LMFDB - Embedded newform 151.2.c.a.32.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(32,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(6))

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("151.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.c (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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 10 x^{10} + x^{9} + 68 x^{8} + 6 x^{7} + 179 x^{6} + 211 x^{5} + 266 x^{4} + 128 x^{3} + \cdots + 1 $ x^12 - x^11 + 10x^10 + x^9 + 68x^8 + 6x^7 + 179x^6 + 211x^5 + 266x^4 + 128x^3 + 47x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			32.5
Root			$-0.182744 - 0.316521i$ of defining polynomial
Character	$\chi$	$=$	151.32
Dual form			151.2.c.a.118.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368036 + 0.637457i) q^{2} +1.32785 q^{3} +(0.729099 - 1.26284i) q^{4} +(-0.697137 - 1.20748i) q^{5} +(0.488697 + 0.846448i) q^{6} +(-0.120119 - 0.208053i) q^{7} +2.54548 q^{8} -1.23681 q^{9} +O(q^{10})$	\(q+(0.368036 + 0.637457i) q^{2} +1.32785 q^{3} +(0.729099 - 1.26284i) q^{4} +(-0.697137 - 1.20748i) q^{5} +(0.488697 + 0.846448i) q^{6} +(-0.120119 - 0.208053i) q^{7} +2.54548 q^{8} -1.23681 q^{9} +(0.513143 - 0.888790i) q^{10} +(0.0188183 + 0.0325942i) q^{11} +(0.968134 - 1.67686i) q^{12} +(-3.10511 + 5.37821i) q^{13} +(0.0884165 - 0.153142i) q^{14} +(-0.925694 - 1.60335i) q^{15} +(-0.521367 - 0.903034i) q^{16} +(2.51569 + 4.35731i) q^{17} +(-0.455192 - 0.788415i) q^{18} -3.37259 q^{19} -2.03313 q^{20} +(-0.159500 - 0.276263i) q^{21} +(-0.0138516 + 0.0239917i) q^{22} +(3.23165 + 5.59738i) q^{23} +3.38002 q^{24} +(1.52800 - 2.64657i) q^{25} -4.57118 q^{26} -5.62585 q^{27} -0.350315 q^{28} +4.31718 q^{29} +(0.681378 - 1.18018i) q^{30} +(-2.94890 - 5.10765i) q^{31} +(2.92925 - 5.07361i) q^{32} +(0.0249879 + 0.0432803i) q^{33} +(-1.85173 + 3.20729i) q^{34} +(-0.167479 + 0.290082i) q^{35} +(-0.901758 + 1.56189i) q^{36} +(-5.07925 - 8.79752i) q^{37} +(-1.24124 - 2.14989i) q^{38} +(-4.12313 + 7.14147i) q^{39} +(-1.77455 - 3.07361i) q^{40} -0.953705 q^{41} +(0.117404 - 0.203350i) q^{42} +(-1.56517 + 2.71096i) q^{43} +0.0548815 q^{44} +(0.862228 + 1.49342i) q^{45} +(-2.37873 + 4.12008i) q^{46} +(0.791018 - 1.37008i) q^{47} +(-0.692298 - 1.19909i) q^{48} +(3.47114 - 6.01220i) q^{49} +2.24944 q^{50} +(3.34046 + 5.78585i) q^{51} +(4.52787 + 7.84250i) q^{52} -9.65415 q^{53} +(-2.07052 - 3.58624i) q^{54} +(0.0262378 - 0.0454453i) q^{55} +(-0.305762 - 0.529595i) q^{56} -4.47830 q^{57} +(1.58888 + 2.75202i) q^{58} +6.45322 q^{59} -2.69969 q^{60} +(1.01486 - 1.75778i) q^{61} +(2.17061 - 3.75960i) q^{62} +(0.148565 + 0.257322i) q^{63} +2.22681 q^{64} +8.65876 q^{65} +(-0.0183929 + 0.0318574i) q^{66} +9.75088 q^{67} +7.33675 q^{68} +(4.29115 + 7.43248i) q^{69} -0.246554 q^{70} +(-1.85813 + 3.21837i) q^{71} -3.14829 q^{72} -0.595531 q^{73} +(3.73869 - 6.47561i) q^{74} +(2.02896 - 3.51425i) q^{75} +(-2.45895 + 4.25903i) q^{76} +(0.00452088 - 0.00783039i) q^{77} -6.06984 q^{78} -4.91715 q^{79} +(-0.726929 + 1.25908i) q^{80} -3.75986 q^{81} +(-0.350998 - 0.607947i) q^{82} +11.4868 q^{83} -0.465166 q^{84} +(3.50756 - 6.07528i) q^{85} -2.30416 q^{86} +5.73257 q^{87} +(0.0479016 + 0.0829681i) q^{88} +(-1.10000 + 1.90526i) q^{89} +(-0.634662 + 1.09927i) q^{90} +1.49194 q^{91} +9.42476 q^{92} +(-3.91570 - 6.78219i) q^{93} +1.16449 q^{94} +(2.35116 + 4.07233i) q^{95} +(3.88960 - 6.73699i) q^{96} +(0.973937 + 1.68691i) q^{97} +5.11003 q^{98} +(-0.0232747 - 0.0403129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 2 q^{3} - 10 q^{4} - 7 q^{5} - 5 q^{6} - 6 q^{7} + 22 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 2 * q^3 - 10 * q^4 - 7 * q^5 - 5 * q^6 - 6 * q^7 + 22 * q^9	\( 12 q - 4 q^{2} - 2 q^{3} - 10 q^{4} - 7 q^{5} - 5 q^{6} - 6 q^{7} + 22 q^{9} - 17 q^{10} + 6 q^{11} + 24 q^{12} - 3 q^{13} + q^{14} + 2 q^{15} - 10 q^{16} + 5 q^{17} - 5 q^{18} - 12 q^{19} - 4 q^{20} + 11 q^{21} - 9 q^{22} + 18 q^{23} + 2 q^{24} - 5 q^{25} - 60 q^{26} - 56 q^{27} + 80 q^{28} + 34 q^{29} + 44 q^{30} + 8 q^{31} + 11 q^{32} - 19 q^{33} - 2 q^{34} + 18 q^{35} - 55 q^{36} + 2 q^{37} + 18 q^{38} + 6 q^{39} - 24 q^{40} + 18 q^{41} - 31 q^{42} - 9 q^{43} - 32 q^{44} - 3 q^{45} + 6 q^{46} + 7 q^{47} + 47 q^{48} - 6 q^{49} + 24 q^{50} + 13 q^{51} - 4 q^{52} - 40 q^{53} + 18 q^{54} + 6 q^{55} - 6 q^{56} + 12 q^{57} + 17 q^{58} - 46 q^{59} - 46 q^{60} + 12 q^{61} + 37 q^{62} - 19 q^{63} - 12 q^{64} - 44 q^{65} + 11 q^{66} + 20 q^{67} - 20 q^{68} - 8 q^{69} + 30 q^{70} + 29 q^{71} - 18 q^{72} - 18 q^{73} + 47 q^{74} + 44 q^{75} + 28 q^{76} - q^{77} + 50 q^{78} - 4 q^{79} - 2 q^{80} + 68 q^{81} - q^{82} + 2 q^{83} - 88 q^{84} - 15 q^{85} - 2 q^{86} - 74 q^{87} - 31 q^{88} - 39 q^{89} - 89 q^{90} + 10 q^{91} - 48 q^{92} - 3 q^{93} + 64 q^{94} + 8 q^{95} + 6 q^{96} - 4 q^{97} - 6 q^{98} + 42 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 - 10 * q^4 - 7 * q^5 - 5 * q^6 - 6 * q^7 + 22 * q^9 - 17 * q^10 + 6 * q^11 + 24 * q^12 - 3 * q^13 + q^14 + 2 * q^15 - 10 * q^16 + 5 * q^17 - 5 * q^18 - 12 * q^19 - 4 * q^20 + 11 * q^21 - 9 * q^22 + 18 * q^23 + 2 * q^24 - 5 * q^25 - 60 * q^26 - 56 * q^27 + 80 * q^28 + 34 * q^29 + 44 * q^30 + 8 * q^31 + 11 * q^32 - 19 * q^33 - 2 * q^34 + 18 * q^35 - 55 * q^36 + 2 * q^37 + 18 * q^38 + 6 * q^39 - 24 * q^40 + 18 * q^41 - 31 * q^42 - 9 * q^43 - 32 * q^44 - 3 * q^45 + 6 * q^46 + 7 * q^47 + 47 * q^48 - 6 * q^49 + 24 * q^50 + 13 * q^51 - 4 * q^52 - 40 * q^53 + 18 * q^54 + 6 * q^55 - 6 * q^56 + 12 * q^57 + 17 * q^58 - 46 * q^59 - 46 * q^60 + 12 * q^61 + 37 * q^62 - 19 * q^63 - 12 * q^64 - 44 * q^65 + 11 * q^66 + 20 * q^67 - 20 * q^68 - 8 * q^69 + 30 * q^70 + 29 * q^71 - 18 * q^72 - 18 * q^73 + 47 * q^74 + 44 * q^75 + 28 * q^76 - q^77 + 50 * q^78 - 4 * q^79 - 2 * q^80 + 68 * q^81 - q^82 + 2 * q^83 - 88 * q^84 - 15 * q^85 - 2 * q^86 - 74 * q^87 - 31 * q^88 - 39 * q^89 - 89 * q^90 + 10 * q^91 - 48 * q^92 - 3 * q^93 + 64 * q^94 + 8 * q^95 + 6 * q^96 - 4 * q^97 - 6 * q^98 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.368036	+	0.637457i	0.260241	+	0.450750i	0.966306	−	0.257397i	$-0.0828647\pi$
$2$	0.368036	+	0.637457i	0.260241	+	0.450750i	−0.706065	+	0.708147i	$0.749531\pi$
$3$	1.32785			0.766635			0.383318	−	0.923617i	$-0.374782\pi$
$3$	1.32785			0.766635			0.383318	+	0.923617i	$0.374782\pi$
$4$	0.729099	−	1.26284i	0.364549	−	0.631418i
$5$	−0.697137	−	1.20748i	−0.311769	−	0.540000i	0.666976	−	0.745079i	$-0.267588\pi$
$5$	−0.697137	−	1.20748i	−0.311769	−	0.540000i	−0.978745	+	0.205079i	$0.934255\pi$
$6$	0.488697	+	0.846448i	0.199510	+	0.345561i
$7$	−0.120119	−	0.208053i	−0.0454008	−	0.0786365i	0.842432	−	0.538803i	$-0.181123\pi$
$7$	−0.120119	−	0.208053i	−0.0454008	−	0.0786365i	−0.887833	+	0.460166i	$0.847790\pi$
$8$	2.54548			0.899964
$9$	−1.23681			−0.412271
$10$	0.513143	−	0.888790i	0.162270	−	0.281060i
$11$	0.0188183	+	0.0325942i	0.00567393	+	0.00982753i	0.868848	−	0.495078i	$-0.164861\pi$
$11$	0.0188183	+	0.0325942i	0.00567393	+	0.00982753i	−0.863175	+	0.504906i	$0.831527\pi$
$12$	0.968134	−	1.67686i	0.279476	−	0.484067i
$13$	−3.10511	+	5.37821i	−0.861204	+	1.49165i	0.00956445	+	0.999954i	$0.496955\pi$
$13$	−3.10511	+	5.37821i	−0.861204	+	1.49165i	−0.870768	+	0.491694i	$0.836378\pi$
$14$	0.0884165	−	0.153142i	0.0236303	−	0.0409289i
$15$	−0.925694	−	1.60335i	−0.239013	−	0.413983i
$16$	−0.521367	−	0.903034i	−0.130342	−	0.225759i
$17$	2.51569	+	4.35731i	0.610145	+	1.05680i	0.991216	+	0.132256i	$0.0422221\pi$
$17$	2.51569	+	4.35731i	0.610145	+	1.05680i	−0.381071	+	0.924546i	$0.624445\pi$
$18$	−0.455192	−	0.788415i	−0.107290	−	0.185831i
$19$	−3.37259			−0.773726			−0.386863	−	0.922137i	$-0.626441\pi$
$19$	−3.37259			−0.773726			−0.386863	+	0.922137i	$0.626441\pi$
$20$	−2.03313			−0.454621
$21$	−0.159500	−	0.276263i	−0.0348059	−	0.0602855i
$22$	−0.0138516	+	0.0239917i	−0.00295317	+	0.00511505i
$23$	3.23165	+	5.59738i	0.673845	+	1.16713i	0.976805	+	0.214131i	$0.0686918\pi$
$23$	3.23165	+	5.59738i	0.673845	+	1.16713i	−0.302960	+	0.953003i	$0.597975\pi$
$24$	3.38002			0.689944
$25$	1.52800	−	2.64657i	0.305600	−	0.529315i
$26$	−4.57118			−0.896482
