	+	0.840773i
$795$	6.58411	−	4.78364i	0.233514	−	0.169658i
$796$	−1.59925	−	4.92198i	−0.0566838	−	0.174455i
$797$	−28.2369	−	20.5153i	−1.00020	−	0.726688i	−0.0380694	−	0.999275i	$-0.512121\pi$
$797$	−28.2369	−	20.5153i	−1.00020	−	0.726688i	−0.962131	+	0.272587i	$0.912121\pi$
$798$	4.59751	+	3.34029i	0.162750	+	0.118245i
$799$	32.0826	−	23.3094i	1.13500	−	0.824626i
$800$	−25.4195			−0.898716
$801$	67.3261			2.37885
$802$	10.0887	−	7.32988i	0.356245	−	0.258827i
$803$	5.70683	−	17.5638i	0.201390	−	0.619813i
$804$	5.58503	+	17.1889i	0.196969	+	0.606207i
$805$	5.61703			0.197974
$806$	1.10643	+	4.31885i	0.0389722	+	0.152125i
$807$	−26.3643			−0.928068
$808$	−7.38562	−	22.7306i	−0.259825	−	0.799660i
$809$	−5.56917	+	17.1401i	−0.195802	+	0.602615i	0.804165	+	0.594406i	$0.202613\pi$
$809$	−5.56917	+	17.1401i	−0.195802	+	0.602615i	−0.999966	+	0.00820867i	$0.997387\pi$
$810$	11.4523	−	8.32060i	0.402394	−	0.292356i
$811$	51.0860			1.79387			0.896936	−	0.442161i	$-0.145788\pi$
$811$	51.0860			1.79387			0.896936	+	0.442161i	$0.145788\pi$
$812$	−3.60373			−0.126466
$813$	7.29225	−	5.29813i	0.255750	−	0.185813i
$814$	−30.4905	−	22.1527i	−1.06869	−	0.776451i
$815$	0.983913	+	0.714855i	0.0344650	+	0.0250403i
$816$	−2.00098	−	6.15839i	−0.0700483	−	0.215587i
$817$	12.0770	−	8.77443i	0.422520	−	0.306979i
$818$	−7.21836	−	22.2158i	−0.252384	−	0.776758i
$819$	−1.73239	+	5.33174i	−0.0605345	+	0.186306i
$820$	3.75864	+	2.73081i	0.131257	+	0.0953640i
$821$	15.5456	−	47.8445i	0.542546	−	1.66979i	−0.184207	−	0.982888i	$-0.558972\pi$
$821$	15.5456	−	47.8445i	0.542546	−	1.66979i	0.726753	−	0.686899i	$-0.241028\pi$
$822$	5.58034	−	17.1745i	0.194637	−	0.599031i
$823$	30.6416	+	22.2624i	1.06810	+	0.776020i	0.975570	−	0.219690i	$-0.0705046\pi$
$823$	30.6416	+	22.2624i	1.06810	+	0.776020i	0.0925301	+	0.995710i	$0.470505\pi$
$824$	11.3061	−	34.7967i	0.393868	−	1.21220i
$825$	25.1733	+	77.4756i	0.876423	+	2.69735i
$826$	1.25305	−	0.910391i	0.0435990	−	0.0316765i
$827$	−8.41683	−	25.9043i	−0.292682	−	0.900782i	−0.983990	−	0.178222i	$-0.942965\pi$
$827$	−8.41683	−	25.9043i	−0.292682	−	0.900782i	0.691309	−	0.722560i	$-0.257035\pi$
$828$	−72.8291	−	52.9135i	−2.53099	−	1.83887i
$829$	8.40218	+	6.10454i	0.291820	+	0.212019i	0.724056	−	0.689741i	$-0.242275\pi$
$829$	8.40218	+	6.10454i	0.291820	+	0.212019i	−0.432237	+	0.901760i	$0.642275\pi$
$830$	8.08114	−	5.87129i	0.280500	−	0.203795i
$831$	0.785649			0.0272538
$832$	−3.54084			−0.122756
$833$	18.5627	−	13.4866i	0.643161	−	0.467284i
$834$	3.82847	−	11.7828i	0.132569	−	0.408006i
$835$	−1.64100	−	5.05049i	−0.0567893	−	0.174780i
