LMFDB - Embedded newform 122.2.e.a.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(9,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("122.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.e (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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} + 10 x^{9} + 34 x^{8} - 107 x^{7} + 287 x^{6} - 358 x^{5} + 1201 x^{4} + \cdots + 81 $ x^12 - x^11 + 11x^10 + 10x^9 + 34x^8 - 107x^7 + 287x^6 - 358x^5 + 1201x^4 - 1164x^3 + 981x^2 - 405x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$0.234038 + 0.720296i$ of defining polynomial
Character	$\chi$	$=$	122.81
Dual form			122.2.e.a.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.0749786 + 0.230760i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.59188 - 1.15657i) q^{5} +(0.196297 - 0.142618i) q^{6} +(0.425021 - 1.30808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37942 - 1.72875i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.0749786 + 0.230760i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.59188 - 1.15657i) q^{5} +(0.196297 - 0.142618i) q^{6} +(0.425021 - 1.30808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37942 - 1.72875i) q^{9} +(-1.59188 - 1.15657i) q^{10} -3.19312 q^{11} +(-0.196297 - 0.142618i) q^{12} +3.05378 q^{13} -1.37540 q^{14} +(0.386248 + 0.280625i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.15900 + 3.74824i) q^{17} +(-2.37942 - 1.72875i) q^{18} +(0.628481 + 1.93426i) q^{19} +(-0.608045 + 1.87137i) q^{20} +0.333721 q^{21} +(0.986727 + 3.03683i) q^{22} +(-0.156233 + 0.113510i) q^{23} +(-0.0749786 + 0.230760i) q^{24} +(-0.348651 + 1.07304i) q^{25} +(-0.943671 - 2.90432i) q^{26} +(1.16622 + 0.847310i) q^{27} +(0.425021 + 1.30808i) q^{28} +2.56445 q^{29} +(0.147533 - 0.454061i) q^{30} +(-2.70018 + 8.31029i) q^{31} -1.00000 q^{32} +(-0.239415 - 0.736844i) q^{33} +(5.15900 + 3.74824i) q^{34} +(-0.836304 - 2.57388i) q^{35} +(-0.908858 + 2.79718i) q^{36} +(-1.71345 + 5.27345i) q^{37} +(1.64538 - 1.19544i) q^{38} +(0.228969 + 0.704693i) q^{39} +1.96767 q^{40} +(2.65641 - 8.17560i) q^{41} +(-0.103125 - 0.317387i) q^{42} +(-3.33983 - 2.42653i) q^{43} +(2.58328 - 1.87687i) q^{44} +(1.78834 - 5.50394i) q^{45} +(0.156233 + 0.113510i) q^{46} -8.97402 q^{47} +0.242636 q^{48} +(4.13269 + 3.00257i) q^{49} +1.12826 q^{50} +(-1.25176 - 0.909456i) q^{51} +(-2.47056 + 1.79497i) q^{52} +(-3.95739 - 2.87521i) q^{53} +(0.445457 - 1.37098i) q^{54} +(-5.08306 + 3.69306i) q^{55} +(1.11272 - 0.808439i) q^{56} +(-0.399229 + 0.290057i) q^{57} +(-0.792460 - 2.43894i) q^{58} +(-0.931478 - 2.86679i) q^{59} -0.477428 q^{60} +(3.71961 - 6.86764i) q^{61} +8.73795 q^{62} +(-1.25004 - 3.84723i) q^{63} +(0.309017 + 0.951057i) q^{64} +(4.86126 - 3.53192i) q^{65} +(-0.626797 + 0.455395i) q^{66} +(7.53424 - 5.47394i) q^{67} +(1.97056 - 6.06477i) q^{68} +(-0.0379078 - 0.0275416i) q^{69} +(-2.18947 + 1.59074i) q^{70} +(-2.87886 - 2.09162i) q^{71} +2.94113 q^{72} +(-6.52753 - 4.74253i) q^{73} +5.54484 q^{74} -0.273756 q^{75} +(-1.64538 - 1.19544i) q^{76} +(-1.35714 + 4.17685i) q^{77} +(0.599447 - 0.435524i) q^{78} +(10.9510 + 7.95637i) q^{79} +(-0.608045 - 1.87137i) q^{80} +(2.61849 - 8.05889i) q^{81} -8.59634 q^{82} +(1.78615 + 5.49720i) q^{83} +(-0.269986 + 0.196156i) q^{84} +(-3.87743 + 11.9335i) q^{85} +(-1.27570 + 3.92621i) q^{86} +(0.192279 + 0.591774i) q^{87} +(-2.58328 - 1.87687i) q^{88} +(4.16333 + 12.8134i) q^{89} -5.78718 q^{90} +(1.29792 - 3.99460i) q^{91} +(0.0596759 - 0.183663i) q^{92} -2.12014 q^{93} +(2.77312 + 8.53480i) q^{94} +(3.23758 + 2.35224i) q^{95} +(-0.0749786 - 0.230760i) q^{96} +(1.41627 - 4.35883i) q^{97} +(1.57855 - 4.85826i) q^{98} +(-7.59777 + 5.52010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9} + 6 q^{10} - 4 q^{11} + q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 7 q^{17} + 7 q^{18} - 6 q^{19} + 4 q^{20} - 56 q^{21} - q^{22} + 8 q^{23} + 4 q^{24} - 21 q^{25} - 7 q^{26} + 2 q^{27} + 10 q^{28} + 30 q^{29} + 3 q^{30} + q^{31} - 12 q^{32} + 21 q^{33} - 7 q^{34} + 5 q^{35} - 2 q^{36} - 14 q^{38} - 21 q^{39} - 4 q^{40} + 2 q^{41} - 14 q^{42} - 8 q^{43} + q^{44} + 49 q^{45} - 8 q^{46} - 10 q^{47} + 6 q^{48} - 3 q^{49} - 44 q^{50} + 8 q^{51} - 3 q^{52} + 8 q^{53} + 8 q^{54} + 13 q^{55} + 10 q^{56} + 5 q^{57} + 25 q^{58} + 4 q^{59} - 18 q^{60} - 26 q^{61} + 34 q^{62} + 29 q^{63} - 3 q^{64} + 3 q^{65} + 29 q^{66} + 33 q^{67} - 3 q^{68} + 26 q^{69} + 20 q^{70} - 13 q^{71} - 18 q^{72} - 38 q^{73} + 30 q^{74} - 8 q^{75} + 14 q^{76} - 23 q^{77} - 9 q^{78} + 26 q^{79} + 4 q^{80} + 20 q^{81} - 42 q^{82} + 18 q^{83} + 14 q^{84} - 5 q^{85} - 12 q^{86} - 66 q^{87} - q^{88} + 2 q^{89} - 14 q^{90} + 17 q^{91} + 8 q^{92} - 68 q^{93} + 20 q^{94} + 65 q^{95} + 4 q^{96} - 4 q^{97} - 7 q^{98} - 50 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9 + 6 * q^10 - 4 * q^11 + q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 7 * q^17 + 7 * q^18 - 6 * q^19 + 4 * q^20 - 56 * q^21 - q^22 + 8 * q^23 + 4 * q^24 - 21 * q^25 - 7 * q^26 + 2 * q^27 + 10 * q^28 + 30 * q^29 + 3 * q^30 + q^31 - 12 * q^32 + 21 * q^33 - 7 * q^34 + 5 * q^35 - 2 * q^36 - 14 * q^38 - 21 * q^39 - 4 * q^40 + 2 * q^41 - 14 * q^42 - 8 * q^43 + q^44 + 49 * q^45 - 8 * q^46 - 10 * q^47 + 6 * q^48 - 3 * q^49 - 44 * q^50 + 8 * q^51 - 3 * q^52 + 8 * q^53 + 8 * q^54 + 13 * q^55 + 10 * q^56 + 5 * q^57 + 25 * q^58 + 4 * q^59 - 18 * q^60 - 26 * q^61 + 34 * q^62 + 29 * q^63 - 3 * q^64 + 3 * q^65 + 29 * q^66 + 33 * q^67 - 3 * q^68 + 26 * q^69 + 20 * q^70 - 13 * q^71 - 18 * q^72 - 38 * q^73 + 30 * q^74 - 8 * q^75 + 14 * q^76 - 23 * q^77 - 9 * q^78 + 26 * q^79 + 4 * q^80 + 20 * q^81 - 42 * q^82 + 18 * q^83 + 14 * q^84 - 5 * q^85 - 12 * q^86 - 66 * q^87 - q^88 + 2 * q^89 - 14 * q^90 + 17 * q^91 + 8 * q^92 - 68 * q^93 + 20 * q^94 + 65 * q^95 + 4 * q^96 - 4 * q^97 - 7 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.0749786	+	0.230760i	0.0432889	+	0.133230i	0.970365	−	0.241643i	$-0.0776864\pi$
$3$	0.0749786	+	0.230760i	0.0432889	+	0.133230i	−0.927076	+	0.374873i	$0.877686\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.59188	−	1.15657i	0.711911	−	0.517234i	−0.171878	−	0.985118i	$-0.554984\pi$
$5$	1.59188	−	1.15657i	0.711911	−	0.517234i	0.883790	+	0.467884i	$0.154984\pi$
$6$	0.196297	−	0.142618i	0.0801377	−	0.0582235i
$7$	0.425021	−	1.30808i	0.160643	−	0.494408i	−0.838046	−	0.545600i	$-0.816302\pi$
$7$	0.425021	−	1.30808i	0.160643	−	0.494408i	0.998689	+	0.0511915i	$0.0163019\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.37942	−	1.72875i	0.793141	−	0.576251i
$10$	−1.59188	−	1.15657i	−0.503397	−	0.365740i
$11$	−3.19312			−0.962760			−0.481380	−	0.876512i	$-0.659864\pi$
$11$	−3.19312			−0.962760			−0.481380	+	0.876512i	$0.659864\pi$
$12$	−0.196297	−	0.142618i	−0.0566659	−	0.0411702i
$13$	3.05378			0.846968			0.423484	−	0.905904i	$-0.360807\pi$
$13$	3.05378			0.846968			0.423484	+	0.905904i	$0.360807\pi$
$14$	−1.37540			−0.367591
$15$	0.386248	+	0.280625i	0.0997287	+	0.0724571i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−5.15900	+	3.74824i	−1.25124	+	0.909081i	−0.998293	−	0.0583991i	$-0.981400\pi$
$17$	−5.15900	+	3.74824i	−1.25124	+	0.909081i	−0.252949	+	0.967480i	$0.581400\pi$
$18$	−2.37942	−	1.72875i	−0.560835	−	0.407471i
$19$	0.628481	+	1.93426i	0.144183	+	0.443751i	0.996905	−	0.0786147i	$-0.0250497\pi$
$19$	0.628481	+	1.93426i	0.144183	+	0.443751i	−0.852722	+	0.522365i	$0.825050\pi$
$20$	−0.608045	+	1.87137i	−0.135963	+	0.418451i
$21$	0.333721			0.0728239
$22$	0.986727	+	3.03683i	0.210371	+	0.647455i
$23$	−0.156233	+	0.113510i	−0.0325769	+	0.0236685i	−0.603955	−	0.797019i	$-0.706409\pi$
$23$	−0.156233	+	0.113510i	−0.0325769	+	0.0236685i	0.571378	+	0.820687i	$0.306409\pi$
$24$	−0.0749786	+	0.230760i	−0.0153049	+	0.0471038i
$25$	−0.348651	+	1.07304i	−0.0697302	+	0.214607i
$26$	−0.943671	−	2.90432i	−0.185069	−	0.569584i
$27$	1.16622	+	0.847310i	0.224440	+	0.163065i
$28$	0.425021	+	1.30808i	0.0803215	+	0.247204i
$29$	2.56445			0.476207			0.238104	−	0.971240i	$-0.423474\pi$
$29$	2.56445			0.476207			0.238104	+	0.971240i	$0.423474\pi$
$30$	0.147533	−	0.454061i	0.0269358	−	0.0828999i
$31$	−2.70018	+	8.31029i	−0.484966	+	1.49257i	0.347065	+	0.937841i	$0.387178\pi$
$31$	−2.70018	+	8.31029i	−0.484966	+	1.49257i	−0.832030	+	0.554730i	$0.812822\pi$
$32$	−1.00000			−0.176777
$33$	−0.239415	−	0.736844i	−0.0416769	−	0.128268i
$34$	5.15900	+	3.74824i	0.884762	+	0.642817i
$35$	−0.836304	−	2.57388i	−0.141361	−	0.435065i
$36$	−0.908858	+	2.79718i	−0.151476	+	0.466196i
$37$	−1.71345	+	5.27345i	−0.281689	+	0.866950i	0.705682	+	0.708528i	$0.250641\pi$
$37$	−1.71345	+	5.27345i	−0.281689	+	0.866950i	−0.987372	+	0.158422i	$0.949359\pi$
$38$	1.64538	−	1.19544i	0.266917	−	0.193926i
$39$	0.228969	+	0.704693i	0.0366643	+	0.112841i
$40$	1.96767			0.311117
$41$	2.65641	−	8.17560i	0.414862	−	1.27681i	−0.497512	−	0.867457i	$-0.665753\pi$
$41$	2.65641	−	8.17560i	0.414862	−	1.27681i	0.912374	−	0.409357i	$-0.134247\pi$
$42$	−0.103125	−	0.317387i	−0.0159126	−	0.0489739i
$43$	−3.33983	−	2.42653i	−0.509319	−	0.370042i	0.303246	−	0.952912i	$-0.401930\pi$
$43$	−3.33983	−	2.42653i	−0.509319	−	0.370042i	−0.812565	+	0.582870i	$0.801930\pi$
$44$	2.58328	−	1.87687i	0.389445	−	0.282948i
$45$	1.78834	−	5.50394i	0.266590	−	0.820478i
$46$	0.156233	+	0.113510i	0.0230354	+	0.0167362i
$47$	−8.97402			−1.30900			−0.654498	−	0.756064i	$-0.727120\pi$
