LMFDB - Embedded newform 585.2.i.e.391.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.8
Root			$1.79305 - 1.53983i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.e.196.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29305 + 2.23963i) q^{2} +(1.68259 - 0.410979i) q^{3} +(-2.34397 + 4.05987i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.09611 + 3.23696i) q^{6} +(2.13745 + 3.70217i) q^{7} -6.95128 q^{8} +(2.66219 - 1.38302i) q^{9} +O(q^{10})$	\(q+(1.29305 + 2.23963i) q^{2} +(1.68259 - 0.410979i) q^{3} +(-2.34397 + 4.05987i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.09611 + 3.23696i) q^{6} +(2.13745 + 3.70217i) q^{7} -6.95128 q^{8} +(2.66219 - 1.38302i) q^{9} +2.58610 q^{10} +(-2.19223 - 3.79706i) q^{11} +(-2.27540 + 7.79440i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-5.52766 + 9.57419i) q^{14} +(0.485374 - 1.66265i) q^{15} +(-4.30043 - 7.44856i) q^{16} +0.619151 q^{17} +(6.53980 + 4.17402i) q^{18} -2.61288 q^{19} +(2.34397 + 4.05987i) q^{20} +(5.11795 + 5.35077i) q^{21} +(5.66934 - 9.81959i) q^{22} +(-2.71443 + 4.70154i) q^{23} +(-11.6961 + 2.85683i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.58610 q^{26} +(3.91098 - 3.42115i) q^{27} -20.0404 q^{28} +(-3.47887 - 6.02558i) q^{29} +(4.35134 - 1.06284i) q^{30} +(3.44304 - 5.96353i) q^{31} +(4.17008 - 7.22278i) q^{32} +(-5.24913 - 5.48791i) q^{33} +(0.800595 + 1.38667i) q^{34} +4.27489 q^{35} +(-0.625222 + 14.0499i) q^{36} -4.02164 q^{37} +(-3.37859 - 5.85188i) q^{38} +(0.485374 - 1.66265i) q^{39} +(-3.47564 + 6.01998i) q^{40} +(2.03714 - 3.52842i) q^{41} +(-5.36597 + 18.3811i) q^{42} +(5.01845 + 8.69221i) q^{43} +20.5541 q^{44} +(0.133368 - 2.99703i) q^{45} -14.0396 q^{46} +(0.202993 + 0.351595i) q^{47} +(-10.2970 - 10.7655i) q^{48} +(-5.63736 + 9.76419i) q^{49} +(1.29305 - 2.23963i) q^{50} +(1.04178 - 0.254458i) q^{51} +(2.34397 + 4.05987i) q^{52} -8.71205 q^{53} +(12.7192 + 4.33542i) q^{54} -4.38446 q^{55} +(-14.8580 - 25.7348i) q^{56} +(-4.39639 + 1.07384i) q^{57} +(8.99672 - 15.5828i) q^{58} +(5.36073 - 9.28505i) q^{59} +(5.61245 + 5.86776i) q^{60} +(-2.53609 - 4.39263i) q^{61} +17.8081 q^{62} +(10.8105 + 6.89975i) q^{63} +4.36679 q^{64} +(-0.500000 - 0.866025i) q^{65} +(5.50350 - 18.8523i) q^{66} +(-7.27894 + 12.6075i) q^{67} +(-1.45127 + 2.51367i) q^{68} +(-2.63503 + 9.02632i) q^{69} +(5.52766 + 9.57419i) q^{70} +6.57523 q^{71} +(-18.5056 + 9.61373i) q^{72} +16.7313 q^{73} +(-5.20019 - 9.00700i) q^{74} +(-1.19721 - 1.25167i) q^{75} +(6.12450 - 10.6079i) q^{76} +(9.37156 - 16.2320i) q^{77} +(4.35134 - 1.06284i) q^{78} +(-7.27288 - 12.5970i) q^{79} -8.60086 q^{80} +(5.17453 - 7.36371i) q^{81} +10.5365 q^{82} +(1.52057 + 2.63370i) q^{83} +(-33.7197 + 8.23620i) q^{84} +(0.309576 - 0.536201i) q^{85} +(-12.9782 + 22.4790i) q^{86} +(-8.32989 - 8.70881i) q^{87} +(15.2388 + 26.3944i) q^{88} +7.27070 q^{89} +(6.88470 - 3.57663i) q^{90} +4.27489 q^{91} +(-12.7251 - 22.0405i) q^{92} +(3.34233 - 11.4492i) q^{93} +(-0.524962 + 0.909260i) q^{94} +(-1.30644 + 2.26282i) q^{95} +(4.04810 - 13.8668i) q^{96} +(4.81738 + 8.34394i) q^{97} -29.1576 q^{98} +(-11.0875 - 7.07660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * 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 $

$2$	1.29305	+	2.23963i	0.914326	+	1.58366i	0.807885	+	0.589340i	$0.200612\pi$
$2$	1.29305	+	2.23963i	0.914326	+	1.58366i	0.106440	+	0.994319i	$0.466055\pi$
$3$	1.68259	−	0.410979i	0.971442	−	0.237279i
$3$	1.68259	−	0.410979i	0.971442	−	0.237279i
$4$	−2.34397	+	4.05987i	−1.17198	+	2.02993i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.09611	+	3.23696i	1.26398	+	1.32148i
$7$	2.13745	+	3.70217i	0.807879	+	1.39929i	0.914330	+	0.404969i	$0.132718\pi$
$7$	2.13745	+	3.70217i	0.807879	+	1.39929i	−0.106451	+	0.994318i	$0.533949\pi$
$8$	−6.95128			−2.45765
$9$	2.66219	−	1.38302i	0.887397	−	0.461006i
$10$	2.58610			0.817798
$11$	−2.19223	−	3.79706i	−0.660983	−	1.14486i	−0.980358	−	0.197227i	$-0.936806\pi$
$11$	−2.19223	−	3.79706i	−0.660983	−	1.14486i	0.319375	−	0.947628i	$-0.396527\pi$
$12$	−2.27540	+	7.79440i	−0.656852	+	2.25005i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−5.52766	+	9.57419i	−1.47733	+	2.55881i
$15$	0.485374	−	1.66265i	0.125323	−	0.429295i
$16$	−4.30043	−	7.44856i	−1.07511	−	1.86214i
$17$	0.619151			0.150166			0.0750831	−	0.997177i	$-0.476078\pi$
$17$	0.619151			0.150166			0.0750831	+	0.997177i	$0.476078\pi$
$18$	6.53980	+	4.17402i	1.54145	+	0.983825i
$19$	−2.61288			−0.599435			−0.299718	−	0.954028i	$-0.596892\pi$
$19$	−2.61288			−0.599435			−0.299718	+	0.954028i	$0.596892\pi$
$20$	2.34397	+	4.05987i	0.524127	+	0.907814i
$21$	5.11795	+	5.35077i	1.11683	+	1.16763i
$22$	5.66934	−	9.81959i	1.20871	−	2.09354i
$23$	−2.71443	+	4.70154i	−0.565998	+	0.980338i	0.430958	+	0.902372i	$0.358176\pi$
$23$	−2.71443	+	4.70154i	−0.565998	+	0.980338i	−0.996956	+	0.0779658i	$0.975157\pi$
$24$	−11.6961	+	2.85683i	−2.38746	+	0.583148i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.58610			0.507177
$27$	3.91098	−	3.42115i	0.752668	−	0.658401i
$28$	−20.0404			−3.78728
$29$	−3.47887	−	6.02558i	−0.646010	−	1.11892i	−0.984067	−	0.177796i	$-0.943103\pi$
$29$	−3.47887	−	6.02558i	−0.646010	−	1.11892i	0.338057	−	0.941125i	$-0.390230\pi$
$30$	4.35134	−	1.06284i	0.794443	−	0.194046i
$31$	3.44304	−	5.96353i	0.618389	−	1.07108i	−0.371391	−	0.928477i	$-0.621119\pi$
$31$	3.44304	−	5.96353i	0.618389	−	1.07108i	0.989780	−	0.142605i	$-0.0455477\pi$
$32$	4.17008	−	7.22278i	0.737172	−	1.27682i
$33$	−5.24913	−	5.48791i	−0.913757	−	0.955323i
$34$	0.800595	+	1.38667i	0.137301	+	0.237812i
$35$	4.27489			0.722589
$36$	−0.625222	+	14.0499i	−0.104204	+	2.34165i
$37$	−4.02164			−0.661154			−0.330577	−	0.943779i	$-0.607243\pi$
$37$	−4.02164			−0.661154			−0.330577	+	0.943779i	$0.607243\pi$
$38$	−3.37859	−	5.85188i	−0.548079	−	0.949301i
$39$	0.485374	−	1.66265i	0.0777221	−	0.266237i
$40$	−3.47564	+	6.01998i	−0.549547	+	0.951843i
$41$	2.03714	−	3.52842i	0.318147	−	0.551047i	−0.661954	−	0.749544i	$-0.730273\pi$
$41$	2.03714	−	3.52842i	0.318147	−	0.551047i	0.980101	+	0.198497i	$0.0636060\pi$
$42$	−5.36597	+	18.3811i	−0.827987	+	2.83627i
$43$	5.01845	+	8.69221i	0.765307	+	1.32555i	0.940084	+	0.340942i	$0.110746\pi$
$43$	5.01845	+	8.69221i	0.765307	+	1.32555i	−0.174778	+	0.984608i	$0.555921\pi$
$44$	20.5541			3.09864
$45$	0.133368	−	2.99703i	0.0198814	−	0.446771i
$46$	−14.0396			−2.07003
$47$	0.202993	+	0.351595i	0.0296096	+	0.0512854i	0.880450	−	0.474138i	$-0.157240\pi$
$47$	0.202993	+	0.351595i	0.0296096	+	0.0512854i	−0.850841	+	0.525423i	$0.823907\pi$
$48$	−10.2970	−	10.7655i	−1.48625	−	1.55386i
$49$	−5.63736	+	9.76419i	−0.805337	+	1.39488i
$50$	1.29305	−	2.23963i	0.182865	−	0.316732i
$51$	1.04178	−	0.254458i	0.145878	−	0.0356313i
$52$	2.34397	+	4.05987i	0.325050	+	0.563003i
$53$	−8.71205			−1.19669			−0.598346	−	0.801238i	$-0.704175\pi$
$53$	−8.71205			−1.19669			−0.598346	+	0.801238i	$0.704175\pi$
$54$	12.7192	+	4.33542i	1.73087	+	0.589976i
$55$	−4.38446			−0.591201
$56$	−14.8580	−	25.7348i	−1.98548	−	3.43895i
$57$	−4.39639	+	1.07384i	−0.582316	+	0.142233i
$58$	8.99672	−	15.5828i	1.18133	−	2.04612i
$59$	5.36073	−	9.28505i	0.697907	−	1.20881i	−0.271284	−	0.962499i	$-0.587448\pi$
$59$	5.36073	−	9.28505i	0.697907	−	1.20881i	0.969191	−	0.246311i	$-0.0792185\pi$
$60$	5.61245	+	5.86776i	0.724564	+	0.757524i
$61$	−2.53609	−	4.39263i	−0.324713	−	0.562419i	0.656742	−	0.754116i	$-0.271934\pi$
$61$	−2.53609	−	4.39263i	−0.324713	−	0.562419i	−0.981454	+	0.191697i	$0.938601\pi$
$62$	17.8081			2.26164
$63$	10.8105	+	6.89975i	1.36199	+	0.869287i
$64$	4.36679			0.545849
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	5.50350	−	18.8523i	0.677435	−	2.32056i
$67$	−7.27894	+	12.6075i	−0.889264	+	1.54025i	−0.0485164	+	0.998822i	$0.515449\pi$
$67$	−7.27894	+	12.6075i	−0.889264	+	1.54025i	−0.840747	+	0.541428i	$0.817884\pi$
$68$	−1.45127	+	2.51367i	−0.175992	+	0.304828i
$69$	−2.63503	+	9.02632i	−0.317221	+	1.08664i
$70$	5.52766	+	9.57419i	0.660682	+	1.14433i
$71$	6.57523			0.780336			0.390168	−	0.920744i	$-0.372417\pi$
$71$	6.57523			0.780336			0.390168	+	0.920744i	$0.372417\pi$
$72$	−18.5056	+	9.61373i	−2.18091	+	1.13299i
$73$	16.7313			1.95825			0.979125	−	0.203257i	$-0.0651527\pi$
$73$	16.7313			1.95825			0.979125	+	0.203257i	$0.0651527\pi$
$74$	−5.20019	−	9.00700i	−0.604510	−	1.04704i
$75$	−1.19721	−	1.25167i	−0.138242	−	0.144531i
$76$	6.12450	−	10.6079i	0.702528	−	1.21681i
$77$	9.37156	−	16.2320i	1.06799	−	1.84981i