$836$	−22.7573			−0.787078
$837$	−58.7483	−	48.6539i	−2.03064	−	1.68172i
$838$	9.39002			0.324373
$839$	5.61878	+	17.2928i	0.193982	+	0.597015i	0.999987	+	0.00510632i	$0.00162540\pi$
$839$	5.61878	+	17.2928i	0.193982	+	0.597015i	−0.806005	+	0.591909i	$0.798375\pi$
$840$	−1.64300	+	5.05663i	−0.0566889	+	0.174470i
$841$	13.8811	−	10.0852i	0.478658	−	0.347766i
$842$	−23.5481			−0.811520
$843$	36.1256			1.24423
$844$	20.0659	−	14.5787i	0.690696	−	0.501820i
$845$	0.647416	+	0.470375i	0.0222718	+	0.0161814i
$846$	52.1735	+	37.9063i	1.79376	+	1.30324i
$847$	5.47380	+	16.8466i	0.188082	+	0.578857i
$848$	1.44774	−	1.05184i	0.0497155	−	0.0361204i
$849$	−1.21930	−	3.75263i	−0.0418464	−	0.128790i
$850$	−3.86380	+	11.8916i	−0.132527	+	0.407877i
$851$	59.4892	+	43.2215i	2.03926	+	1.48161i
$852$	−6.94814	+	21.3842i	−0.238039	+	0.732609i
$853$	3.48312	−	10.7199i	0.119260	−	0.367043i	−0.873552	−	0.486731i	$-0.838189\pi$
$853$	3.48312	−	10.7199i	0.119260	−	0.367043i	0.992812	+	0.119687i	$0.0381892\pi$
$854$	−4.41388	−	3.20687i	−0.151040	−	0.109737i
$855$	−5.16790	+	15.9052i	−0.176738	+	0.543945i
$856$	−9.85032	−	30.3162i	−0.336677	−	1.03619i
$857$	29.5346	−	21.4582i	1.00888	−	0.732997i	0.0449096	−	0.998991i	$-0.485700\pi$
$857$	29.5346	−	21.4582i	1.00888	−	0.732997i	0.963975	+	0.265994i	$0.0857000\pi$
$858$	4.62365	+	14.2301i	0.157849	+	0.485809i
$859$	35.9929	+	26.1503i	1.22806	+	0.892238i	0.996743	−	0.0806403i	$-0.0256965\pi$
$859$	35.9929	+	26.1503i	1.22806	+	0.892238i	0.231317	+	0.972878i	$0.425697\pi$
$860$	4.57112	+	3.32112i	0.155874	+	0.113249i
$861$	−8.53878	+	6.20379i	−0.291001	+	0.211425i
$862$	−15.0026			−0.510990
$863$	−34.0617			−1.15947			−0.579737	−	0.814803i	$-0.696845\pi$
$863$	−34.0617			−1.15947			−0.579737	+	0.814803i	$0.696845\pi$
$864$	64.6257	−	46.9533i	2.19861	−	1.59738i
$865$	−0.760645	+	2.34103i	−0.0258627	+	0.0795973i
$866$	2.52799	+	7.78036i	0.0859047	+	0.264387i
$867$	13.3698			0.454061
$868$	5.81899	+	0.369232i	0.197509	+	0.0125325i
$869$	−76.7239			−2.60268
$870$	2.18417	+	6.72217i	0.0740502	+	0.227903i
$871$	−1.28230	+	3.94652i	−0.0434492	+	0.133723i
$872$	−15.0009	+	10.8988i	−0.507994	+	0.369079i
$873$	44.4101			1.50305
$874$	−20.9515			−0.708695
$875$	−4.67002	+	3.39297i	−0.157876	+	0.114703i
$876$	−11.1626	−	8.11013i	−0.377150	−	0.274016i
$877$	−9.55809	−	6.94436i	−0.322754	−	0.234494i	0.414596	−	0.910006i	$-0.363923\pi$
$877$	−9.55809	−	6.94436i	−0.322754	−	0.234494i	−0.737350	+	0.675511i	$0.763923\pi$
$878$	−1.13505	−	3.49331i	−0.0383059	−	0.117894i
$879$	−16.1717	+	11.7494i	−0.545458	+	0.396299i