$27$	−5.62585			−1.08270
$28$	−0.350315			−0.0662033
$29$	4.31718			0.801681			0.400840	−	0.916148i	$-0.368718\pi$
$29$	4.31718			0.801681			0.400840	+	0.916148i	$0.368718\pi$
$30$	0.681378	−	1.18018i	0.124402	−	0.215471i
$31$	−2.94890	−	5.10765i	−0.529638	−	0.917361i	−0.999402	−	0.0345685i	$-0.988994\pi$
$31$	−2.94890	−	5.10765i	−0.529638	−	0.917361i	0.469764	−	0.882792i	$-0.344339\pi$
$32$	2.92925	−	5.07361i	0.517823	−	0.896895i
$33$	0.0249879	+	0.0432803i	0.00434983	+	0.00753413i
$34$	−1.85173	+	3.20729i	−0.317569	+	0.550046i
$35$	−0.167479	+	0.290082i	−0.0283091	+	0.0490329i
$36$	−0.901758	+	1.56189i	−0.150293	+	0.260315i
$37$	−5.07925	−	8.79752i	−0.835023	−	1.44630i	−0.894011	−	0.448044i	$-0.852121\pi$
$37$	−5.07925	−	8.79752i	−0.835023	−	1.44630i	0.0589882	−	0.998259i	$-0.481213\pi$
$38$	−1.24124	−	2.14989i	−0.201355	−	0.348758i
$39$	−4.12313	+	7.14147i	−0.660229	+	1.14355i
$40$	−1.77455	−	3.07361i	−0.280581	−	0.485981i
$41$	−0.953705			−0.148944			−0.0744719	−	0.997223i	$-0.523727\pi$
$41$	−0.953705			−0.148944			−0.0744719	+	0.997223i	$0.523727\pi$
$42$	0.117404	−	0.203350i	0.0181158	−	0.0313775i
$43$	−1.56517	+	2.71096i	−0.238687	+	0.413417i	−0.960338	−	0.278840i	$-0.910050\pi$
$43$	−1.56517	+	2.71096i	−0.238687	+	0.413417i	0.721651	+	0.692257i	$0.243384\pi$
$44$	0.0548815			0.00827370
$45$	0.862228	+	1.49342i	0.128533	+	0.222626i
$46$	−2.37873	+	4.12008i	−0.350724	+	0.607472i
$47$	0.791018	−	1.37008i	0.115382	−	0.199847i	−0.802550	−	0.596584i	$-0.796524\pi$
$47$	0.791018	−	1.37008i	0.115382	−	0.199847i	0.917932	+	0.396737i	$0.129857\pi$
$48$	−0.692298	−	1.19909i	−0.0999246	−	0.173074i
$49$	3.47114	−	6.01220i	0.495878	−	0.858885i
$50$	2.24944			0.318118
$51$	3.34046	+	5.78585i	0.467759	+	0.810182i
$52$	4.52787	+	7.84250i	0.627902	+	1.08756i
$53$	−9.65415			−1.32610			−0.663050	−	0.748575i	$-0.730738\pi$
$53$	−9.65415			−1.32610			−0.663050	+	0.748575i	$0.730738\pi$
$54$	−2.07052	−	3.58624i	−0.281762	−	0.488026i
$55$	0.0262378	−	0.0454453i	0.00353791	−	0.00612784i
$56$	−0.305762	−	0.529595i	−0.0408591	−	0.0707701i
$57$	−4.47830			−0.593166
$58$	1.58888	+	2.75202i	0.208630	+	0.361358i
$59$	6.45322			0.840138			0.420069	−	0.907492i	$-0.362006\pi$
$59$	6.45322			0.840138			0.420069	+	0.907492i	$0.362006\pi$
$60$	−2.69969			−0.348528
$61$	1.01486	−	1.75778i	0.129939	−	0.225061i	−0.793714	−	0.608292i	$-0.791855\pi$
$61$	1.01486	−	1.75778i	0.129939	−	0.225061i	0.923653	+	0.383230i	$0.125188\pi$
$62$	2.17061	−	3.75960i	0.275667	−	0.477470i
$63$	0.148565	+	0.257322i	0.0187174	+	0.0324195i
$64$	2.22681			0.278351
$65$	8.65876			1.07399
$66$	−0.0183929	+	0.0318574i	−0.00226401	+	0.00392138i
$67$	9.75088			1.19126			0.595630	−	0.803259i	$-0.296903\pi$
$67$	9.75088			1.19126			0.595630	+	0.803259i	$0.296903\pi$
$68$	7.33675			0.889712
$69$	4.29115	+	7.43248i	0.516593	+	0.894766i
$70$	−0.246554			−0.0294688
$71$	−1.85813	+	3.21837i	−0.220519	+	0.381951i	−0.954966	−	0.296716i	$-0.904109\pi$
$71$	−1.85813	+	3.21837i	−0.220519	+	0.381951i	0.734447	+	0.678667i	$0.237442\pi$
$72$	−3.14829			−0.371029
$73$	−0.595531			−0.0697016			−0.0348508	−	0.999393i	$-0.511096\pi$
$73$	−0.595531			−0.0697016			−0.0348508	+	0.999393i	$0.511096\pi$
$74$	3.73869	−	6.47561i	0.434614	−	0.752774i
$75$	2.02896	−	3.51425i	0.234284	−	0.405791i
$76$	−2.45895	+	4.25903i	−0.282061	+	0.488545i
$77$	0.00452088	−	0.00783039i	0.000515202	−	0.000892355i
$78$	−6.06984			−0.687274
$79$	−4.91715			−0.553223			−0.276611	−	0.960982i	$-0.589211\pi$
$79$	−4.91715			−0.553223			−0.276611	+	0.960982i	$0.589211\pi$
$80$	−0.726929	+	1.25908i	−0.0812731	+	0.140769i
$81$	−3.75986			−0.417762
$82$	−0.350998	−	0.607947i	−0.0387613	−	0.0671365i
$83$	11.4868			1.26084			0.630421	−	0.776253i	$-0.282882\pi$
$83$	11.4868			1.26084			0.630421	+	0.776253i	$0.282882\pi$
$84$	−0.465166			−0.0507538
$85$	3.50756	−	6.07528i	0.380449	−	0.658957i
$86$	−2.30416			−0.248464
$87$	5.73257			0.614597
$88$	0.0479016	+	0.0829681i	0.00510633	+	0.00884442i
$89$	−1.10000	+	1.90526i	−0.116600	+	0.201957i	−0.918418	−	0.395611i	$-0.870533\pi$
$89$	−1.10000	+	1.90526i	−0.116600	+	0.201957i	0.801818	+	0.597568i	$0.203866\pi$
$90$	−0.634662	+	1.09927i	−0.0668992	+	0.115873i
$91$	1.49194			0.156397
$92$	9.42476			0.982599
$93$	−3.91570	−	6.78219i	−0.406039	−	0.703281i
$94$	1.16449			0.120108
$95$	2.35116	+	4.07233i	0.241224	+	0.417812i
$96$	3.88960	−	6.73699i	0.396981	−	0.687591i
$97$	0.973937	+	1.68691i	0.0988883	+	0.171280i	0.911225	−	0.411910i	$-0.135138\pi$
$97$	0.973937	+	1.68691i	0.0988883	+	0.171280i	−0.812336	+	0.583189i	$0.801805\pi$
$98$	5.11003			0.516190
$99$	−0.0232747	−	0.0403129i	−0.00233919	−	0.00405160i
$100$	−2.22813	−	3.85923i	−0.222813	−	0.385923i
$101$	−13.5873			−1.35199			−0.675994	−	0.736907i	$-0.736286\pi$
$101$	−13.5873			−1.35199			−0.675994	+	0.736907i	$0.736286\pi$
$102$	−2.45882	+	4.25881i	−0.243460	+	0.421685i
$103$	6.63128	+	11.4857i	0.653399	+	1.13172i	0.982293	+	0.187354i	$0.0599910\pi$
$103$	6.63128	+	11.4857i	0.653399	+	1.13172i	−0.328893	+	0.944367i	$0.606676\pi$
$104$	−7.90402	+	13.6902i	−0.775053	+	1.34243i
$105$	−0.222387	+	0.385186i	−0.0217028	+	0.0375903i
$106$	−3.55308	−	6.15411i	−0.345105	−	0.597740i
$107$	9.46932			0.915434			0.457717	−	0.889098i	$-0.348667\pi$
$107$	9.46932			0.915434			0.457717	+	0.889098i	$0.348667\pi$
$108$	−4.10180	+	7.10453i	−0.394696	+	0.683634i
$109$	−5.42925	+	9.40373i	−0.520028	+	0.900714i	0.479701	+	0.877432i	$0.340745\pi$
$109$	−5.42925	+	9.40373i	−0.520028	+	0.900714i	−0.999729	+	0.0232824i	$0.992588\pi$
$110$	0.0386259			0.00368284
$111$	−6.74448	−	11.6818i	−0.640158	−	1.10879i
$112$	−0.125252	+	0.216944i	−0.0118352	+	0.0204992i
$113$	−2.88394	−	4.99513i	−0.271298	−	0.469902i	0.697896	−	0.716199i	$-0.254120\pi$
$113$	−2.88394	−	4.99513i	−0.271298	−	0.469902i	−0.969194	+	0.246297i	$0.920786\pi$
$114$	−1.64818	−	2.85473i	−0.154366	−	0.267370i
$115$	4.50580	−	7.80428i	0.420168	−	0.727753i
$116$	3.14765	−	5.45189i	0.292252	−	0.506196i
$117$	3.84044	−	6.65184i	0.355049	−	0.614963i
$118$	2.37502	+	4.11365i	0.218638	+	0.378692i
$119$	0.604366	−	1.04679i	0.0554022	−	0.0959594i
$120$	−2.35634	−	4.08130i	−0.215103	−	0.372570i
$121$	5.49929	−	9.52505i	0.499936	−	0.865914i
$122$	1.49402			0.135262
$123$	−1.26638			−0.114186
$124$	−8.60016			−0.772317
$125$	−11.2323			−1.00464
$126$	−0.109355	+	0.189408i	−0.00974208	+	0.0168738i
$127$	−14.8230			−1.31532			−0.657662	−	0.753313i	$-0.728455\pi$
$127$	−14.8230			−1.31532			−0.657662	+	0.753313i	$0.728455\pi$
$128$	−5.03895	−	8.72772i	−0.445384	−	0.771428i
$129$	−2.07832	+	3.59975i	−0.182986	+	0.316940i
$130$	3.18674	+	5.51959i	0.279495	+	0.484100i
$131$	0.562257			0.0491246			0.0245623	−	0.999698i	$-0.492181\pi$
$131$	0.562257			0.0491246			0.0245623	+	0.999698i	$0.492181\pi$
$132$	0.0728745			0.00634291
$133$	0.405114	+	0.701677i	0.0351278	+	0.0608431i
$134$	3.58868	+	6.21577i	0.310014	+	0.536961i
$135$	3.92199	+	6.79309i	0.337551	+	0.584656i
$136$	6.40365	+	11.0915i	0.549109	+	0.951084i
$137$	8.66910	−	15.0153i	0.740651	−	1.28285i	−0.211548	−	0.977368i	$-0.567851\pi$
$137$	8.66910	−	15.0153i	0.740651	−	1.28285i	0.952199	−	0.305478i	$-0.0988161\pi$
$138$	−3.15859	+	5.47085i	−0.268877	+	0.465709i
$139$	−8.27620	+	14.3348i	−0.701978	+	1.21586i	0.265793	+	0.964030i	$0.414366\pi$
$139$	−8.27620	+	14.3348i	−0.701978	+	1.21586i	−0.967771	+	0.251832i	$0.918967\pi$
$140$	0.244218	+	0.422997i	0.0206402	+	0.0357498i
$141$	1.05035	−	1.81927i	0.0884558	−	0.153210i
$142$	−2.73543			−0.229553
$143$	−0.233732			−0.0195456
$144$	0.644833	+	1.11688i	0.0537361	+	0.0930737i
$145$	−3.00967	−	5.21290i	−0.249939	−	0.432908i
$146$	−0.219177	−	0.379625i	−0.0181392	−	0.0314180i
$147$	4.60916	−	7.98330i	0.380157	−	0.658451i
$148$	−14.8131			−1.21763
$149$	−0.0391047	−	0.0677314i	−0.00320358	−	0.00554877i	0.864419	−	0.502772i	$-0.167686\pi$
$149$	−0.0391047	−	0.0677314i	−0.00320358	−	0.00554877i	−0.867623	+	0.497223i	$0.834353\pi$
$150$	2.98692			0.243881
$151$	8.34280	−	9.02207i	0.678927	−	0.734205i
$151$	8.34280	−	9.02207i	0.678927	−	0.734205i
$152$	−8.58489			−0.696326
$153$	−3.11144	−	5.38917i	−0.251545	−	0.435689i