$78$	4.35134	−	1.06284i	0.492693	−	0.120342i
$79$	−7.27288	−	12.5970i	−0.818263	−	1.41727i	−0.906961	−	0.421214i	$-0.861604\pi$
$79$	−7.27288	−	12.5970i	−0.818263	−	1.41727i	0.0886982	−	0.996059i	$-0.471729\pi$
$80$	−8.60086			−0.961605
$81$	5.17453	−	7.36371i	0.574948	−	0.818190i
$82$	10.5365			1.16356
$83$	1.52057	+	2.63370i	0.166904	+	0.289086i	0.937330	−	0.348444i	$-0.113290\pi$
$83$	1.52057	+	2.63370i	0.166904	+	0.289086i	−0.770426	+	0.637530i	$0.779956\pi$
$84$	−33.7197	+	8.23620i	−3.67912	+	0.898643i
$85$	0.309576	−	0.536201i	0.0335782	−	0.0581591i
$86$	−12.9782	+	22.4790i	−1.39948	+	2.42397i
$87$	−8.32989	−	8.70881i	−0.893058	−	0.933682i
$88$	15.2388	+	26.3944i	1.62446	+	2.81365i
$89$	7.27070			0.770693			0.385347	−	0.922772i	$-0.374082\pi$
$89$	7.27070			0.770693			0.385347	+	0.922772i	$0.374082\pi$
$90$	6.88470	−	3.57663i	0.725712	−	0.377009i
$91$	4.27489			0.448131
$92$	−12.7251	−	22.0405i	−1.32668	−	2.29788i
$93$	3.34233	−	11.4492i	0.346584	−	1.18722i
$94$	−0.524962	+	0.909260i	−0.0541457	+	0.0937830i
$95$	−1.30644	+	2.26282i	−0.134038	+	0.232160i
$96$	4.04810	−	13.8668i	0.413157	−	1.41527i
$97$	4.81738	+	8.34394i	0.489130	+	0.847199i	0.999922	−	0.0125059i	$-0.00398085\pi$
$97$	4.81738	+	8.34394i	0.489130	+	0.847199i	−0.510791	+	0.859705i	$0.670648\pi$
$98$	−29.1576			−2.94536
$99$	−11.0875	−	7.07660i	−1.11434	−	0.711225i
$100$	4.68793			0.468793
$101$	−3.89976	−	6.75458i	−0.388041	−	0.672106i	0.604145	−	0.796874i	$-0.293515\pi$
$101$	−3.89976	−	6.75458i	−0.388041	−	0.672106i	−0.992186	+	0.124768i	$0.960181\pi$
$102$	1.91696	+	2.00417i	0.189808	+	0.198442i
$103$	−0.496621	+	0.860172i	−0.0489335	+	0.0847553i	−0.889455	−	0.457023i	$-0.848916\pi$
$103$	−0.496621	+	0.860172i	−0.0489335	+	0.0847553i	0.840521	+	0.541779i	$0.182249\pi$
$104$	−3.47564	+	6.01998i	−0.340814	+	0.590308i
$105$	7.19288	−	1.75689i	0.701953	−	0.171455i
$106$	−11.2651	−	19.5118i	−1.09417	−	1.89515i
$107$	4.24171			0.410062			0.205031	−	0.978755i	$-0.434270\pi$
$107$	4.24171			0.410062			0.205031	+	0.978755i	$0.434270\pi$
$108$	4.72223	+	23.8971i	0.454397	+	2.29950i
$109$	4.72247			0.452330			0.226165	−	0.974089i	$-0.427381\pi$
$109$	4.72247			0.452330			0.226165	+	0.974089i	$0.427381\pi$
$110$	−5.66934	−	9.81959i	−0.540550	−	0.936261i
$111$	−6.76676	+	1.65281i	−0.642272	+	0.156878i
$112$	18.3839	−	31.8418i	1.73711	−	3.00877i
$113$	1.77704	−	3.07792i	0.167170	−	0.289546i	−0.770254	−	0.637737i	$-0.779871\pi$
$113$	1.77704	−	3.07792i	0.167170	−	0.289546i	0.937424	+	0.348191i	$0.113204\pi$
$114$	−8.08977	−	8.45777i	−0.757676	−	0.792143i
$115$	2.71443	+	4.70154i	0.253122	+	0.438420i
$116$	32.6174			3.02845
$117$	0.133368	−	2.99703i	0.0123299	−	0.277076i
$118$	27.7268			2.55246
$119$	1.32340	+	2.29220i	0.121316	+	0.210126i
$120$	−3.37397	+	11.5576i	−0.308000	+	1.05506i
$121$	−4.11176	+	7.12178i	−0.373797	+	0.647435i
$122$	6.55858	−	11.3598i	0.593786	−	1.02847i
$123$	1.97755	−	6.77410i	0.178309	−	0.610800i
$124$	16.1408	+	27.9566i	1.44948	+	2.51058i
$125$	−1.00000			−0.0894427
$126$	−1.47443	+	33.1332i	−0.131353	+	2.95174i
$127$	−13.6413			−1.21047			−0.605234	−	0.796048i	$-0.706920\pi$
$127$	−13.6413			−1.21047			−0.605234	+	0.796048i	$0.706920\pi$
$128$	−2.69366	−	4.66556i	−0.238088	−	0.412381i
$129$	12.0163	+	12.5629i	1.05798	+	1.10610i
$130$	1.29305	−	2.23963i	0.113408	−	0.196429i
$131$	−4.18118	+	7.24202i	−0.365312	+	0.632738i	−0.988826	−	0.149073i	$-0.952371\pi$
$131$	−4.18118	+	7.24202i	−0.365312	+	0.632738i	0.623514	+	0.781812i	$0.285704\pi$
$132$	34.5840	−	8.44730i	3.01015	−	0.735244i
$133$	−5.58489	−	9.67331i	−0.484271	−	0.838782i
$134$	−37.6482			−3.25231
$135$	−1.00732	−	5.09758i	−0.0866960	−	0.438730i
$136$	−4.30389			−0.369056
$137$	3.37544	+	5.84643i	0.288383	+	0.499494i	0.973424	−	0.229010i	$-0.0735489\pi$
$137$	3.37544	+	5.84643i	0.288383	+	0.499494i	−0.685041	+	0.728505i	$0.740216\pi$
$138$	−23.6229	+	5.76999i	−2.01091	+	0.491174i
$139$	−1.75288	+	3.03608i	−0.148678	+	0.257517i	−0.930739	−	0.365684i	$-0.880835\pi$
$139$	−1.75288	+	3.03608i	−0.148678	+	0.257517i	0.782061	+	0.623201i	$0.214168\pi$
$140$	−10.0202	+	17.3555i	−0.846862	+	1.46681i
$141$	0.486052	+	0.508162i	0.0409330	+	0.0427950i
$142$	8.50211	+	14.7261i	0.713481	+	1.23579i
$143$	−4.38446			−0.366647
$144$	−21.7500	−	13.8819i	−1.81250	−	1.15683i
$145$	−6.95774			−0.577809
$146$	21.6344	+	37.4720i	1.79048	+	3.10120i
$147$	−5.47246	+	18.7459i	−0.451361	+	1.54614i
$148$	9.42660	−	16.3273i	0.774861	−	1.34210i
$149$	−6.13951	+	10.6339i	−0.502968	+	0.871166i	0.497026	+	0.867736i	$0.334425\pi$
$149$	−6.13951	+	10.6339i	−0.502968	+	0.871166i	−0.999994	+	0.00343063i	$0.998908\pi$
$150$	1.25523	−	4.29979i	0.102489	−	0.351076i
$151$	8.34821	+	14.4595i	0.679367	+	1.17670i	0.975172	+	0.221450i	$0.0710791\pi$
$151$	8.34821	+	14.4595i	0.679367	+	1.17670i	−0.295804	+	0.955249i	$0.595588\pi$
$152$	18.1628			1.47320
$153$	1.64830	−	0.856297i	0.133257	−	0.0692275i
$154$	48.4717			3.90596
$155$	−3.44304	−	5.96353i	−0.276552	−	0.479002i
$156$	5.61245	+	5.86776i	0.449356	+	0.469797i
$157$	−3.99844	+	6.92550i	−0.319110	+	0.552715i	−0.980303	−	0.197501i	$-0.936717\pi$
$157$	−3.99844	+	6.92550i	−0.319110	+	0.552715i	0.661192	+	0.750216i	$0.270051\pi$
$158$	18.8084	−	32.5771i	1.49632	−	2.59170i
$159$	−14.6588	+	3.58048i	−1.16252	+	0.283950i
$160$	−4.17008	−	7.22278i	−0.329674	−	0.571011i
$161$	−23.2078			−1.82903
$162$	23.1829	+	2.06738i	1.82142	+	0.162429i
$163$	−17.3723			−1.36071			−0.680353	−	0.732885i	$-0.738173\pi$
$163$	−17.3723			−1.36071			−0.680353	+	0.732885i	$0.738173\pi$
$164$	9.54996	+	16.5410i	0.745727	+	1.29164i
$165$	−7.37724	+	1.80192i	−0.574317	+	0.140280i
$166$	−3.93234	+	6.81102i	−0.305209	+	0.528637i
$167$	−2.13795	+	3.70303i	−0.165439	+	0.286549i	−0.936811	−	0.349835i	$-0.886238\pi$
$167$	−2.13795	+	3.70303i	−0.165439	+	0.286549i	0.771372	+	0.636385i	$0.219571\pi$
$168$	−35.5763	−	37.1947i	−2.74477	−	2.86963i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	1.60119			0.122806
$171$	−6.95598	+	3.61365i	−0.531937	+	0.276343i
$172$	−47.0523			−3.58771
$173$	−6.47793	−	11.2201i	−0.492508	−	0.853049i	0.507455	−	0.861679i	$-0.330587\pi$
$173$	−6.47793	−	11.2201i	−0.492508	−	0.853049i	−0.999963	+	0.00862929i	$0.997253\pi$
$174$	8.73355	−	29.9168i	0.662089	−	2.26799i
$175$	2.13745	−	3.70217i	0.161576	−	0.279857i
$176$	−18.8551	+	32.6579i	−1.42125	+	2.46169i
$177$	5.20392	−	17.8260i	0.391150	−	1.33989i
$178$	9.40140	+	16.2837i	0.704665	+	1.22051i
$179$	18.8530			1.40914			0.704571	−	0.709633i	$-0.251139\pi$
$179$	18.8530			1.40914			0.704571	+	0.709633i	$0.251139\pi$
$180$	11.8550	+	7.56641i	0.883616	+	0.563967i
$181$	−21.2593			−1.58019			−0.790097	−	0.612982i	$-0.789970\pi$
$181$	−21.2593			−1.58019			−0.790097	+	0.612982i	$0.789970\pi$
$182$	5.52766	+	9.57419i	0.409737	+	0.709686i
$183$	−6.07246	−	6.34870i	−0.448889	−	0.469309i
$184$	18.8688	−	32.6817i	1.39102	−	2.40933i
$185$	−2.01082	+	3.48284i	−0.147838	+	0.256064i
$186$	29.9637	−	7.31878i	2.19705	−	0.536639i
$187$	−1.35732	−	2.35095i	−0.0992573	−	0.171919i
$188$	−1.90324			−0.138808
$189$	21.0252	+	7.16655i	1.52936	+	0.521290i
$190$	−6.75717			−0.490217
$191$	7.70849	+	13.3515i	0.557767	+	0.966081i	0.997682	+	0.0680415i	$0.0216750\pi$
$191$	7.70849	+	13.3515i	0.557767	+	0.966081i	−0.439916	+	0.898039i	$0.644992\pi$
$192$	7.34751	−	1.79466i	0.530261	−	0.129519i
$193$	−0.944008	+	1.63507i	−0.0679512	+	0.117695i	−0.897999	−	0.439997i	$-0.854980\pi$
$193$	−0.944008	+	1.63507i	−0.0679512	+	0.117695i	0.830048	+	0.557692i	$0.188313\pi$
$194$	−12.4582	+	21.5783i	−0.894449	+	1.54923i
$195$	−1.19721	−	1.25167i	−0.0857341	−	0.0896341i
$196$	−26.4276	−	45.7739i	−1.88768	−	3.26956i
$197$	−10.8597			−0.773723			−0.386862	−	0.922138i	$-0.626441\pi$
$197$	−10.8597			−0.773723			−0.386862	+	0.922138i	$0.626441\pi$
$198$	1.51222	−	33.9824i	0.107469	−	2.41502i
$199$	−1.20110			−0.0851436			−0.0425718	−	0.999093i	$-0.513555\pi$
$199$	−1.20110			−0.0851436			−0.0425718	+	0.999093i	$0.513555\pi$
$200$	3.47564	+	6.01998i	0.245765	+	0.425677i
$201$	−7.06602	+	24.2047i	−0.498399	+	1.70727i
$202$	10.0852	−	17.4681i	0.709591	−	1.22905i
$203$	14.8718	−	25.7587i	1.04380	−	1.80791i
$204$	−1.40882	+	4.82591i	−0.0986370	+	0.337882i
$205$	−2.03714	−	3.52842i	−0.142280	−	0.246436i
$206$	−2.56863			−0.178965
$207$	−0.724038	+	16.2705i	−0.0503241	+	1.13088i
$208$	−8.60086			−0.596362
$209$	5.72803	+	9.92125i	0.396216	+	0.686267i
$210$	13.2356	+	13.8376i	0.913340	+	0.954888i
$211$	0.117606	−	0.203699i	0.00809632	−	0.0140232i	−0.861949	−	0.506995i	$-0.830756\pi$