$47$	−8.97402			−1.30900			−0.654498	+	0.756064i	$0.727120\pi$
$48$	0.242636			0.0350215
$49$	4.13269	+	3.00257i	0.590384	+	0.428939i
$50$	1.12826			0.159560
$51$	−1.25176	−	0.909456i	−0.175281	−	0.127349i
$52$	−2.47056	+	1.79497i	−0.342606	+	0.248918i
$53$	−3.95739	−	2.87521i	−0.543590	−	0.394941i	0.281827	−	0.959465i	$-0.409060\pi$
$53$	−3.95739	−	2.87521i	−0.543590	−	0.394941i	−0.825416	+	0.564524i	$0.809060\pi$
$54$	0.445457	−	1.37098i	0.0606191	−	0.186566i
$55$	−5.08306	+	3.69306i	−0.685400	+	0.497972i
$56$	1.11272	−	0.808439i	0.148694	−	0.108032i
$57$	−0.399229	+	0.290057i	−0.0528792	+	0.0384190i
$58$	−0.792460	−	2.43894i	−0.104055	−	0.320249i
$59$	−0.931478	−	2.86679i	−0.121268	−	0.373225i	0.871935	−	0.489622i	$-0.162865\pi$
$59$	−0.931478	−	2.86679i	−0.121268	−	0.373225i	−0.993203	+	0.116398i	$0.962865\pi$
$60$	−0.477428			−0.0616357
$61$	3.71961	−	6.86764i	0.476248	−	0.879311i
$61$	3.71961	−	6.86764i	0.476248	−	0.879311i
$62$	8.73795			1.10972
$63$	−1.25004	−	3.84723i	−0.157491	−	0.484706i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	4.86126	−	3.53192i	0.602966	−	0.438080i
$66$	−0.626797	+	0.455395i	−0.0771534	+	0.0560552i
$67$	7.53424	−	5.47394i	0.920453	−	0.668749i	−0.0231834	−	0.999731i	$-0.507380\pi$
$67$	7.53424	−	5.47394i	0.920453	−	0.668749i	0.943637	+	0.330983i	$0.107380\pi$
$68$	1.97056	−	6.06477i	0.238966	−	0.735462i
$69$	−0.0379078	−	0.0275416i	−0.00456357	−	0.00331562i
$70$	−2.18947	+	1.59074i	−0.261692	+	0.190130i
$71$	−2.87886	−	2.09162i	−0.341658	−	0.248229i	0.403703	−	0.914890i	$-0.367723\pi$
$71$	−2.87886	−	2.09162i	−0.341658	−	0.248229i	−0.745361	+	0.666661i	$0.767723\pi$
$72$	2.94113			0.346615
$73$	−6.52753	−	4.74253i	−0.763990	−	0.555071i	0.136142	−	0.990689i	$-0.456530\pi$
$73$	−6.52753	−	4.74253i	−0.763990	−	0.555071i	−0.900131	+	0.435618i	$0.856530\pi$
$74$	5.54484			0.644574
$75$	−0.273756			−0.0316106
$76$	−1.64538	−	1.19544i	−0.188738	−	0.137127i
$77$	−1.35714	+	4.17685i	−0.154661	+	0.475997i
$78$	0.599447	−	0.435524i	0.0678740	−	0.0493134i
$79$	10.9510	+	7.95637i	1.23208	+	0.895162i	0.997045	−	0.0768240i	$-0.0244780\pi$
$79$	10.9510	+	7.95637i	1.23208	+	0.895162i	0.235040	+	0.971986i	$0.424478\pi$
$80$	−0.608045	−	1.87137i	−0.0679815	−	0.209225i
$81$	2.61849	−	8.05889i	0.290944	−	0.895432i
$82$	−8.59634			−0.949306
$83$	1.78615	+	5.49720i	0.196055	+	0.603396i	0.999963	+	0.00864163i	$0.00275075\pi$
$83$	1.78615	+	5.49720i	0.196055	+	0.603396i	−0.803907	+	0.594755i	$0.797249\pi$
$84$	−0.269986	+	0.196156i	−0.0294579	+	0.0214024i
$85$	−3.87743	+	11.9335i	−0.420566	+	1.29437i
$86$	−1.27570	+	3.92621i	−0.137562	+	0.423374i
$87$	0.192279	+	0.591774i	0.0206145	+	0.0634449i
$88$	−2.58328	−	1.87687i	−0.275379	−	0.200075i
$89$	4.16333	+	12.8134i	0.441312	+	1.35822i	0.886478	+	0.462770i	$0.153145\pi$
$89$	4.16333	+	12.8134i	0.441312	+	1.35822i	−0.445166	+	0.895448i	$0.646855\pi$
$90$	−5.78718			−0.610022
$91$	1.29792	−	3.99460i	0.136059	−	0.418748i
$92$	0.0596759	−	0.183663i	0.00622164	−	0.0191482i
$93$	−2.12014			−0.219848
$94$	2.77312	+	8.53480i	0.286026	+	0.880297i
$95$	3.23758	+	2.35224i	0.332169	+	0.241335i
$96$	−0.0749786	−	0.230760i	−0.00765247	−	0.0235519i
$97$	1.41627	−	4.35883i	0.143800	−	0.442572i	−0.853054	−	0.521822i	$-0.825252\pi$
$97$	1.41627	−	4.35883i	0.143800	−	0.442572i	0.996855	+	0.0792498i	$0.0252525\pi$
$98$	1.57855	−	4.85826i	0.159457	−	0.490759i
$99$	−7.59777	+	5.52010i	−0.763605	+	0.554791i
$100$	−0.348651	−	1.07304i	−0.0348651	−	0.107304i
$101$	1.43816			0.143103			0.0715513	−	0.997437i	$-0.477205\pi$
$101$	1.43816			0.143103			0.0715513	+	0.997437i	$0.477205\pi$
$102$	−0.478129	+	1.47153i	−0.0473419	+	0.145703i
$103$	1.39720	+	4.30013i	0.137670	+	0.423704i	0.995996	−	0.0894007i	$-0.0284952\pi$
$103$	1.39720	+	4.30013i	0.137670	+	0.423704i	−0.858326	+	0.513105i	$0.828495\pi$
$104$	2.47056	+	1.79497i	0.242259	+	0.176011i
$105$	0.531244	−	0.385972i	0.0518441	−	0.0376670i
$106$	−1.51159	+	4.65219i	−0.146819	+	0.451861i
$107$	−12.6770	−	9.21038i	−1.22553	−	0.890401i	−0.228985	−	0.973430i	$-0.573541\pi$
$107$	−12.6770	−	9.21038i	−1.22553	−	0.890401i	−0.996547	+	0.0830284i	$0.973541\pi$
$108$	−1.44153			−0.138711
$109$	1.49824			0.143506			0.0717528	−	0.997422i	$-0.477141\pi$
$109$	1.49824			0.143506			0.0717528	+	0.997422i	$0.477141\pi$
$110$	5.08306	+	3.69306i	0.484651	+	0.352120i
$111$	−1.34538			−0.127697
$112$	−1.11272	−	0.808439i	−0.105142	−	0.0763903i
$113$	−4.84065	+	3.51694i	−0.455370	+	0.330846i	−0.791712	−	0.610894i	$-0.790810\pi$
$113$	−4.84065	+	3.51694i	−0.455370	+	0.330846i	0.336342	+	0.941740i	$0.390810\pi$
$114$	0.399229	+	0.290057i	0.0373912	+	0.0271663i
$115$	−0.117423	+	0.361390i	−0.0109497	+	0.0336998i
$116$	−2.07469	+	1.50735i	−0.192630	+	0.139954i
$117$	7.26624	−	5.27924i	0.671765	−	0.488066i
$118$	−2.43864	+	1.77178i	−0.224495	+	0.163105i
$119$	2.71031	+	8.34148i	0.248454	+	0.764662i
$120$	0.147533	+	0.454061i	0.0134679	+	0.0414499i
$121$	−0.804016			−0.0730923
$122$	−7.68094	−	1.41535i	−0.695399	−	0.128139i
$123$	2.08578			0.188068
$124$	−2.70018	−	8.31029i	−0.242483	−	0.746286i
$125$	3.72626	+	11.4682i	0.333286	+	1.02575i
$126$	−3.27265	+	2.37772i	−0.291551	+	0.211824i
$127$	−4.96091	+	3.60431i	−0.440210	+	0.319831i	−0.785718	−	0.618584i	$-0.787706\pi$
$127$	−4.96091	+	3.60431i	−0.440210	+	0.319831i	0.345509	+	0.938416i	$0.387706\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	0.309531	−	0.952638i	0.0272527	−	0.0838751i
$130$	−4.86126	−	3.53192i	−0.426361	−	0.309769i
$131$	4.45843	−	3.23924i	0.389534	−	0.283013i	−0.375730	−	0.926729i	$-0.622608\pi$
$131$	4.45843	−	3.23924i	0.389534	−	0.283013i	0.765265	+	0.643716i	$0.222608\pi$
$132$	0.626797	+	0.455395i	0.0545557	+	0.0396370i
$133$	2.79729			0.242556
$134$	−7.53424	−	5.47394i	−0.650859	−	0.472877i
$135$	2.83646			0.244124
$136$	−6.37688			−0.546813
$137$	5.24027	+	3.80728i	0.447707	+	0.325278i	0.788690	−	0.614792i	$-0.210760\pi$
$137$	5.24027	+	3.80728i	0.447707	+	0.325278i	−0.340983	+	0.940069i	$0.610760\pi$
$138$	−0.0144795	+	0.0445633i	−0.00123258	+	0.00379348i
$139$	18.8267	−	13.6784i	1.59686	−	1.16018i	0.703643	−	0.710553i	$-0.251555\pi$
$139$	18.8267	−	13.6784i	1.59686	−	1.16018i	0.893214	−	0.449632i	$-0.148445\pi$
$140$	2.18947	+	1.59074i	0.185044	+	0.134442i
$141$	−0.672859	−	2.07085i	−0.0566650	−	0.174397i
$142$	−1.09963	+	3.38431i	−0.0922787	+	0.284005i
$143$	−9.75109			−0.815427
$144$	−0.908858	−	2.79718i	−0.0757382	−	0.233098i
$145$	4.08231	−	2.96597i	0.339017	−	0.246310i
$146$	−2.49329	+	7.67357i	−0.206347	+	0.635069i
$147$	−0.383012	+	1.17879i	−0.0315903	+	0.0972248i
$148$	−1.71345	−	5.27345i	−0.140845	−	0.433475i
$149$	−14.5381	−	10.5626i	−1.19101	−	0.865321i	−0.197641	−	0.980275i	$-0.563328\pi$
$149$	−14.5381	−	10.5626i	−1.19101	−	0.865321i	−0.993371	+	0.114954i	$0.963328\pi$
$150$	0.0845952	+	0.260357i	0.00690717	+	0.0212581i
$151$	−13.0719			−1.06377			−0.531887	−	0.846815i	$-0.678517\pi$
$151$	−13.0719			−1.06377			−0.531887	+	0.846815i	$0.678517\pi$
$152$	−0.628481	+	1.93426i	−0.0509765	+	0.156890i
$153$	−5.79568	+	17.8373i	−0.468553	+	1.44206i
$154$	4.39180			0.353902
$155$	5.31307	+	16.3519i	0.426756	+	1.31342i
$156$	−0.599447	−	0.435524i	−0.0479942	−	0.0348698i
$157$	0.797924	+	2.45576i	0.0636813	+	0.195991i	0.977835	−	0.209377i	$-0.0671435\pi$
$157$	0.797924	+	2.45576i	0.0636813	+	0.195991i	−0.914154	+	0.405368i	$0.867144\pi$
$158$	4.18291	−	12.8737i	0.332775	−	1.02417i
$159$	0.366766	−	1.12879i	0.0290864	−	0.0895188i
$160$	−1.59188	+	1.15657i	−0.125849	+	0.0914349i
$161$	0.0820781	+	0.252610i	0.00646866	+	0.0199085i
$162$	−8.47362			−0.665750
$163$	4.08472	−	12.5715i	0.319940	−	0.984674i	−0.653733	−	0.756725i	$-0.726798\pi$
$163$	4.08472	−	12.5715i	0.319940	−	0.984674i	0.973673	−	0.227949i	$-0.0732018\pi$
$164$	2.65641	+	8.17560i	0.207431	+	0.638407i
$165$	−1.23333	−	0.896069i	−0.0960148	−	0.0697589i
$166$	4.67620	−	3.39746i	0.362943	−	0.263694i
$167$	6.37997	−	19.6355i	0.493697	−	1.51944i	−0.325281	−	0.945617i	$-0.605459\pi$
$167$	6.37997	−	19.6355i	0.493697	−	1.51944i	0.818978	−	0.573825i	$-0.194541\pi$
$168$	0.269986	+	0.196156i	0.0208299	+	0.0151338i
$169$	−3.67440			−0.282646
$170$	12.5476			0.962359
$171$	4.83928	+	3.51595i	0.370069	+	0.268871i
$172$	4.12826			0.314777
$173$	1.16390	+	0.845624i	0.0884898	+	0.0642916i	0.631150	−	0.775660i	$-0.282583\pi$
$173$	1.16390	+	0.845624i	0.0884898	+	0.0642916i	−0.542661	+	0.839952i	$0.682583\pi$
$174$	0.503393	−	0.365737i	0.0381622	−	0.0277264i
$175$	1.25544	+	0.912128i	0.0949021	+	0.0689504i
$176$	−0.986727	+	3.03683i	−0.0743773	+	0.228910i
$177$	0.591702	−	0.429896i	0.0444750	−	0.0323130i
$178$	10.8997	−	7.91912i	0.816970	−	0.593563i
$179$	20.6559	−	15.0074i	1.54390	−	1.12171i	0.596067	−	0.802935i	$-0.296729\pi$
$179$	20.6559	−	15.0074i	1.54390	−	1.12171i	0.947831	−	0.318772i	$-0.103271\pi$
$180$	1.78834	+	5.50394i	0.133295	+	0.410239i
$181$	−1.57791	−	4.85630i	−0.117285	−	0.360966i	0.875132	−	0.483885i	$-0.160775\pi$
$181$	−1.57791	−	4.85630i	−0.117285	−	0.360966i	−0.992417	+	0.122919i	$0.960775\pi$
$182$	−4.20017			−0.311337
$183$	1.86367	+	0.343413i	0.137766	+	0.0253859i
$184$	−0.193115			−0.0142366
$185$	3.37151	+	10.3764i	0.247878	+	0.762891i
$186$	0.655159	+	2.01637i	0.0480386	+	0.147848i
$187$	16.4733	−	11.9685i	1.20465	−	0.875227i
$188$	7.26013	−	5.27480i	0.529500	−	0.384704i
$189$	1.60402	−	1.16539i	0.116675	−	0.0847696i