$154$	0.00665538			0.000536306
$155$	−4.11158	+	7.12146i	−0.330250	+	0.572009i
$156$	6.01233	+	10.4137i	0.481372	+	0.833761i
$157$	1.70552	+	2.95405i	0.136116	+	0.235759i	0.926023	−	0.377467i	$-0.123205\pi$
$157$	1.70552	+	2.95405i	0.136116	+	0.235759i	−0.789907	+	0.613226i	$0.789871\pi$
$158$	−1.80969	−	3.13448i	−0.143971	−	0.249365i
$159$	−12.8193			−1.01663
$160$	−8.16835			−0.645765
$161$	0.776366	−	1.34471i	0.0611862	−	0.105978i
$162$	−1.38376	−	2.39675i	−0.108719	−	0.188306i
$163$	−7.48220	+	12.9596i	−0.586051	+	1.01507i	0.408692	+	0.912672i	$0.365985\pi$
$163$	−7.48220	+	12.9596i	−0.586051	+	1.01507i	−0.994743	+	0.102398i	$0.967348\pi$
$164$	−0.695345	+	1.20437i	−0.0542973	+	0.0940458i
$165$	0.0348399	−	0.0603445i	0.00271229	−	0.00469782i
$166$	4.22757	+	7.32236i	0.328123	+	0.568325i
$167$	3.47772	+	6.02359i	0.269114	+	0.466120i	0.968633	−	0.248494i	$-0.0799357\pi$
$167$	3.47772	+	6.02359i	0.269114	+	0.466120i	−0.699519	+	0.714614i	$0.746602\pi$
$168$	−0.406006	−	0.703223i	−0.0313240	−	0.0542548i
$169$	−12.7835	−	22.1416i	−0.983343	−	1.70320i
$170$	5.16364			0.396033
$171$	4.17127			0.318985
$172$	2.28233	+	3.95311i	0.174026	+	0.301422i
$173$	4.60116	−	7.96944i	0.349819	−	0.605905i	−0.636398	−	0.771361i	$-0.719576\pi$
$173$	4.60116	−	7.96944i	0.349819	−	0.605905i	0.986217	+	0.165456i	$0.0529096\pi$
$174$	2.10980	+	3.65427i	0.159943	+	0.277030i
$175$	−0.734169			−0.0554980
$176$	0.0196225	−	0.0339871i	0.00147910	−	0.00256187i
$177$	8.56891			0.644079
$178$	−1.61936			−0.121376
$179$	−14.5958			−1.09094			−0.545472	−	0.838129i	$-0.683650\pi$
$179$	−14.5958			−1.09094			−0.545472	+	0.838129i	$0.683650\pi$
$180$	2.51460			0.187427
$181$	−3.84200	+	6.65454i	−0.285574	+	0.494628i	−0.972748	−	0.231864i	$-0.925517\pi$
$181$	−3.84200	+	6.65454i	−0.285574	+	0.494628i	0.687175	+	0.726492i	$0.258851\pi$
$182$	0.549086	+	0.951046i	0.0407010	+	0.0704962i
$183$	1.34758	−	2.33407i	0.0996158	−	0.172540i
$184$	8.22611	+	14.2480i	0.606437	+	1.05038i
$185$	−7.08186	+	12.2661i	−0.520669	+	0.901825i
$186$	2.88224	−	4.99219i	0.211336	−	0.366045i
$187$	−0.0946820	+	0.163994i	−0.00692383	+	0.0119924i
$188$	−1.15346	−	1.99785i	−0.0841248	−	0.145708i
$189$	0.675774	+	1.17047i	0.0491553	+	0.0851395i
$190$	−1.73062	+	2.99753i	−0.125553	+	0.217464i
$191$	7.60994	+	13.1808i	0.550636	+	0.953729i	0.998229	+	0.0594917i	$0.0189480\pi$
$191$	7.60994	+	13.1808i	0.550636	+	0.953729i	−0.447593	+	0.894237i	$0.647719\pi$
$192$	2.95687			0.213394
$193$	6.18993	−	10.7213i	0.445561	−	0.771735i	−0.552530	−	0.833493i	$-0.686337\pi$
$193$	6.18993	−	10.7213i	0.445561	−	0.771735i	0.998091	+	0.0617584i	$0.0196708\pi$
$194$	−0.716888	+	1.24169i	−0.0514696	+	0.0891479i
$195$	11.4975			0.823356
$196$	−5.06161	−	8.76697i	−0.361544	−	0.626212i
$197$	12.2296	−	21.1823i	0.871323	−	1.50918i	0.0106938	−	0.999943i	$-0.496596\pi$
$197$	12.2296	−	21.1823i	0.871323	−	1.50918i	0.860629	−	0.509232i	$-0.170071\pi$
$198$	0.0171318	−	0.0296732i	0.00121751	−	0.00210878i
$199$	−3.75069	−	6.49638i	−0.265879	−	0.460516i	0.701914	−	0.712261i	$-0.252329\pi$
$199$	−3.75069	−	6.49638i	−0.265879	−	0.460516i	−0.967794	+	0.251745i	$0.918996\pi$
$200$	3.88950	−	6.73681i	0.275029	−	0.476364i
$201$	12.9477			0.913261
$202$	−5.00063	−	8.66134i	−0.351843	−	0.609410i
$203$	−0.518577	−	0.898201i	−0.0363970	−	0.0630414i
$204$	9.74211			0.682084
$205$	0.664863	+	1.15158i	0.0464361	+	0.0804296i
$206$	−4.88110	+	8.45432i	−0.340082	+	0.589040i
$207$	−3.99694	−	6.92290i	−0.277807	−	0.481175i
$208$	6.47562			0.449003
$209$	−0.0634664	−	0.109927i	−0.00439007	−	0.00760382i
$210$	−0.327386			−0.0225918
$211$	17.0979			1.17707			0.588534	−	0.808472i	$-0.299705\pi$
$211$	17.0979			1.17707			0.588534	+	0.808472i	$0.299705\pi$
$212$	−7.03883	+	12.1916i	−0.483429	+	0.837323i
$213$	−2.46732	+	4.27352i	−0.169058	+	0.292817i
$214$	3.48505	+	6.03629i	0.238233	+	0.412632i
$215$	4.36456			0.297661
$216$	−14.3205			−0.974388
$217$	−0.708440	+	1.22705i	−0.0480920	+	0.0832978i
$218$	−7.99264			−0.541330
$219$	−0.790776			−0.0534357
$220$	−0.0382599	−	0.0662682i	−0.00257949	−	0.00446780i
$221$	−31.2460			−2.10184
$222$	4.96443	−	8.59864i	0.333191	−	0.577103i
$223$	17.5092			1.17250			0.586252	−	0.810129i	$-0.300603\pi$
$223$	17.5092			1.17250			0.586252	+	0.810129i	$0.300603\pi$
$224$	−1.40744			−0.0940383
$225$	−1.88985	+	3.27331i	−0.125990	+	0.218221i
$226$	2.12279	−	3.67678i	0.141206	−	0.244575i
$227$	2.96517	−	5.13583i	0.196805	−	0.340877i	−0.750686	−	0.660660i	$-0.770277\pi$
$227$	2.96517	−	5.13583i	0.196805	−	0.340877i	0.947491	+	0.319783i	$0.103610\pi$
$228$	−3.26512	+	5.65536i	−0.216238	+	0.374535i
$229$	10.2577			0.677846			0.338923	−	0.940814i	$-0.389937\pi$
$229$	10.2577			0.677846			0.338923	+	0.940814i	$0.389937\pi$
$230$	6.63319			0.437380
$231$	0.00600305	−	0.0103976i	0.000394972	−	0.000684111i
$232$	10.9893			0.721484
$233$	9.85597	+	17.0710i	0.645686	+	1.11836i	0.984143	+	0.177379i	$0.0567619\pi$
$233$	9.85597	+	17.0710i	0.645686	+	1.11836i	−0.338456	+	0.940982i	$0.609905\pi$
$234$	5.65369			0.369593
$235$	−2.20579			−0.143890
$236$	4.70503	−	8.14936i	0.306272	−	0.530478i
$237$	−6.52924			−0.424120
$238$	0.889715			0.0576716
$239$	3.31738	+	5.74587i	0.214583	+	0.371669i	0.953144	−	0.302518i	$-0.0978273\pi$
$239$	3.31738	+	5.74587i	0.214583	+	0.371669i	−0.738560	+	0.674187i	$0.764494\pi$
$240$	−0.965253	+	1.67187i	−0.0623068	+	0.107919i
$241$	3.13898	−	5.43687i	0.202199	−	0.350220i	−0.747037	−	0.664782i	$-0.768524\pi$
$241$	3.13898	−	5.43687i	0.202199	−	0.350220i	0.949237	+	0.314562i	$0.101858\pi$
$242$	8.09575			0.520415
$243$	11.8850			0.762425
$244$	−1.47986	−	2.56319i	−0.0947384	−	0.164092i
$245$	−9.67945			−0.618397
$246$	−0.466073	−	0.807262i	−0.0297157	−	0.0514692i
$247$	10.4723	−	18.1385i	0.666336	−	1.15413i
$248$	−7.50638	−	13.0014i	−0.476656	−	0.825592i
$249$	15.2528			0.966606
$250$	−4.13388	−	7.16010i	−0.261450	−	0.452844i
$251$	10.7190	+	18.5659i	0.676579	+	1.17187i	0.976005	+	0.217750i	$0.0698717\pi$
$251$	10.7190	+	18.5659i	0.676579	+	1.17187i	−0.299425	+	0.954120i	$0.596795\pi$
$252$	0.433274			0.0272937
$253$	−0.121628	+	0.210666i	−0.00764669	+	0.0132445i
$254$	−5.45538	−	9.44900i	−0.342301	−	0.592883i
$255$	4.65752	−	8.06707i	0.291665	−	0.505179i
$256$	5.93584	−	10.2812i	0.370990	−	0.642574i
$257$	−5.02192	−	8.69823i	−0.313259	−	0.542580i	0.665807	−	0.746124i	$-0.268087\pi$
$257$	−5.02192	−	8.69823i	−0.313259	−	0.542580i	−0.979066	+	0.203544i	$0.934754\pi$
$258$	−3.05958			−0.190481
$259$	−1.22023	+	2.11350i	−0.0758215	+	0.131327i
$260$	6.31309	−	10.9346i	0.391521	−	0.678135i
$261$	−5.33954			−0.330509
$262$	0.206931	+	0.358415i	0.0127842	+	0.0221430i
$263$	−14.9592	+	25.9102i	−0.922426	+	1.59769i	−0.126777	+	0.991931i	$0.540463\pi$
$263$	−14.9592	+	25.9102i	−0.922426	+	1.59769i	−0.795649	+	0.605758i	$0.792870\pi$
$264$	0.0636062	+	0.110169i	0.00391469	+	0.00678045i
$265$	6.73027	+	11.6572i	0.413437	+	0.716094i
$266$	−0.298193	+	0.516485i	−0.0182834	+	0.0316678i
$267$	−1.46064	+	2.52990i	−0.0893896	+	0.154827i
$268$	7.10935	−	12.3138i	0.434273	−	0.752182i
$269$	−0.809850	−	1.40270i	−0.0493774	−	0.0855242i	0.840280	−	0.542152i	$-0.182390\pi$
$269$	−0.809850	−	1.40270i	−0.0493774	−	0.0855242i	−0.889658	+	0.456628i	$0.849057\pi$
$270$	−2.88687	+	5.00021i	−0.175689	+	0.304303i
$271$	6.02883	+	10.4422i	0.366226	+	0.634321i	0.988972	−	0.148102i	$-0.0473165\pi$
$271$	6.02883	+	10.4422i	0.366226	+	0.634321i	−0.622747	+	0.782424i	$0.713983\pi$
$272$	2.62320	−	4.54351i	0.159055	−	0.275491i
$273$	1.98107			0.119900
$274$	12.7622			0.770991
$275$	0.115017			0.00693581
$276$	12.5147			0.753295
$277$	−7.05484	+	12.2193i	−0.423884	+	0.734189i	−0.996316	−	0.0857637i	$-0.972667\pi$
$277$	−7.05484	+	12.2193i	−0.423884	+	0.734189i	0.572431	+	0.819953i	$0.306000\pi$
$278$	−12.1838			−0.730734
$279$	3.64724	+	6.31720i	0.218354	+	0.378201i
$280$	−0.426316	+	0.738400i	−0.0254772	+	0.0441279i
$281$	11.8645	+	20.5498i	0.707774	+	1.22590i	0.965681	+	0.259731i	$0.0836340\pi$
$281$	11.8645	+	20.5498i	0.707774	+	1.22590i	−0.257907	+	0.966170i	$0.583033\pi$
$282$	1.54627			0.0920793