$211$	0.117606	−	0.203699i	0.00809632	−	0.0140232i	0.870045	+	0.492972i	$0.164089\pi$
$212$	20.4208	−	35.3698i	1.40250	−	2.42921i
$213$	11.0634	−	2.70228i	0.758051	−	0.185157i
$214$	5.48476	+	9.49988i	0.374930	+	0.649398i
$215$	10.0369			0.684511
$216$	−27.1863	+	23.7814i	−1.84979	+	1.61812i
$217$	29.4373			1.99833
$218$	6.10639	+	10.5766i	0.413577	+	0.716337i
$219$	28.1519	−	6.87622i	1.90233	−	0.464652i
$220$	10.2770	−	17.8004i	0.692878	−	1.20010i
$221$	0.309576	−	0.536201i	0.0208243	−	0.0360688i
$222$	−12.4515	−	13.0179i	−0.835687	−	0.873703i
$223$	8.37747	+	14.5102i	0.560997	+	0.971675i	0.997410	+	0.0719287i	$0.0229154\pi$
$223$	8.37747	+	14.5102i	0.560997	+	0.971675i	−0.436413	+	0.899747i	$0.643751\pi$
$224$	35.6533			2.38218
$225$	−2.52882	−	1.61402i	−0.168588	−	0.107601i
$226$	9.19121			0.611390
$227$	−11.4002	−	19.7457i	−0.756656	−	1.31057i	−0.944547	−	0.328377i	$-0.893498\pi$
$227$	−11.4002	−	19.7457i	−0.756656	−	1.31057i	0.187891	−	0.982190i	$-0.439835\pi$
$228$	5.94535	−	20.3658i	0.393740	−	1.34876i
$229$	3.48739	−	6.04033i	0.230453	−	0.399156i	−0.727488	−	0.686120i	$-0.759313\pi$
$229$	3.48739	−	6.04033i	0.230453	−	0.399156i	0.957942	+	0.286964i	$0.0926459\pi$
$230$	−7.01981	+	12.1587i	−0.462872	+	0.801718i
$231$	9.09743	−	31.1633i	0.598567	−	2.05039i
$232$	24.1826	+	41.8855i	1.58766	+	2.74992i
$233$	−8.63201			−0.565502			−0.282751	−	0.959193i	$-0.591247\pi$
$233$	−8.63201			−0.565502			−0.282751	+	0.959193i	$0.591247\pi$
$234$	6.88470	−	3.57663i	0.450067	−	0.233811i
$235$	0.405987			0.0264836
$236$	25.1307	+	43.5277i	1.63587	+	2.83341i
$237$	−17.4144	−	18.2065i	−1.13118	−	1.18264i
$238$	−3.42246	+	5.92787i	−0.221845	+	0.384247i
$239$	1.53550	−	2.65957i	0.0993235	−	0.172033i	−0.812081	−	0.583544i	$-0.801665\pi$
$239$	1.53550	−	2.65957i	0.0993235	−	0.172033i	0.911405	+	0.411511i	$0.134999\pi$
$240$	−14.4717	+	3.53478i	−0.934143	+	0.228169i
$241$	−2.91634	−	5.05125i	−0.187858	−	0.325379i	0.756678	−	0.653788i	$-0.226821\pi$
$241$	−2.91634	−	5.05125i	−0.187858	−	0.325379i	−0.944536	+	0.328408i	$0.893488\pi$
$242$	−21.2669			−1.36709
$243$	5.68026	−	14.5167i	0.364389	−	0.931247i
$244$	23.7780			1.52223
$245$	5.63736	+	9.76419i	0.360157	+	0.623811i
$246$	17.7286	−	4.33028i	1.13033	−	0.276089i
$247$	−1.30644	+	2.26282i	−0.0831267	+	0.143980i
$248$	−23.9336	+	41.4541i	−1.51978	+	2.63234i
$249$	3.64088	+	3.80650i	0.230731	+	0.241227i
$250$	−1.29305	−	2.23963i	−0.0817798	−	0.141647i
$251$	−23.7101			−1.49657			−0.748285	−	0.663378i	$-0.769122\pi$
$251$	−23.7101			−1.49657			−0.748285	+	0.663378i	$0.769122\pi$
$252$	−53.3514	+	27.7162i	−3.36082	+	1.74596i
$253$	23.8027			1.49646
$254$	−17.6389	−	30.5514i	−1.10676	−	1.91697i
$255$	0.300520	−	1.02943i	0.0188193	−	0.0644656i
$256$	11.3329	−	19.6291i	0.708305	−	1.22682i
$257$	−9.65384	+	16.7209i	−0.602190	+	1.04302i	0.390299	+	0.920688i	$0.372372\pi$
$257$	−9.65384	+	16.7209i	−0.602190	+	1.04302i	−0.992489	+	0.122335i	$0.960962\pi$
$258$	−12.5986	+	43.1566i	−0.784355	+	2.68681i
$259$	−8.59604	−	14.8888i	−0.534132	−	0.925144i
$260$	4.68793			0.290733
$261$	−17.5949	−	11.2299i	−1.08910	−	0.695114i
$262$	−21.6260			−1.33606
$263$	5.85985	+	10.1496i	0.361334	+	0.625848i	0.988181	−	0.153294i	$-0.0489882\pi$
$263$	5.85985	+	10.1496i	0.361334	+	0.625848i	−0.626847	+	0.779142i	$0.715655\pi$
$264$	36.4882	+	38.1480i	2.24569	+	2.34785i
$265$	−4.35603	+	7.54486i	−0.267589	+	0.463477i
$266$	14.4431	−	25.0162i	0.885563	−	1.53384i
$267$	12.2336	−	2.98811i	0.748683	−	0.182869i
$268$	−34.1232	−	59.1031i	−2.08440	−	3.61029i
$269$	−17.0088			−1.03705			−0.518524	−	0.855063i	$-0.673518\pi$
$269$	−17.0088			−1.03705			−0.518524	+	0.855063i	$0.673518\pi$
$270$	10.1142	−	8.84745i	0.615530	−	0.538439i
$271$	−12.4840			−0.758348			−0.379174	−	0.925325i	$-0.623792\pi$
$271$	−12.4840			−0.758348			−0.379174	+	0.925325i	$0.623792\pi$
$272$	−2.66262	−	4.61179i	−0.161445	−	0.279631i
$273$	7.19288	−	1.75689i	0.435333	−	0.106332i
$274$	−8.72924	+	15.1195i	−0.527353	+	0.913401i
$275$	−2.19223	+	3.79706i	−0.132197	+	0.228971i
$276$	−30.4692	−	31.8553i	−1.83403	−	1.91746i
$277$	−10.1444	−	17.5705i	−0.609516	−	1.05571i	−0.991320	−	0.131469i	$-0.958031\pi$
$277$	−10.1444	−	17.5705i	−0.609516	−	1.05571i	0.381805	−	0.924243i	$-0.375303\pi$
$278$	−9.06628			−0.543759
$279$	0.918386	−	20.6378i	0.0549823	−	1.23556i
$280$	−29.7160			−1.77587
$281$	4.18725	+	7.25252i	0.249790	+	0.432649i	0.963467	−	0.267825i	$-0.0863050\pi$
$281$	4.18725	+	7.25252i	0.249790	+	0.432649i	−0.713677	+	0.700475i	$0.752972\pi$
$282$	−0.509606	+	1.74566i	−0.0303466	+	0.103952i
$283$	1.11281	−	1.92745i	0.0661498	−	0.114575i	−0.831054	−	0.556192i	$-0.812262\pi$
$283$	1.11281	−	1.92745i	0.0661498	−	0.114575i	0.897203	+	0.441617i	$0.145595\pi$
$284$	−15.4121	+	26.6946i	−0.914541	+	1.58403i
$285$	−1.26822	+	4.34431i	−0.0751231	+	0.257335i
$286$	−5.66934	−	9.81959i	−0.335235	−	0.580644i
$287$	17.4171			1.02810
$288$	1.11231	−	24.9957i	0.0655436	−	1.47289i
$289$	−16.6167			−0.977450
$290$	−8.99672	−	15.5828i	−0.528305	−	0.915052i
$291$	11.5348	+	12.0596i	0.676184	+	0.706944i
$292$	−39.2176	+	67.9269i	−2.29504	+	3.97512i
$293$	1.26944	−	2.19873i	0.0741613	−	0.128451i	−0.826560	−	0.562849i	$-0.809705\pi$
$293$	1.26944	−	2.19873i	0.0741613	−	0.128451i	0.900721	+	0.434398i	$0.143039\pi$
$294$	−49.0601	+	11.9832i	−2.86125	+	0.698873i
$295$	−5.36073	−	9.28505i	−0.312114	−	0.540596i
$296$	27.9555			1.62488
$297$	−21.5641	−	7.35024i	−1.25127	−	0.426504i
$298$	−31.7548			−1.83951
$299$	2.71443	+	4.70154i	0.156980	+	0.271897i
$300$	7.88785	−	1.92664i	0.455405	−	0.111235i
$301$	−21.4533	+	37.1583i	−1.23655	+	2.14177i
$302$	−21.5893	+	37.3938i	−1.24233	+	2.15177i
$303$	−9.33768	−	9.76245i	−0.536436	−	0.560838i
$304$	11.2365	+	19.4622i	0.644457	+	1.11623i
$305$	−5.07217			−0.290432
$306$	4.04913	+	2.58435i	0.231473	+	0.147737i
$307$	19.2343			1.09776			0.548881	−	0.835901i	$-0.315054\pi$
$307$	19.2343			1.09776			0.548881	+	0.835901i	$0.315054\pi$
$308$	43.9332	+	76.0946i	2.50333	+	4.33589i
$309$	−0.482094	+	1.65141i	−0.0274254	+	0.0939457i
$310$	8.90407	−	15.4223i	0.505717	−	0.875928i
$311$	−4.38021	+	7.58674i	−0.248379	+	0.430205i	−0.963076	−	0.269229i	$-0.913231\pi$
$311$	−4.38021	+	7.58674i	−0.248379	+	0.430205i	0.714697	+	0.699434i	$0.246564\pi$
$312$	−3.37397	+	11.5576i	−0.191014	+	0.654318i
$313$	6.08910	+	10.5466i	0.344176	+	0.596131i	0.985204	−	0.171387i	$-0.0548248\pi$
$313$	6.08910	+	10.5466i	0.344176	+	0.596131i	−0.641027	+	0.767518i	$0.721491\pi$
$314$	−20.6808			−1.16708
$315$	11.3806	−	5.91225i	0.641223	−	0.333117i
$316$	68.1896			3.83596
$317$	−8.66227	−	15.0035i	−0.486521	−	0.842680i	0.513359	−	0.858174i	$-0.328401\pi$
$317$	−8.66227	−	15.0035i	−0.486521	−	0.842680i	−0.999880	+	0.0154945i	$0.995068\pi$
$318$	−26.9735	−	28.2005i	−1.51260	−	1.58141i
$319$	−15.2530	+	26.4189i	−0.854003	+	1.47918i
$320$	2.18340	−	3.78175i	0.122056	−	0.211407i
$321$	7.13705	−	1.74326i	0.398351	−	0.0972992i
$322$	−30.0089	−	51.9770i	−1.67233	−	2.89656i
$323$	−1.61777			−0.0900149
$324$	17.7668	+	38.2682i	0.987043	+	2.12601i
$325$	−1.00000			−0.0554700
$326$	−22.4633	−	38.9076i	−1.24413	−	2.15489i
$327$	7.94596	−	1.94084i	0.439412	−	0.107329i
$328$	−14.1607	+	24.5270i	−0.781894	+	1.35428i
$329$	−0.867775	+	1.50303i	−0.0478420	+	0.0828647i
$330$	−13.5748	−	14.1923i	−0.747268	−	0.781261i
$331$	−1.23037	−	2.13106i	−0.0676272	−	0.117134i	0.830229	−	0.557422i	$-0.188210\pi$
$331$	−1.23037	−	2.13106i	−0.0676272	−	0.117134i	−0.897856	+	0.440288i	$0.854876\pi$
$332$	−14.2566			−0.782434
$333$	−10.7064	+	5.56200i	−0.586706	+	0.304796i
$334$	−11.0579			−0.605062
$335$	7.27894	+	12.6075i	0.397691	+	0.688821i
$336$	17.8461	−	61.1320i	0.973586	−	3.33502i
$337$	−10.3743	+	17.9688i	−0.565123	+	0.978821i	0.431915	+	0.901914i	$0.357838\pi$
$337$	−10.3743	+	17.9688i	−0.565123	+	0.978821i	−0.997038	+	0.0769073i	$0.975495\pi$
$338$	1.29305	−	2.23963i	0.0703328	−	0.121820i
$339$	1.72506	−	5.90919i	0.0936922	−	0.320943i
$340$	1.45127	+	2.51367i	0.0787062	+	0.136323i
$341$	−30.1918			−1.63498
$342$	−17.0877	−	10.9062i	−0.923997	−	0.589739i
$343$	−18.2739			−0.986700
$344$	−34.8846	−	60.4220i	−1.88085	−	3.25773i
$345$	6.49950	+	6.79516i	0.349921	+	0.365839i
$346$	16.7526	−	29.0164i	0.900626	−	1.55993i
$347$	6.29383	−	10.9012i	0.337871	−	0.585209i	−0.646161	−	0.763201i	$-0.723627\pi$
$347$	6.29383	−	10.9012i	0.337871	−	0.585209i	0.984032	+	0.177992i	$0.0569601\pi$
$348$	54.8816	−	13.4051i	2.94196	−	0.718588i