$190$	1.23665	−	3.80600i	0.0897157	−	0.276116i
$191$	19.6124	+	14.2493i	1.41911	+	1.03104i	0.991918	+	0.126878i	$0.0404956\pi$
$191$	19.6124	+	14.2493i	1.41911	+	1.03104i	0.427187	+	0.904163i	$0.359504\pi$
$192$	−0.196297	+	0.142618i	−0.0141665	+	0.0102926i
$193$	−21.3281	−	15.4957i	−1.53523	−	1.11541i	−0.953242	−	0.302208i	$-0.902276\pi$
$193$	−21.3281	−	15.4957i	−1.53523	−	1.11541i	−0.581985	−	0.813199i	$-0.697724\pi$
$194$	−4.58315			−0.329051
$195$	1.17952	+	0.856969i	0.0844670	+	0.0613688i
$196$	−5.10828			−0.364877
$197$	−21.6330			−1.54129			−0.770644	−	0.637266i	$-0.780065\pi$
$197$	−21.6330			−1.54129			−0.770644	+	0.637266i	$0.780065\pi$
$198$	7.59777	+	5.52010i	0.539950	+	0.392297i
$199$	−6.58132	+	20.2552i	−0.466538	+	1.43586i	0.390501	+	0.920603i	$0.372302\pi$
$199$	−6.58132	+	20.2552i	−0.466538	+	1.43586i	−0.857038	+	0.515253i	$0.827698\pi$
$200$	−0.912780	+	0.663174i	−0.0645433	+	0.0468935i
$201$	1.82808	+	1.32817i	0.128943	+	0.0936822i
$202$	−0.444417	−	1.36777i	−0.0312691	−	0.0962363i
$203$	1.08995	−	3.35451i	0.0764993	−	0.235441i
$204$	1.54726			0.108330
$205$	−5.22696	−	16.0869i	−0.365066	−	1.12356i
$206$	3.65791	−	2.65763i	0.254859	−	0.185166i
$207$	−0.175514	+	0.540178i	−0.0121991	+	0.0375449i
$208$	0.943671	−	2.90432i	0.0654318	−	0.201379i
$209$	−2.00681	−	6.17633i	−0.138814	−	0.427226i
$210$	−0.531244	−	0.385972i	−0.0366593	−	0.0266346i
$211$	−5.76023	−	17.7282i	−0.396551	−	1.22046i	−0.927747	−	0.373209i	$-0.878257\pi$
$211$	−5.76023	−	17.7282i	−0.396551	−	1.22046i	0.531197	−	0.847249i	$-0.321743\pi$
$212$	4.89161			0.335957
$213$	0.266809	−	0.821154i	0.0182815	−	0.0562645i
$214$	−4.84219	+	14.9027i	−0.331005	+	1.01873i
$215$	−8.12307			−0.553989
$216$	0.445457	+	1.37098i	0.0303095	+	0.0932832i
$217$	9.72290	+	7.06410i	0.660033	+	0.479542i
$218$	−0.462983	−	1.42491i	−0.0313571	−	0.0965074i
$219$	0.604963	−	1.86188i	0.0408796	−	0.125814i
$220$	1.94156	−	5.97550i	0.130900	−	0.402868i
$221$	−15.7545	+	11.4463i	−1.05976	+	0.769962i
$222$	0.415744	+	1.27953i	0.0279029	+	0.0858763i
$223$	−25.4956			−1.70731			−0.853657	−	0.520835i	$-0.825621\pi$
$223$	−25.4956			−1.70731			−0.853657	+	0.520835i	$0.825621\pi$
$224$	−0.425021	+	1.30808i	−0.0283979	+	0.0873999i
$225$	1.02543	+	3.15594i	0.0683618	+	0.210396i
$226$	4.84065	+	3.51694i	0.321995	+	0.233943i
$227$	10.4392	−	7.58454i	0.692876	−	0.503404i	−0.184729	−	0.982790i	$-0.559141\pi$
$227$	10.4392	−	7.58454i	0.692876	−	0.503404i	0.877604	+	0.479386i	$0.159141\pi$
$228$	0.152492	−	0.469322i	0.0100990	−	0.0310816i
$229$	11.9543	+	8.68534i	0.789965	+	0.573943i	0.907953	−	0.419072i	$-0.137644\pi$
$229$	11.9543	+	8.68534i	0.789965	+	0.573943i	−0.117988	+	0.993015i	$0.537644\pi$
$230$	0.379988			0.0250556
$231$	−1.06561			−0.0701119
$232$	2.07469	+	1.50735i	0.136210	+	0.0989623i
$233$	−24.7369			−1.62057			−0.810283	−	0.586039i	$-0.800686\pi$
$233$	−24.7369			−1.62057			−0.810283	+	0.586039i	$0.800686\pi$
$234$	−7.26624	−	5.27924i	−0.475009	−	0.345114i
$235$	−14.2856	+	10.3791i	−0.931888	+	0.677057i
$236$	2.43864	+	1.77178i	0.158742	+	0.115333i
$237$	−1.01492	+	3.12362i	−0.0659264	+	0.202901i
$238$	7.09568	−	5.15532i	0.459945	−	0.334170i
$239$	−6.48035	+	4.70825i	−0.419179	+	0.304551i	−0.777307	−	0.629121i	$-0.783415\pi$
$239$	−6.48035	+	4.70825i	−0.419179	+	0.304551i	0.358128	+	0.933672i	$0.383415\pi$
$240$	0.386248	−	0.280625i	0.0249322	−	0.0181143i
$241$	−0.469854	−	1.44606i	−0.0302660	−	0.0931491i	0.934782	−	0.355221i	$-0.115594\pi$
$241$	−0.469854	−	1.44606i	−0.0302660	−	0.0931491i	−0.965048	+	0.262072i	$0.915594\pi$
$242$	0.248455	+	0.764664i	0.0159713	+	0.0491545i
$243$	6.38059			0.409315
$244$	1.02747	+	7.74237i	0.0657768	+	0.495655i
$245$	10.0514			0.642162
$246$	−0.644541	−	1.98369i	−0.0410944	−	0.126476i
$247$	1.91925	+	5.90683i	0.122119	+	0.375843i
$248$	−7.06915	+	5.13604i	−0.448892	+	0.326139i
$249$	−1.13461	+	0.824345i	−0.0719032	+	0.0522407i
$250$	9.75546	−	7.08776i	0.616990	−	0.448269i
$251$	6.36794	−	19.5985i	0.401941	−	1.23705i	−0.521482	−	0.853262i	$-0.674621\pi$
$251$	6.36794	−	19.5985i	0.401941	−	1.23705i	0.923423	−	0.383784i	$-0.125379\pi$
$252$	3.27265	+	2.37772i	0.206158	+	0.149782i
$253$	0.498871	−	0.362451i	0.0313638	−	0.0227871i
$254$	4.96091	+	3.60431i	0.311275	+	0.226155i
$255$	−3.04450			−0.190654
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.30220			−0.0812291			−0.0406145	−	0.999175i	$-0.512932\pi$
$257$	−1.30220			−0.0812291			−0.0406145	+	0.999175i	$0.512932\pi$
$258$	−1.00166			−0.0623608
$259$	6.16985	+	4.48266i	0.383376	+	0.278539i
$260$	−1.85684	+	5.71476i	−0.115156	+	0.354414i
$261$	6.10192	−	4.43330i	0.377699	−	0.274415i
$262$	−4.45843	−	3.23924i	−0.275442	−	0.200121i
$263$	1.76420	+	5.42964i	0.108785	+	0.334806i	0.990600	−	0.136789i	$-0.0436783\pi$
$263$	1.76420	+	5.42964i	0.108785	+	0.334806i	−0.881815	+	0.471595i	$0.843678\pi$
$264$	0.239415	−	0.736844i	0.0147350	−	0.0453496i
$265$	−9.62509			−0.591265
$266$	−0.864411	−	2.66038i	−0.0530005	−	0.163119i
$267$	−2.64467	+	1.92146i	−0.161851	+	0.117592i
$268$	−2.87782	+	8.85703i	−0.175791	+	0.541029i
$269$	−8.12237	+	24.9981i	−0.495230	+	1.52416i	0.321369	+	0.946954i	$0.395857\pi$
$269$	−8.12237	+	24.9981i	−0.495230	+	1.52416i	−0.816599	+	0.577206i	$0.804143\pi$
$270$	−0.876515	−	2.69764i	−0.0533430	−	0.164173i
$271$	−1.91811	−	1.39359i	−0.116517	−	0.0846544i	0.528001	−	0.849244i	$-0.322942\pi$
$271$	−1.91811	−	1.39359i	−0.116517	−	0.0846544i	−0.644518	+	0.764589i	$0.722942\pi$
$272$	1.97056	+	6.06477i	0.119483	+	0.367731i
$273$	1.01911			0.0616795
$274$	2.00161	−	6.16031i	0.120921	−	0.372158i
$275$	1.11328	−	3.42633i	0.0671335	−	0.206616i
$276$	0.0468567			0.00282044
$277$	−4.89821	−	15.0751i	−0.294305	−	0.905777i	−0.983454	−	0.181158i	$-0.942016\pi$
$277$	−4.89821	−	15.0751i	−0.294305	−	0.905777i	0.689149	−	0.724620i	$-0.257984\pi$
$278$	−18.8267	−	13.6784i	−1.12915	−	0.820375i
$279$	7.94156	+	24.4416i	0.475449	+	1.46328i
$280$	0.836304	−	2.57388i	0.0499787	−	0.153819i
$281$	−9.03997	+	27.8222i	−0.539279	+	1.65973i	0.194937	+	0.980816i	$0.437550\pi$
$281$	−9.03997	+	27.8222i	−0.539279	+	1.65973i	−0.734217	+	0.678915i	$0.762450\pi$
$282$	−1.76157	+	1.27985i	−0.104900	+	0.0762142i
$283$	4.29109	+	13.2066i	0.255079	+	0.785051i	0.993814	+	0.111056i	$0.0354232\pi$
$283$	4.29109	+	13.2066i	0.255079	+	0.785051i	−0.738736	+	0.673995i	$0.764577\pi$
$284$	3.55847			0.211156
$285$	−0.300054	+	0.923473i	−0.0177737	+	0.0547018i
$286$	3.01325	+	9.27383i	0.178177	+	0.548373i
$287$	−9.56532	−	6.94961i	−0.564623	−	0.410223i
$288$	−2.37942	+	1.72875i	−0.140209	+	0.101868i
$289$	7.31276	−	22.5064i	0.430162	−	1.32390i
$290$	−4.08231	−	2.96597i	−0.239721	−	0.174168i
$291$	1.11204			0.0651887
$292$	8.06847			0.472172
$293$	8.76061	+	6.36496i	0.511801	+	0.371845i	0.813506	−	0.581556i	$-0.197556\pi$
$293$	8.76061	+	6.36496i	0.511801	+	0.371845i	−0.301706	+	0.953401i	$0.597556\pi$
$294$	1.23945			0.0722863
$295$	−4.79845	−	3.48628i	−0.279377	−	0.202979i
$296$	−4.48587	+	3.25917i	−0.260736	+	0.189436i
$297$	−3.72388	−	2.70556i	−0.216082	−	0.156992i
$298$	−5.55308	+	17.0906i	−0.321681	+	0.990033i
$299$	−0.477103	+	0.346636i	−0.0275916	+	0.0200465i
$300$	0.221473	−	0.160910i	0.0127868	−	0.00929012i
$301$	−4.59360	+	3.33744i	−0.264771	+	0.192367i
$302$	4.03943	+	12.4321i	0.232443	+	0.715387i
$303$	0.107831	+	0.331871i	0.00619476	+	0.0190655i
$304$	2.03381			0.116647
$305$	−2.02172	−	15.2345i	−0.115763	−	0.872323i
$306$	18.7552			1.07216
$307$	0.979154	+	3.01353i	0.0558833	+	0.171991i	0.975102	−	0.221756i	$-0.0711787\pi$
$307$	0.979154	+	3.01353i	0.0558833	+	0.171991i	−0.919219	+	0.393747i	$0.871179\pi$
$308$	−1.35714	−	4.17685i	−0.0773304	−	0.237998i
$309$	−0.887540	+	0.644835i	−0.0504904	+	0.0366834i
$310$	13.9098	−	10.1061i	0.790023	−	0.573985i
$311$	8.71969	−	6.33523i	0.494448	−	0.359238i	−0.312444	−	0.949936i	$-0.601148\pi$
$311$	8.71969	−	6.33523i	0.494448	−	0.359238i	0.806892	+	0.590698i	$0.201148\pi$
$312$	−0.228969	+	0.704693i	−0.0129628	+	0.0398954i
$313$	16.7834	+	12.1939i	0.948654	+	0.689237i	0.950488	−	0.310761i	$-0.100584\pi$
$313$	16.7834	+	12.1939i	0.948654	+	0.689237i	−0.00183441	+	0.999998i	$0.500584\pi$
$314$	2.08899	−	1.51774i	0.117889	−	0.0856511i
$315$	−6.43952	−	4.67858i	−0.362826	−	0.263608i
$316$	−13.5362			−0.761470
$317$	12.8435	+	9.33133i	0.721362	+	0.524100i	0.886819	−	0.462117i	$-0.152910\pi$
$317$	12.8435	+	9.33133i	0.721362	+	0.524100i	−0.165457	+	0.986217i	$0.552910\pi$
$318$	−1.18688			−0.0665569
$319$	−8.18860			−0.458473
$320$	1.59188	+	1.15657i	0.0889889	+	0.0646542i
$321$	1.17489	−	3.61593i	0.0655758	−	0.201822i
$322$	0.214883	−	0.156122i	0.0119750	−	0.00870033i
$323$	−10.4924	−	7.62319i	−0.583814	−	0.424165i
$324$	2.61849	+	8.05889i	0.145472	+	0.447716i
$325$	−1.06471	+	3.27683i	−0.0590592	+	0.181766i
$326$	−13.2184			−0.732101
$327$	0.112336	+	0.345735i	0.00621221	+	0.0191192i
$328$	6.95458	−	5.05280i	0.384003	−	0.278994i
$329$	−3.81415	+	11.7387i	−0.210281	+	0.647178i
$330$	−0.471091	+	1.44987i	−0.0259327	+	0.0798127i
$331$	−7.50503	−	23.0981i	−0.412514	−	1.26959i	−0.914456	−	0.404686i	$-0.867381\pi$
$331$	−7.50503	−	23.0981i	−0.412514	−	1.26959i	0.501942	−	0.864901i	$-0.332619\pi$
$332$	−4.67620	−	3.39746i	−0.256640	−	0.186460i
$333$	5.03947	+	15.5099i	0.276161	+	0.849937i
$334$	−20.6460			−1.12970
$335$	5.66262	−	17.4277i	0.309382	−	0.952179i
$336$	0.103125	−	0.317387i	0.00562595	−	0.0173149i