$283$	−20.2256			−1.20229			−0.601144	−	0.799141i	$-0.705288\pi$
$283$	−20.2256			−1.20229			−0.601144	+	0.799141i	$0.705288\pi$
$284$	2.70952	+	4.69302i	0.160780	+	0.278480i
$285$	3.12199	+	5.40745i	0.184931	+	0.320310i
$286$	−0.0860217	−	0.148994i	−0.00508657	−	0.00881020i
$287$	0.114558	+	0.198421i	0.00676217	+	0.0117124i
$288$	−3.62293	+	6.27510i	−0.213483	+	0.369764i
$289$	−4.15741	+	7.20085i	−0.244554	+	0.423580i
$290$	2.21533	−	3.83707i	0.130089	−	0.225321i
$291$	1.29324	+	2.23996i	0.0758112	+	0.131309i
$292$	−0.434201	+	0.752057i	−0.0254097	+	0.0440108i
$293$	−33.3603			−1.94893			−0.974465	−	0.224540i	$-0.927912\pi$
$293$	−33.3603			−1.94893			−0.974465	+	0.224540i	$0.927912\pi$
$294$	6.78535			0.395730
$295$	−4.49878	−	7.79211i	−0.261929	−	0.453674i
$296$	−12.9291	−	22.3939i	−0.751491	−	1.30162i
$297$	−0.105869	−	0.183370i	−0.00614314	−	0.0106402i
$298$	0.0287839	−	0.0498552i	0.00166741	−	0.00288803i
$299$	−40.1385			−2.32127
$300$	−2.95862	−	5.12448i	−0.170816	−	0.295862i
$301$	0.752030			0.0433463
$302$	8.82164	+	1.99773i	0.507628	+	0.114957i
$303$	−18.0419			−1.03648
$304$	1.75836	+	3.04557i	0.100849	+	0.174675i
$305$	−2.82998			−0.162044
$306$	2.29024	−	3.96682i	0.130925	−	0.226768i
$307$	−9.92832	−	17.1963i	−0.566639	−	0.981448i	−0.996895	−	0.0787407i	$-0.974910\pi$
$307$	−9.92832	−	17.1963i	−0.566639	−	0.981448i	0.430256	−	0.902707i	$-0.358423\pi$
$308$	−0.00659233	−	0.0114182i	−0.000375633	−	0.000650615i
$309$	8.80535	+	15.2513i	0.500919	+	0.867617i
$310$	−6.05284			−0.343778
$311$	−31.1499			−1.76635			−0.883175	−	0.469043i	$-0.844599\pi$
$311$	−31.1499			−1.76635			−0.883175	+	0.469043i	$0.844599\pi$
$312$	−10.4954	+	18.1785i	−0.594182	+	1.02915i
$313$	16.2177	+	28.0899i	0.916679	+	1.58773i	0.804424	+	0.594055i	$0.202474\pi$
$313$	16.2177	+	28.0899i	0.916679	+	1.58773i	0.112255	+	0.993679i	$0.464193\pi$
$314$	−1.25539	+	2.17440i	−0.0708457	+	0.122708i
$315$	0.207140	−	0.358778i	0.0116710	−	0.0202148i
$316$	−3.58509	+	6.20956i	−0.201677	+	0.349315i
$317$	−14.5155	−	25.1416i	−0.815272	−	1.41209i	−0.909132	−	0.416508i	$-0.863254\pi$
$317$	−14.5155	−	25.1416i	−0.815272	−	1.41209i	0.0938597	−	0.995585i	$-0.470079\pi$
$318$	−4.71796	−	8.17174i	−0.264570	−	0.458248i
$319$	0.0812420	+	0.140715i	0.00454868	+	0.00787854i
$320$	−1.55239	−	2.68882i	−0.0867813	−	0.150310i
$321$	12.5738			0.701803
$322$	1.14292			0.0636926
$323$	−8.48441	−	14.6954i	−0.472085	−	0.817676i
$324$	−2.74131	+	4.74809i	−0.152295	+	0.263783i
$325$	9.48923	+	16.4358i	0.526368	+	0.911695i
$326$	−11.0149			−0.610058
$327$	−7.20923	+	12.4868i	−0.398671	+	0.690519i
$328$	−2.42764			−0.134044
$329$	−0.380066			−0.0209537
$330$	0.0512894			0.00282339
$331$	−9.92556			−0.545558			−0.272779	−	0.962077i	$-0.587943\pi$
$331$	−9.92556			−0.545558			−0.272779	+	0.962077i	$0.587943\pi$
$332$	8.37503	−	14.5060i	0.459639	−	0.796118i
$333$	6.28208	+	10.8809i	0.344256	+	0.596268i
$334$	−2.55986	+	4.43380i	−0.140069	+	0.242607i
$335$	−6.79770	−	11.7740i	−0.371398	−	0.643280i
$336$	−0.166317	+	0.288069i	−0.00907331	+	0.0157154i
$337$	14.7440	−	25.5374i	0.803159	−	1.39111i	−0.114367	−	0.993439i	$-0.536484\pi$
$337$	14.7440	−	25.5374i	0.803159	−	1.39111i	0.917527	−	0.397674i	$-0.130183\pi$
$338$	9.40955	−	16.2978i	0.511812	−	0.886485i
$339$	−3.82944	−	6.63278i	−0.207987	−	0.360243i
$340$	−5.11472	−	8.85896i	−0.277385	−	0.480444i
$341$	0.110987	−	0.192234i	0.00601026	−	0.0104101i
$342$	1.53518	+	2.65900i	0.0830129	+	0.143783i
$343$	−3.34947			−0.180855
$344$	−3.98412	+	6.90070i	−0.214810	+	0.372061i
$345$	5.98303	−	10.3629i	0.322116	−	0.557921i
$346$	6.77357			0.364149
$347$	13.9958	+	24.2414i	0.751334	+	1.30135i	0.947177	+	0.320713i	$0.103922\pi$
$347$	13.9958	+	24.2414i	0.751334	+	1.30135i	−0.195843	+	0.980635i	$0.562744\pi$
$348$	4.17961	−	7.23930i	0.224051	−	0.388067i
$349$	−12.8197	+	22.2044i	−0.686225	+	1.18858i	0.286826	+	0.957983i	$0.407400\pi$
$349$	−12.8197	+	22.2044i	−0.686225	+	1.18858i	−0.973050	+	0.230593i	$0.925933\pi$
$350$	−0.270201	−	0.468001i	−0.0144428	−	0.0250157i
$351$	17.4689	−	30.2571i	0.932422	−	1.61500i
$352$	0.220494			0.0117523
$353$	9.82720	+	17.0212i	0.523049	+	0.905948i	0.999640	+	0.0268227i	$0.00853895\pi$
$353$	9.82720	+	17.0212i	0.523049	+	0.905948i	−0.476591	+	0.879125i	$0.658128\pi$
$354$	3.15367	+	5.46232i	0.167616	+	0.290319i
$355$	5.18148			0.275004
$356$	1.60402	+	2.77824i	0.0850129	+	0.147247i
$357$	0.802508	−	1.38998i	0.0424732	−	0.0735658i
$358$	−5.37180	−	9.30423i	−0.283908	−	0.491744i
$359$	−6.37812			−0.336624			−0.168312	−	0.985734i	$-0.553832\pi$
$359$	−6.37812			−0.336624			−0.168312	+	0.985734i	$0.553832\pi$
$360$	2.19479	+	3.80148i	0.115675	+	0.200356i
$361$	−7.62560			−0.401348
$362$	−5.65598			−0.297272
$363$	7.30224	−	12.6478i	0.383268	−	0.663840i
$364$	1.08777	−	1.88407i	0.0570146	−	0.0987521i
$365$	0.415166	+	0.719089i	0.0217308	+	0.0376389i
$366$	1.98383			0.103696
$367$	−2.54195			−0.132689			−0.0663443	−	0.997797i	$-0.521134\pi$
$367$	−2.54195			−0.132689			−0.0663443	+	0.997797i	$0.521134\pi$
$368$	3.36975	−	5.83658i	0.175660	−	0.304253i
$369$	1.17955			0.0614052
$370$	−10.4255			−0.541997
$371$	1.15965	+	2.00857i	0.0602060	+	0.104280i
$372$	−11.4197			−0.592085
$373$	13.9079	−	24.0892i	0.720125	−	1.24729i	−0.240824	−	0.970569i	$-0.577418\pi$
$373$	13.9079	−	24.0892i	0.720125	−	1.24729i	0.960949	−	0.276724i	$-0.0892489\pi$
$374$	−0.139386			−0.00720746
$375$	−14.9148			−0.770196
$376$	2.01352	−	3.48753i	0.103840	−	0.179855i
$377$	−13.4053	+	23.2187i	−0.690410	+	1.19583i
$378$	−0.497418	+	0.861554i	−0.0255844	+	0.0443135i
$379$	8.49899	−	14.7207i	0.436564	−	0.756150i	−0.560858	−	0.827912i	$-0.689529\pi$
$379$	8.49899	−	14.7207i	0.436564	−	0.756150i	0.997422	+	0.0717615i	$0.0228620\pi$
$380$	6.85691			0.351752
$381$	−19.6827			−1.00837
$382$	−5.60147	+	9.70202i	−0.286596	+	0.496399i
$383$	27.1981			1.38976			0.694879	−	0.719127i	$-0.255458\pi$
$383$	27.1981			1.38976			0.694879	+	0.719127i	$0.255458\pi$
$384$	−6.69097	−	11.5891i	−0.341447	−	0.591404i
$385$	−0.0126067			−0.000642496
$386$	9.11248			0.463813
$387$	1.93583	−	3.35295i	0.0984035	−	0.170440i
$388$	2.84038			0.144199
$389$	1.94800			0.0987676			0.0493838	−	0.998780i	$-0.484274\pi$
$389$	1.94800			0.0987676			0.0493838	+	0.998780i	$0.484274\pi$
$390$	4.23151	+	7.32919i	0.214271	+	0.371128i
$391$	−16.2597	+	28.1626i	−0.822286	+	1.42424i
$392$	8.83574	−	15.3039i	0.446272	−	0.772966i
$393$	0.746594			0.0376607
$394$	18.0037			0.907015
$395$	3.42793	+	5.93735i	0.172478	+	0.298740i
$396$	−0.0678781			−0.00341101
$397$	−9.72297	−	16.8407i	−0.487982	−	0.845209i	0.511923	−	0.859032i	$-0.328933\pi$
$397$	−9.72297	−	16.8407i	−0.487982	−	0.845209i	−0.999904	+	0.0138223i	$0.995600\pi$
$398$	2.76078	−	4.78181i	0.138385	−	0.239690i
$399$	0.537930	+	0.931723i	0.0269302	+	0.0466445i
$400$	−3.18660			−0.159330
$401$	−3.98368	−	6.89993i	−0.198935	−	0.344566i	0.749248	−	0.662289i	$-0.230415\pi$
$401$	−3.98368	−	6.89993i	−0.198935	−	0.344566i	−0.948184	+	0.317723i	$0.897082\pi$
$402$	4.76523	+	8.25361i	0.237668	+	0.411653i
$403$	36.6267			1.82451
$404$	−9.90650	+	17.1586i	−0.492867	+	0.853670i
$405$	2.62114	+	4.53994i	0.130245	+	0.225592i
$406$	0.381710	−	0.661141i	0.0189440	−	0.0328119i
$407$	0.191165	−	0.331108i	0.00947572	−	0.0164124i
$408$	8.50310	+	14.7278i	0.420966	+	0.729135i
$409$	14.6667			0.725221			0.362611	−	0.931941i	$-0.381885\pi$
$409$	14.6667			0.725221			0.362611	+	0.931941i	$0.381885\pi$
$410$	−0.489388	+	0.847644i	−0.0241691	+	0.0418622i
$411$	11.5113	−	19.9381i	0.567809	−	0.983474i
$412$	19.3394			0.952785
$413$	−0.775156	−	1.34261i	−0.0381429	−	0.0660655i
$414$	2.94204	−	5.09576i	0.144593	−	0.250443i
$415$	−8.00789	−	13.8701i	−0.393092	−	0.680855i
$416$	18.1913	+	31.5082i	0.891902	+	1.54482i
$417$	−10.9896	+	19.0345i	−0.538161	+	0.932122i
$418$	0.0467159	−	0.0809143i	0.00228495	−	0.00395765i
$419$	−15.6699	+	27.1410i	−0.765524	+	1.32593i	0.174445	+	0.984667i	$0.444187\pi$
$419$	−15.6699	+	27.1410i	−0.765524	+	1.32593i	−0.939969	+	0.341259i	$0.889147\pi$
$420$	0.324285	+	0.561678i	0.0158235	+	0.0274071i