$349$	9.98642	+	17.2970i	0.534561	+	0.925887i	0.999184	+	0.0403782i	$0.0128563\pi$
$349$	9.98642	+	17.2970i	0.534561	+	0.925887i	−0.464624	+	0.885508i	$0.653810\pi$
$350$	11.0553			0.590932
$351$	−1.00732	−	5.09758i	−0.0537665	−	0.272089i
$352$	−36.5671			−1.94903
$353$	−2.94467	−	5.10031i	−0.156729	−	0.271462i	0.776958	−	0.629552i	$-0.216762\pi$
$353$	−2.94467	−	5.10031i	−0.156729	−	0.271462i	−0.933687	+	0.358090i	$0.883428\pi$
$354$	46.6527	−	11.3951i	2.47956	−	0.605645i
$355$	3.28761	−	5.69431i	0.174488	−	0.302223i
$356$	−17.0423	+	29.5181i	−0.903240	+	1.56446i
$357$	3.16879	+	3.31293i	0.167710	+	0.175339i
$358$	24.3780	+	42.2239i	1.28842	+	2.23160i
$359$	17.8334			0.941209			0.470605	−	0.882344i	$-0.344036\pi$
$359$	17.8334			0.941209			0.470605	+	0.882344i	$0.344036\pi$
$360$	−0.927080	+	20.8332i	−0.0488614	+	1.09801i
$361$	−12.1729			−0.640677
$362$	−27.4894	−	47.6131i	−1.44481	−	2.50249i
$363$	−3.99149	+	13.6729i	−0.209499	+	0.717639i
$364$	−10.0202	+	17.3555i	−0.525202	+	0.909676i
$365$	8.36565	−	14.4897i	0.437878	−	0.758427i
$366$	6.36673	−	21.8093i	0.332795	−	1.13999i
$367$	14.9165	+	25.8361i	0.778633	+	1.34863i	0.932730	+	0.360576i	$0.117420\pi$
$367$	14.9165	+	25.8361i	0.778633	+	1.34863i	−0.154097	+	0.988056i	$0.549247\pi$
$368$	46.6929			2.43404
$369$	0.543379	−	12.2107i	0.0282872	−	0.635665i
$370$	−10.4004			−0.540690
$371$	−18.6215	−	32.2535i	−0.966783	−	1.67452i
$372$	38.6478	+	40.4059i	2.00380	+	2.09495i
$373$	7.28970	−	12.6261i	0.377446	−	0.653756i	−0.613244	−	0.789894i	$-0.710136\pi$
$373$	7.28970	−	12.6261i	0.377446	−	0.653756i	0.990690	+	0.136138i	$0.0434690\pi$
$374$	3.51018	−	6.07981i	0.181507	−	0.314379i
$375$	−1.68259	+	0.410979i	−0.0868884	+	0.0212229i
$376$	−1.41106	−	2.44403i	−0.0727700	−	0.126041i
$377$	−6.95774			−0.358342
$378$	11.1362	+	56.3554i	0.572784	+	2.89861i
$379$	20.7048			1.06353			0.531766	−	0.846891i	$-0.321529\pi$
$379$	20.7048			1.06353			0.531766	+	0.846891i	$0.321529\pi$
$380$	−6.12450	−	10.6079i	−0.314180	−	0.544176i
$381$	−22.9526	+	5.60628i	−1.17590	+	0.287219i
$382$	−19.9350	+	34.5284i	−1.01996	+	1.76663i
$383$	12.7832	−	22.1412i	0.653193	−	1.13136i	−0.329150	−	0.944277i	$-0.606762\pi$
$383$	12.7832	−	22.1412i	0.653193	−	1.13136i	0.982344	−	0.187086i	$-0.0599043\pi$
$384$	−6.44977	−	6.74317i	−0.329138	−	0.344111i
$385$	−9.37156	−	16.2320i	−0.477619	−	0.827260i
$386$	−4.88260			−0.248518
$387$	25.3816	+	16.1997i	1.29022	+	0.823479i
$388$	−45.1671			−2.29301
$389$	8.56520	+	14.8354i	0.434273	+	0.752183i	0.997236	−	0.0742992i	$-0.0236720\pi$
$389$	8.56520	+	14.8354i	0.434273	+	0.752183i	−0.562963	+	0.826482i	$0.690339\pi$
$390$	1.25523	−	4.29979i	0.0635610	−	0.217728i
$391$	−1.68064	+	2.91096i	−0.0849939	+	0.147214i
$392$	39.1868	−	67.8736i	1.97923	−	3.42813i
$393$	−4.05888	+	13.9037i	−0.204743	+	0.701349i
$394$	−14.0422	−	24.3218i	−0.707435	−	1.22531i
$395$	−14.5458			−0.731877
$396$	54.7189	−	28.4266i	2.74973	−	1.42849i
$397$	−15.8337			−0.794669			−0.397334	−	0.917674i	$-0.630065\pi$
$397$	−15.8337			−0.794669			−0.397334	+	0.917674i	$0.630065\pi$
$398$	−1.55308	−	2.69002i	−0.0778490	−	0.134838i
$399$	−13.3726	−	13.9809i	−0.669467	−	0.699920i
$400$	−4.30043	+	7.44856i	−0.215021	+	0.372428i
$401$	17.0554	−	29.5408i	0.851706	−	1.47520i	−0.0279624	−	0.999609i	$-0.508902\pi$
$401$	17.0554	−	29.5408i	0.851706	−	1.47520i	0.879668	−	0.475588i	$-0.157765\pi$
$402$	−63.3463	+	15.4726i	−3.15943	+	0.771705i
$403$	−3.44304	−	5.96353i	−0.171510	−	0.297065i
$404$	36.5636			1.81911
$405$	−3.78990	−	8.16313i	−0.188321	−	0.405629i
$406$	76.9200			3.81748
$407$	8.81637	+	15.2704i	0.437011	+	0.756926i
$408$	−7.24167	+	1.76881i	−0.358516	+	0.0875692i
$409$	9.57264	−	16.5803i	0.473336	−	0.819843i	−0.526198	−	0.850362i	$-0.676383\pi$
$409$	9.57264	−	16.5803i	0.473336	−	0.819843i	0.999534	+	0.0305196i	$0.00971618\pi$
$410$	5.26825	−	9.12487i	0.260180	−	0.450645i
$411$	8.08223	+	8.44989i	0.398667	+	0.416802i
$412$	−2.32812	−	4.03243i	−0.114698	−	0.198664i
$413$	45.8331			2.25530
$414$	−37.3761	+	19.4170i	−1.83694	+	0.954294i
$415$	3.04113			0.149283
$416$	−4.17008	−	7.22278i	−0.204455	−	0.354126i
$417$	−1.70161	+	5.82887i	−0.0833282	+	0.285441i
$418$	−14.8133	+	25.6574i	−0.724542	+	1.25494i
$419$	−3.56749	+	6.17908i	−0.174284	+	0.301868i	−0.939913	−	0.341414i	$-0.889094\pi$
$419$	−3.56749	+	6.17908i	−0.174284	+	0.301868i	0.765630	+	0.643282i	$0.222428\pi$
$420$	−9.72710	+	33.3202i	−0.474634	+	1.62586i
$421$	13.0809	+	22.6568i	0.637524	+	1.10422i	0.985974	+	0.166896i	$0.0533745\pi$
$421$	13.0809	+	22.6568i	0.637524	+	1.10422i	−0.348451	+	0.937327i	$0.613292\pi$
$422$	0.608282			0.0296107
$423$	1.02667	+	0.655269i	0.0499183	+	0.0318603i
$424$	60.5599			2.94105
$425$	−0.309576	−	0.536201i	−0.0150166	−	0.0260096i
$426$	20.3577	+	21.2837i	0.986332	+	1.03120i
$427$	10.8415	−	18.7780i	0.524657	−	0.908732i
$428$	−9.94244	+	17.2208i	−0.480586	+	0.832399i
$429$	−7.37724	+	1.80192i	−0.356176	+	0.0869978i
$430$	12.9782	+	22.4790i	0.625866	+	1.08403i
$431$	−12.4211			−0.598302			−0.299151	−	0.954206i	$-0.596703\pi$
$431$	−12.4211			−0.598302			−0.299151	+	0.954206i	$0.596703\pi$
$432$	−42.3015	−	14.4187i	−2.03523	−	0.693721i
$433$	−6.04541			−0.290524			−0.145262	−	0.989393i	$-0.546402\pi$
$433$	−6.04541			−0.290524			−0.145262	+	0.989393i	$0.546402\pi$
$434$	38.0640	+	65.9287i	1.82713	+	3.16468i
$435$	−11.7070	+	2.85949i	−0.561307	+	0.137102i
$436$	−11.0693	+	19.1726i	−0.530124	+	0.918201i
$437$	7.09248	−	12.2845i	0.339279	−	0.587649i
$438$	51.8020	+	54.1585i	2.47520	+	2.58779i
$439$	14.3382	+	24.8345i	0.684326	+	1.18529i	0.973648	+	0.228055i	$0.0732366\pi$
$439$	14.3382	+	24.8345i	0.684326	+	1.18529i	−0.289323	+	0.957232i	$0.593430\pi$
$440$	30.4776			1.45296
$441$	−1.50369	+	33.7907i	−0.0716042	+	1.60908i
$442$	1.60119			0.0761608
$443$	4.57498	+	7.92410i	0.217364	+	0.376485i	0.954001	−	0.299803i	$-0.0969209\pi$
$443$	4.57498	+	7.92410i	0.217364	+	0.376485i	−0.736637	+	0.676288i	$0.763588\pi$
$444$	9.15086	−	31.3463i	0.434280	−	1.48763i
$445$	3.63535	−	6.29661i	0.172332	−	0.298488i
$446$	−21.6650	+	37.5249i	−1.02587	+	1.77686i
$447$	−5.95992	+	20.4157i	−0.281895	+	0.965631i
$448$	9.33379	+	16.1666i	0.440980	+	0.763800i
$449$	35.4645			1.67367			0.836837	−	0.547452i	$-0.184402\pi$
$449$	35.4645			1.67367			0.836837	+	0.547452i	$0.184402\pi$
$450$	0.344904	−	7.75064i	0.0162589	−	0.365369i
$451$	−17.8635			−0.841160
$452$	8.33064	+	14.4291i	0.391840	+	0.678687i
$453$	19.9891	+	20.8984i	0.939172	+	0.981895i
$454$	29.4820	−	51.0644i	1.38366	−	2.39657i
$455$	2.13745	−	3.70217i	0.100205	−	0.173560i
$456$	30.5605	−	7.46455i	1.43113	−	0.349560i
$457$	−4.70631	−	8.15156i	−0.220152	−	0.381314i	0.734702	−	0.678390i	$-0.237322\pi$
$457$	−4.70631	−	8.15156i	−0.220152	−	0.381314i	−0.954854	+	0.297076i	$0.903989\pi$
$458$	18.0375			0.842837
$459$	2.42149	−	2.11821i	0.113025	−	0.0988696i
$460$	−25.4502			−1.18662
$461$	10.2513	+	17.7557i	0.477450	+	0.826967i	0.999666	−	0.0258461i	$-0.00822797\pi$
$461$	10.2513	+	17.7557i	0.477450	+	0.826967i	−0.522216	+	0.852813i	$0.674895\pi$
$462$	81.5577	−	19.9209i	3.79441	−	0.926802i
$463$	18.8916	−	32.7211i	0.877965	−	1.52068i	0.0243951	−	0.999702i	$-0.492234\pi$
$463$	18.8916	−	32.7211i	0.877965	−	1.52068i	0.853570	−	0.520978i	$-0.174433\pi$
$464$	−29.9213	+	51.8251i	−1.38906	+	2.40592i
$465$	−8.24411	−	8.61913i	−0.382311	−	0.399703i
$466$	−11.1616	−	19.3325i	−0.517053	−	0.895562i
$467$	−12.8882			−0.596394			−0.298197	−	0.954504i	$-0.596385\pi$
$467$	−12.8882			−0.596394			−0.298197	+	0.954504i	$0.596385\pi$
$468$	11.8550	+	7.56641i	0.547996	+	0.349757i
$469$	−62.2334			−2.87367
$470$	0.524962	+	0.909260i	0.0242147	+	0.0419411i
$471$	−3.88148	+	13.2960i	−0.178849	+	0.612649i
$472$	−37.2639	+	64.5429i	−1.71521	+	2.97083i
$473$	22.0032	−	38.1107i	1.01171	−	1.75233i
$474$	18.2583	−	62.5437i	0.838629	−	2.87273i
$475$	1.30644	+	2.26282i	0.0599435	+	0.103825i
$476$	−12.4080			−0.568722
$477$	−23.1932	+	12.0489i	−1.06194	+	0.551682i
$478$	7.94194			0.363256
$479$	−10.0940	−	17.4833i	−0.461207	−	0.798835i	0.537814	−	0.843063i	$-0.319250\pi$
$479$	−10.0940	−	17.4833i	−0.461207	−	0.798835i	−0.999021	+	0.0442289i	$0.985917\pi$
$480$	−9.98493	−	10.4391i	−0.455748	−	0.476479i
$481$	−2.01082	+	3.48284i	−0.0916855	+	0.158804i
$482$	7.54195	−	13.0630i	0.343527	−	0.595006i
$483$	−39.0492	+	9.53794i	−1.77680	+	0.433991i
$484$	−19.2757	−	33.3865i	−0.876167	−	1.51757i
$485$	9.63475			0.437492
$486$	39.8569	−	6.04917i	1.80795	−	0.274396i