$337$	12.7569			0.694915			0.347457	−	0.937696i	$-0.387045\pi$
$337$	12.7569			0.694915			0.347457	+	0.937696i	$0.387045\pi$
$338$	1.13545	+	3.49456i	0.0617604	+	0.190079i
$339$	−1.17451	−	0.853335i	−0.0637909	−	0.0463468i
$340$	−3.87743	−	11.9335i	−0.210283	−	0.647185i
$341$	8.62197	−	26.5357i	0.466906	−	1.43699i
$342$	1.84844	−	5.68892i	0.0999523	−	0.307622i
$343$	13.4731	−	9.78880i	0.727481	−	0.528546i
$344$	−1.27570	−	3.92621i	−0.0687812	−	0.211687i
$345$	−0.0921986			−0.00496381
$346$	0.444571	−	1.36825i	0.0239003	−	0.0735575i
$347$	9.20786	+	28.3389i	0.494304	+	1.52131i	0.818039	+	0.575163i	$0.195061\pi$
$347$	9.20786	+	28.3389i	0.494304	+	1.52131i	−0.323735	+	0.946148i	$0.604939\pi$
$348$	−0.503393	−	0.365737i	−0.0269847	−	0.0196055i
$349$	18.3334	−	13.3200i	0.981364	−	0.713002i	0.0233507	−	0.999727i	$-0.492567\pi$
$349$	18.3334	−	13.3200i	0.981364	−	0.713002i	0.958013	+	0.286725i	$0.0925666\pi$
$350$	0.479534	−	1.47585i	0.0256322	−	0.0788877i
$351$	3.56139	+	2.58750i	0.190093	+	0.138111i
$352$	3.19312			0.170194
$353$	22.5930			1.20250			0.601251	−	0.799060i	$-0.294669\pi$
$353$	22.5930			1.20250			0.601251	+	0.799060i	$0.294669\pi$
$354$	−0.591702	−	0.429896i	−0.0314486	−	0.0228487i
$355$	−7.00191			−0.371623
$356$	−10.8997	−	7.91912i	−0.577685	−	0.419713i
$357$	−1.72167	+	1.25086i	−0.0911203	+	0.0662028i
$358$	−20.6559	−	15.0074i	−1.09170	−	0.793167i
$359$	−1.99912	+	6.15265i	−0.105509	+	0.324725i	−0.989850	−	0.142118i	$-0.954609\pi$
$359$	−1.99912	+	6.15265i	−0.105509	+	0.324725i	0.884340	+	0.466843i	$0.154609\pi$
$360$	4.68193	−	3.40162i	0.246759	−	0.179281i
$361$	12.0249	−	8.73662i	0.632891	−	0.459822i
$362$	−4.13102	+	3.00136i	−0.217121	+	0.157748i
$363$	−0.0602840	−	0.185535i	−0.00316409	−	0.00973806i
$364$	1.29792	+	3.99460i	0.0680297	+	0.209374i
$365$	−15.8761			−0.830994
$366$	−0.249300	−	1.87858i	−0.0130311	−	0.0981948i
$367$	35.1856			1.83667			0.918336	−	0.395801i	$-0.129533\pi$
$367$	35.1856			1.83667			0.918336	+	0.395801i	$0.129533\pi$
$368$	0.0596759	+	0.183663i	0.00311082	+	0.00957412i
$369$	−7.81285	−	24.0455i	−0.406721	−	1.25176i
$370$	8.82672	−	6.41299i	0.458880	−	0.333395i
$371$	−5.44299	+	3.95456i	−0.282586	+	0.205311i
$372$	1.71523	−	1.24619i	0.0889305	−	0.0646118i
$373$	3.55206	−	10.9321i	0.183919	−	0.566043i	−0.816009	−	0.578039i	$-0.803818\pi$
$373$	3.55206	−	10.9321i	0.183919	−	0.566043i	0.999928	+	0.0119952i	$0.00381829\pi$
$374$	−16.4733	−	11.9685i	−0.851814	−	0.618879i
$375$	−2.36702	+	1.71974i	−0.122233	+	0.0888072i
$376$	−7.26013	−	5.27480i	−0.374413	−	0.272027i
$377$	7.83129			0.403332
$378$	−1.60402	−	1.16539i	−0.0825019	−	0.0599411i
$379$	−24.8400			−1.27594			−0.637971	−	0.770060i	$-0.720226\pi$
$379$	−24.8400			−1.27594			−0.637971	+	0.770060i	$0.720226\pi$
$380$	−4.00187			−0.205292
$381$	−1.20370	−	0.874536i	−0.0616672	−	0.0448038i
$382$	7.49128	−	23.0558i	0.383287	−	1.17964i
$383$	15.5030	−	11.2636i	0.792165	−	0.575541i	−0.116440	−	0.993198i	$-0.537148\pi$
$383$	15.5030	−	11.2636i	0.792165	−	0.575541i	0.908605	+	0.417656i	$0.137148\pi$
$384$	0.196297	+	0.142618i	0.0100172	+	0.00727793i
$385$	2.67041	+	8.21869i	0.136097	+	0.418863i
$386$	−8.14659	+	25.0726i	−0.414651	+	1.27616i
$387$	−12.1417			−0.617199
$388$	1.41627	+	4.35883i	0.0719002	+	0.221286i
$389$	−14.3393	+	10.4181i	−0.727032	+	0.528219i	−0.888623	−	0.458638i	$-0.848337\pi$
$389$	−14.3393	+	10.4181i	−0.727032	+	0.528219i	0.161591	+	0.986858i	$0.448337\pi$
$390$	0.450535	−	1.38661i	0.0228137	−	0.0702135i
$391$	0.380546	−	1.17120i	0.0192450	−	0.0592301i
$392$	1.57855	+	4.85826i	0.0797286	+	0.245379i
$393$	1.08177	+	0.785955i	0.0545683	+	0.0396462i
$394$	6.68497	+	20.5742i	0.336784	+	1.03651i
$395$	26.6348			1.34014
$396$	2.90209	−	8.93171i	0.145835	−	0.448836i
$397$	−0.966982	+	2.97606i	−0.0485314	+	0.149364i	−0.972385	−	0.233381i	$-0.925021\pi$
$397$	−0.966982	+	2.97606i	−0.0485314	+	0.149364i	0.923854	+	0.382745i	$0.125021\pi$
$398$	21.2976			1.06755
$399$	0.209737	+	0.645505i	0.0105000	+	0.0323156i
$400$	0.912780	+	0.663174i	0.0456390	+	0.0331587i
$401$	−1.62759	−	5.00920i	−0.0812779	−	0.250148i	0.902157	−	0.431407i	$-0.141983\pi$
$401$	−1.62759	−	5.00920i	−0.0812779	−	0.250148i	−0.983435	+	0.181259i	$0.941983\pi$
$402$	0.698263	−	2.14903i	0.0348262	−	0.107184i
$403$	−8.24576	+	25.3778i	−0.410750	+	1.26416i
$404$	−1.16350	+	0.845331i	−0.0578862	+	0.0420568i
$405$	−5.15234	−	15.8573i	−0.256022	−	0.787954i
$406$	−3.52715			−0.175049
$407$	5.47124	−	16.8387i	0.271199	−	0.834665i
$408$	−0.478129	−	1.47153i	−0.0236709	−	0.0728516i
$409$	−12.2307	−	8.88613i	−0.604769	−	0.439391i	0.242799	−	0.970077i	$-0.421934\pi$
$409$	−12.2307	−	8.88613i	−0.604769	−	0.439391i	−0.847569	+	0.530686i	$0.821934\pi$
$410$	−13.6843	+	9.94226i	−0.675822	+	0.491013i
$411$	−0.485661	+	1.49471i	−0.0239559	+	0.0737287i
$412$	−3.65791	−	2.65763i	−0.180212	−	0.130932i
$413$	−4.14590			−0.204006
$414$	0.567976			0.0279145
$415$	9.20123	+	6.68509i	0.451671	+	0.328158i
$416$	−3.05378			−0.149724
$417$	4.56803	+	3.31886i	0.223697	+	0.162525i
$418$	−5.25390	+	3.81718i	−0.256977	+	0.186704i
$419$	−9.86994	−	7.17093i	−0.482178	−	0.350323i	0.319990	−	0.947421i	$-0.396320\pi$
$419$	−9.86994	−	7.17093i	−0.482178	−	0.350323i	−0.802168	+	0.597098i	$0.796320\pi$
$420$	−0.202917	+	0.624515i	−0.00990135	+	0.0304732i
$421$	−2.68543	+	1.95108i	−0.130880	+	0.0950896i	−0.651299	−	0.758821i	$-0.725776\pi$
$421$	−2.68543	+	1.95108i	−0.130880	+	0.0950896i	0.520419	+	0.853911i	$0.325776\pi$
$422$	−15.0805	+	10.9566i	−0.734106	+	0.533359i
$423$	−21.3530	+	15.5138i	−1.03822	+	0.754309i
$424$	−1.51159	−	4.65219i	−0.0734093	−	0.225931i
$425$	−2.22331	−	6.84263i	−0.107846	−	0.331916i
$426$	−0.863412			−0.0418325
$427$	−7.40252	−	7.78445i	−0.358233	−	0.376716i
$428$	15.6696			0.757421
$429$	−0.731123	−	2.25016i	−0.0352989	−	0.108639i
$430$	2.51017	+	7.72550i	0.121051	+	0.372557i
$431$	26.2661	−	19.0835i	1.26520	−	0.919218i	0.266195	−	0.963919i	$-0.414234\pi$
$431$	26.2661	−	19.0835i	1.26520	−	0.919218i	0.999000	+	0.0447010i	$0.0142335\pi$
$432$	1.16622	−	0.847310i	0.0561099	−	0.0407662i
$433$	−10.1119	+	7.34670i	−0.485945	+	0.353060i	−0.803623	−	0.595139i	$-0.797097\pi$
$433$	−10.1119	+	7.34670i	−0.485945	+	0.353060i	0.317678	+	0.948199i	$0.397097\pi$
$434$	3.71382	−	11.4300i	0.178269	−	0.548655i
$435$	0.990514	+	0.719651i	0.0474915	+	0.0345046i
$436$	−1.21210	+	0.880645i	−0.0580493	+	0.0421753i
$437$	−0.317749	−	0.230858i	−0.0152000	−	0.0110434i
$438$	−1.95770			−0.0935425
$439$	11.2422	+	8.16796i	0.536562	+	0.389835i	0.822807	−	0.568321i	$-0.192407\pi$
$439$	11.2422	+	8.16796i	0.536562	+	0.389835i	−0.286244	+	0.958157i	$0.592407\pi$
$440$	−6.28301			−0.299531
$441$	15.0241			0.715434
$442$	15.7545	+	11.4463i	0.749365	+	0.544445i
$443$	−8.00009	+	24.6218i	−0.380096	+	1.16982i	0.559880	+	0.828574i	$0.310847\pi$
$443$	−8.00009	+	24.6218i	−0.380096	+	1.16982i	−0.939976	+	0.341241i	$0.889153\pi$
$444$	1.08843	−	0.790792i	0.0516547	−	0.0375293i
$445$	21.4471	+	15.5822i	1.01669	+	0.738669i
$446$	7.87859	+	24.2478i	0.373062	+	1.14817i
$447$	1.34738	−	4.14680i	0.0637287	−	0.196137i
$448$	1.37540			0.0649815
$449$	−6.83147	−	21.0251i	−0.322397	−	0.992237i	−0.972602	−	0.232477i	$-0.925317\pi$
$449$	−6.83147	−	21.0251i	−0.322397	−	0.992237i	0.650205	−	0.759759i	$-0.274683\pi$
$450$	2.68460	−	1.95048i	0.126553	−	0.0919464i
$451$	−8.48223	+	26.1056i	−0.399413	+	1.22927i
$452$	1.84896	−	5.69052i	0.0869679	−	0.267660i
$453$	−0.980111	−	3.01647i	−0.0460496	−	0.141726i
$454$	−10.4392	−	7.58454i	−0.489937	−	0.355960i
$455$	−2.55389	−	7.86007i	−0.119728	−	0.368486i
$456$	−0.493474			−0.0231091
$457$	−6.03598	+	18.5768i	−0.282351	+	0.868987i	0.704829	+	0.709377i	$0.251024\pi$
$457$	−6.03598	+	18.5768i	−0.282351	+	0.868987i	−0.987180	+	0.159610i	$0.948976\pi$
$458$	4.56615	−	14.0532i	0.213362	−	0.656662i
$459$	−9.19247			−0.429068
$460$	−0.117423	−	0.361390i	−0.00547486	−	0.0168499i
$461$	12.3639	+	8.98287i	0.575842	+	0.418374i	0.837223	−	0.546862i	$-0.184178\pi$
$461$	12.3639	+	8.98287i	0.575842	+	0.418374i	−0.261380	+	0.965236i	$0.584178\pi$
$462$	0.329291	+	1.01345i	0.0153200	+	0.0471502i
$463$	−7.95177	+	24.4730i	−0.369550	+	1.13736i	0.577532	+	0.816368i	$0.304016\pi$
$463$	−7.95177	+	24.4730i	−0.369550	+	1.13736i	−0.947082	+	0.320991i	$0.895984\pi$
$464$	0.792460	−	2.43894i	0.0367890	−	0.113225i
$465$	−3.37501	+	2.45209i	−0.156512	+	0.113713i
$466$	7.64411	+	23.5261i	0.354106	+	1.08983i
$467$	5.10358			0.236166			0.118083	−	0.993004i	$-0.462325\pi$
$467$	5.10358			0.236166			0.118083	+	0.993004i	$0.462325\pi$
$468$	−2.77546	+	8.54198i	−0.128296	+	0.394853i
$469$	−3.95815	−	12.1819i	−0.182770	−	0.562510i
$470$	14.2856	+	10.3791i	0.658945	+	0.478751i
$471$	−0.506864	+	0.368258i	−0.0233551	+	0.0169685i
$472$	0.931478	−	2.86679i	0.0428747	−	0.131955i
$473$	10.6645	+	7.74819i	0.490353	+	0.356262i
$474$	3.28436			0.150856
$475$	−2.29466			−0.105286
$476$	−7.09568	−	5.15532i	−0.325230	−	0.236294i
$477$	−14.3868			−0.658728
$478$	6.48035	+	4.70825i	0.296404	+	0.215350i
$479$	−6.48975	+	4.71508i	−0.296524	+	0.215437i	−0.726093	−	0.687597i	$-0.758666\pi$
$479$	−6.48975	+	4.71508i	−0.296524	+	0.215437i	0.429569	+	0.903034i	$0.358666\pi$
$480$	−0.386248	−	0.280625i	−0.0176297	−	0.0128087i
$481$	−5.23250	+	16.1040i	−0.238582	+	0.734279i
$482$	−1.23009	+	0.893716i	−0.0560293	+	0.0407076i