$421$	−8.64013	+	14.9652i	−0.421094	+	0.729357i	−0.996047	−	0.0888300i	$-0.971687\pi$
$421$	−8.64013	+	14.9652i	−0.421094	+	0.729357i	0.574952	+	0.818187i	$0.305021\pi$
$422$	6.29265	+	10.8992i	0.306321	+	0.530564i
$423$	−0.978341	+	1.69454i	−0.0475686	+	0.0823912i
$424$	−24.5745			−1.19344
$425$	15.3759			0.745841
$426$	−3.63225			−0.175983
$427$	−0.487615			−0.0235974
$428$	6.90407	−	11.9582i	0.333721	−	0.578021i
$429$	−0.310361			−0.0149844
$430$	1.60632	+	2.78222i	0.0774635	+	0.134171i
$431$	4.62496	−	8.01067i	0.222777	−	0.385860i	−0.732874	−	0.680365i	$-0.761821\pi$
$431$	4.62496	−	8.01067i	0.222777	−	0.385860i	0.955650	+	0.294505i	$0.0951547\pi$
$432$	2.93314	+	5.08034i	0.141121	+	0.244428i
$433$	1.87372			0.0900453			0.0450226	−	0.998986i	$-0.485664\pi$
$433$	1.87372			0.0900453			0.0450226	+	0.998986i	$0.485664\pi$
$434$	−1.04293			−0.0500621
$435$	−3.99639	−	6.92195i	−0.191612	−	0.331882i
$436$	7.91691	+	13.7125i	0.379151	+	0.656710i
$437$	−10.8990	−	18.8777i	−0.521372	−	0.903042i
$438$	−0.291034	−	0.504086i	−0.0139061	−	0.0240862i
$439$	14.3184	−	24.8003i	0.683382	−	1.18365i	−0.290560	−	0.956857i	$-0.593842\pi$
$439$	14.3184	−	24.8003i	0.683382	−	1.18365i	0.973942	−	0.226796i	$-0.0728250\pi$
$440$	0.0667880	−	0.115680i	0.00318399	−	0.00551484i
$441$	−4.29315	+	7.43596i	−0.204436	+	0.354093i
$442$	−11.4997	−	19.9180i	−0.546984	−	0.947404i
$443$	12.9029	−	22.3484i	0.613034	−	1.06181i	−0.377692	−	0.925931i	$-0.623282\pi$
$443$	12.9029	−	22.3484i	0.613034	−	1.06181i	0.990726	−	0.135874i	$-0.0433844\pi$
$444$	−19.6696			−0.933477
$445$	3.06741			0.145409
$446$	6.44402	+	11.1614i	0.305133	+	0.528506i
$447$	−0.0519252	−	0.0899371i	−0.00245598	−	0.00425388i
$448$	−0.267483	−	0.463294i	−0.0126374	−	0.0218886i
$449$	7.03710	−	12.1886i	0.332101	−	0.575216i	−0.650822	−	0.759230i	$-0.725576\pi$
$449$	7.03710	−	12.1886i	0.332101	−	0.575216i	0.982924	+	0.184014i	$0.0589090\pi$
$450$	−2.78213			−0.131151
$451$	−0.0179471	−	0.0310853i	−0.000845096	−	0.00146375i
$452$	−8.41070			−0.395606
$453$	11.0780	−	11.9800i	0.520490	−	0.562868i
$454$	4.36516			0.204867
$455$	−1.04008	−	1.80148i	−0.0487599	−	0.0844546i
$456$	−11.3994			−0.533828
$457$	−3.85698	+	6.68049i	−0.180422	+	0.312500i	−0.942024	−	0.335545i	$-0.891080\pi$
$457$	−3.85698	+	6.68049i	−0.180422	+	0.312500i	0.761602	+	0.648045i	$0.224413\pi$
$458$	3.77520	+	6.53883i	0.176403	+	0.305540i
$459$	−14.1529	−	24.5136i	−0.660602	−	1.14420i
$460$	−6.57035	−	11.3802i	−0.306344	−	0.530604i
$461$	9.47120			0.441118			0.220559	−	0.975374i	$-0.429212\pi$
$461$	9.47120			0.441118			0.220559	+	0.975374i	$0.429212\pi$
$462$	0.00883736			0.000411151
$463$	−8.25734	+	14.3021i	−0.383751	+	0.664676i	−0.991595	−	0.129380i	$-0.958701\pi$
$463$	−8.25734	+	14.3021i	−0.383751	+	0.664676i	0.607844	+	0.794056i	$0.292035\pi$
$464$	−2.25084	−	3.89856i	−0.104492	−	0.180986i
$465$	−5.45956	+	9.45624i	−0.253181	+	0.438523i
$466$	−7.25471	+	12.5655i	−0.336068	+	0.582087i
$467$	−10.4625	+	18.1216i	−0.484146	+	0.838566i	−0.999834	−	0.0182108i	$-0.994203\pi$
$467$	−10.4625	+	18.1216i	−0.484146	+	0.838566i	0.515688	+	0.856776i	$0.327536\pi$
$468$	−5.60012	−	9.69970i	−0.258866	−	0.448369i
$469$	−1.17127	−	2.02870i	−0.0540841	−	0.0936765i
$470$	−0.811812	−	1.40610i	−0.0374461	−	0.0648585i
$471$	2.26468	+	3.92254i	0.104351	+	0.180741i
$472$	16.4266			0.756094
$473$	−0.117815			−0.00541716
$474$	−2.40300	−	4.16212i	−0.110373	−	0.191172i
$475$	−5.15332	+	8.92582i	−0.236451	+	0.409545i
$476$	−0.881285	−	1.52643i	−0.0403936	−	0.0699638i
$477$	11.9404			0.546712
$478$	−2.44183	+	4.22937i	−0.111687	+	0.193447i
$479$	−3.05129			−0.139417			−0.0697085	−	0.997567i	$-0.522207\pi$
$479$	−3.05129			−0.139417			−0.0697085	+	0.997567i	$0.522207\pi$
$480$	−10.8463			−0.495066
$481$	63.0866			2.87650
$482$	4.62103			0.210482
$483$	1.03090	−	1.78557i	0.0469075	−	0.0812462i
$484$	−8.01905	−	13.8894i	−0.364502	−	0.631337i
$485$	1.35793	−	2.35201i	0.0616606	−	0.106799i
$486$	4.37412	+	7.57620i	0.198414	+	0.343663i
$487$	0.605624	−	1.04897i	0.0274434	−	0.0475334i	−0.851978	−	0.523578i	$-0.824597\pi$
$487$	0.605624	−	1.04897i	0.0274434	−	0.0475334i	0.879421	+	0.476045i	$0.157930\pi$
$488$	2.58330	−	4.47441i	0.116941	−	0.202547i
$489$	−9.93525	+	17.2084i	−0.449288	+	0.778189i
$490$	−3.56239	−	6.17024i	−0.160932	−	0.278743i
$491$	−0.165029	−	0.285839i	−0.00744766	−	0.0128997i	0.862278	−	0.506436i	$-0.169037\pi$
$491$	−0.165029	−	0.285839i	−0.00744766	−	0.0128997i	−0.869725	+	0.493536i	$0.835704\pi$
$492$	−0.923315	+	1.59923i	−0.0416263	+	0.0720988i
$493$	10.8607	+	18.8113i	0.489141	+	0.847218i
$494$	15.4167			0.693631
$495$	−0.0324513	+	0.0562073i	−0.00145858	+	0.00252633i
$496$	−3.07492	+	5.32592i	−0.138068	+	0.239141i
$497$	0.892788			0.0400470
$498$	5.61358	+	9.72300i	0.251550	+	0.435698i
$499$	9.80863	−	16.9890i	0.439095	−	0.760534i	−0.558525	−	0.829488i	$-0.688633\pi$
$499$	9.80863	−	16.9890i	0.439095	−	0.760534i	0.997620	+	0.0689532i	$0.0219659\pi$
$500$	−8.18943	+	14.1845i	−0.366243	+	0.634351i
$501$	4.61790	+	7.99843i	0.206312	+	0.357344i
$502$	−7.88998	+	13.6659i	−0.352147	+	0.609937i
$503$	23.4012			1.04341			0.521705	−	0.853126i	$-0.325296\pi$
$503$	23.4012			1.04341			0.521705	+	0.853126i	$0.325296\pi$
$504$	0.378170	+	0.655009i	0.0168450	+	0.0291764i
$505$	9.47222	+	16.4064i	0.421508	+	0.730074i
$506$	−0.179054			−0.00795993
$507$	−16.9745	−	29.4007i	−0.753865	−	1.30573i
$508$	−10.8074	+	18.7190i	−0.479501	+	0.830519i
$509$	4.67055	+	8.08963i	0.207019	+	0.358567i	0.950774	−	0.309885i	$-0.100291\pi$
$509$	4.67055	+	8.08963i	0.207019	+	0.358567i	−0.743755	+	0.668452i	$0.766957\pi$
$510$	6.85655			0.303613
$511$	0.0715347	+	0.123902i	0.00316451	+	0.00548109i
$512$	−11.4174			−0.504582
$513$	18.9737			0.837711
$514$	3.69650	−	6.40252i	0.163046	−	0.282403i
$515$	9.24582	−	16.0142i	0.407419	−	0.705671i
$516$	3.03060	+	5.24915i	0.133415	+	0.231081i
$517$	0.0595424			0.00261867
$518$	−1.79636			−0.0789274
$519$	6.10965	−	10.5822i	0.268184	−	0.464508i
$520$	22.0407			0.966550
$521$	−14.3651			−0.629349			−0.314674	−	0.949200i	$-0.601895\pi$
$521$	−14.3651			−0.629349			−0.314674	+	0.949200i	$0.601895\pi$
$522$	−1.96515	−	3.40373i	−0.0860121	−	0.148977i
$523$	−24.9594			−1.09140			−0.545700	−	0.837981i	$-0.683736\pi$
$523$	−24.9594			−1.09140			−0.545700	+	0.837981i	$0.683736\pi$
$524$	0.409941	−	0.710039i	0.0179084	−	0.0310182i
$525$	−0.974867			−0.0425467
$526$	−22.0222			−0.960212
$527$	14.8371	−	25.6985i	0.646312	−	1.11945i
$528$	0.0260557	−	0.0451298i	0.00113393	−	0.00196402i
$529$	−9.38709	+	16.2589i	−0.408134	+	0.706910i
$530$	−4.95396	+	8.58052i	−0.215186	+	0.372714i
$531$	−7.98142			−0.346364
$532$	1.18147			0.0512233
$533$	2.96136	−	5.12923i	0.128271	−	0.222172i
$534$	−2.15027			−0.0930514
$535$	−6.60141	−	11.4340i	−0.285404	−	0.494334i
$536$	24.8207			1.07209
$537$	−19.3811			−0.836356
$538$	0.596108	−	1.03249i	0.0257001	−	0.0445138i
$539$	0.261284			0.0112543
$540$	11.4381			0.492216
$541$	−21.7611	−	37.6914i	−0.935584	−	1.62048i	−0.773590	−	0.633687i	$-0.781541\pi$
$541$	−21.7611	−	37.6914i	−0.935584	−	1.62048i	−0.161994	−	0.986792i	$-0.551792\pi$
$542$	−4.43766	+	7.68625i	−0.190614	+	0.330153i
$543$	−5.10160	+	8.83623i	−0.218931	+	0.379199i
$544$	29.4763			1.26379
$545$	15.1397			0.648514
$546$	0.729105	+	1.26285i	0.0312028	+	0.0540449i
$547$	2.86957			0.122694			0.0613470	−	0.998117i	$-0.480460\pi$
$547$	2.86957			0.122694			0.0613470	+	0.998117i	$0.480460\pi$
$548$	−12.6413	−	21.8953i	−0.540008	−	0.935321i
$549$	−1.25519	+	2.17405i	−0.0535701	+	0.0927861i
$550$	0.0423305	+	0.0733186i	0.00180498	+	0.00312632i
$551$	−14.5601			−0.620282
$552$	10.9230	+	18.9193i	0.464916	+	0.805257i
$553$	0.590645	+	1.02303i	0.0251168	+	0.0435035i
$554$	−10.3857			−0.441248
$555$	−9.40366	+	16.2876i	−0.399163	+	0.691371i
$556$	12.0683	+	20.9030i	0.511811	+	0.886483i
$557$	−4.24234	+	7.34796i	−0.179754	+	0.311343i	−0.941796	−	0.336184i	$-0.890863\pi$
$557$	−4.24234	+	7.34796i	−0.179754	+	0.311343i	0.762042	+	0.647527i	$0.224197\pi$
$558$	−2.68463	+	4.64992i	−0.113649	+	0.196847i
$559$	−9.72008	−	16.8357i	−0.411116	−	0.712073i
$560$	0.349273			0.0147595