$487$	15.1480			0.686423			0.343212	−	0.939258i	$-0.388485\pi$
$487$	15.1480			0.686423			0.343212	+	0.939258i	$0.388485\pi$
$488$	17.6290	+	30.5344i	0.798029	+	1.38223i
$489$	−29.2304	+	7.13967i	−1.32185	+	0.322867i
$490$	−14.5788	+	25.2512i	−0.658603	+	1.14073i
$491$	5.74374	−	9.94845i	0.259211	−	0.448967i	−0.706820	−	0.707394i	$-0.749871\pi$
$491$	5.74374	−	9.94845i	0.259211	−	0.448967i	0.966031	+	0.258427i	$0.0832040\pi$
$492$	22.8666	+	23.9068i	1.03091	+	1.07780i
$493$	−2.15395	−	3.73074i	−0.0970089	−	0.168024i
$494$	−6.75717			−0.304020
$495$	−11.6723	+	6.06379i	−0.524630	+	0.272547i
$496$	−59.2263			−2.65934
$497$	14.0542	+	24.3426i	0.630417	+	1.09191i
$498$	−3.81732	+	13.0762i	−0.171058	+	0.585960i
$499$	6.56005	−	11.3623i	0.293668	−	0.508648i	−0.681006	−	0.732278i	$-0.738457\pi$
$499$	6.56005	−	11.3623i	0.293668	−	0.508648i	0.974674	+	0.223630i	$0.0717906\pi$
$500$	2.34397	−	4.05987i	0.104825	−	0.181563i
$501$	−2.07541	+	7.10933i	−0.0927225	+	0.317621i
$502$	−30.6584	−	53.1019i	−1.36835	−	2.37006i
$503$	7.80396			0.347961			0.173981	−	0.984749i	$-0.444337\pi$
$503$	7.80396			0.347961			0.173981	+	0.984749i	$0.444337\pi$
$504$	−75.1464	−	47.9621i	−3.34729	−	2.13640i
$505$	−7.79952			−0.347074
$506$	30.7781	+	53.3092i	1.36825	+	2.36988i
$507$	−1.19721	−	1.25167i	−0.0531700	−	0.0555887i
$508$	31.9747	−	55.3818i	1.41865	−	2.45717i
$509$	−10.9919	+	19.0385i	−0.487205	+	0.843865i	−0.999892	−	0.0147114i	$-0.995317\pi$
$509$	−10.9919	+	19.0385i	−0.487205	+	0.843865i	0.512686	+	0.858576i	$0.328650\pi$
$510$	2.69414	−	0.658056i	0.119298	−	0.0291392i
$511$	35.7623	+	61.9421i	1.58203	+	2.74016i
$512$	47.8414			2.11431
$513$	−10.2189	+	8.93905i	−0.451175	+	0.394669i
$514$	−49.9316			−2.20239
$515$	0.496621	+	0.860172i	0.0218837	+	0.0379037i
$516$	−79.1696	+	19.3375i	−3.48525	+	0.851288i
$517$	0.890017	−	1.54155i	0.0391429	−	0.0677975i
$518$	22.2303	−	38.5039i	0.976742	−	1.69177i
$519$	−15.5109	−	16.2165i	−0.680854	−	0.711826i
$520$	3.47564	+	6.01998i	0.152417	+	0.263994i
$521$	12.1706			0.533205			0.266603	−	0.963807i	$-0.414099\pi$
$521$	12.1706			0.533205			0.266603	+	0.963807i	$0.414099\pi$
$522$	2.39975	−	53.9269i	0.105034	−	2.36032i
$523$	32.5468			1.42317			0.711587	−	0.702598i	$-0.247977\pi$
$523$	32.5468			1.42317			0.711587	+	0.702598i	$0.247977\pi$
$524$	−19.6011	−	33.9501i	−0.856279	−	1.48312i
$525$	2.07492	−	7.10766i	0.0905571	−	0.310204i
$526$	−15.1542	+	26.2478i	−0.660753	+	1.14446i
$527$	2.13177	−	3.69233i	0.0928612	−	0.160840i
$528$	−18.3035	+	62.6988i	−0.796559	+	2.72862i
$529$	−3.23629	−	5.60543i	−0.140708	−	0.243714i
$530$	−22.5303			−0.978653
$531$	1.42990	−	32.1326i	0.0620524	−	1.39443i
$532$	52.3632			2.27023
$533$	−2.03714	−	3.52842i	−0.0882382	−	0.152833i
$534$	22.5109	+	23.5349i	0.974143	+	1.01846i
$535$	2.12086	−	3.67343i	0.0916927	−	0.158816i
$536$	50.5979	−	87.6381i	2.18550	−	3.78539i
$537$	31.7219	−	7.74821i	1.36890	−	0.334360i
$538$	−21.9933	−	38.0936i	−0.948199	−	1.64233i
$539$	49.4336			2.12925
$540$	23.0566	+	7.85899i	0.992199	+	0.338197i
$541$	−16.3865			−0.704511			−0.352256	−	0.935904i	$-0.614585\pi$
$541$	−16.3865			−0.704511			−0.352256	+	0.935904i	$0.614585\pi$
$542$	−16.1424	−	27.9595i	−0.693378	−	1.20097i
$543$	−35.7707	+	8.73715i	−1.53507	+	0.374947i
$544$	2.58191	−	4.47200i	0.110698	−	0.191735i
$545$	2.36123	−	4.08978i	0.101144	−	0.175187i
$546$	13.2356	+	13.8376i	0.566430	+	0.592196i
$547$	−9.53335	−	16.5122i	−0.407616	−	0.706012i	0.587006	−	0.809583i	$-0.300307\pi$
$547$	−9.53335	−	16.5122i	−0.407616	−	0.706012i	−0.994622	+	0.103570i	$0.966973\pi$
$548$	−31.6477			−1.35192
$549$	−12.8266	−	8.18657i	−0.547427	−	0.349394i
$550$	−11.3387			−0.483483
$551$	9.08986	+	15.7441i	0.387241	+	0.670721i
$552$	18.3168	−	62.7444i	0.779616	−	2.67058i
$553$	31.0908	−	53.8508i	1.32211	−	2.28997i
$554$	26.2344	−	45.4393i	1.11459	−	1.93053i
$555$	−1.95200	+	6.68659i	−0.0828579	+	0.283830i
$556$	−8.21740	−	14.2330i	−0.348495	−	0.603612i
$557$	−38.2913			−1.62245			−0.811227	−	0.584732i	$-0.801200\pi$
$557$	−38.2913			−1.62245			−0.811227	+	0.584732i	$0.801200\pi$
$558$	47.4087	−	24.6290i	2.00697	−	1.04263i
$559$	10.0369			0.424516
$560$	−18.3839	−	31.8418i	−0.776860	−	1.34556i
$561$	−3.25001	−	3.39785i	−0.137215	−	0.143457i
$562$	−10.8287	+	18.7558i	−0.456779	+	0.791165i
$563$	−5.17040	+	8.95540i	−0.217906	+	0.377425i	−0.954168	−	0.299272i	$-0.903256\pi$
$563$	−5.17040	+	8.95540i	−0.217906	+	0.377425i	0.736261	+	0.676697i	$0.236589\pi$
$564$	−3.20236	+	0.782192i	−0.134844	+	0.0329362i
$565$	−1.77704	−	3.07792i	−0.0747605	−	0.129489i
$566$	5.75569			0.241930
$567$	38.3220	+	3.41743i	1.60937	+	0.143518i
$568$	−45.7062			−1.91779
$569$	13.0134	+	22.5398i	0.545548	+	0.944917i	0.998572	+	0.0534187i	$0.0170118\pi$
$569$	13.0134	+	22.5398i	0.545548	+	0.944917i	−0.453024	+	0.891498i	$0.649655\pi$
$570$	−11.3695	+	2.77706i	−0.476217	+	0.116318i
$571$	16.1620	−	27.9933i	0.676357	−	1.17148i	−0.299713	−	0.954029i	$-0.596891\pi$
$571$	16.1620	−	27.9933i	0.676357	−	1.17148i	0.976070	−	0.217456i	$-0.0697757\pi$
$572$	10.2770	−	17.8004i	0.429705	−	0.744270i
$573$	18.4574	+	19.2970i	0.771069	+	0.806144i
$574$	22.5212	+	39.0078i	0.940016	+	1.62816i
$575$	5.42887			0.226399
$576$	11.6252	−	6.03935i	0.484385	−	0.251640i
$577$	12.4808			0.519581			0.259790	−	0.965665i	$-0.416347\pi$
$577$	12.4808			0.519581			0.259790	+	0.965665i	$0.416347\pi$
$578$	−21.4862	−	37.2152i	−0.893708	−	1.54795i
$579$	−0.916394	+	3.13911i	−0.0380841	+	0.130457i
$580$	16.3087	−	28.2475i	0.677182	−	1.17291i
$581$	−6.50026	+	11.2588i	−0.269676	+	0.467093i
$582$	−12.0938	+	41.4274i	−0.501305	+	1.71722i
$583$	19.0988	+	33.0802i	0.790993	+	1.37004i
$584$	−116.304			−4.81269
$585$	−2.52882	−	1.61402i	−0.104554	−	0.0667314i
$586$	6.56579			0.271230
$587$	12.5975	+	21.8195i	0.519955	+	0.900588i	0.999731	+	0.0231969i	$0.00738446\pi$
$587$	12.5975	+	21.8195i	0.519955	+	0.900588i	−0.479776	+	0.877391i	$0.659282\pi$
$588$	−63.2788	−	66.1573i	−2.60957	−	2.72828i
$589$	−8.99625	+	15.5820i	−0.370684	+	0.642044i
$590$	13.8634	−	24.0121i	0.570747	−	0.988563i
$591$	−18.2724	+	4.46312i	−0.751627	+	0.183588i
$592$	17.2948	+	29.9554i	0.710811	+	1.23116i
$593$	−38.4456			−1.57877			−0.789385	−	0.613898i	$-0.789601\pi$
$593$	−38.4456			−1.57877			−0.789385	+	0.613898i	$0.789601\pi$
$594$	−11.4216	−	57.7998i	−0.468635	−	2.37156i
$595$	2.64681			0.108508
$596$	−28.7816	−	49.8512i	−1.17894	−	2.04198i
$597$	−2.02095	+	0.493627i	−0.0827120	+	0.0202028i
$598$	−7.01981	+	12.1587i	−0.287061	+	0.497205i
$599$	23.6618	−	40.9834i	0.966795	−	1.67454i	0.262082	−	0.965045i	$-0.415591\pi$
$599$	23.6618	−	40.9834i	0.966795	−	1.67454i	0.704713	−	0.709493i	$-0.251076\pi$
$600$	8.32215	+	8.70072i	0.339750	+	0.355205i
$601$	−20.0328	−	34.6979i	−0.817156	−	1.41536i	−0.907770	−	0.419469i	$-0.862216\pi$
$601$	−20.0328	−	34.6979i	−0.817156	−	1.41536i	0.0906140	−	0.995886i	$-0.471117\pi$
$602$	−110.961			−4.52244
$603$	−1.94156	+	43.6304i	−0.0790664	+	1.77677i
$604$	−78.2717			−3.18483
$605$	4.11176	+	7.12178i	0.167167	+	0.289542i
$606$	9.79018	−	33.5363i	0.397699	−	1.36232i
$607$	−10.3060	+	17.8505i	−0.418306	+	0.724528i	−0.995769	−	0.0918893i	$-0.970709\pi$
$607$	−10.3060	+	17.8505i	−0.418306	+	0.724528i	0.577463	+	0.816417i	$0.304043\pi$
$608$	−10.8959	+	18.8723i	−0.441887	+	0.765371i
$609$	14.4368	−	49.4532i	0.585008	−	2.00395i
$610$	−6.55858	−	11.3598i	−0.265549	−	0.459945i
$611$	0.405987			0.0164245
$612$	−0.387107	+	8.69901i	−0.0156479	+	0.351637i
$613$	−4.02465			−0.162554			−0.0812770	−	0.996692i	$-0.525900\pi$
$613$	−4.02465			−0.162554			−0.0812770	+	0.996692i	$0.525900\pi$
$614$	24.8710	+	43.0778i	1.00371	+	1.73848i
$615$	−4.87777	−	5.09966i	−0.196691	−	0.205638i
$616$	−65.1443	+	112.833i	−2.62474	+	4.54618i
$617$	−14.9120	+	25.8283i	−0.600334	+	1.03981i	0.392436	+	0.919779i	$0.371632\pi$
$617$	−14.9120	+	25.8283i	−0.600334	+	1.03981i	−0.992770	+	0.120030i	$0.961701\pi$
$618$	−4.32193	+	1.05565i	−0.173854	+	0.0424646i
$619$	23.7693	+	41.1696i	0.955368	+	1.65475i	0.733524	+	0.679664i	$0.237874\pi$
$619$	23.7693	+	41.1696i	0.955368	+	1.65475i	0.221844	+	0.975082i	$0.428792\pi$
$620$	32.2815			1.29646
$621$	5.46858	+	27.6741i	0.219447	+	1.11052i
$622$	−22.6554			−0.908397
$623$	15.5407	+	26.9174i	0.622627	+	1.07842i
$624$	−14.4717	+	3.53478i	−0.579331	+	0.141504i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.7471	+	27.2747i	−0.629379	+	1.09012i
$627$	13.7153	+	14.3392i	0.547738	+	0.572654i