$483$	−0.0521384	+	0.0378807i	−0.00237238	+	0.00172363i
$484$	0.650462	−	0.472589i	0.0295665	−	0.0214813i
$485$	−2.78676	−	8.57676i	−0.126540	−	0.389451i
$486$	−1.97171	−	6.06831i	−0.0894387	−	0.275264i
$487$	−22.9043			−1.03789			−0.518945	−	0.854807i	$-0.673675\pi$
$487$	−22.9043			−1.03789			−0.518945	+	0.854807i	$0.673675\pi$
$488$	7.04593	−	3.36970i	0.318954	−	0.152539i
$489$	3.20726			0.145038
$490$	−3.10606	−	9.55948i	−0.140318	−	0.431853i
$491$	3.34360	+	10.2905i	0.150894	+	0.464406i	0.997722	−	0.0674624i	$-0.0214903\pi$
$491$	3.34360	+	10.2905i	0.150894	+	0.464406i	−0.846827	+	0.531868i	$0.821490\pi$
$492$	−1.68743	+	1.22599i	−0.0760752	+	0.0552719i
$493$	−13.2300	+	9.61218i	−0.595850	+	0.432911i
$494$	5.02465	−	3.65062i	0.226070	−	0.164249i
$495$	−5.71037	+	17.5747i	−0.256662	+	0.789924i
$496$	7.06915	+	5.13604i	0.317414	+	0.230615i
$497$	−3.95958	+	2.87680i	−0.177612	+	0.129042i
$498$	1.13461	+	0.824345i	0.0508432	+	0.0369398i
$499$	−17.2837			−0.773726			−0.386863	−	0.922137i	$-0.626441\pi$
$499$	−17.2837			−0.773726			−0.386863	+	0.922137i	$0.626441\pi$
$500$	−9.75546	−	7.08776i	−0.436278	−	0.316974i
$501$	5.00946			0.223806
$502$	−20.6071			−0.919739
$503$	−17.7453	−	12.8927i	−0.791224	−	0.574858i	0.117102	−	0.993120i	$-0.462639\pi$
$503$	−17.7453	−	12.8927i	−0.791224	−	0.574858i	−0.908327	+	0.418262i	$0.862639\pi$
$504$	1.25004	−	3.84723i	0.0556813	−	0.171369i
$505$	2.28939	−	1.66334i	0.101876	−	0.0740175i
$506$	−0.498871	−	0.362451i	−0.0221775	−	0.0161129i
$507$	−0.275501	−	0.847905i	−0.0122354	−	0.0376568i
$508$	1.89490	−	5.83190i	0.0840726	−	0.258749i
$509$	23.1388			1.02561			0.512806	−	0.858505i	$-0.328606\pi$
$509$	23.1388			1.02561			0.512806	+	0.858505i	$0.328606\pi$
$510$	0.940803	+	2.89549i	0.0416595	+	0.128215i
$511$	−8.97795	+	6.52286i	−0.397161	+	0.288555i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.905974	+	2.78830i	−0.0399997	+	0.123107i
$514$	0.402402	+	1.23847i	0.0177492	+	0.0546264i
$515$	7.19757	+	5.22934i	0.317163	+	0.230432i
$516$	0.309531	+	0.952638i	0.0136263	+	0.0419376i
$517$	28.6551			1.26025
$518$	2.35667	−	7.25310i	0.103546	−	0.318683i
$519$	−0.107869	+	0.331986i	−0.00473492	+	0.0145726i
$520$	6.00885			0.263506
$521$	3.16697	+	9.74693i	0.138747	+	0.427021i	0.996154	−	0.0876189i	$-0.0279258\pi$
$521$	3.16697	+	9.74693i	0.138747	+	0.427021i	−0.857407	+	0.514639i	$0.827926\pi$
$522$	−6.10192	−	4.43330i	−0.267074	−	0.194040i
$523$	3.11809	+	9.59650i	0.136345	+	0.419626i	0.995797	−	0.0915906i	$-0.0291951\pi$
$523$	3.11809	+	9.59650i	0.136345	+	0.419626i	−0.859452	+	0.511216i	$0.829195\pi$
$524$	−1.70297	+	5.24119i	−0.0743945	+	0.228963i
$525$	−0.116352	+	0.358095i	−0.00507802	+	0.0156285i
$526$	4.61873	−	3.35570i	0.201386	−	0.146316i
$527$	−17.2187	−	52.9937i	−0.750058	−	2.30844i
$528$	−0.774764			−0.0337173
$529$	−7.09587	+	21.8388i	−0.308516	+	0.949514i
$530$	2.97432	+	9.15400i	0.129196	+	0.397625i
$531$	−7.17235	−	5.21102i	−0.311254	−	0.226139i
$532$	−2.26306	+	1.64421i	−0.0981160	+	0.0712855i
$533$	8.11212	−	24.9665i	0.351375	−	1.08142i
$534$	2.64467	+	1.92146i	0.114446	+	0.0831498i
$535$	−30.8328			−1.33302
$536$	9.31283			0.402253
$537$	5.01187	+	3.64134i	0.216278	+	0.157135i
$538$	26.2845			1.13321
$539$	−13.1961	−	9.58756i	−0.568398	−	0.412965i
$540$	−2.29475	+	1.66723i	−0.0987502	+	0.0717462i
$541$	−25.5416	−	18.5571i	−1.09812	−	0.797831i	−0.117368	−	0.993088i	$-0.537446\pi$
$541$	−25.5416	−	18.5571i	−1.09812	−	0.797831i	−0.980752	+	0.195258i	$0.937446\pi$
$542$	−0.732652	+	2.25487i	−0.0314701	+	0.0968550i
$543$	1.00233	−	0.728237i	0.0430142	−	0.0312516i
$544$	5.15900	−	3.74824i	0.221190	−	0.160704i
$545$	2.38503	−	1.73282i	0.102163	−	0.0742260i
$546$	−0.314923	−	0.969233i	−0.0134775	−	0.0414793i
$547$	−3.96291	−	12.1966i	−0.169442	−	0.521489i	0.829894	−	0.557921i	$-0.188401\pi$
$547$	−3.96291	−	12.1966i	−0.169442	−	0.521489i	−0.999336	+	0.0364321i	$0.988401\pi$
$548$	−6.47733			−0.276698
$549$	−3.02191	−	22.7713i	−0.128972	−	0.971856i
$550$	−3.60266			−0.153618
$551$	1.61171	+	4.96033i	0.0686612	+	0.211317i
$552$	−0.0144795	−	0.0445633i	−0.000616289	−	0.00189674i
$553$	15.0620	−	10.9432i	0.640501	−	0.465351i
$554$	−12.8237	+	9.31695i	−0.544826	+	0.395839i
$555$	−2.14168	+	1.55602i	−0.0909092	+	0.0660494i
$556$	−7.19115	+	22.1321i	−0.304973	+	0.938609i
$557$	27.0079	+	19.6224i	1.14436	+	0.831427i	0.987721	−	0.156229i	$-0.0499338\pi$
$557$	27.0079	+	19.6224i	1.14436	+	0.831427i	0.156640	+	0.987656i	$0.449934\pi$
$558$	20.7913	−	15.1057i	0.880165	−	0.639477i
$559$	−10.1991	−	7.41010i	−0.431377	−	0.313414i
$560$	−2.70634			−0.114364
$561$	3.99701	+	2.90400i	0.168754	+	0.122607i
$562$	29.2540			1.23400
$563$	−0.897868			−0.0378406			−0.0189203	−	0.999821i	$-0.506023\pi$
$563$	−0.897868			−0.0378406			−0.0189203	+	0.999821i	$0.506023\pi$
$564$	1.76157	+	1.27985i	0.0741754	+	0.0538916i
$565$	−3.63816	+	11.1971i	−0.153058	+	0.471065i
$566$	11.2342	−	8.16213i	0.472209	−	0.343080i
$567$	−9.42877	−	6.85040i	−0.395971	−	0.287690i
$568$	−1.09963	−	3.38431i	−0.0461393	−	0.142002i
$569$	3.11941	−	9.60056i	0.130772	−	0.402476i	−0.864136	−	0.503258i	$-0.832134\pi$
$569$	3.11941	−	9.60056i	0.130772	−	0.402476i	0.994909	+	0.100782i	$0.0321345\pi$
$570$	0.970997			0.0406706
$571$	−4.90181	−	15.0862i	−0.205134	−	0.631339i	−0.999708	−	0.0241708i	$-0.992305\pi$
$571$	−4.90181	−	15.0862i	−0.205134	−	0.631339i	0.794573	−	0.607168i	$-0.207695\pi$
$572$	7.88880	−	5.73155i	0.329847	−	0.239648i
$573$	−1.81765	+	5.59416i	−0.0759336	+	0.233699i
$574$	−3.65363	+	11.2447i	−0.152499	+	0.469345i
$575$	−0.0673298	−	0.207220i	−0.00280785	−	0.00864166i
$576$	2.37942	+	1.72875i	0.0991426	+	0.0720313i
$577$	−8.68822	−	26.7396i	−0.361695	−	1.11318i	−0.952025	−	0.306021i	$-0.901002\pi$
$577$	−8.68822	−	26.7396i	−0.361695	−	1.11318i	0.590329	−	0.807163i	$-0.298998\pi$
$578$	−23.6646			−0.984317
$579$	1.97666	−	6.08352i	0.0821470	−	0.252822i
$580$	−1.55930	+	4.79904i	−0.0647465	+	0.199269i
$581$	7.94994			0.329819
$582$	−0.343638	−	1.05761i	−0.0142442	−	0.0438393i
$583$	12.6364	+	9.18089i	0.523347	+	0.380234i
$584$	−2.49329	−	7.67357i	−0.103173	−	0.317535i
$585$	5.46120	−	16.8078i	0.225793	−	0.694919i
$586$	3.34626	−	10.2987i	0.138233	−	0.425436i
$587$	−24.0662	+	17.4851i	−0.993320	+	0.721689i	−0.960646	−	0.277777i	$-0.910402\pi$
$587$	−24.0662	+	17.4851i	−0.993320	+	0.721689i	−0.0326740	+	0.999466i	$0.510402\pi$
$588$	−0.383012	−	1.17879i	−0.0157951	−	0.0486124i
$589$	−17.7713			−0.732254
$590$	−1.83284	+	5.64092i	−0.0754570	+	0.232233i
$591$	−1.62201	−	4.99204i	−0.0667207	−	0.205345i
$592$	4.48587	+	3.25917i	0.184368	+	0.133951i
$593$	11.1630	−	8.11037i	0.458408	−	0.333053i	−0.334498	−	0.942396i	$-0.608567\pi$
$593$	11.1630	−	8.11037i	0.458408	−	0.333053i	0.792906	+	0.609343i	$0.208567\pi$
$594$	−1.42240	+	4.37769i	−0.0583616	+	0.179619i
$595$	13.9620	+	10.1440i	0.572386	+	0.415863i
$596$	17.9701			0.736086
$597$	−5.16756			−0.211494
$598$	0.477103	+	0.346636i	0.0195102	+	0.0141750i
$599$	7.93338			0.324149			0.162075	−	0.986779i	$-0.448182\pi$
$599$	7.93338			0.324149			0.162075	+	0.986779i	$0.448182\pi$
$600$	−0.221473	−	0.160910i	−0.00904160	−	0.00656911i
$601$	11.8375	−	8.60045i	0.482862	−	0.350819i	−0.319571	−	0.947562i	$-0.603539\pi$
$601$	11.8375	−	8.60045i	0.482862	−	0.350819i	0.802433	+	0.596743i	$0.203539\pi$
$602$	4.59360	+	3.33744i	0.187221	+	0.136024i
$603$	8.46404	−	26.0496i	0.344682	−	1.06082i
$604$	10.5754	−	7.68346i	0.430306	−	0.312635i
$605$	−1.27990	+	0.929900i	−0.0520353	+	0.0378058i
$606$	0.282307	−	0.205108i	0.0114679	−	0.00833193i
$607$	10.6418	+	32.7522i	0.431938	+	1.32937i	0.896192	+	0.443667i	$0.146323\pi$
$607$	10.6418	+	32.7522i	0.431938	+	1.32937i	−0.464253	+	0.885702i	$0.653677\pi$
$608$	−0.628481	−	1.93426i	−0.0254883	−	0.0784448i
$609$	0.855812			0.0346792
$610$	−13.8641	+	6.63048i	−0.561341	+	0.268460i
$611$	−27.4047			−1.10868
$612$	−5.79568	−	17.8373i	−0.234276	−	0.721029i
$613$	3.66490	+	11.2794i	0.148024	+	0.455571i	0.997387	−	0.0722375i	$-0.0230140\pi$
$613$	3.66490	+	11.2794i	0.148024	+	0.455571i	−0.849364	+	0.527808i	$0.823014\pi$
$614$	2.56346	−	1.86246i	0.103453	−	0.0751628i
$615$	3.32031	−	2.41235i	0.133888	−	0.0972753i
$616$	−3.55304	+	2.58144i	−0.143156	+	0.104009i
$617$	3.37178	−	10.3773i	0.135743	−	0.417773i	−0.859962	−	0.510358i	$-0.829513\pi$
$617$	3.37178	−	10.3773i	0.135743	−	0.417773i	0.995705	+	0.0925847i	$0.0295129\pi$
$618$	0.887540	+	0.644835i	0.0357021	+	0.0259391i
$619$	25.7081	−	18.6780i	1.03330	−	0.750733i	0.0643299	−	0.997929i	$-0.479509\pi$
$619$	25.7081	−	18.6780i	1.03330	−	0.750733i	0.968966	+	0.247196i	$0.0795090\pi$
$620$	−13.9098	−	10.1061i	−0.558630	−	0.405869i
$621$	−0.278381			−0.0111711
$622$	−8.71969	−	6.33523i	−0.349628	−	0.254019i
$623$	18.5305			0.742408
$624$	0.740958			0.0296620
$625$	14.6317	+	10.6305i	0.585267	+	0.425221i
$626$	6.41069	−	19.7301i	0.256223	−	0.788572i
$627$	1.27478	−	0.926185i	0.0509100	−	0.0369883i
$628$	−2.08899	−	1.51774i	−0.0833599	−	0.0605645i
$629$	−10.9265	−	33.6282i	−0.435666	−	1.34084i
$630$	−2.45968	+	7.57010i	−0.0979958	+	0.301600i
$631$	18.5458			0.738296			0.369148	−	0.929371i	$-0.379650\pi$
$631$	18.5458			0.738296			0.369148	+	0.929371i	$0.379650\pi$
$632$	4.18291	+	12.8737i	0.166387	+	0.512087i
$633$	3.65907	−	2.65847i	0.145435	−	0.105665i
$634$	4.90577	−	15.0984i	0.194833	−	0.599635i
$635$	−3.72855	+	11.4753i	−0.147963	+	0.455383i