$561$	−0.125724	+	0.217760i	−0.00530805	+	0.00919382i
$562$	−8.73310	+	15.1262i	−0.368384	+	0.638059i
$563$	−21.5709			−0.909106			−0.454553	−	0.890720i	$-0.650201\pi$
$563$	−21.5709			−0.909106			−0.454553	+	0.890720i	$0.650201\pi$
$564$	−1.53162	−	2.65285i	−0.0644930	−	0.111705i
$565$	−4.02100	+	6.96458i	−0.169165	+	0.293002i
$566$	−7.44376	−	12.8930i	−0.312884	−	0.541932i
$567$	0.451632	+	0.782249i	0.0189667	+	0.0328514i
$568$	−4.72984	+	8.19231i	−0.198459	+	0.343742i
$569$	5.46349	−	9.46304i	0.229041	−	0.396711i	−0.728483	−	0.685064i	$-0.759774\pi$
$569$	5.46349	−	9.46304i	0.229041	−	0.396711i	0.957524	+	0.288353i	$0.0931075\pi$
$570$	−2.29801	+	3.98027i	−0.0962531	+	0.166715i
$571$	−13.7074	−	23.7419i	−0.573637	−	0.993569i	−0.996188	−	0.0872297i	$-0.972199\pi$
$571$	−13.7074	−	23.7419i	−0.573637	−	0.993569i	0.422551	−	0.906339i	$-0.361135\pi$
$572$	−0.170413	+	0.295165i	−0.00712534	+	0.0123415i
$573$	10.1049	+	17.5021i	0.422137	+	0.731162i
$574$	−0.0843233	+	0.146052i	−0.00351959	+	0.00609610i
$575$	19.7518			0.823708
$576$	−2.75414			−0.114756
$577$	−40.9286			−1.70388			−0.851941	−	0.523638i	$-0.824574\pi$
$577$	−40.9286			−1.70388			−0.851941	+	0.523638i	$0.824574\pi$
$578$	−6.12032			−0.254572
$579$	8.21931	−	14.2363i	0.341583	−	0.591639i
$580$	−8.77738			−0.364461
$581$	−1.37979	−	2.38986i	−0.0572433	−	0.0991482i
$582$	−0.951920	+	1.64877i	−0.0394584	+	0.0683439i
$583$	−0.181675	−	0.314670i	−0.00752419	−	0.0130323i
$584$	−1.51591			−0.0627289
$585$	−10.7093			−0.442773
$586$	−12.2778	−	21.2658i	−0.507191	−	0.878481i
$587$	7.36278	+	12.7527i	0.303894	+	0.526360i	0.977015	−	0.213173i	$-0.0683797\pi$
$587$	7.36278	+	12.7527i	0.303894	+	0.526360i	−0.673120	+	0.739533i	$0.735046\pi$
$588$	−6.72106	−	11.6412i	−0.277172	−	0.480076i
$589$	9.94545	+	17.2260i	0.409795	+	0.709786i
$590$	3.31143	−	5.73556i	0.136329	−	0.236129i
$591$	16.2391	−	28.1269i	0.667987	−	1.15699i
$592$	−5.29631	+	9.17347i	−0.217677	+	0.377027i
$593$	−4.02205	−	6.96639i	−0.165166	−	0.286075i	0.771548	−	0.636171i	$-0.219483\pi$
$593$	−4.02205	−	6.96639i	−0.165166	−	0.286075i	−0.936714	+	0.350095i	$0.886149\pi$
$594$	0.0779272	−	0.134974i	0.00319739	−	0.00553804i
$595$	−1.68530			−0.0690907
$596$	−0.114045			−0.00467146
$597$	−4.98036	−	8.62623i	−0.203832	−	0.353048i
$598$	−14.7724	−	25.5866i	−0.604090	−	1.04631i
$599$	11.8321	+	20.4939i	0.483448	+	0.837357i	0.999819	−	0.0190082i	$-0.00605086\pi$
$599$	11.8321	+	20.4939i	0.483448	+	0.837357i	−0.516371	+	0.856365i	$0.672718\pi$
$600$	5.16467	−	8.94548i	0.210847	−	0.365198i
$601$	0.831941			0.0339356			0.0169678	−	0.999856i	$-0.494599\pi$
$601$	0.831941			0.0339356			0.0169678	+	0.999856i	$0.494599\pi$
$602$	0.276774	+	0.479387i	0.0112805	+	0.0195384i
$603$	−12.0600			−0.491121
$604$	−5.31067	−	17.1136i	−0.216088	−	0.696341i
$605$	−15.3350			−0.623458
$606$	−6.64008	−	11.5010i	−0.269735	−	0.467195i
$607$	19.0597			0.773608			0.386804	−	0.922162i	$-0.373579\pi$
$607$	19.0597			0.773608			0.386804	+	0.922162i	$0.373579\pi$
$608$	−9.87917	+	17.1112i	−0.400653	+	0.693952i
$609$	−0.688593	−	1.19268i	−0.0279032	−	0.0483297i
$610$	−1.04153	−	1.80399i	−0.0421705	−	0.0730414i
$611$	4.91240	+	8.50853i	0.198735	+	0.344218i
$612$	−9.07418			−0.366802
$613$	−25.1883			−1.01735			−0.508674	−	0.860959i	$-0.669864\pi$
$613$	−25.1883			−1.01735			−0.508674	+	0.860959i	$0.669864\pi$
$614$	7.30796	−	12.6578i	0.294925	−	0.510826i
$615$	0.882839	+	1.52912i	0.0355995	+	0.0616602i
$616$	0.0115078	−	0.0199321i	0.000463663	−	0.000803088i
$617$	−17.2472	+	29.8731i	−0.694347	+	1.20264i	0.276053	+	0.961142i	$0.410973\pi$
$617$	−17.2472	+	29.8731i	−0.694347	+	1.20264i	−0.970400	+	0.241502i	$0.922360\pi$
$618$	−6.48137	+	11.2261i	−0.260719	+	0.451579i
$619$	−18.3127	−	31.7185i	−0.736048	−	1.27487i	−0.954262	−	0.298972i	$-0.903356\pi$
$619$	−18.3127	−	31.7185i	−0.736048	−	1.27487i	0.218214	−	0.975901i	$-0.429977\pi$
$620$	5.99549	+	10.3845i	0.240785	+	0.417051i
$621$	−18.1808	−	31.4900i	−0.729570	−	1.26365i
$622$	−11.4643	−	19.8568i	−0.459677	−	0.796183i
$623$	0.528526			0.0211749
$624$	8.59865			0.344222
$625$	0.190433	+	0.329840i	0.00761732	+	0.0131936i
$626$	−11.9374	+	20.6762i	−0.477115	+	0.826387i
$627$	−0.0842740	−	0.145967i	−0.00336558	−	0.00582935i
$628$	4.97398			0.198483
$629$	25.5556	−	44.2637i	1.01897	−	1.76491i
$630$	0.304941			0.0121491
$631$	−11.2498			−0.447849			−0.223924	−	0.974607i	$-0.571887\pi$
$631$	−11.2498			−0.447849			−0.223924	+	0.974607i	$0.571887\pi$
$632$	−12.5165			−0.497881
$633$	22.7035			0.902382
$634$	10.6845	−	18.5060i	0.424334	−	0.734969i
$635$	10.3336	+	17.8984i	0.410077	+	0.710275i
$636$	−9.34651	+	16.1886i	−0.370613	+	0.641921i
$637$	21.5566	+	37.3371i	0.854103	+	1.47935i
$638$	−0.0598000	+	0.103577i	−0.00236750	+	0.00410064i
$639$	2.29816	−	3.98052i	0.0909136	−	0.157467i
$640$	−7.02568	+	12.1688i	−0.277714	+	0.481015i
$641$	16.7182	+	28.9567i	0.660328	+	1.14372i	0.980530	+	0.196372i	$0.0629159\pi$
$641$	16.7182	+	28.9567i	0.660328	+	1.14372i	−0.320202	+	0.947349i	$0.603751\pi$
$642$	4.62763	+	8.01529i	0.182638	+	0.316338i
$643$	−19.1670	+	33.1982i	−0.755873	+	1.30921i	0.189066	+	0.981964i	$0.439454\pi$
$643$	−19.1670	+	33.1982i	−0.755873	+	1.30921i	−0.944939	+	0.327246i	$0.893879\pi$
$644$	−1.13210	−	1.96085i	−0.0446108	−	0.0772682i
$645$	5.79549			0.228197
$646$	6.24514	−	10.8169i	0.245712	−	0.425585i
$647$	−8.97868	+	15.5515i	−0.352988	+	0.611394i	−0.986772	−	0.162117i	$-0.948168\pi$
$647$	−8.97868	+	15.5515i	−0.352988	+	0.611394i	0.633783	+	0.773511i	$0.281501\pi$
$648$	−9.57066			−0.375971
$649$	0.121439	+	0.210338i	0.00476688	+	0.00825648i
$650$	−6.98476	+	12.0980i	−0.273965	+	0.474521i
$651$	−0.940702	+	1.62934i	−0.0368690	+	0.0638590i
$652$	10.9105	+	18.8976i	0.427289	+	0.740087i
$653$	1.44459	−	2.50211i	0.0565312	−	0.0979150i	−0.836375	−	0.548158i	$-0.815329\pi$
$653$	1.44459	−	2.50211i	0.0565312	−	0.0979150i	0.892906	+	0.450243i	$0.148663\pi$
$654$	−10.6130			−0.415002
$655$	−0.391970	−	0.678912i	−0.0153155	−	0.0265273i
$656$	0.497231	+	0.861229i	0.0194136	+	0.0336253i
$657$	0.736560			0.0287359
$658$	−0.139878	−	0.242276i	−0.00545302	−	0.00944490i
$659$	−8.29200	+	14.3622i	−0.323011	+	0.559471i	−0.981108	−	0.193462i	$-0.938028\pi$
$659$	−8.29200	+	14.3622i	−0.323011	+	0.559471i	0.658097	+	0.752933i	$0.271362\pi$
$660$	−0.0508035	−	0.0879943i	−0.00197752	−	0.00342517i
$661$	−7.13379			−0.277472			−0.138736	−	0.990329i	$-0.544304\pi$
$661$	−7.13379			−0.277472			−0.138736	+	0.990329i	$0.544304\pi$
$662$	−3.65296	−	6.32712i	−0.141977	−	0.245911i
$663$	−41.4901			−1.61134
$664$	29.2395			1.13471
$665$	0.564839	−	0.978331i	0.0219035	−	0.0379380i
$666$	−4.62406	+	8.00911i	−0.179179	+	0.310347i
$667$	13.9516	+	24.1649i	0.540209	+	0.935669i
$668$	10.1424			0.392422
$669$	23.2496			0.898882
$670$	5.00360	−	8.66648i	0.193306	−	0.334815i
$671$	0.0763914			0.00294906
$672$	−1.86887			−0.0720931
$673$	−9.71380	−	16.8248i	−0.374440	−	0.648548i	0.615803	−	0.787900i	$-0.288832\pi$
$673$	−9.71380	−	16.8248i	−0.374440	−	0.648548i	−0.990243	+	0.139351i	$0.955498\pi$
$674$	21.7054			0.836060
$675$	−8.59631	+	14.8892i	−0.330872	+	0.573087i
$676$	−37.2816			−1.43391
$677$	17.1277			0.658271			0.329136	−	0.944283i	$-0.393243\pi$
$677$	17.1277			0.658271			0.329136	+	0.944283i	$0.393243\pi$
$678$	2.81875	−	4.88221i	0.108253	−	0.187500i
$679$	0.233977	−	0.405260i	0.00897922	−	0.0155525i
$680$	8.92845	−	15.4645i	0.342390	−	0.593038i
$681$	3.93730	−	6.81961i	0.150878	−	0.261328i
$682$	0.163388			0.00625646
$683$	39.1779			1.49910			0.749550	−	0.661948i	$-0.230270\pi$
$683$	39.1779			1.49910			0.749550	+	0.661948i	$0.230270\pi$
$684$	3.04126	−	5.26763i	0.116286	−	0.201413i
$685$	−24.1742			−0.923649
$686$	−1.23273	−	2.13515i	−0.0470658	−	0.0815203i
$687$	13.6207			0.519661
$688$	3.26412			0.124443
$689$	29.9772	−	51.9221i	1.14204	−	1.97807i
$690$	8.80789			0.335311
$691$	−43.8813			−1.66932			−0.834662	−	0.550762i	$-0.814337\pi$
$691$	−43.8813			−1.66932			−0.834662	+	0.550762i	$0.814337\pi$
$692$	−6.70939	−	11.6210i	−0.255053	−	0.441765i
$693$	−0.00559147	+	0.00968472i	−0.000212403	+	0.000367892i