$628$	−18.7444	−	32.4663i	−0.747984	−	1.29555i
$629$	−2.49000			−0.0992830
$630$	27.9569	+	17.8435i	1.11383	+	0.710901i
$631$	32.2213			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$631$	32.2213			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$632$	50.5558	+	87.5652i	2.01100	+	3.48316i
$633$	0.114166	−	0.391075i	0.00453768	−	0.0155438i
$634$	22.4015	−	38.8006i	0.889678	−	1.54097i
$635$	−6.82064	+	11.8137i	−0.270669	+	0.468812i
$636$	19.8234	−	67.9052i	0.786050	−	2.69262i
$637$	5.63736	+	9.76419i	0.223360	+	0.386871i
$638$	−78.8916			−3.12335
$639$	17.5045	−	9.09365i	0.692468	−	0.359739i
$640$	−5.38732			−0.212953
$641$	−1.75107	−	3.03295i	−0.0691632	−	0.119794i	0.829370	−	0.558700i	$-0.188700\pi$
$641$	−1.75107	−	3.03295i	−0.0691632	−	0.119794i	−0.898533	+	0.438906i	$0.855366\pi$
$642$	13.1328	+	13.7302i	0.518312	+	0.541889i
$643$	−0.0115697	+	0.0200394i	−0.000456266	+	0.000790276i	−0.866253	−	0.499605i	$-0.833479\pi$
$643$	−0.0115697	+	0.0200394i	−0.000456266	+	0.000790276i	0.865797	+	0.500395i	$0.166812\pi$
$644$	54.3984	−	94.2207i	2.14360	−	3.71282i
$645$	16.8880	−	4.12496i	0.664963	−	0.162420i
$646$	−2.09186	−	3.62320i	−0.0823030	−	0.142553i
$647$	−20.8611			−0.820136			−0.410068	−	0.912055i	$-0.634495\pi$
$647$	−20.8611			−0.820136			−0.410068	+	0.912055i	$0.634495\pi$
$648$	−35.9696	+	51.1872i	−1.41302	+	2.01082i
$649$	−47.0078			−1.84522
$650$	−1.29305	−	2.23963i	−0.0507177	−	0.0878456i
$651$	49.5308	−	12.0981i	1.94126	−	0.474163i
$652$	40.7202	−	70.5294i	1.59472	−	2.76214i
$653$	−5.47824	+	9.48859i	−0.214380	+	0.371317i	−0.953081	−	0.302716i	$-0.902106\pi$
$653$	−5.47824	+	9.48859i	−0.214380	+	0.371317i	0.738700	+	0.674034i	$0.235440\pi$
$654$	14.6213	+	15.2864i	0.571738	+	0.597746i
$655$	4.18118	+	7.24202i	0.163372	+	0.282969i
$656$	−35.0422			−1.36817
$657$	44.5419	−	23.1397i	1.73775	−	0.902765i
$658$	−4.48831			−0.174973
$659$	17.0546	+	29.5395i	0.664354	+	1.15070i	0.979460	+	0.201639i	$0.0646267\pi$
$659$	17.0546	+	29.5395i	0.664354	+	1.15070i	−0.315106	+	0.949057i	$0.602040\pi$
$660$	9.97642	−	34.1743i	0.388332	−	1.33023i
$661$	12.0901	−	20.9406i	0.470249	−	0.814495i	−0.529172	−	0.848514i	$-0.677497\pi$
$661$	12.0901	−	20.9406i	0.470249	−	0.814495i	0.999421	+	0.0340194i	$0.0108308\pi$
$662$	3.18186	−	5.51115i	0.123667	−	0.214197i
$663$	0.300520	−	1.02943i	0.0116712	−	0.0399799i
$664$	−10.5699	−	18.3076i	−0.410191	−	0.710471i
$665$	−11.1698			−0.433145
$666$	−26.3007	−	16.7864i	−1.01913	−	0.650460i
$667$	37.7726			1.46256
$668$	−10.0226	−	17.3596i	−0.387784	−	0.671662i
$669$	20.0592	+	20.9717i	0.775534	+	0.810813i
$670$	−18.8241	+	32.6043i	−0.727238	+	1.25961i
$671$	−11.1194	+	19.2593i	−0.429259	+	0.743498i
$672$	59.9897	−	14.6528i	2.31415	−	0.565243i
$673$	−9.66073	−	16.7329i	−0.372394	−	0.645005i	0.617539	−	0.786540i	$-0.288130\pi$
$673$	−9.66073	−	16.7329i	−0.372394	−	0.645005i	−0.989933	+	0.141535i	$0.954796\pi$
$674$	−53.6579			−2.06683
$675$	−4.91829	−	1.67643i	−0.189305	−	0.0645258i
$676$	4.68793			0.180305
$677$	19.1367	+	33.1457i	0.735483	+	1.27389i	0.954511	+	0.298175i	$0.0963779\pi$
$677$	19.1367	+	33.1457i	0.735483	+	1.27389i	−0.219028	+	0.975718i	$0.570289\pi$
$678$	15.4650	−	3.77740i	0.593930	−	0.145070i
$679$	−20.5938	+	35.6695i	−0.790316	+	1.36887i
$680$	−2.15195	+	3.72728i	−0.0825234	+	0.142935i
$681$	−27.2968	−	28.5386i	−1.04602	−	1.09360i
$682$	−39.0396	−	67.6185i	−1.49490	−	2.58925i
$683$	0.692198			0.0264862			0.0132431	−	0.999912i	$-0.495784\pi$
$683$	0.692198			0.0264862			0.0132431	+	0.999912i	$0.495784\pi$
$684$	1.63363	−	36.7107i	0.0624633	−	1.40367i
$685$	6.75088			0.257938
$686$	−23.6292	−	40.9269i	−0.902165	−	1.56260i
$687$	3.38538	−	11.5966i	0.129160	−	0.442439i
$688$	43.1630	−	74.7605i	1.64557	−	2.85022i
$689$	−4.35603	+	7.54486i	−0.165951	+	0.287436i
$690$	−6.81447	+	23.3430i	−0.259422	+	0.888652i
$691$	16.4956	+	28.5711i	0.627520	+	1.08690i	0.988048	+	0.154148i	$0.0492634\pi$
$691$	16.4956	+	28.5711i	0.627520	+	1.08690i	−0.360527	+	0.932749i	$0.617403\pi$
$692$	60.7363			2.30885
$693$	2.49974	−	56.1738i	0.0949571	−	2.13386i
$694$	32.5530			1.23569
$695$	1.75288	+	3.03608i	0.0664907	+	0.115165i
$696$	57.9033	+	60.5373i	2.19482	+	2.29466i
$697$	1.26130	−	2.18463i	0.0477750	−	0.0827487i
$698$	−25.8259	+	44.7318i	−0.977526	+	1.69312i
$699$	−14.5241	+	3.54758i	−0.549352	+	0.134182i
$700$	10.0202	+	17.3555i	0.378728	+	0.655977i
$701$	−18.7776			−0.709219			−0.354610	−	0.935014i	$-0.615386\pi$
$701$	−18.7776			−0.709219			−0.354610	+	0.935014i	$0.615386\pi$
$702$	10.1142	−	8.84745i	0.381735	−	0.333926i
$703$	10.5081			0.396319
$704$	−9.57303	−	16.5810i	−0.360797	−	0.624919i
$705$	0.683107	−	0.166852i	0.0257273	−	0.00628402i
$706$	7.61522	−	13.1899i	0.286603	−	0.496410i
$707$	16.6711	−	28.8751i	0.626980	−	1.08596i
$708$	60.1736	+	62.9109i	2.26146	+	2.36434i
$709$	−4.04721	−	7.00997i	−0.151996	−	0.263265i	0.779965	−	0.625823i	$-0.215237\pi$
$709$	−4.04721	−	7.00997i	−0.151996	−	0.263265i	−0.931961	+	0.362558i	$0.881903\pi$
$710$	17.0042			0.638157
$711$	−36.7837	−	23.4771i	−1.37949	−	0.880460i
$712$	−50.5407			−1.89409
$713$	18.6918	+	32.3752i	0.700014	+	1.21246i
$714$	−3.32235	+	11.3807i	−0.124336	+	0.425912i
$715$	−2.19223	+	3.79706i	−0.0819848	+	0.142002i
$716$	−44.1909	+	76.5409i	−1.65149	+	2.86047i
$717$	1.49059	−	5.10602i	0.0556670	−	0.190688i
$718$	23.0595	+	39.9402i	0.860572	+	1.49055i
$719$	31.8467			1.18768			0.593840	−	0.804583i	$-0.297611\pi$
$719$	31.8467			1.18768			0.593840	+	0.804583i	$0.297611\pi$
$720$	−22.8971	+	11.8951i	−0.853325	+	0.443305i
$721$	−4.24600			−0.158129
$722$	−15.7402	−	27.2627i	−0.585788	−	1.01461i
$723$	−6.98295	−	7.30060i	−0.259699	−	0.271512i
$724$	49.8312	−	86.3101i	1.85196	−	3.20769i
$725$	−3.47887	+	6.02558i	−0.129202	+	0.223784i
$726$	−35.7834	+	8.74026i	−1.32805	+	0.324381i
$727$	10.1546	+	17.5883i	0.376613	+	0.652313i	0.990567	−	0.137029i	$-0.0437552\pi$
$727$	10.1546	+	17.5883i	0.376613	+	0.652313i	−0.613954	+	0.789342i	$0.710422\pi$
$728$	−29.7160			−1.10135
$729$	3.59145	−	26.7601i	0.133017	−	0.991114i
$730$	43.2689			1.60145
$731$	3.10718	+	5.38180i	0.114923	+	0.199053i
$732$	40.0085	−	9.77227i	1.47876	−	0.361194i
$733$	7.15966	−	12.4009i	0.264448	−	0.458037i	−0.702971	−	0.711219i	$-0.748144\pi$
$733$	7.15966	−	12.4009i	0.264448	−	0.458037i	0.967419	+	0.253181i	$0.0814769\pi$
$734$	−38.5755	+	66.8147i	−1.42385	+	2.46618i
$735$	13.4982	+	14.1122i	0.497889	+	0.520538i
$736$	22.6388	+	39.2115i	0.834477	+	1.44536i
$737$	63.8285			2.35115
$738$	28.0502	−	14.5721i	1.03254	−	0.536408i
$739$	−32.7316			−1.20405			−0.602025	−	0.798477i	$-0.705639\pi$
$739$	−32.7316			−1.20405			−0.602025	+	0.798477i	$0.705639\pi$
$740$	−9.42660	−	16.3273i	−0.346529	−	0.600205i
$741$	−1.26822	+	4.34431i	−0.0465894	+	0.159592i
$742$	48.1573	−	83.4108i	1.76791	−	3.06211i
$743$	−19.4753	+	33.7323i	−0.714481	+	1.23752i	0.248678	+	0.968586i	$0.420004\pi$
$743$	−19.4753	+	33.7323i	−0.714481	+	1.23752i	−0.963159	+	0.268931i	$0.913330\pi$
$744$	−23.2335	+	79.5863i	−0.851780	+	2.91778i
$745$	6.13951	+	10.6339i	0.224934	+	0.389597i
$746$	37.7038			1.38044
$747$	7.69049	+	4.90844i	0.281380	+	0.179590i
$748$	12.7261			0.465312
$749$	9.06644	+	15.7035i	0.331280	+	0.573795i
$750$	−3.09611	−	3.23696i	−0.113054	−	0.118197i
$751$	11.5075	−	19.9316i	0.419916	−	0.727316i	−0.576015	−	0.817439i	$-0.695393\pi$
$751$	11.5075	−	19.9316i	0.419916	−	0.727316i	0.995931	+	0.0901237i	$0.0287263\pi$
$752$	1.74592	−	3.02401i	0.0636670	−	0.110274i
$753$	−39.8943	+	9.74437i	−1.45383	+	0.355105i
$754$	−8.99672	−	15.5828i	−0.327641	−	0.567491i
$755$	16.6964			0.607645
$756$	−78.3776	+	68.5613i	−2.85056	+	2.49355i
$757$	41.6474			1.51370			0.756850	−	0.653588i	$-0.226737\pi$
$757$	41.6474			1.51370			0.756850	+	0.653588i	$0.226737\pi$
$758$	26.7723	+	46.3710i	0.972415	+	1.68427i
$759$	40.0500	−	9.78241i	1.45372	−	0.355079i
$760$	9.08142	−	15.7295i	0.329418	−	0.570568i
$761$	−3.44431	+	5.96571i	−0.124856	+	0.216257i	−0.921677	−	0.387959i	$-0.873180\pi$
$761$	−3.44431	+	5.96571i	−0.124856	+	0.216257i	0.796821	+	0.604216i	$0.206514\pi$
$762$	−42.2349	−	44.1562i	−1.53001	−	1.59961i
$763$	10.0940	+	17.4834i	0.365428	+	0.632940i
$764$	−72.2738			−2.61477
$765$	0.0825751	−	1.85562i	0.00298551	−	0.0670900i
$766$	66.1176			2.38893
$767$	−5.36073	−	9.28505i	−0.193565	−	0.335264i
$768$	11.0014	−	37.6853i	0.396978	−	1.35985i
$769$	4.78387	−	8.28591i	0.172511	−	0.298797i	−0.766786	−	0.641903i	$-0.778145\pi$
$769$	4.78387	−	8.28591i	0.172511	−	0.298797i	0.939297	+	0.343105i	$0.111479\pi$