$636$	0.366766	+	1.12879i	0.0145432	+	0.0447594i
$637$	12.6203	+	9.16921i	0.500036	+	0.363297i
$638$	2.53042	+	7.78782i	0.100180	+	0.308323i
$639$	−10.4659			−0.414025
$640$	0.608045	−	1.87137i	0.0240351	−	0.0739724i
$641$	−3.19010	+	9.81812i	−0.126001	+	0.387793i	−0.994082	−	0.108630i	$-0.965353\pi$
$641$	−3.19010	+	9.81812i	−0.126001	+	0.387793i	0.868081	+	0.496423i	$0.165353\pi$
$642$	−3.80202			−0.150054
$643$	10.8682	+	33.4490i	0.428601	+	1.31910i	0.899504	+	0.436913i	$0.143928\pi$
$643$	10.8682	+	33.4490i	0.428601	+	1.31910i	−0.470902	+	0.882185i	$0.656072\pi$
$644$	−0.214883	−	0.156122i	−0.00846758	−	0.00615206i
$645$	−0.609056	−	1.87448i	−0.0239816	−	0.0738077i
$646$	−4.00775	+	12.3346i	−0.157683	+	0.485297i
$647$	6.49513	−	19.9900i	0.255350	−	0.785887i	−0.738410	−	0.674352i	$-0.764423\pi$
$647$	6.49513	−	19.9900i	0.255350	−	0.785887i	0.993760	−	0.111535i	$-0.0355767\pi$
$648$	6.85530	−	4.98067i	0.269302	−	0.195659i
$649$	2.97432	+	9.15400i	0.116752	+	0.359326i
$650$	3.44546			0.135142
$651$	−0.901105	+	2.77332i	−0.0353171	+	0.108695i
$652$	4.08472	+	12.5715i	0.159970	+	0.492337i
$653$	36.2525	+	26.3390i	1.41867	+	1.03072i	0.991989	+	0.126321i	$0.0403171\pi$
$653$	36.2525	+	26.3390i	1.41867	+	1.03072i	0.426680	+	0.904403i	$0.359683\pi$
$654$	0.294100	−	0.213676i	0.0115002	−	0.00835540i
$655$	3.35088	−	10.3130i	0.130930	−	0.402961i
$656$	−6.95458	−	5.05280i	−0.271531	−	0.197279i
$657$	−23.7304			−0.925811
$658$	12.3428			0.481174
$659$	23.8084	+	17.2978i	0.927445	+	0.673828i	0.945366	−	0.326011i	$-0.105705\pi$
$659$	23.8084	+	17.2978i	0.927445	+	0.673828i	−0.0179209	+	0.999839i	$0.505705\pi$
$660$	1.52448			0.0593404
$661$	−25.0968	−	18.2339i	−0.976154	−	0.709217i	−0.0193081	−	0.999814i	$-0.506146\pi$
$661$	−25.0968	−	18.2339i	−0.976154	−	0.709217i	−0.956846	+	0.290596i	$0.906146\pi$
$662$	−19.6484	+	14.2754i	−0.763658	+	0.554830i
$663$	−3.82260	−	2.77728i	−0.148458	−	0.107861i
$664$	−1.78615	+	5.49720i	−0.0693160	+	0.213333i
$665$	4.45296	−	3.23527i	0.172678	−	0.125458i
$666$	13.1935	−	9.58564i	0.511238	−	0.371436i
$667$	−0.400653	+	0.291092i	−0.0155134	+	0.0112711i
$668$	6.37997	+	19.6355i	0.246848	+	0.759721i
$669$	−1.91163	−	5.88339i	−0.0739078	−	0.227465i
$670$	−18.3246			−0.707941
$671$	−11.8772	+	21.9292i	−0.458512	+	0.846566i
$672$	−0.333721			−0.0128736
$673$	−6.21755	−	19.1357i	−0.239669	−	0.737626i	−0.996468	−	0.0839775i	$-0.973238\pi$
$673$	−6.21755	−	19.1357i	−0.239669	−	0.737626i	0.756799	−	0.653648i	$-0.226762\pi$
$674$	−3.94211	−	12.1326i	−0.151844	−	0.467329i
$675$	−1.31580	+	0.955985i	−0.0506452	+	0.0367959i
$676$	2.97265	−	2.15976i	0.114333	−	0.0830676i
$677$	1.80415	−	1.31079i	0.0693392	−	0.0503779i	−0.552576	−	0.833463i	$-0.686355\pi$
$677$	1.80415	−	1.31079i	0.0693392	−	0.0503779i	0.621915	+	0.783085i	$0.286355\pi$
$678$	−0.448625	+	1.38072i	−0.0172293	+	0.0530264i
$679$	−5.09976	−	3.70519i	−0.195711	−	0.142192i
$680$	−10.1512	+	7.37531i	−0.389282	+	0.282830i
$681$	2.53293	+	1.84028i	0.0970621	+	0.0705197i
$682$	−27.9013			−1.06840
$683$	9.01944	+	6.55301i	0.345119	+	0.250744i	0.746819	−	0.665028i	$-0.231580\pi$
$683$	9.01944	+	6.55301i	0.345119	+	0.250744i	−0.401699	+	0.915772i	$0.631580\pi$
$684$	−5.98168			−0.228715
$685$	12.7453			0.486972
$686$	−13.4731	−	9.78880i	−0.514407	−	0.373738i
$687$	−1.10791	+	3.40980i	−0.0422695	+	0.130092i
$688$	−3.33983	+	2.42653i	−0.127330	+	0.0925106i
$689$	−12.0850	−	8.78029i	−0.460403	−	0.334502i
$690$	0.0284909	+	0.0876861i	0.00108463	+	0.00333815i
$691$	−0.123239	+	0.379292i	−0.00468825	+	0.0144289i	−0.953373	−	0.301794i	$-0.902415\pi$
$691$	−0.123239	+	0.379292i	−0.00468825	+	0.0144289i	0.948685	+	0.316223i	$0.102415\pi$
$692$	−1.43866			−0.0546897
$693$	3.99153	+	12.2847i	0.151626	+	0.466656i
$694$	24.1065	−	17.5144i	0.915070	−	0.664837i
$695$	14.1498	−	43.5487i	0.536734	−	1.65190i
$696$	−0.192279	+	0.591774i	−0.00728832	+	0.0224312i
$697$	16.9396	+	52.1348i	0.641634	+	1.97475i
$698$	−18.3334	−	13.3200i	−0.693929	−	0.504169i
$699$	−1.85473	−	5.70829i	−0.0701525	−	0.215907i
$700$	−1.55180			−0.0586527
$701$	−7.88907	+	24.2801i	−0.297966	+	0.917046i	0.684243	+	0.729254i	$0.260133\pi$
$701$	−7.88907	+	24.2801i	−0.297966	+	0.917046i	−0.982209	+	0.187791i	$0.939867\pi$
$702$	1.36033	−	4.18667i	0.0513424	−	0.158016i
$703$	−11.2771			−0.425325
$704$	−0.986727	−	3.03683i	−0.0371887	−	0.114455i
$705$	−3.46619	−	2.51834i	−0.130544	−	0.0948460i
$706$	−6.98161	−	21.4872i	−0.262756	−	0.808681i
$707$	0.611250	−	1.88124i	0.0229884	−	0.0707511i
$708$	−0.226010	+	0.695587i	−0.00849397	+	0.0261418i
$709$	14.6864	−	10.6703i	0.551558	−	0.400730i	−0.276802	−	0.960927i	$-0.589275\pi$
$709$	14.6864	−	10.6703i	0.551558	−	0.400730i	0.828360	+	0.560197i	$0.189275\pi$
$710$	2.16371	+	6.65921i	0.0812025	+	0.249916i
$711$	39.8117			1.49305
$712$	−4.16333	+	12.8134i	−0.156027	+	0.480203i
$713$	−0.521445	−	1.60484i	−0.0195283	−	0.0601018i
$714$	1.72167	+	1.25086i	0.0644318	+	0.0468124i
$715$	−15.5226	+	11.2778i	−0.580512	+	0.421766i
$716$	−7.88987	+	24.2825i	−0.294858	+	0.907480i
$717$	−1.57237	−	1.14239i	−0.0587211	−	0.0426633i
$718$	6.46928			0.241432
$719$	−21.5791			−0.804766			−0.402383	−	0.915471i	$-0.631818\pi$
$719$	−21.5791			−0.804766			−0.402383	+	0.915471i	$0.631818\pi$
$720$	−4.68193	−	3.40162i	−0.174485	−	0.126771i
$721$	6.21876			0.231599
$722$	−12.0249	−	8.73662i	−0.447522	−	0.325143i
$723$	0.298465	−	0.216848i	0.0111000	−	0.00806465i
$724$	4.13102	+	3.00136i	0.153528	+	0.111545i
$725$	−0.894100	+	2.75176i	−0.0332060	+	0.102198i
$726$	−0.157825	+	0.114667i	−0.00585745	+	0.00425569i
$727$	−19.2820	+	14.0092i	−0.715129	+	0.519571i	−0.884824	−	0.465925i	$-0.845722\pi$
$727$	−19.2820	+	14.0092i	−0.715129	+	0.519571i	0.169695	+	0.985497i	$0.445722\pi$
$728$	3.39801	−	2.46880i	0.125939	−	0.0914997i
$729$	−7.37707	−	22.7043i	−0.273225	−	0.840899i
$730$	4.90599	+	15.0991i	0.181579	+	0.558842i
$731$	26.3254			0.973680
$732$	−1.70959	+	0.817611i	−0.0631884	+	0.0302198i
$733$	−41.4489			−1.53095			−0.765475	−	0.643466i	$-0.777496\pi$
$733$	−41.4489			−1.53095			−0.765475	+	0.643466i	$0.777496\pi$
$734$	−10.8729	−	33.4635i	−0.401328	−	1.23516i
$735$	0.753642	+	2.31947i	0.0277985	+	0.0855550i
$736$	0.156233	−	0.113510i	0.00575884	−	0.00418404i
$737$	−24.0577	+	17.4789i	−0.886176	+	0.643845i
$738$	−20.4543	+	14.8609i	−0.752934	+	0.547038i
$739$	−7.25211	+	22.3197i	−0.266773	+	0.821044i	0.724506	+	0.689268i	$0.242068\pi$
$739$	−7.25211	+	22.3197i	−0.266773	+	0.821044i	−0.991280	+	0.131776i	$0.957932\pi$
$740$	−8.82672	−	6.41299i	−0.324477	−	0.235746i
$741$	−1.21916	+	0.885771i	−0.0447870	+	0.0325396i
$742$	5.44299	+	3.95456i	0.199819	+	0.145177i
$743$	21.4187			0.785776			0.392888	−	0.919586i	$-0.371476\pi$
$743$	21.4187			0.785776			0.392888	+	0.919586i	$0.371476\pi$
$744$	−1.71523	−	1.24619i	−0.0628834	−	0.0456874i
$745$	−35.3594			−1.29547
$746$	−11.4947			−0.420851
$747$	13.7533	+	9.99236i	0.503207	+	0.365601i
$748$	−6.29224	+	19.3655i	−0.230067	+	0.708073i
$749$	−17.4359	+	12.6679i	−0.637095	+	0.462877i
$750$	2.36702	+	1.71974i	0.0864315	+	0.0627962i
$751$	4.64746	+	14.3034i	0.169588	+	0.521938i	0.999345	−	0.0361865i	$-0.0115210\pi$
$751$	4.64746	+	14.3034i	0.169588	+	0.521938i	−0.829757	+	0.558125i	$0.811521\pi$
$752$	−2.77312	+	8.53480i	−0.101125	+	0.311232i
$753$	5.00002			0.182211
$754$	−2.42000	−	7.44800i	−0.0881313	−	0.271240i
$755$	−20.8089	+	15.1185i	−0.757313	+	0.550220i
$756$	−0.612681	+	1.88564i	−0.0222830	+	0.0685800i
$757$	4.17395	−	12.8461i	0.151705	−	0.466899i	−0.846107	−	0.533012i	$-0.821060\pi$
$757$	4.17395	−	12.8461i	0.151705	−	0.466899i	0.997812	+	0.0661133i	$0.0210599\pi$
$758$	7.67597	+	23.6242i	0.278804	+	0.858070i
$759$	0.121044	+	0.0879437i	0.00439362	+	0.00319215i
$760$	1.23665	+	3.80600i	0.0448578	+	0.138058i
$761$	−27.3461			−0.991297			−0.495648	−	0.868523i	$-0.665070\pi$
$761$	−27.3461			−0.991297			−0.495648	+	0.868523i	$0.665070\pi$
$762$	−0.459771	+	1.41503i	−0.0166557	+	0.0512611i
$763$	0.636786	−	1.95982i	0.0230532	−	0.0709504i
$764$	−24.2423			−0.877056
$765$	11.4040	+	35.0979i	0.412313	+	1.26897i
$766$	−15.5030	−	11.2636i	−0.560145	−	0.406969i
$767$	−2.84453	−	8.75457i	−0.102710	−	0.316109i
$768$	0.0749786	−	0.230760i	0.00270556	−	0.00832685i
$769$	9.85410	−	30.3278i	0.355348	−	1.09365i	−0.600460	−	0.799655i	$-0.705016\pi$
$769$	9.85410	−	30.3278i	0.355348	−	1.09365i	0.955808	−	0.293993i	$-0.0949843\pi$
$770$	6.99123	−	5.07943i	0.251947	−	0.183050i
$771$	−0.0976372	−	0.300496i	−0.00351632	−	0.0108221i
$772$	26.3629			0.948823
$773$	6.49843	−	20.0001i	0.233732	−	0.719354i	−0.763555	−	0.645743i	$-0.776548\pi$
$773$	6.49843	−	20.0001i	0.233732	−	0.719354i	0.997287	−	0.0736111i	$-0.0234523\pi$
$774$	3.75200	+	11.5475i	0.134863	+	0.415065i
$775$	−7.97583	−	5.79478i	−0.286500	−	0.208155i
$776$	3.70784	−	2.69391i	0.133104	−	0.0967056i
$777$	−0.571814	+	1.75986i	−0.0205137	+	0.0631347i
$778$	14.3393	+	10.4181i	0.514089	+	0.373507i
$779$	17.4833			0.626404
$780$	−1.45796			−0.0522035
$781$	9.19254	+	6.67877i	0.328935	+	0.238985i
$782$	−1.23147			−0.0440373
$783$	2.99072	+	2.17289i	0.106880	+	0.0776527i
$784$	4.13269	−	3.00257i	0.147596	−	0.107235i
$785$	4.11046	+	2.98642i	0.146708	+	0.106590i
$786$	0.413201	−	1.27170i	0.0147384	−	0.0453601i
$787$	15.5632	−	11.3074i	0.554770	−	0.403064i	−0.274771	−	0.961510i	$-0.588602\pi$