$694$	−10.3019	+	17.8434i	−0.391055	+	0.677328i
$695$	23.0786			0.875421
$696$	14.5922			0.553115
$697$	−2.39923	−	4.15559i	−0.0908773	−	0.157404i
$698$	−18.8725			−0.714335
$699$	13.0873	+	22.6678i	0.495006	+	0.857375i
$700$	−0.535282	+	0.927135i	−0.0202317	+	0.0350424i
$701$	8.41689	+	14.5785i	0.317902	+	0.550622i	0.980050	−	0.198751i	$-0.0636885\pi$
$701$	8.41689	+	14.5785i	0.317902	+	0.550622i	−0.662148	+	0.749373i	$0.730355\pi$
$702$	25.7168			0.970617
$703$	17.1302	+	29.6705i	0.646079	+	1.11904i
$704$	0.0419047	+	0.0725811i	0.00157934	+	0.00273550i
$705$	−2.92896			−0.110311
$706$	−7.23353	+	12.5288i	−0.272238	+	0.471529i
$707$	1.63210	+	2.82688i	0.0613814	+	0.106316i
$708$	6.24758	−	10.8211i	0.234799	−	0.406683i
$709$	−16.1128	+	27.9083i	−0.605130	+	1.04812i	0.386900	+	0.922121i	$0.373546\pi$
$709$	−16.1128	+	27.9083i	−0.605130	+	1.04812i	−0.992031	+	0.125995i	$0.959788\pi$
$710$	1.90697	+	3.30297i	0.0715674	+	0.123958i
$711$	6.08159			0.228078
$712$	−2.80004	+	4.84981i	−0.104936	+	0.181754i
$713$	19.0596	−	33.0122i	0.713788	−	1.23632i
$714$	1.18141			0.0442131
$715$	0.162943	+	0.282225i	0.00609372	+	0.0105546i
$716$	−10.6418	+	18.4322i	−0.397703	+	0.688842i
$717$	4.40498	+	7.62965i	0.164507	+	0.284935i
$718$	−2.34738	−	4.06578i	−0.0876034	−	0.151734i
$719$	26.3760	−	45.6845i	0.983658	−	1.70375i	0.335902	−	0.941897i	$-0.390959\pi$
$719$	26.3760	−	45.6845i	0.983658	−	1.70375i	0.647755	−	0.761848i	$-0.275708\pi$
$720$	0.899074	−	1.55724i	0.0335065	−	0.0580350i
$721$	1.59309	−	2.75931i	0.0593297	−	0.102762i
$722$	−2.80650	−	4.86100i	−0.104447	−	0.180908i
$723$	4.16810	−	7.21936i	0.155013	−	0.268491i
$724$	5.60239	+	9.70363i	0.208211	+	0.360633i
$725$	6.59666	−	11.4257i	0.244994	−	0.424341i
$726$	10.7500			0.398968
$727$	19.4928			0.722949			0.361474	−	0.932382i	$-0.382273\pi$
$727$	19.4928			0.722949			0.361474	+	0.932382i	$0.382273\pi$
$728$	3.79770			0.140752
$729$	27.0611			1.00226
$730$	−0.305593	+	0.529302i	−0.0113105	+	0.0195903i
$731$	−15.7500			−0.582534
$732$	−1.96503	−	3.40354i	−0.0726298	−	0.125798i
$733$	−19.7821	+	34.2636i	−0.730668	+	1.26555i	0.225929	+	0.974144i	$0.427458\pi$
$733$	−19.7821	+	34.2636i	−0.730668	+	1.26555i	−0.956598	+	0.291411i	$0.905875\pi$
$734$	−0.935529	−	1.62038i	−0.0345310	−	0.0598095i
$735$	−12.8529			−0.474085
$736$	37.8652			1.39573
$737$	0.183495	+	0.317822i	0.00675911	+	0.0117071i
$738$	0.434119	+	0.751916i	0.0159801	+	0.0276784i
$739$	−3.93686	−	6.81885i	−0.144820	−	0.250835i	0.784486	−	0.620147i	$-0.212927\pi$
$739$	−3.93686	−	6.81885i	−0.144820	−	0.250835i	−0.929306	+	0.369311i	$0.879594\pi$
$740$	10.3268	+	17.8865i	0.379619	+	0.657520i
$741$	13.9056	−	24.0853i	0.510836	−	0.884795i
$742$	−0.853586	+	1.47845i	−0.0313361	+	0.0542758i
$743$	12.5686	−	21.7694i	0.461096	−	0.798642i	−0.537919	−	0.842996i	$-0.680790\pi$
$743$	12.5686	−	21.7694i	0.461096	−	0.798642i	0.999016	+	0.0443538i	$0.0141229\pi$
$744$	−9.96735	−	17.2640i	−0.365421	−	0.632928i
$745$	−0.0545227	+	0.0944361i	−0.00199756	+	0.00345987i
$746$	20.4745			0.749624
$747$	−14.2070			−0.519808
$748$	0.138065	+	0.239136i	0.00504816	+	0.00874367i
$749$	−1.13745	−	1.97012i	−0.0415614	−	0.0719865i
$750$	−5.48918	−	9.50754i	−0.200437	−	0.347166i
$751$	18.4748	−	31.9992i	0.674153	−	1.16767i	−0.302562	−	0.953130i	$-0.597842\pi$
$751$	18.4748	−	31.9992i	0.674153	−	1.16767i	0.976716	−	0.214538i	$-0.0688247\pi$
$752$	−1.64964			−0.0601563
$753$	14.2333	+	24.6528i	0.518689	+	0.898396i
$754$	−19.7346			−0.718692
$755$	−16.7100	−	3.78412i	−0.608140	−	0.137718i
$756$	1.97082			0.0716781
$757$	12.9334	+	22.4013i	0.470073	+	0.814190i	0.999414	−	0.0342188i	$-0.0108943\pi$
$757$	12.9334	+	22.4013i	0.470073	+	0.814190i	−0.529341	+	0.848409i	$0.677561\pi$
$758$	12.5117			0.454447
$759$	−0.161504	+	0.279733i	−0.00586222	+	0.0101537i
$760$	5.98484	+	10.3660i	0.217093	+	0.376016i
$761$	−7.84858	−	13.5941i	−0.284511	−	0.492787i	0.687980	−	0.725730i	$-0.258498\pi$
$761$	−7.84858	−	13.5941i	−0.284511	−	0.492787i	−0.972490	+	0.232943i	$0.925164\pi$
$762$	−7.24393	−	12.5469i	−0.262420	−	0.454525i
$763$	2.60863			0.0944387
$764$	22.1936			0.802936
$765$	−4.33820	+	7.51398i	−0.156848	+	0.271669i
$766$	10.0099	+	17.3376i	0.361672	+	0.626434i
$767$	−20.0380	+	34.7068i	−0.723530	+	1.25319i
$768$	7.88191	−	13.6519i	0.284414	−	0.492619i
$769$	24.0886	−	41.7227i	0.868657	−	1.50456i	0.00528810	−	0.999986i	$-0.498317\pi$
$769$	24.0886	−	41.7227i	0.868657	−	1.50456i	0.863369	−	0.504573i	$-0.168350\pi$
$770$	−0.00463972	−	0.00803622i	−0.000167204	−	0.000289605i
$771$	−6.66836	−	11.5499i	−0.240155	−	0.415961i
$772$	−9.02615	−	15.6337i	−0.324858	−	0.562671i
$773$	−10.1856	−	17.6419i	−0.366350	−	0.634536i	0.622642	−	0.782507i	$-0.286059\pi$
$773$	−10.1856	−	17.6419i	−0.366350	−	0.634536i	−0.988992	+	0.147970i	$0.952726\pi$
$774$	2.84982			0.102434
$775$	−18.0237			−0.647430
$776$	2.47914	+	4.29400i	0.0889959	+	0.154145i
$777$	−1.62028	+	2.80642i	−0.0581274	+	0.100680i
$778$	0.716935	+	1.24177i	0.0257034	+	0.0445195i
$779$	3.21646			0.115242
$780$	8.38284	−	14.5195i	0.300154	−	0.519882i
$781$	−0.139867			−0.00500484
$782$	−23.9366			−0.855970
$783$	−24.2878			−0.867977
$784$	−7.23896			−0.258534
$785$	2.37797	−	4.11876i	0.0848733	−	0.147005i
$786$	0.274773	+	0.475922i	0.00980085	+	0.0169756i
$787$	13.0469	−	22.5979i	0.465072	−	0.805528i	−0.534133	−	0.845400i	$-0.679362\pi$
$787$	13.0469	−	22.5979i	0.465072	−	0.805528i	0.999205	+	0.0398727i	$0.0126952\pi$
$788$	−17.8332	−	30.8880i	−0.635280	−	1.10034i
$789$	−19.8636	+	34.4048i	−0.707164	+	1.22484i
$790$	−2.52320	+	4.37032i	−0.0897716	+	0.155489i
$791$	−0.692833	+	1.20002i	−0.0246343	+	0.0426679i
$792$	−0.0592453	−	0.102616i	−0.00210519	−	0.00364630i
$793$	6.30249	+	10.9162i	0.223808	+	0.387647i
$794$	7.15681	−	12.3960i	0.253986	−	0.439916i
$795$	8.93679	+	15.4790i	0.316955	+	0.548983i
$796$	−10.9385			−0.387704
$797$	−20.0250	+	34.6843i	−0.709322	+	1.22858i	0.255787	+	0.966733i	$0.417666\pi$
$797$	−20.0250	+	34.6843i	−0.709322	+	1.22858i	−0.965109	+	0.261849i	$0.915668\pi$
$798$	−0.395956	+	0.685816i	−0.0140167	+	0.0242776i
$799$	7.95984			0.281599
$800$	−8.95178	−	15.5049i	−0.316493	−	0.548182i
$801$	1.36050	−	2.35645i	0.0480708	−	0.0832610i
$802$	2.93228	−	5.07885i	0.103542	−	0.179340i
$803$	−0.0112069	−	0.0194109i	−0.000395482	−	0.000684994i
$804$	9.44016	−	16.3508i	0.332929	−	0.576649i
$805$	−2.16493			−0.0763039
$806$	13.4800	+	23.3480i	0.474811	+	0.822397i
$807$	−1.07536	−	1.86258i	−0.0378545	−	0.0655659i
$808$	−34.5863			−1.21674
$809$	−25.5777	−	44.3019i	−0.899264	−	1.55757i	−0.828437	−	0.560082i	$-0.810770\pi$
$809$	−25.5777	−	44.3019i	−0.899264	−	1.55757i	−0.0708269	−	0.997489i	$-0.522564\pi$
$810$	−1.92935	+	3.34173i	−0.0677903	+	0.117416i
$811$	20.6810	+	35.8205i	0.726207	+	1.25783i	0.958475	+	0.285176i	$0.0920521\pi$
$811$	20.6810	+	35.8205i	0.726207	+	1.25783i	−0.232268	+	0.972652i	$0.574615\pi$
$812$	−1.51237			−0.0530740
$813$	8.00539	+	13.8657i	0.280761	+	0.486293i
$814$	0.281423			0.00986388
$815$	20.8645			0.730851
$816$	3.48322	−	6.03311i	0.121937	−	0.211201i
$817$	5.27870	−	9.14297i	0.184678	−	0.319872i
$818$	5.39788	+	9.34940i	0.188732	+	0.326894i
$819$	−1.84524			−0.0644781
$820$	1.93900			0.0677130
$821$	0.109484	−	0.189631i	0.00382100	−	0.00661817i	−0.864109	−	0.503305i	$-0.832117\pi$
$821$	0.109484	−	0.189631i	0.00382100	−	0.00661817i	0.867930	+	0.496687i	$0.165450\pi$
$822$	16.9463			0.591069
$823$	31.6607			1.10362			0.551811	−	0.833969i	$-0.313937\pi$
$823$	31.6607			1.10362			0.551811	+	0.833969i	$0.313937\pi$
$824$	16.8798	+	29.2367i	0.588036	+	1.01851i
$825$	0.152726			0.00531723
$826$	0.570571	−	0.988258i	0.0198527	−	0.0343859i
$827$	−23.4356			−0.814936			−0.407468	−	0.913220i	$-0.633588\pi$
$827$	−23.4356			−0.814936			−0.407468	+	0.913220i	$0.633588\pi$
$828$	−11.6567			−0.405097
$829$	15.2991	−	26.4988i	0.531360	−	0.920342i	−0.467970	−	0.883744i	$-0.655015\pi$
$829$	15.2991	−	26.4988i	0.531360	−	0.920342i	0.999330	−	0.0365979i	$-0.0116521\pi$
$830$	5.89439	−	10.2094i	0.204597	−	0.354373i
$831$	−9.36778	+	16.2255i	−0.324965	+	0.562855i