$770$	24.2358	−	41.9777i	0.873399	−	1.51277i
$771$	−9.37145	+	32.1019i	−0.337504	+	1.15612i
$772$	−4.42545	−	7.66510i	−0.159275	−	0.275873i
$773$	−10.5131			−0.378131			−0.189066	−	0.981964i	$-0.560546\pi$
$773$	−10.5131			−0.378131			−0.189066	+	0.981964i	$0.560546\pi$
$774$	−3.46177	+	77.7924i	−0.124431	+	2.79619i
$775$	−6.88609			−0.247356
$776$	−33.4869	−	58.0010i	−1.20211	−	2.08212i
$777$	−20.5826	−	21.5189i	−0.738396	−	0.771985i
$778$	−22.1505	+	38.3658i	−0.794134	+	1.37548i
$779$	−5.32279	+	9.21934i	−0.190709	+	0.330317i
$780$	7.88785	−	1.92664i	0.282430	−	0.0689849i
$781$	−14.4144	−	24.9665i	−0.515789	−	0.893372i
$782$	−8.69264			−0.310848
$783$	−34.2202	−	11.6642i	−1.22293	−	0.416843i
$784$	96.9722			3.46329
$785$	3.99844	+	6.92550i	0.142710	+	0.247182i
$786$	−36.3875	+	8.88782i	−1.29790	+	0.317018i
$787$	18.0600	−	31.2808i	0.643769	−	1.11504i	−0.340816	−	0.940130i	$-0.610703\pi$
$787$	18.0600	−	31.2808i	0.643769	−	1.11504i	0.984584	−	0.174910i	$-0.0559634\pi$
$788$	25.4548	−	44.0891i	0.906791	−	1.57061i
$789$	14.0310	+	14.6692i	0.499515	+	0.522238i
$790$	−18.8084	−	32.5771i	−0.669174	−	1.15904i
$791$	15.1933			0.540211
$792$	77.0725	+	49.1914i	2.73865	+	1.74794i
$793$	−5.07217			−0.180118
$794$	−20.4738	−	35.4616i	−0.726586	−	1.25848i
$795$	−4.22861	+	14.4851i	−0.149973	+	0.513734i
$796$	2.81533	−	4.87630i	0.0997869	−	0.172836i
$797$	7.37462	−	12.7732i	0.261223	−	0.452451i	−0.705344	−	0.708865i	$-0.749208\pi$
$797$	7.37462	−	12.7732i	0.261223	−	0.452451i	0.966567	+	0.256414i	$0.0825410\pi$
$798$	14.0206	−	48.0277i	0.496325	−	1.70016i
$799$	0.125684	+	0.217690i	0.00444636	+	0.00770133i
$800$	−8.34015			−0.294869
$801$	19.3560	−	10.0555i	0.683911	−	0.355294i
$802$	88.2140			3.11495
$803$	−36.6789	−	63.5297i	−1.29437	−	2.24192i
$804$	−81.7053	−	85.4221i	−2.88152	−	3.01260i
$805$	−11.6039	+	20.0986i	−0.408984	+	0.708381i
$806$	8.90407	−	15.4223i	0.313633	−	0.543227i
$807$	−28.6188	+	6.99029i	−1.00743	+	0.246070i
$808$	27.1083	+	46.9530i	0.953667	+	1.65180i
$809$	1.81657			0.0638672			0.0319336	−	0.999490i	$-0.489833\pi$
$809$	1.81657			0.0638672			0.0319336	+	0.999490i	$0.489833\pi$
$810$	13.3819	−	19.0433i	0.470191	−	0.669114i
$811$	−33.3279			−1.17030			−0.585151	−	0.810924i	$-0.698965\pi$
$811$	−33.3279			−1.17030			−0.585151	+	0.810924i	$0.698965\pi$
$812$	69.7180	+	120.755i	2.44662	+	4.23767i
$813$	−21.0054	+	5.13066i	−0.736691	+	0.179940i
$814$	−22.8001	+	39.4909i	−0.799142	+	1.38415i
$815$	−8.68616	+	15.0449i	−0.304263	+	0.526999i
$816$	−6.37543	−	6.66544i	−0.223185	−	0.233337i
$817$	−13.1126	−	22.7117i	−0.458752	−	0.794581i
$818$	49.5117			1.73113
$819$	11.3806	−	5.91225i	0.397670	−	0.206591i
$820$	19.0999			0.666998
$821$	−17.7439	−	30.7333i	−0.619266	−	1.07260i	−0.989620	−	0.143709i	$-0.954097\pi$
$821$	−17.7439	−	30.7333i	−0.619266	−	1.07260i	0.370354	−	0.928891i	$-0.379236\pi$
$822$	−8.47390	+	29.0274i	−0.295561	+	1.01245i
$823$	8.28999	−	14.3587i	0.288971	−	0.500512i	−0.684594	−	0.728925i	$-0.740020\pi$
$823$	8.28999	−	14.3587i	0.288971	−	0.500512i	0.973564	+	0.228413i	$0.0733536\pi$
$824$	3.45215	−	5.97929i	0.120261	−	0.208299i
$825$	−2.12811	+	7.28984i	−0.0740912	+	0.253800i
$826$	59.2645	+	102.649i	2.06208	+	3.57162i
$827$	8.93071			0.310551			0.155276	−	0.987871i	$-0.450373\pi$
$827$	8.93071			0.310551			0.155276	+	0.987871i	$0.450373\pi$
$828$	−64.3590	−	41.0770i	−2.23663	−	1.42752i
$829$	12.9059			0.448240			0.224120	−	0.974562i	$-0.428049\pi$
$829$	12.9059			0.448240			0.224120	+	0.974562i	$0.428049\pi$
$830$	3.93234	+	6.81102i	0.136494	+	0.236414i
$831$	−24.2899	−	25.3948i	−0.842607	−	0.880937i
$832$	2.18340	−	3.78175i	0.0756957	−	0.131109i
$833$	−3.49038	+	6.04551i	−0.120934	+	0.209464i
$834$	−15.2548	+	3.72605i	−0.528230	+	0.129023i
$835$	2.13795	+	3.70303i	0.0739867	+	0.128149i
$836$	−53.7053			−1.85744
$837$	−6.93647	−	35.1024i	−0.239759	−	1.21332i
$838$	−18.4518			−0.637408
$839$	−17.4959	−	30.3039i	−0.604027	−	1.04621i	−0.992204	−	0.124621i	$-0.960229\pi$
$839$	−17.4959	−	30.3039i	−0.604027	−	1.04621i	0.388178	−	0.921585i	$-0.373105\pi$
$840$	−49.9997	+	12.2127i	−1.72515	+	0.421377i
$841$	−9.70506	+	16.8097i	−0.334657	+	0.579644i
$842$	−33.8286	+	58.5928i	−1.16581	+	2.01924i
$843$	10.0260	+	10.4821i	0.345315	+	0.361024i
$844$	0.551328	+	0.954929i	0.0189775	+	0.0328700i
$845$	−1.00000			−0.0344010
$846$	−0.140026	+	3.14666i	−0.00481421	+	0.108184i
$847$	−35.1547			−1.20793
$848$	37.4656	+	64.8922i	1.28657	+	2.22841i
$849$	1.08026	−	3.70044i	0.0370744	−	0.126999i
$850$	0.800595	−	1.38667i	0.0274602	−	0.0475624i
$851$	10.9165	−	18.9079i	0.374212	−	0.648154i
$852$	−14.9613	+	51.2500i	−0.512565	+	1.75580i
$853$	10.5784	+	18.3223i	0.362198	+	0.627345i	0.988322	−	0.152378i	$-0.0486933\pi$
$853$	10.5784	+	18.3223i	0.362198	+	0.627345i	−0.626125	+	0.779723i	$0.715360\pi$
$854$	56.0745			1.91883
$855$	−0.348475	+	7.83088i	−0.0119176	+	0.267811i
$856$	−29.4853			−1.00779
$857$	5.81524	+	10.0723i	0.198645	+	0.344063i	0.948089	−	0.318004i	$-0.103013\pi$
$857$	5.81524	+	10.0723i	0.198645	+	0.344063i	−0.749444	+	0.662067i	$0.769679\pi$
$858$	−13.5748	−	14.1923i	−0.463436	−	0.484518i
$859$	−0.890335	+	1.54211i	−0.0303778	+	0.0526160i	−0.880815	−	0.473461i	$-0.843004\pi$
$859$	−0.890335	+	1.54211i	−0.0303778	+	0.0526160i	0.850437	+	0.526077i	$0.176338\pi$
$860$	−23.5262	+	40.7485i	−0.802236	+	1.38951i
$861$	29.3057	−	7.15806i	0.998737	−	0.243946i
$862$	−16.0611	−	27.8186i	−0.547043	−	0.947506i
$863$	−7.65256			−0.260496			−0.130248	−	0.991481i	$-0.541577\pi$
$863$	−7.65256			−0.260496			−0.130248	+	0.991481i	$0.541577\pi$
$864$	−8.40117	−	42.5146i	−0.285814	−	1.44638i
$865$	−12.9559			−0.440513
$866$	−7.81703	−	13.5395i	−0.265633	−	0.460091i
$867$	−27.9589	+	6.82910i	−0.949536	+	0.231928i
$868$	−69.0000	+	119.512i	−2.34201	+	4.05649i
$869$	−31.8877	+	55.2311i	−1.08172	+	1.87359i
$870$	−21.5420	−	22.5219i	−0.730341	−	0.763564i
$871$	7.27894	+	12.6075i	0.246637	+	0.427188i
$872$	−32.8272			−1.11167
$873$	24.3646	+	15.5507i	0.824616	+	0.526310i
$874$	36.6838			1.24085
$875$	−2.13745	−	3.70217i	−0.0722589	−	0.125156i
$876$	−38.0705	+	130.411i	−1.28628	+	4.40616i
$877$	−3.39612	+	5.88225i	−0.114679	+	0.198629i	−0.917651	−	0.397387i	$-0.869917\pi$
$877$	−3.39612	+	5.88225i	−0.114679	+	0.198629i	0.802973	+	0.596016i	$0.203251\pi$
$878$	−37.0801	+	64.2246i	−1.25139	+	2.16748i
$879$	1.23230	−	4.22127i	0.0415646	−	0.142380i
$880$	18.8551	+	32.6579i	0.635604	+	1.10090i
$881$	8.06104			0.271583			0.135792	−	0.990737i	$-0.456642\pi$
$881$	8.06104			0.271583			0.135792	+	0.990737i	$0.456642\pi$
$882$	−77.6231	+	40.3254i	−2.61370	+	1.35783i
$883$	15.7753			0.530882			0.265441	−	0.964127i	$-0.414482\pi$
$883$	15.7753			0.530882			0.265441	+	0.964127i	$0.414482\pi$
$884$	1.45127	+	2.51367i	0.0488115	+	0.0845440i
$885$	−12.8358	−	13.4197i	−0.431472	−	0.451100i
$886$	−11.8314	+	20.4925i	−0.397483	+	0.688460i
$887$	8.88157	−	15.3833i	0.298214	−	0.516522i	−0.677513	−	0.735510i	$-0.736942\pi$
$887$	8.88157	−	15.3833i	0.298214	−	0.516522i	0.975727	+	0.218989i	$0.0702757\pi$
$888$	47.0376	−	11.4892i	1.57848	−	0.385551i
$889$	−29.1575	−	50.5023i	−0.977911	−	1.69379i
$890$	18.8028			0.630271
$891$	−39.3042	−	3.50502i	−1.31674	−	0.117423i
$892$	−78.5461			−2.62992
$893$	−0.530397	−	0.918674i	−0.0177490	−	0.0307422i
$894$	−53.4302	+	13.0506i	−1.78697	+	0.436477i
$895$	9.42652	−	16.3272i	0.315094	−	0.545758i
$896$	11.5151	−	19.9448i	0.384693	−	0.666308i
$897$	6.49950	+	6.79516i	0.217012	+	0.226884i
$898$	45.8575	+	79.4274i	1.53028	+	2.65053i
$899$	−47.9116			−1.59794
$900$	12.4802	−	6.48349i	0.416006	−	0.216116i
$901$	−5.39408			−0.179703
$902$	−23.0984	−	40.0077i	−0.769094	−	1.33211i
$903$	−20.8258	+	71.3389i	−0.693039	+	2.37401i
$904$	−12.3527	+	21.3955i	−0.410844	+	0.711603i
$905$	−10.6297	+	18.4111i	−0.353342	+	0.612006i
$906$	−20.9578	+	71.7911i	−0.696277	+	2.38510i
$907$	−24.3180	−	42.1199i	−0.807464	−	1.39857i	−0.914615	−	0.404327i	$-0.867506\pi$
$907$	−24.3180	−	42.1199i	−0.807464	−	1.39857i	0.107150	−	0.994243i	$-0.465827\pi$
$908$	106.887			3.54715
$909$	−19.7236	−	12.5886i	−0.654191	−	0.417536i
$910$	11.0553			0.366480
$911$	−9.32994	−	16.1599i	−0.309115	−	0.535402i	0.669054	−	0.743214i	$-0.266699\pi$
$911$	−9.32994	−	16.1599i	−0.309115	−	0.535402i	−0.978169	+	0.207811i	$0.933366\pi$
$912$	26.9049	+	28.1288i	0.890911	+	0.931438i
$913$	6.66687	−	11.5474i	0.220641	−	0.382162i
$914$	12.1710	−	21.0808i	0.402581	−	0.697290i