$787$	15.5632	−	11.3074i	0.554770	−	0.403064i	0.829541	+	0.558446i	$0.188602\pi$
$788$	17.5015	−	12.7156i	0.623464	−	0.452973i
$789$	−1.12067	+	0.814214i	−0.0398969	+	0.0289868i
$790$	−8.23061	−	25.3312i	−0.292832	−	0.901244i
$791$	2.54306	+	7.82674i	0.0904208	+	0.278287i
$792$	−9.39136			−0.333707
$793$	11.3589	−	20.9723i	0.403366	−	0.744748i
$794$	3.12922			0.111052
$795$	−0.721676	−	2.22109i	−0.0255952	−	0.0787739i
$796$	−6.58132	−	20.2552i	−0.233269	−	0.717928i
$797$	−15.9937	+	11.6201i	−0.566524	+	0.411604i	−0.833841	−	0.552005i	$-0.813863\pi$
$797$	−15.9937	+	11.6201i	−0.566524	+	0.411604i	0.267317	+	0.963609i	$0.413863\pi$
$798$	0.549099	−	0.398944i	0.0194379	−	0.0141225i
$799$	46.2970	−	33.6367i	1.63787	−	1.18998i
$800$	0.348651	−	1.07304i	0.0123267	−	0.0379376i
$801$	32.0575	+	23.2911i	1.13270	+	0.822952i
$802$	−4.26108	+	3.09586i	−0.150464	+	0.109319i
$803$	20.8432	+	15.1434i	0.735539	+	0.534400i
$804$	−2.25963			−0.0796908
$805$	0.422820	+	0.307197i	0.0149024	+	0.0108273i
$806$	26.6838			0.939898
$807$	−6.37757			−0.224501
$808$	1.16350	+	0.845331i	0.0409317	+	0.0297387i
$809$	−4.92946	+	15.1713i	−0.173310	+	0.533395i	−0.999552	−	0.0299209i	$-0.990474\pi$
$809$	−4.92946	+	15.1713i	−0.173310	+	0.533395i	0.826242	+	0.563316i	$0.190474\pi$
$810$	−13.4890	+	9.80033i	−0.473955	+	0.344348i
$811$	2.60583	+	1.89325i	0.0915030	+	0.0664808i	0.632596	−	0.774482i	$-0.281989\pi$
$811$	2.60583	+	1.89325i	0.0915030	+	0.0664808i	−0.541093	+	0.840963i	$0.681989\pi$
$812$	1.08995	+	3.35451i	0.0382497	+	0.117720i
$813$	0.177768	−	0.547112i	0.00623458	−	0.0191881i
$814$	−17.7053			−0.620570
$815$	−8.03740	−	24.7366i	−0.281538	−	0.866484i
$816$	−1.25176	+	0.909456i	−0.0438203	+	0.0318373i
$817$	2.59453	−	7.98515i	0.0907711	−	0.279365i
$818$	−4.67171	+	14.3781i	−0.163343	+	0.502717i
$819$	−3.81736	−	11.7486i	−0.133389	−	0.410530i
$820$	13.6843	+	9.94226i	0.477878	+	0.347199i
$821$	0.308223	+	0.948614i	0.0107571	+	0.0331069i	0.956291	−	0.292417i	$-0.0944594\pi$
$821$	0.308223	+	0.948614i	0.0107571	+	0.0331069i	−0.945534	+	0.325524i	$0.894459\pi$
$822$	1.57163			0.0548170
$823$	−9.59560	+	29.5322i	−0.334482	+	1.02943i	0.632495	+	0.774564i	$0.282031\pi$
$823$	−9.59560	+	29.5322i	−0.334482	+	1.02943i	−0.966977	+	0.254865i	$0.917969\pi$
$824$	−1.39720	+	4.30013i	−0.0486736	+	0.149802i
$825$	0.874134			0.0304334
$826$	1.28115	+	3.94298i	0.0445770	+	0.137194i
$827$	8.09740	+	5.88311i	0.281574	+	0.204576i	0.719604	−	0.694385i	$-0.244323\pi$
$827$	8.09740	+	5.88311i	0.281574	+	0.204576i	−0.438030	+	0.898961i	$0.644323\pi$
$828$	−0.175514	−	0.540178i	−0.00609954	−	0.0187725i
$829$	−11.5333	+	35.4957i	−0.400567	+	1.23282i	0.523974	+	0.851734i	$0.324449\pi$
$829$	−11.5333	+	35.4957i	−0.400567	+	1.23282i	−0.924541	+	0.381083i	$0.875551\pi$
$830$	3.51456	−	10.8167i	0.121992	−	0.375453i
$831$	3.11148	−	2.26063i	0.107936	−	0.0784202i
$832$	0.943671	+	2.90432i	0.0327159	+	0.100689i
$833$	−32.5749			−1.12865
$834$	1.74483	−	5.37004i	0.0604185	−	0.185949i
$835$	−12.5537	−	38.6363i	−0.434439	−	1.33707i
$836$	5.25390	+	3.81718i	0.181710	+	0.132020i
$837$	−10.1904	+	7.40376i	−0.352232	+	0.255911i
$838$	−3.76998	+	11.6028i	−0.130232	+	0.400813i
$839$	−0.0938912	−	0.0682159i	−0.00324148	−	0.00235508i	0.586163	−	0.810193i	$-0.300638\pi$
$839$	−0.0938912	−	0.0682159i	−0.00324148	−	0.00235508i	−0.589405	+	0.807838i	$0.700638\pi$
$840$	0.656654			0.0226567
$841$	−22.4236			−0.773227
$842$	2.68543	+	1.95108i	0.0925459	+	0.0672385i
$843$	−7.09806			−0.244470
$844$	15.0805	+	10.9566i	0.519092	+	0.377142i
$845$	−5.84921	+	4.24970i	−0.201219	+	0.146194i
$846$	21.3530	+	15.5138i	0.734131	+	0.533377i
$847$	−0.341724	+	1.05172i	−0.0117418	+	0.0361375i
$848$	−3.95739	+	2.87521i	−0.135897	+	0.0987353i
$849$	−2.72582	+	1.98043i	−0.0935499	+	0.0679680i
$850$	−5.82069	+	4.22898i	−0.199648	+	0.145053i
$851$	−0.330893	−	1.01838i	−0.0113429	−	0.0349097i
$852$	0.266809	+	0.821154i	0.00914073	+	0.0281323i
$853$	43.5595			1.49145			0.745725	−	0.666254i	$-0.232103\pi$
$853$	43.5595			1.49145			0.745725	+	0.666254i	$0.232103\pi$
$854$	−5.11595	+	9.44574i	−0.175064	+	0.323227i
$855$	11.7700			0.402526
$856$	−4.84219	−	14.9027i	−0.165503	−	0.509364i
$857$	4.82666	+	14.8549i	0.164875	+	0.507434i	0.999027	−	0.0441007i	$-0.0140423\pi$
$857$	4.82666	+	14.8549i	0.164875	+	0.507434i	−0.834152	+	0.551535i	$0.814042\pi$
$858$	−1.91410	+	1.39068i	−0.0653464	+	0.0474770i
$859$	−39.6170	+	28.7834i	−1.35171	+	0.982078i	−0.352790	+	0.935702i	$0.614767\pi$
$859$	−39.6170	+	28.7834i	−1.35171	+	0.982078i	−0.998924	+	0.0463756i	$0.985233\pi$
$860$	6.57170	−	4.77462i	0.224093	−	0.162813i
$861$	0.886501	−	2.72837i	0.0302119	−	0.0929826i
$862$	−26.2661	−	19.0835i	−0.894628	−	0.649985i
$863$	7.35390	−	5.34292i	0.250330	−	0.181875i	−0.455543	−	0.890214i	$-0.650555\pi$
$863$	7.35390	−	5.34292i	0.250330	−	0.181875i	0.705873	+	0.708339i	$0.250555\pi$
$864$	−1.16622	−	0.847310i	−0.0396757	−	0.0288261i
$865$	2.83082			0.0962507
$866$	10.1119	+	7.34670i	0.343615	+	0.249651i
$867$	5.74188			0.195004
$868$	−12.0182			−0.407923
$869$	−34.9678	−	25.4056i	−1.18620	−	0.861826i
$870$	0.378343	−	1.16442i	0.0128270	−	0.0394775i
$871$	23.0079	−	16.7162i	0.779594	−	0.566408i
$872$	1.21210	+	0.880645i	0.0410470	+	0.0298224i
$873$	−4.16543	−	12.8199i	−0.140979	−	0.433887i
$874$	−0.121369	+	0.373536i	−0.00410537	+	0.0126350i
$875$	16.5851			0.560679
$876$	0.604963	+	1.86188i	0.0204398	+	0.0629072i
$877$	1.35864	−	0.987110i	0.0458780	−	0.0333323i	−0.564610	−	0.825358i	$-0.690973\pi$
$877$	1.35864	−	0.987110i	0.0458780	−	0.0333323i	0.610488	+	0.792026i	$0.290973\pi$
$878$	4.29415	−	13.2160i	0.144921	−	0.446020i
$879$	−0.811922	+	2.49884i	−0.0273854	+	0.0842837i
$880$	1.94156	+	5.97550i	0.0654499	+	0.201434i
$881$	7.07597	+	5.14099i	0.238395	+	0.173204i	0.700568	−	0.713586i	$-0.252930\pi$
$881$	7.07597	+	5.14099i	0.238395	+	0.173204i	−0.462173	+	0.886790i	$0.652930\pi$
$882$	−4.64270	−	14.2888i	−0.156328	−	0.481128i
$883$	52.0042			1.75008			0.875040	−	0.484050i	$-0.160835\pi$
$883$	52.0042			1.75008			0.875040	+	0.484050i	$0.160835\pi$
$884$	6.01768	−	18.5205i	0.202396	−	0.622912i
$885$	0.444714	−	1.36869i	0.0149489	−	0.0460080i
$886$	25.8888			0.869753
$887$	−13.8233	−	42.5437i	−0.464140	−	1.42848i	−0.860061	−	0.510192i	$-0.829574\pi$
$887$	−13.8233	−	42.5437i	−0.464140	−	1.42848i	0.395921	−	0.918285i	$-0.370426\pi$
$888$	−1.08843	−	0.790792i	−0.0365254	−	0.0265372i
$889$	2.60624	+	8.02119i	0.0874105	+	0.269022i
$890$	8.19207	−	25.2126i	0.274599	−	0.845128i
$891$	−8.36114	+	25.7330i	−0.280109	+	0.862087i
$892$	20.6264	−	14.9860i	0.690623	−	0.501767i
$893$	−5.64000	−	17.3581i	−0.188735	−	0.580868i
$894$	−4.36020			−0.145827
$895$	15.5247	−	47.7801i	0.518933	−	1.59711i
$896$	−0.425021	−	1.30808i	−0.0141990	−	0.0436999i
$897$	−0.115762	−	0.0841063i	−0.00386519	−	0.00280823i
$898$	−17.8850	+	12.9942i	−0.596831	+	0.433623i
$899$	−6.92448	+	21.3113i	−0.230944	+	0.710773i
$900$	−2.68460	−	1.95048i	−0.0894868	−	0.0650159i
$901$	31.1932			1.03920
$902$	27.4491			0.913955
$903$	−1.11457	−	0.809784i	−0.0370906	−	0.0269479i
$904$	−5.98337			−0.199004
$905$	−8.12849	−	5.90570i	−0.270200	−	0.196312i
$906$	−2.56596	+	1.86428i	−0.0852484	+	0.0619366i
$907$	−48.4429	−	35.1958i	−1.60852	−	1.16866i	−0.867910	−	0.496722i	$-0.834537\pi$
$907$	−48.4429	−	35.1958i	−1.60852	−	1.16866i	−0.740610	−	0.671936i	$-0.765463\pi$
$908$	−3.98743	+	12.2720i	−0.132327	+	0.407262i
$909$	3.42200	−	2.48623i	0.113501	−	0.0824630i
$910$	−6.68617	+	4.85779i	−0.221645	+	0.161034i
$911$	−19.6407	+	14.2698i	−0.650724	+	0.472779i	−0.863518	−	0.504318i	$-0.831744\pi$
$911$	−19.6407	+	14.2698i	−0.650724	+	0.472779i	0.212794	+	0.977097i	$0.431744\pi$
$912$	0.152492	+	0.469322i	0.00504951	+	0.0155408i
$913$	−5.70338	−	17.5532i	−0.188754	−	0.580926i
$914$	19.5328			0.646089
$915$	3.36393	−	1.60879i	0.111208	−	0.0531850i
$916$	−14.7764			−0.488225
$917$	−2.34226	−	7.20873i	−0.0773482	−	0.238053i
$918$	2.84063	+	8.74255i	0.0937547	+	0.288547i
$919$	20.7050	−	15.0431i	0.682995	−	0.496225i	−0.191355	−	0.981521i	$-0.561288\pi$
$919$	20.7050	−	15.0431i	0.682995	−	0.496225i	0.874350	+	0.485296i	$0.161288\pi$
$920$	−0.307416	+	0.223351i	−0.0101352	+	0.00736367i
$921$	−0.621987	+	0.451900i	−0.0204952	+	0.0148906i
$922$	4.72257	−	14.5346i	0.155530	−	0.478671i
$923$	−8.79143	−	6.38735i	−0.289373	−	0.210242i
$924$	0.862096	−	0.626349i	0.0283609	−	0.0206054i
$925$	−5.06122	−	3.67719i	−0.166412	−	0.120905i
$926$	25.7325			0.845622
$927$	10.7584	+	7.81642i	0.353351	+	0.256725i
$928$	−2.56445			−0.0841823
$929$	48.7821			1.60049			0.800244	−	0.599674i	$-0.204703\pi$
$929$	48.7821			1.60049			0.800244	+	0.599674i	$0.204703\pi$
$930$	3.37501	+	2.45209i	0.110671	+	0.0804072i
$931$	−3.21046	+	9.88077i	−0.105218	+	0.323829i
$932$	20.0125	−	14.5400i	0.655532	−	0.476272i
$933$	2.11571	+	1.53715i	0.0692652	+	0.0503241i
$934$	−1.57709	−	4.85379i	−0.0516041	−	0.158821i
$935$	12.3811	−	38.1050i	0.404904	−	1.24617i
$936$	8.98157			0.293572
$937$	15.5377	+	47.8202i	0.507595	+	1.56222i	0.796363	+	0.604819i	$0.206754\pi$
$937$	15.5377	+	47.8202i	0.507595	+	1.56222i	−0.288768	+	0.957399i	$0.593246\pi$
$938$	−10.3626	+	7.52885i	−0.338350	+	0.245826i
$939$	−1.55546	+	4.78722i	−0.0507606	+	0.156225i
$940$	5.45661	−	16.7937i	0.177975	−	0.547750i
$941$	5.66349	+	17.4304i	0.184625	+	0.568216i	0.999942	−	0.0107987i	$-0.00343739\pi$