$880$	−0.813089	−	2.50243i	−0.0274092	−	0.0843570i
$881$	8.11209	−	24.9664i	0.273303	−	0.841141i	−0.716360	−	0.697731i	$-0.754193\pi$
$881$	8.11209	−	24.9664i	0.273303	−	0.841141i	0.989663	−	0.143410i	$-0.0458067\pi$
$882$	30.1872	+	21.9323i	1.01646	+	0.738498i
$883$	−8.71190	+	26.8125i	−0.293179	+	0.902311i	0.690648	+	0.723191i	$0.257325\pi$
$883$	−8.71190	+	26.8125i	−0.293179	+	0.902311i	−0.983827	+	0.179121i	$0.942675\pi$
$884$	1.50397	−	4.62873i	0.0505839	−	0.155681i
$885$	5.20831	+	3.78406i	0.175075	+	0.127200i
$886$	−7.85934	+	24.1886i	−0.264040	+	0.812631i
$887$	2.94726	+	9.07073i	0.0989593	+	0.304565i	0.988265	−	0.152747i	$-0.0488120\pi$
$887$	2.94726	+	9.07073i	0.0989593	+	0.304565i	−0.889306	+	0.457313i	$0.848812\pi$
$888$	−56.3102	+	40.9118i	−1.88965	+	1.37291i
$889$	3.32566	+	10.2353i	0.111539	+	0.343282i
$890$	4.79815	+	3.48606i	0.160834	+	0.116853i
$891$	−104.187	−	75.6966i	−3.49041	−	2.53593i
$892$	9.77391	−	7.10116i	0.327255	−	0.237764i
$893$	−31.8082			−1.06442
$894$	−19.4822			−0.651581
$895$	−10.0588	+	7.30816i	−0.336229	+	0.244285i
$896$	−2.10199	+	6.46926i	−0.0702225	+	0.216123i
$897$	−9.02108	−	27.7640i	−0.301205	−	0.927014i
$898$	21.1751			0.706623
$899$	16.1828	−	10.2577i	0.539725	−	0.342114i
$900$	43.0915			1.43638
$901$	−3.51170	−	10.8079i	−0.116992	−	0.360063i
$902$	−6.16308	+	18.9680i	−0.205208	+	0.631566i
$903$	−10.3846	+	7.54483i	−0.345577	+	0.251076i
$904$	25.9775			0.863999
$905$	−0.0950365			−0.00315912
$906$	19.6270	−	14.2599i	0.652065	−	0.473753i
$907$	34.8163	+	25.2955i	1.15606	+	0.839924i	0.989274	−	0.146069i	$-0.0466623\pi$
$907$	34.8163	+	25.2955i	1.15606	+	0.839924i	0.166782	+	0.985994i	$0.446662\pi$
$908$	−21.4016	−	15.5492i	−0.710238	−	0.516018i
$909$	19.9753	+	61.4778i	0.662540	+	2.03909i
$910$	−0.399533	+	0.290278i	−0.0132444	+	0.00962262i
$911$	2.03407	+	6.26022i	0.0673917	+	0.207410i	0.979081	−	0.203469i	$-0.0652217\pi$
$911$	2.03407	+	6.26022i	0.0673917	+	0.207410i	−0.911690	+	0.410880i	$0.865222\pi$
$912$	−1.60498	+	4.93962i	−0.0531462	+	0.163567i
$913$	−73.5180	−	53.4140i	−2.43309	−	1.76774i
$914$	−3.10587	+	9.55887i	−0.102733	+	0.316179i
$915$	7.00770	−	21.5675i	0.231667	−	0.712999i
$916$	2.93161	+	2.12994i	0.0968631	+	0.0703752i
$917$	−2.22712	+	6.85436i	−0.0735459	+	0.226351i
$918$	−12.1421	−	37.3696i	−0.400750	−	1.23338i
$919$	29.7315	−	21.6012i	0.980750	−	0.712557i	0.0228739	−	0.999738i	$-0.492718\pi$
$919$	29.7315	−	21.6012i	0.980750	−	0.712557i	0.957876	+	0.287182i	$0.0927184\pi$
$920$	−6.05742	−	18.6428i	−0.199707	−	0.614636i
$921$	−24.7418	−	17.9760i	−0.815270	−	0.592328i
$922$	−7.27668	−	5.28682i	−0.239645	−	0.174112i