$915$	−8.53437	+	2.08456i	−0.282137	+	0.0689134i
$916$	16.3486	+	28.3167i	0.540174	+	0.935609i
$917$	−35.7482			−1.18051
$918$	7.87512	+	2.68428i	0.259918	+	0.0885944i
$919$	−13.8812			−0.457898			−0.228949	−	0.973438i	$-0.573529\pi$
$919$	−13.8812			−0.457898			−0.228949	+	0.973438i	$0.573529\pi$
$920$	−18.8688	−	32.6817i	−0.622085	−	1.07748i
$921$	32.3634	−	7.90492i	1.06641	−	0.260476i
$922$	−26.5109	+	45.9182i	−0.873089	+	1.51223i
$923$	3.28761	−	5.69431i	0.108213	−	0.187431i
$924$	105.195	+	109.980i	3.46065	+	3.61808i
$925$	2.01082	+	3.48284i	0.0661154	+	0.114515i
$926$	97.7111			3.21099
$927$	−0.132467	+	2.97678i	−0.00435078	+	0.0977702i
$928$	−58.0286			−1.90488
$929$	−8.83587	−	15.3042i	−0.289895	−	0.502114i	0.683889	−	0.729586i	$-0.260287\pi$
$929$	−8.83587	−	15.3042i	−0.289895	−	0.502114i	−0.973785	+	0.227472i	$0.926954\pi$
$930$	8.64362	−	29.6087i	0.283435	−	0.970909i
$931$	14.7297	−	25.5126i	0.482747	−	0.836143i
$932$	20.2331	−	35.0448i	0.662758	−	1.14793i
$933$	−4.25208	+	14.5655i	−0.139207	+	0.476854i
$934$	−16.6651	−	28.8648i	−0.545299	−	0.944485i
$935$	−2.71465			−0.0887784
$936$	−0.927080	+	20.8332i	−0.0303025	+	0.680955i
$937$	33.4041			1.09126			0.545632	−	0.838025i	$-0.316290\pi$
$937$	33.4041			1.09126			0.545632	+	0.838025i	$0.316290\pi$
$938$	−80.4710	−	139.380i	−2.62747	−	4.55091i
$939$	14.5799	+	15.2431i	0.475797	+	0.497441i
$940$	−0.951619	+	1.64825i	−0.0310384	+	0.0537601i
$941$	28.9473	−	50.1383i	0.943656	−	1.63446i	0.185236	−	0.982694i	$-0.440695\pi$
$941$	28.9473	−	50.1383i	0.943656	−	1.63446i	0.758420	−	0.651766i	$-0.225972\pi$
$942$	−34.7972	+	8.49937i	−1.13375	+	0.276924i
$943$	11.0593	+	19.1553i	0.360142	+	0.623784i
$944$	−92.2136			−3.00130
$945$	16.7190	−	14.6251i	0.543869	−	0.475753i
$946$	113.805			3.70013
$947$	27.3142	+	47.3096i	0.887593	+	1.53736i	0.842712	+	0.538364i	$0.180957\pi$
$947$	27.3142	+	47.3096i	0.887593	+	1.53736i	0.0448808	+	0.998992i	$0.485709\pi$
$948$	114.735	−	28.0245i	3.72641	−	0.910194i
$949$	8.36565	−	14.4897i	0.271561	−	0.470357i
$950$	−3.37859	+	5.85188i	−0.109616	+	0.189860i
$951$	−20.7411	−	21.6846i	−0.672577	−	0.703173i
$952$	−9.19934	−	15.9337i	−0.298152	−	0.516415i
$953$	19.7207			0.638815			0.319407	−	0.947618i	$-0.396516\pi$
$953$	19.7207			0.638815			0.319407	+	0.947618i	$0.396516\pi$
$954$	−56.9751	−	36.3643i	−1.84464	−	1.17734i
$955$	15.4170			0.498882
$956$	7.19834	+	12.4679i	0.232811	+	0.403240i
$957$	−14.8068	+	50.7208i	−0.478636	+	1.63957i
$958$	26.1042	−	45.2138i	0.843388	−	1.46079i
$959$	−14.4296	+	24.9929i	−0.465958	+	0.807062i
$960$	2.11953	−	7.26046i	0.0684075	−	0.234330i
$961$	−8.20911	−	14.2186i	−0.264810	−	0.458665i
$962$	−10.4004			−0.335322
$963$	11.2923	−	5.86636i	0.363888	−	0.189041i
$964$	27.3432			0.880665
$965$	0.944008	+	1.63507i	0.0303887	+	0.0526347i
$966$	−71.8541	−	75.1227i	−2.31187	−	2.41703i
$967$	17.6087	−	30.4992i	0.566259	−	0.980790i	−0.430672	−	0.902508i	$-0.641723\pi$
$967$	17.6087	−	30.4992i	0.566259	−	0.980790i	0.996931	−	0.0782812i	$-0.0249432\pi$
$968$	28.5820	−	49.5055i	0.918661	−	1.59117i
$969$	−2.72203	+	0.664869i	−0.0874443	+	0.0213587i
$970$	12.4582	+	21.5783i	0.400010	+	0.692837i
$971$	−13.9711			−0.448354			−0.224177	−	0.974548i	$-0.571969\pi$
$971$	−13.9711			−0.448354			−0.224177	+	0.974548i	$0.571969\pi$
$972$	45.6216	+	57.0878i	1.46331	+	1.83109i
$973$	−14.9868			−0.480454
$974$	19.5872	+	33.9260i	0.627614	+	1.08706i
$975$	−1.68259	+	0.410979i	−0.0538859	+	0.0131619i
$976$	−21.8125	+	37.7804i	−0.698201	+	1.20932i
$977$	−18.2453	+	31.6017i	−0.583718	+	1.01103i	0.411316	+	0.911493i	$0.365069\pi$
$977$	−18.2453	+	31.6017i	−0.583718	+	1.01103i	−0.995034	+	0.0995362i	$0.968264\pi$
$978$	−53.7867	−	56.2334i	−1.71991	−	1.79815i
$979$	−15.9391	−	27.6073i	−0.509415	−	0.882333i
$980$	−52.8551			−1.68839
$981$	12.5721	−	6.53125i	0.401397	−	0.208527i
$982$	29.7078			0.948015
$983$	8.75026	+	15.1559i	0.279090	+	0.483398i	0.971159	−	0.238433i	$-0.0766339\pi$
$983$	8.75026	+	15.1559i	0.279090	+	0.483398i	−0.692069	+	0.721832i	$0.743301\pi$
$984$	−13.7465	+	47.0886i	−0.438222	+	1.50113i
$985$	−5.42986	+	9.40480i	−0.173010	+	0.299662i
$986$	5.57033	−	9.64809i	0.177395	−	0.307258i
$987$	−0.842391	+	2.88561i	−0.0268136	+	0.0918501i
$988$	−6.12450	−	10.6079i	−0.194846	−	0.337484i
$989$	−54.4890			−1.73265
$990$	−28.6735	−	18.3008i	−0.911304	−	0.581638i
$991$	18.8114			0.597565			0.298783	−	0.954321i	$-0.403419\pi$
$991$	18.8114			0.597565			0.298783	+	0.954321i	$0.403419\pi$
$992$	−28.7155	−	49.7367i	−0.911719	−	1.57914i
$993$	−2.94603	−	3.08004i	−0.0934893	−	0.0977421i
$994$	−36.3456	+	62.9525i	−1.15281	+	1.99673i
$995$	−0.600549	+	1.04018i	−0.0190387	+	0.0329760i
$996$	−23.9880	+	5.85918i	−0.760089	+	0.185655i
$997$	−1.76712	−	3.06074i	−0.0559651	−	0.0969345i	0.836686	−	0.547684i	$-0.184490\pi$
$997$	−1.76712	−	3.06074i	−0.0559651	−	0.0969345i	−0.892651	+	0.450749i	$0.851157\pi$
$998$	33.9299			1.07403
$999$	−15.7285	+	13.7586i	−0.497629	+	0.435304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.391.8	yes	16
3.2	odd	2		1755.2.i.f.1171.1		16
9.2	odd	6		1755.2.i.f.586.1		16
9.4	even	3		5265.2.a.bf.1.1		8
9.5	odd	6		5265.2.a.ba.1.8		8
9.7	even	3	inner	585.2.i.e.196.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.8	✓	16	9.7	even	3	inner
585.2.i.e.391.8	yes	16	1.1	even	1	trivial
1755.2.i.f.586.1		16	9.2	odd	6
1755.2.i.f.1171.1		16	3.2	odd	2
5265.2.a.ba.1.8		8	9.5	odd	6
5265.2.a.bf.1.1		8	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(1.29305 + 2.23963i) q^{2} +(1.68259 - 0.410979i) q^{3} +(-2.34397 + 4.05987i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.09611 + 3.23696i) q^{6} +(2.13745 + 3.70217i) q^{7} -6.95128 q^{8} +(2.66219 - 1.38302i) q^{9} +O(q^{10})\)	\(q+(1.29305 + 2.23963i) q^{2} +(1.68259 - 0.410979i) q^{3} +(-2.34397 + 4.05987i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.09611 + 3.23696i) q^{6} +(2.13745 + 3.70217i) q^{7} -6.95128 q^{8} +(2.66219 - 1.38302i) q^{9} +2.58610 q^{10} +(-2.19223 - 3.79706i) q^{11} +(-2.27540 + 7.79440i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-5.52766 + 9.57419i) q^{14} +(0.485374 - 1.66265i) q^{15} +(-4.30043 - 7.44856i) q^{16} +0.619151 q^{17} +(6.53980 + 4.17402i) q^{18} -2.61288 q^{19} +(2.34397 + 4.05987i) q^{20} +(5.11795 + 5.35077i) q^{21} +(5.66934 - 9.81959i) q^{22} +(-2.71443 + 4.70154i) q^{23} +(-11.6961 + 2.85683i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.58610 q^{26} +(3.91098 - 3.42115i) q^{27} -20.0404 q^{28} +(-3.47887 - 6.02558i) q^{29} +(4.35134 - 1.06284i) q^{30} +(3.44304 - 5.96353i) q^{31} +(4.17008 - 7.22278i) q^{32} +(-5.24913 - 5.48791i) q^{33} +(0.800595 + 1.38667i) q^{34} +4.27489 q^{35} +(-0.625222 + 14.0499i) q^{36} -4.02164 q^{37} +(-3.37859 - 5.85188i) q^{38} +(0.485374 - 1.66265i) q^{39} +(-3.47564 + 6.01998i) q^{40} +(2.03714 - 3.52842i) q^{41} +(-5.36597 + 18.3811i) q^{42} +(5.01845 + 8.69221i) q^{43} +20.5541 q^{44} +(0.133368 - 2.99703i) q^{45} -14.0396 q^{46} +(0.202993 + 0.351595i) q^{47} +(-10.2970 - 10.7655i) q^{48} +(-5.63736 + 9.76419i) q^{49} +(1.29305 - 2.23963i) q^{50} +(1.04178 - 0.254458i) q^{51} +(2.34397 + 4.05987i) q^{52} -8.71205 q^{53} +(12.7192 + 4.33542i) q^{54} -4.38446 q^{55} +(-14.8580 - 25.7348i) q^{56} +(-4.39639 + 1.07384i) q^{57} +(8.99672 - 15.5828i) q^{58} +(5.36073 - 9.28505i) q^{59} +(5.61245 + 5.86776i) q^{60} +(-2.53609 - 4.39263i) q^{61} +17.8081 q^{62} +(10.8105 + 6.89975i) q^{63} +4.36679 q^{64} +(-0.500000 - 0.866025i) q^{65} +(5.50350 - 18.8523i) q^{66} +(-7.27894 + 12.6075i) q^{67} +(-1.45127 + 2.51367i) q^{68} +(-2.63503 + 9.02632i) q^{69} +(5.52766 + 9.57419i) q^{70} +6.57523 q^{71} +(-18.5056 + 9.61373i) q^{72} +16.7313 q^{73} +(-5.20019 - 9.00700i) q^{74} +(-1.19721 - 1.25167i) q^{75} +(6.12450 - 10.6079i) q^{76} +(9.37156 - 16.2320i) q^{77} +(4.35134 - 1.06284i) q^{78} +(-7.27288 - 12.5970i) q^{79} -8.60086 q^{80} +(5.17453 - 7.36371i) q^{81} +10.5365 q^{82} +(1.52057 + 2.63370i) q^{83} +(-33.7197 + 8.23620i) q^{84} +(0.309576 - 0.536201i) q^{85} +(-12.9782 + 22.4790i) q^{86} +(-8.32989 - 8.70881i) q^{87} +(15.2388 + 26.3944i) q^{88} +7.27070 q^{89} +(6.88470 - 3.57663i) q^{90} +4.27489 q^{91} +(-12.7251 - 22.0405i) q^{92} +(3.34233 - 11.4492i) q^{93} +(-0.524962 + 0.909260i) q^{94} +(-1.30644 + 2.26282i) q^{95} +(4.04810 - 13.8668i) q^{96} +(4.81738 + 8.34394i) q^{97} -29.1576 q^{98} +(-11.0875 - 7.07660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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