$941$	5.66349	+	17.4304i	0.184625	+	0.568216i	−0.815317	+	0.579015i	$0.803437\pi$
$942$	0.506864	+	0.368258i	0.0165145	+	0.0119985i
$943$	0.512994	+	1.57883i	0.0167054	+	0.0514139i
$944$	−3.01433			−0.0981079
$945$	1.20556	−	3.71032i	0.0392168	−	0.120697i
$946$	4.07346	−	12.5368i	0.132440	−	0.407608i
$947$	−44.4879			−1.44566			−0.722832	−	0.691024i	$-0.757160\pi$
$947$	−44.4879			−1.44566			−0.722832	+	0.691024i	$0.757160\pi$
$948$	−1.01492	−	3.12362i	−0.0329632	−	0.101450i
$949$	−19.9337	−	14.4827i	−0.647074	−	0.470127i
$950$	0.709089	+	2.18235i	0.0230059	+	0.0708048i
$951$	−1.19032	+	3.66342i	−0.0385986	+	0.118794i
$952$	−2.71031	+	8.34148i	−0.0878417	+	0.270349i
$953$	8.61271	−	6.25750i	0.278993	−	0.202700i	−0.439485	−	0.898250i	$-0.644839\pi$
$953$	8.61271	−	6.25750i	0.278993	−	0.202700i	0.718478	+	0.695550i	$0.244839\pi$
$954$	4.44578	+	13.6827i	0.143937	+	0.442994i
$955$	47.7009			1.54357
$956$	2.47527	−	7.61811i	0.0800561	−	0.246387i
$957$	−0.613970	−	1.88960i	−0.0198468	−	0.0610822i
$958$	6.48975	+	4.71508i	0.209674	+	0.152337i
$959$	7.20746	−	5.23653i	0.232741	−	0.169096i
$960$	−0.147533	+	0.454061i	−0.00476162	+	0.0146548i
$961$	−36.6904	−	26.6571i	−1.18356	−	0.859907i
$962$	16.9327			0.545933
$963$	−46.0864			−1.48511
$964$	1.23009	+	0.893716i	0.0396187	+	0.0287847i
$965$	−51.8737			−1.66987
$966$	0.0521384	+	0.0378807i	0.00167752	+	0.00121879i
$967$	47.4240	−	34.4556i	1.52505	−	1.10802i	0.566143	−	0.824307i	$-0.308435\pi$
$967$	47.4240	−	34.4556i	1.52505	−	1.10802i	0.958910	−	0.283709i	$-0.0915650\pi$
$968$	−0.650462	−	0.472589i	−0.0209067	−	0.0151896i
$969$	0.972423	−	2.99281i	0.0312387	−	0.0961429i
$970$	−7.29583	+	5.30073i	−0.234255	+	0.170196i
$971$	−15.7607	+	11.4508i	−0.505786	+	0.367475i	−0.811223	−	0.584737i	$-0.801198\pi$
$971$	−15.7607	+	11.4508i	−0.505786	+	0.367475i	0.305437	+	0.952212i	$0.401198\pi$
$972$	−5.16201	+	3.75042i	−0.165572	+	0.120295i
$973$	−9.89069	−	30.4404i	−0.317081	−	0.975875i
$974$	7.07780	+	21.7832i	0.226787	+	0.697980i
$975$	−0.835992			−0.0267732
$976$	−5.38209	−	5.65978i	−0.172276	−	0.181165i
$977$	−52.0508			−1.66525			−0.832626	−	0.553835i	$-0.813164\pi$
$977$	−52.0508			−1.66525			−0.832626	+	0.553835i	$0.813164\pi$
$978$	−0.991099	−	3.05029i	−0.0316919	−	0.0975375i
$979$	−13.2940	−	40.9147i	−0.424878	−	1.30764i
$980$	−8.13178	+	5.90808i	−0.259760	+	0.188727i
$981$	3.56495	−	2.59009i	0.113820	−	0.0826952i
$982$	8.75366	−	6.35990i	0.279340	−	0.202953i
$983$	−1.44441	+	4.44545i	−0.0460696	+	0.141788i	−0.971445	−	0.237263i	$-0.923750\pi$
$983$	−1.44441	+	4.44545i	−0.0460696	+	0.141788i	0.925376	+	0.379051i	$0.123750\pi$
$984$	1.68743	+	1.22599i	0.0537933	+	0.0390831i
$985$	−34.4372	+	25.0201i	−1.09726	+	0.797206i
$986$	13.2300	+	9.61218i	0.421330	+	0.306114i
$987$	−2.99482			−0.0953261
$988$	−5.02465	−	3.65062i	−0.159855	−	0.116142i
$989$	0.797229			0.0253504
$990$	18.4791			0.587306
$991$	−25.7254	−	18.6906i	−0.817195	−	0.593727i	0.0987124	−	0.995116i	$-0.468528\pi$
$991$	−25.7254	−	18.6906i	−0.817195	−	0.593727i	−0.915908	+	0.401389i	$0.868528\pi$
$992$	2.70018	−	8.31029i	0.0857307	−	0.263852i
$993$	4.76741	−	3.46373i	0.151289	−	0.109918i
$994$	3.95958	+	2.87680i	0.125590	+	0.0912467i
$995$	12.9499	+	39.8557i	0.410539	+	1.26351i
$996$	0.433384	−	1.33382i	0.0137323	−	0.0422636i
$997$	−15.2331			−0.482438			−0.241219	−	0.970471i	$-0.577547\pi$
$997$	−15.2331			−0.482438			−0.241219	+	0.970471i	$0.577547\pi$
$998$	5.34096	+	16.4378i	0.169065	+	0.520329i
$999$	−6.46651	+	4.69820i	−0.204591	+	0.148644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.e.a.81.2	✓	12
3.2	odd	2		1098.2.k.j.325.1		12
4.3	odd	2		976.2.v.b.81.2		12
61.27	even	10		7442.2.a.o.1.3		6
61.34	even	5		7442.2.a.n.1.3		6
61.58	even	5	inner	122.2.e.a.119.2	yes	12
183.119	odd	10		1098.2.k.j.973.1		12
244.119	odd	10		976.2.v.b.241.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.e.a.81.2	✓	12	1.1	even	1	trivial
122.2.e.a.119.2	yes	12	61.58	even	5	inner
976.2.v.b.81.2		12	4.3	odd	2
976.2.v.b.241.2		12	244.119	odd	10
1098.2.k.j.325.1		12	3.2	odd	2
1098.2.k.j.973.1		12	183.119	odd	10
7442.2.a.n.1.3		6	61.34	even	5
7442.2.a.o.1.3		6	61.27	even	10

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.0749786 + 0.230760i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.59188 - 1.15657i) q^{5} +(0.196297 - 0.142618i) q^{6} +(0.425021 - 1.30808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37942 - 1.72875i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.0749786 + 0.230760i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.59188 - 1.15657i) q^{5} +(0.196297 - 0.142618i) q^{6} +(0.425021 - 1.30808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37942 - 1.72875i) q^{9} +(-1.59188 - 1.15657i) q^{10} -3.19312 q^{11} +(-0.196297 - 0.142618i) q^{12} +3.05378 q^{13} -1.37540 q^{14} +(0.386248 + 0.280625i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.15900 + 3.74824i) q^{17} +(-2.37942 - 1.72875i) q^{18} +(0.628481 + 1.93426i) q^{19} +(-0.608045 + 1.87137i) q^{20} +0.333721 q^{21} +(0.986727 + 3.03683i) q^{22} +(-0.156233 + 0.113510i) q^{23} +(-0.0749786 + 0.230760i) q^{24} +(-0.348651 + 1.07304i) q^{25} +(-0.943671 - 2.90432i) q^{26} +(1.16622 + 0.847310i) q^{27} +(0.425021 + 1.30808i) q^{28} +2.56445 q^{29} +(0.147533 - 0.454061i) q^{30} +(-2.70018 + 8.31029i) q^{31} -1.00000 q^{32} +(-0.239415 - 0.736844i) q^{33} +(5.15900 + 3.74824i) q^{34} +(-0.836304 - 2.57388i) q^{35} +(-0.908858 + 2.79718i) q^{36} +(-1.71345 + 5.27345i) q^{37} +(1.64538 - 1.19544i) q^{38} +(0.228969 + 0.704693i) q^{39} +1.96767 q^{40} +(2.65641 - 8.17560i) q^{41} +(-0.103125 - 0.317387i) q^{42} +(-3.33983 - 2.42653i) q^{43} +(2.58328 - 1.87687i) q^{44} +(1.78834 - 5.50394i) q^{45} +(0.156233 + 0.113510i) q^{46} -8.97402 q^{47} +0.242636 q^{48} +(4.13269 + 3.00257i) q^{49} +1.12826 q^{50} +(-1.25176 - 0.909456i) q^{51} +(-2.47056 + 1.79497i) q^{52} +(-3.95739 - 2.87521i) q^{53} +(0.445457 - 1.37098i) q^{54} +(-5.08306 + 3.69306i) q^{55} +(1.11272 - 0.808439i) q^{56} +(-0.399229 + 0.290057i) q^{57} +(-0.792460 - 2.43894i) q^{58} +(-0.931478 - 2.86679i) q^{59} -0.477428 q^{60} +(3.71961 - 6.86764i) q^{61} +8.73795 q^{62} +(-1.25004 - 3.84723i) q^{63} +(0.309017 + 0.951057i) q^{64} +(4.86126 - 3.53192i) q^{65} +(-0.626797 + 0.455395i) q^{66} +(7.53424 - 5.47394i) q^{67} +(1.97056 - 6.06477i) q^{68} +(-0.0379078 - 0.0275416i) q^{69} +(-2.18947 + 1.59074i) q^{70} +(-2.87886 - 2.09162i) q^{71} +2.94113 q^{72} +(-6.52753 - 4.74253i) q^{73} +5.54484 q^{74} -0.273756 q^{75} +(-1.64538 - 1.19544i) q^{76} +(-1.35714 + 4.17685i) q^{77} +(0.599447 - 0.435524i) q^{78} +(10.9510 + 7.95637i) q^{79} +(-0.608045 - 1.87137i) q^{80} +(2.61849 - 8.05889i) q^{81} -8.59634 q^{82} +(1.78615 + 5.49720i) q^{83} +(-0.269986 + 0.196156i) q^{84} +(-3.87743 + 11.9335i) q^{85} +(-1.27570 + 3.92621i) q^{86} +(0.192279 + 0.591774i) q^{87} +(-2.58328 - 1.87687i) q^{88} +(4.16333 + 12.8134i) q^{89} -5.78718 q^{90} +(1.29792 - 3.99460i) q^{91} +(0.0596759 - 0.183663i) q^{92} -2.12014 q^{93} +(2.77312 + 8.53480i) q^{94} +(3.23758 + 2.35224i) q^{95} +(-0.0749786 - 0.230760i) q^{96} +(1.41627 - 4.35883i) q^{97} +(1.57855 - 4.85826i) q^{98} +(-7.59777 + 5.52010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9} + 6 q^{10} - 4 q^{11} + q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 7 q^{17} + 7 q^{18} - 6 q^{19} + 4 q^{20} - 56 q^{21} - q^{22} + 8 q^{23} + 4 q^{24} - 21 q^{25} - 7 q^{26} + 2 q^{27} + 10 q^{28} + 30 q^{29} + 3 q^{30} + q^{31} - 12 q^{32} + 21 q^{33} - 7 q^{34} + 5 q^{35} - 2 q^{36} - 14 q^{38} - 21 q^{39} - 4 q^{40} + 2 q^{41} - 14 q^{42} - 8 q^{43} + q^{44} + 49 q^{45} - 8 q^{46} - 10 q^{47} + 6 q^{48} - 3 q^{49} - 44 q^{50} + 8 q^{51} - 3 q^{52} + 8 q^{53} + 8 q^{54} + 13 q^{55} + 10 q^{56} + 5 q^{57} + 25 q^{58} + 4 q^{59} - 18 q^{60} - 26 q^{61} + 34 q^{62} + 29 q^{63} - 3 q^{64} + 3 q^{65} + 29 q^{66} + 33 q^{67} - 3 q^{68} + 26 q^{69} + 20 q^{70} - 13 q^{71} - 18 q^{72} - 38 q^{73} + 30 q^{74} - 8 q^{75} + 14 q^{76} - 23 q^{77} - 9 q^{78} + 26 q^{79} + 4 q^{80} + 20 q^{81} - 42 q^{82} + 18 q^{83} + 14 q^{84} - 5 q^{85} - 12 q^{86} - 66 q^{87} - q^{88} + 2 q^{89} - 14 q^{90} + 17 q^{91} + 8 q^{92} - 68 q^{93} + 20 q^{94} + 65 q^{95} + 4 q^{96} - 4 q^{97} - 7 q^{98} - 50 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9 + 6 * q^10 - 4 * q^11 + q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 7 * q^17 + 7 * q^18 - 6 * q^19 + 4 * q^20 - 56 * q^21 - q^22 + 8 * q^23 + 4 * q^24 - 21 * q^25 - 7 * q^26 + 2 * q^27 + 10 * q^28 + 30 * q^29 + 3 * q^30 + q^31 - 12 * q^32 + 21 * q^33 - 7 * q^34 + 5 * q^35 - 2 * q^36 - 14 * q^38 - 21 * q^39 - 4 * q^40 + 2 * q^41 - 14 * q^42 - 8 * q^43 + q^44 + 49 * q^45 - 8 * q^46 - 10 * q^47 + 6 * q^48 - 3 * q^49 - 44 * q^50 + 8 * q^51 - 3 * q^52 + 8 * q^53 + 8 * q^54 + 13 * q^55 + 10 * q^56 + 5 * q^57 + 25 * q^58 + 4 * q^59 - 18 * q^60 - 26 * q^61 + 34 * q^62 + 29 * q^63 - 3 * q^64 + 3 * q^65 + 29 * q^66 + 33 * q^67 - 3 * q^68 + 26 * q^69 + 20 * q^70 - 13 * q^71 - 18 * q^72 - 38 * q^73 + 30 * q^74 - 8 * q^75 + 14 * q^76 - 23 * q^77 - 9 * q^78 + 26 * q^79 + 4 * q^80 + 20 * q^81 - 42 * q^82 + 18 * q^83 + 14 * q^84 - 5 * q^85 - 12 * q^86 - 66 * q^87 - q^88 + 2 * q^89 - 14 * q^90 + 17 * q^91 + 8 * q^92 - 68 * q^93 + 20 * q^94 + 65 * q^95 + 4 * q^96 - 4 * q^97 - 7 * q^98 - 50 * q^99

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