$923$	−4.17647	+	3.03438i	−0.137470	+	0.0998778i
$924$	19.5682			0.643747
$925$	−35.1986			−1.15732
$926$	6.41967	−	4.66416i	0.210963	−	0.153274i
$927$	−30.5789	+	94.1121i	−1.00434	+	3.09105i
$928$	6.20035	+	19.0827i	0.203537	+	0.626421i
$929$	4.57148			0.149985			0.0749927	−	0.997184i	$-0.476107\pi$
$929$	4.57148			0.149985			0.0749927	+	0.997184i	$0.476107\pi$
$930$	−2.83806	−	11.0782i	−0.0930637	−	0.363267i
$931$	−18.4040			−0.603166
$932$	10.5500	+	32.4696i	0.345577	+	1.06358i
$933$	−5.35782	+	16.4897i	−0.175407	+	0.539847i
$934$	−2.60065	+	1.88949i	−0.0850960	+	0.0618259i
$935$	−16.7093			−0.546453
$936$	19.5642			0.639475
$937$	−29.7997	+	21.6508i	−0.973515	+	0.707300i	−0.956250	−	0.292551i	$-0.905496\pi$
$937$	−29.7997	+	21.6508i	−0.973515	+	0.707300i	−0.0172652	+	0.999851i	$0.505496\pi$
$938$	−2.07174	−	1.50521i	−0.0676447	−	0.0491468i
$939$	65.9011	+	47.8800i	2.15060	+	1.56250i
$940$	−3.72037	−	11.4501i	−0.121345	−	0.373462i
$941$	−2.09288	+	1.52056i	−0.0682259	+	0.0495690i	−0.621375	−	0.783513i	$-0.713426\pi$
$941$	−2.09288	+	1.52056i	−0.0682259	+	0.0495690i	0.553150	+	0.833082i	$0.313426\pi$
$942$	12.7993	+	39.3920i	0.417022	+	1.28346i
$943$	12.0246	−	37.0079i	0.391575	−	1.20514i
$944$	1.14522	+	0.832052i	0.0372738	+	0.0270810i
$945$	2.61104	−	8.03595i	0.0849371	−	0.261410i
$946$	−7.49532	+	23.0682i	−0.243694	+	0.750013i
$947$	23.8330	+	17.3157i	0.774468	+	0.562684i	0.903314	−	0.428981i	$-0.141127\pi$
$947$	23.8330	+	17.3157i	0.774468	+	0.562684i	−0.128845	+	0.991665i	$0.541127\pi$
$948$	−17.7137	+	54.5172i	−0.575315	+	1.77064i
$949$	−0.978941	−	3.01287i	−0.0317778	−	0.0978020i
$950$	8.11366	−	5.89492i	0.263242	−	0.191257i
$951$	24.8191	+	76.3854i	0.804815	+	2.47697i
$952$	6.00632	+	4.36384i	0.194666	+	0.141433i
$953$	27.2771	+	19.8180i	0.883592	+	0.641967i	0.934199	−	0.356752i	$-0.116116\pi$
$953$	27.2771	+	19.8180i	0.883592	+	0.641967i	−0.0506074	+	0.998719i	$0.516116\pi$
$954$	14.9511	−	10.8626i	0.484060	−	0.351690i
$955$	3.29923			0.106761
$956$	−10.4039			−0.336485
$957$	52.0215	−	37.7958i	1.68161	−	1.22176i
$958$	6.30675	−	19.4102i	0.203762	−	0.627115i
$959$	−1.67562	−	5.15702i	−0.0541085	−	0.166529i
$960$	9.08250			0.293136
$961$	−27.1815	+	14.9052i	−0.876823	+	0.480814i
$962$	−6.46501			−0.208440
$963$	26.6414	+	81.9938i	0.858507	+	2.64221i
$964$	1.21749	−	3.74705i	0.0392128	−	0.120684i
$965$	−3.02852	+	2.20035i	−0.0974917	+	0.0708318i
$966$	18.0155			0.579638
$967$	−12.1794			−0.391664			−0.195832	−	0.980638i	$-0.562741\pi$
$967$	−12.1794			−0.391664			−0.195832	+	0.980638i	$0.562741\pi$
$968$	50.0107	−	36.3349i	1.60741	−	1.16785i
$969$	26.6838	+	19.3869i	0.857207	+	0.622798i
$970$	3.16498	+	2.29949i	0.101621	+	0.0738323i
$971$	9.78863	+	30.1263i	0.314132	+	0.966799i	0.976110	+	0.217276i	$0.0697172\pi$
$971$	9.78863	+	30.1263i	0.314132	+	0.966799i	−0.661978	+	0.749523i	$0.730283\pi$
$972$	−32.6594	+	23.7285i	−1.04755	+	0.761091i
$973$	−1.14958	−	3.53804i	−0.0368539	−	0.113424i
$974$	−7.68772	+	23.6604i	−0.246330	+	0.758127i
$975$	11.3052	+	8.21370i	0.362056	+	0.263049i
$976$	1.54088	−	4.74234i	0.0493223	−	0.151798i
$977$	−7.53499	+	23.1903i	−0.241066	+	0.741924i	0.755193	+	0.655503i	$0.227543\pi$
$977$	−7.53499	+	23.1903i	−0.241066	+	0.741924i	−0.996259	+	0.0864216i	$0.972457\pi$
$978$	3.15570	+	2.29275i	0.100908	+	0.0733141i
$979$	16.6732	−	51.3149i	0.532879	−	1.64003i
$980$	−2.15258	−	6.62495i	−0.0687615	−	0.211626i
$981$	40.5717	−	29.4771i	1.29536	−	0.941131i
$982$	−7.30895	−	22.4946i	−0.233238	−	0.717833i
$983$	24.5438	+	17.8321i	0.782827	+	0.568757i	0.905826	−	0.423650i	$-0.139251\pi$
$983$	24.5438	+	17.8321i	0.782827	+	0.568757i	−0.122999	+	0.992407i	$0.539251\pi$
$984$	29.7985	+	21.6499i	0.949942	+	0.690174i
$985$	−4.56026	+	3.31323i	−0.145302	+	0.105568i
$986$	9.86958			0.314312
$987$	27.3507			0.870584
$988$	−3.15820	+	2.29457i	−0.100476	+	0.0730000i
$989$	14.6239	−	45.0078i	0.465013	−	1.43116i
$990$	−8.39695	−	25.8431i	−0.266873	−	0.821349i
$991$	0.212549			0.00675183			0.00337592	−	0.999994i	$-0.498925\pi$
$991$	0.212549			0.00675183			0.00337592	+	0.999994i	$0.498925\pi$
$992$	−8.05661	−	31.4484i	−0.255798	−	0.998487i
$993$	−26.2041			−0.831562
$994$	−0.984472	−	3.02989i	−0.0312255	−	0.0961023i
$995$	−0.941847	+	2.89871i	−0.0298585	+	0.0918952i
$996$	−54.9276	+	39.9072i	−1.74045	+	1.26451i
$997$	−23.1309			−0.732563			−0.366282	−	0.930504i	$-0.619369\pi$
$997$	−23.1309			−0.732563			−0.366282	+	0.930504i	$0.619369\pi$
$998$	−18.8563			−0.596887
$999$	89.4876	−	65.0166i	2.83126	−	2.05703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.8	✓	48
31.8	even	5	inner	403.2.k.d.287.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.8	✓	48	1.1	even	1	trivial
403.2.k.d.287.8	yes	48	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247442 + 0.761548i) q^{2} +(-0.990504 + 3.04846i) q^{3} +(1.09931 - 0.798693i) q^{4} -0.800250 q^{5} -2.56664 q^{6} +(-0.623500 + 0.452999i) q^{7} +(2.17588 + 1.58087i) q^{8} +(-5.88494 - 4.27566i) q^{9} +O(q^{10})\)	\(q+(0.247442 + 0.761548i) q^{2} +(-0.990504 + 3.04846i) q^{3} +(1.09931 - 0.798693i) q^{4} -0.800250 q^{5} -2.56664 q^{6} +(-0.623500 + 0.452999i) q^{7} +(2.17588 + 1.58087i) q^{8} +(-5.88494 - 4.27566i) q^{9} +(-0.198015 - 0.609429i) q^{10} +(-4.71624 + 3.42655i) q^{11} +(1.34591 + 4.14229i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.499260 - 0.362734i) q^{14} +(0.792650 - 2.43953i) q^{15} +(0.174291 - 0.536412i) q^{16} +(-2.89769 - 2.10530i) q^{17} +(1.79994 - 5.53964i) q^{18} +(0.887777 + 2.73230i) q^{19} +(-0.879719 + 0.639154i) q^{20} +(-0.763369 - 2.34941i) q^{21} +(-3.77648 - 2.74377i) q^{22} +(7.36818 + 5.35329i) q^{23} +(-6.97443 + 5.06722i) q^{24} -4.35960 q^{25} -0.800739 q^{26} +(11.0837 - 8.05278i) q^{27} +(-0.323610 + 0.995969i) q^{28} +(1.06340 + 3.27280i) q^{29} +2.05395 q^{30} +(-1.38176 - 5.39358i) q^{31} +5.83070 q^{32} +(-5.77423 - 17.7713i) q^{33} +(0.886274 - 2.72767i) q^{34} +(0.498955 - 0.362512i) q^{35} -9.88428 q^{36} +8.07381 q^{37} +(-1.86110 + 1.35217i) q^{38} +(-2.59317 - 1.88405i) q^{39} +(-1.74125 - 1.26509i) q^{40} +(-1.32029 - 4.06343i) q^{41} +(1.60030 - 1.16268i) q^{42} +(-1.60569 - 4.94180i) q^{43} +(-2.44783 + 7.53365i) q^{44} +(4.70942 + 3.42160i) q^{45} +(-2.25359 + 6.93585i) q^{46} +(-3.42136 + 10.5299i) q^{47} +(1.46259 + 1.06264i) q^{48} +(-1.97958 + 6.09251i) q^{49} +(-1.07875 - 3.32005i) q^{50} +(9.28808 - 6.74819i) q^{51} +(0.419897 + 1.29231i) q^{52} +(2.56683 + 1.86491i) q^{53} +(8.87515 + 6.44817i) q^{54} +(3.77417 - 2.74209i) q^{55} -2.07279 q^{56} -9.20864 q^{57} +(-2.22927 + 1.61966i) q^{58} +(-0.775572 + 2.38696i) q^{59} +(-1.07707 - 3.31487i) q^{60} +8.84084 q^{61} +(3.76557 - 2.38687i) q^{62} +5.60612 q^{63} +(1.09418 + 3.36754i) q^{64} +(0.247291 - 0.761083i) q^{65} +(12.1049 - 8.79471i) q^{66} +4.14962 q^{67} -4.86694 q^{68} +(-23.6175 + 17.1591i) q^{69} +(0.399533 + 0.290278i) q^{70} +(4.17647 + 3.03438i) q^{71} +(-6.04566 - 18.6066i) q^{72} +(-2.56290 + 1.86206i) q^{73} +(1.99780 + 6.14859i) q^{74} +(4.31820 - 13.2901i) q^{75} +(3.15820 + 2.29457i) q^{76} +(1.38835 - 4.27290i) q^{77} +(0.793135 - 2.44102i) q^{78} +(10.6476 + 7.73591i) q^{79} +(-0.139476 + 0.429264i) q^{80} +(6.82656 + 21.0100i) q^{81} +(2.76780 - 2.01093i) q^{82} +(4.81704 + 14.8253i) q^{83} +(-2.71563 - 1.97302i) q^{84} +(2.31888 + 1.68476i) q^{85} +(3.36610 - 2.44562i) q^{86} -11.0303 q^{87} -15.6789 q^{88} +(-7.48785 + 5.44024i) q^{89} +(-1.44040 + 4.43310i) q^{90} +(-0.238156 - 0.732968i) q^{91} +12.3755 q^{92} +(17.8107 + 1.13014i) q^{93} -8.86560 q^{94} +(-0.710444 - 2.18652i) q^{95} +(-5.77533 + 17.7746i) q^{96} +(-4.93918 + 3.58852i) q^{97} -5.12957 q^{98} +42.4055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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