$832$	−6.91449	+	11.9763i	−0.239717	+	0.415202i
$833$	34.9293			1.21023
$834$	−16.1782			−0.560206
$835$	4.84890	−	8.39854i	0.167803	−	0.290644i
$836$	−0.185093			−0.00640158
$837$	16.5901	+	28.7349i	0.573437	+	0.993223i
$838$	−23.0683			−0.796883
$839$	−46.7284			−1.61324			−0.806621	−	0.591068i	$-0.798706\pi$
$839$	−46.7284			−1.61324			−0.806621	+	0.591068i	$0.798706\pi$
$840$	−0.566083	+	0.980485i	−0.0195317	+	0.0338300i
$841$	−10.3619			−0.357308
$842$	−12.7195			−0.438344
$843$	15.7542	+	27.2871i	0.542605	+	0.939819i
$844$	12.4661	−	21.5919i	0.429100	−	0.743222i
$845$	−17.8236	+	30.8715i	−0.613152	+	1.06201i
$846$	−1.44026			−0.0495172
$847$	−2.64228			−0.0907899
$848$	5.03336	+	8.71803i	0.172846	+	0.299378i
$849$	−26.8566			−0.921716
$850$	5.65889	+	9.80149i	0.194098	+	0.336188i
$851$	32.8287	−	56.8609i	1.12535	−	1.94917i
$852$	3.59784	+	6.23163i	0.123260	+	0.213492i
$853$	33.3246			1.14101			0.570506	−	0.821294i	$-0.306747\pi$
$853$	33.3246			1.14101			0.570506	+	0.821294i	$0.306747\pi$
$854$	−0.179460	−	0.310834i	−0.00614100	−	0.0106365i
$855$	−2.90794	−	5.03671i	−0.0994496	−	0.172252i
$856$	24.1040			0.823858
$857$	4.02176	−	6.96590i	0.137381	−	0.237951i	−0.789124	−	0.614234i	$-0.789465\pi$
$857$	4.02176	−	6.96590i	0.137381	−	0.237951i	0.926504	+	0.376284i	$0.122798\pi$
$858$	−0.114224	−	0.197842i	−0.00389954	−	0.00675421i
$859$	14.5526	−	25.2058i	0.496528	−	0.860011i	−0.503464	−	0.864016i	$-0.667941\pi$
$859$	14.5526	−	25.2058i	0.496528	−	0.860011i	0.999992	+	0.00400467i	$0.00127473\pi$
$860$	3.18220	−	5.51172i	0.108512	−	0.187948i
$861$	0.152116	+	0.263473i	0.00518412	+	0.00897915i
$862$	6.80861			0.231902
$863$	−7.57860	+	13.1265i	−0.257979	+	0.446832i	−0.965700	−	0.259659i	$-0.916390\pi$
$863$	−7.57860	+	13.1265i	−0.257979	+	0.446832i	0.707722	+	0.706491i	$0.249723\pi$
$864$	−16.4795	+	28.5434i	−0.560645	+	0.971065i
$865$	−12.8305			−0.436252
$866$	0.689597	+	1.19442i	0.0234335	+	0.0405879i
$867$	−5.52043	+	9.56166i	−0.187484	+	0.324731i
$868$	1.03305	+	1.78929i	0.0350638	+	0.0607323i
$869$	−0.0925324	−	0.160271i	−0.00313894	−	0.00543681i
$870$	2.94163	−	5.09506i	0.0997307	−	0.172739i
$871$	−30.2776	+	52.4423i	−1.02592	+	1.77694i
$872$	−13.8201	+	23.9370i	−0.468006	+	0.810611i
$873$	−1.20458	−	2.08639i	−0.0407687	−	0.0706135i
$874$	8.02248	−	13.8953i	0.271364	−	0.470017i
$875$	1.34921	+	2.33690i	0.0456117	+	0.0790018i
$876$	−0.576554	+	0.998620i	−0.0194799	+	0.0337402i
$877$	−50.9428			−1.72021			−0.860107	−	0.510113i	$-0.829604\pi$
$877$	−50.9428			−1.72021			−0.860107	+	0.510113i	$0.829604\pi$
$878$	21.0788			0.711376
$879$	−44.2975			−1.49412
$880$	−0.0547182			−0.00184455
$881$	11.0985	−	19.2231i	0.373918	−	0.647644i	−0.616247	−	0.787553i	$-0.711348\pi$
$881$	11.0985	−	19.2231i	0.373918	−	0.647644i	0.990164	+	0.139909i	$0.0446809\pi$
$882$	−6.32014			−0.212810
$883$	−9.28337	−	16.0793i	−0.312410	−	0.541110i	0.666473	−	0.745529i	$-0.267803\pi$
$883$	−9.28337	−	16.0793i	−0.312410	−	0.541110i	−0.978884	+	0.204419i	$0.934470\pi$
$884$	−22.7814	+	39.4586i	−0.766223	+	1.32714i
$885$	−5.97371	−	10.3468i	−0.200804	−	0.347803i
$886$	18.9949			0.638146
$887$	41.6701			1.39914			0.699572	−	0.714562i	$-0.253374\pi$
$887$	41.6701			1.39914			0.699572	+	0.714562i	$0.253374\pi$
$888$	−17.1680	−	29.7358i	−0.576120	−	0.997868i
$889$	1.78052	+	3.08395i	0.0597168	+	0.103433i
$890$	1.12892	+	1.95534i	0.0378414	+	0.0655432i
$891$	−0.0707541	−	0.122550i	−0.00237035	−	0.00410557i
$892$	12.7659	−	22.1113i	0.427435	−	0.740340i
$893$	−2.66778	+	4.62074i	−0.0892740	+	0.154627i
$894$	0.0382207	−	0.0662003i	0.00127829	−	0.00221407i
$895$	10.1753	+	17.6241i	0.340123	+	0.589110i
$896$	−1.21055	+	2.09673i	−0.0404416	+	0.0700470i
$897$	−53.2980			−1.77957
$898$	10.3596			0.345705
$899$	−12.7309	−	22.0506i	−0.424601	−	0.735430i
$900$	2.75577	+	4.77314i	0.0918591	+	0.159105i
$901$	−24.2869	−	42.0661i	−0.809113	−	1.40142i
$902$	0.0132104	−	0.0228810i	0.000439857	−	0.000761855i
$903$	0.998583			0.0332308
$904$	−7.34102	−	12.7150i	−0.244159	−	0.422895i
$905$	10.7136			0.356132
$906$	11.7138	+	2.65269i	0.389166	+	0.0881297i
$907$	−28.7800			−0.955625			−0.477812	−	0.878462i	$-0.658570\pi$
$907$	−28.7800			−0.955625			−0.477812	+	0.878462i	$0.658570\pi$
$908$	−4.32380	−	7.48905i	−0.143490	−	0.248533i
$909$	16.8050			0.557385
$910$	0.765577	−	1.32602i	0.0253786	−	0.0439571i
$911$	23.3824	+	40.4996i	0.774695	+	1.34181i	0.934966	+	0.354738i	$0.115430\pi$
$911$	23.3824	+	40.4996i	0.774695	+	1.34181i	−0.160271	+	0.987073i	$0.551237\pi$
$912$	2.33484	+	4.04406i	0.0773143	+	0.133912i
$913$	0.216162	+	0.374404i	0.00715392	+	0.0123910i
$914$	−5.67803			−0.187813
$915$	−3.75779			−0.124229
$916$	7.47886	−	12.9538i	0.247108	−	0.428004i
$917$	−0.0675379	−	0.116979i	−0.00223030	−	0.00386299i
$918$	10.4176	−	18.0438i	0.343831	−	0.595533i
$919$	−25.5376	+	44.2325i	−0.842409	+	1.45909i	0.0454441	+	0.998967i	$0.485530\pi$
$919$	−25.5376	+	44.2325i	−0.842409	+	1.45909i	−0.887853	+	0.460128i	$0.847804\pi$
$920$	11.4694	−	19.8657i	0.378136	−	0.654952i
$921$	−13.1833	−	22.8342i	−0.434405	−	0.752412i
$922$	3.48575	+	6.03749i	0.114797	+	0.198834i
$923$	−11.5394	−	19.9868i	−0.379824	−	0.657874i
$924$	−0.00875363	−	0.0151617i	−0.000287973	−	0.000498784i
$925$	−31.0444			−1.02073
$926$	−12.1560			−0.399471
$927$	−8.20165	−	14.2057i	−0.269377	−	0.466575i
$928$	12.6461	−	21.9037i	0.415129	−	0.719024i
$929$	13.8468	+	23.9833i	0.454298	+	0.786866i	0.998648	−	0.0519918i	$-0.0165570\pi$
$929$	13.8468	+	23.9833i	0.454298	+	0.786866i	−0.544350	+	0.838858i	$0.683224\pi$
$930$	−8.03727			−0.263552
$931$	−11.7068	+	20.2767i	−0.383674	+	0.664542i
$932$	28.7439			0.941538
$933$	−41.3625			−1.35415
$934$	−15.4023			−0.503978
$935$	0.264025			0.00863455
$936$	9.77578	−	16.9322i	0.319531	−	0.553445i
$937$	20.9558	+	36.2964i	0.684595	+	1.18575i	0.973564	+	0.228414i	$0.0733541\pi$
$937$	20.9558	+	36.2964i	0.684595	+	1.18575i	−0.288969	+	0.957338i	$0.593313\pi$
$938$	0.862138	−	1.49327i	0.0281498	−	0.0487569i
$939$	21.5347	+	37.2992i	0.702758	+	1.21721i
$940$	−1.60824	+	2.78555i	−0.0524550	+	0.0908548i
$941$	−4.56935	+	7.91435i	−0.148957	+	0.258000i	−0.930842	−	0.365422i	$-0.880925\pi$
$941$	−4.56935	+	7.91435i	−0.148957	+	0.258000i	0.781886	+	0.623422i	$0.214258\pi$
$942$	−1.66697	+	2.88727i	−0.0543128	+	0.0940725i
$943$	−3.08204	−	5.33825i	−0.100365	−	0.173837i
$944$	−3.36450	−	5.82748i	−0.109505	−	0.189668i
$945$	0.942214	−	1.63196i	0.0306502	−	0.0530877i
$946$	−0.0433604	−	0.0751024i	−0.00140977	−	0.00244179i
$947$	−13.7974			−0.448356			−0.224178	−	0.974548i	$-0.571970\pi$
$947$	−13.7974			−0.448356			−0.224178	+	0.974548i	$0.571970\pi$
$948$	−4.76046	+	8.24537i	−0.154613	+	0.267797i
$949$	1.84919	−	3.20289i	0.0600273	−	0.103970i
$950$	−7.58644			−0.246137
$951$	−19.2744	−	33.3843i	−0.625016	−	1.08256i
$952$	1.53840	−	2.66459i	0.0498600	−	0.0863600i
$953$	−25.0793	+	43.4386i	−0.812397	+	1.40711i	0.0987845	+	0.995109i	$0.468505\pi$
$953$	−25.0793	+	43.4386i	−0.812397	+	1.40711i	−0.911182	+	0.412005i	$0.864829\pi$
$954$	4.39449	+	7.61148i	0.142277	+	0.246431i
$955$	10.6103	−	18.3776i	0.343342	−	0.594687i
$956$	9.67478			0.312905
$957$	0.107877	+	0.186849i	0.00348717	+	0.00603996i
$958$	−1.12298	−	1.94507i	−0.0362820	−	0.0628423i
$959$	−4.16530			−0.134505
$960$	−2.06134	−	3.57035i	−0.0665296	−	0.115233i
$961$	−1.89204	+	3.27711i	−0.0610336	+	0.105713i
$962$	23.2181	+	40.2150i	0.748583	+	1.29658i
$963$	−11.7118			−0.377406
$964$	−4.57725	−	7.92803i	−0.147423	−	0.255345i
$965$	−17.2609			−0.555649
$966$	1.51763			0.0488290
$967$	11.4677	−	19.8626i	0.368776	−	0.638739i	−0.620598	−	0.784129i	$-0.713110\pi$
$967$	11.4677	−	19.8626i	0.368776	−	0.638739i	0.989375	+	0.145389i	$0.0464435\pi$
$968$	13.9984	−	24.2459i	0.449924	−	0.779292i
$969$	−11.2660	−	19.5133i	−0.361917	−	0.626859i
$970$	1.99908			0.0641865
$971$	−8.99634			−0.288706			−0.144353	−	0.989526i	$-0.546110\pi$
$971$	−8.99634			−0.288706			−0.144353	+	0.989526i	$0.546110\pi$
$972$	8.66536	−	15.0088i	0.277942	−	0.481409i
$973$	3.97652			0.127482
$974$	0.891566			0.0285676
$975$	12.6003	+	21.8243i	0.403532	+	0.698938i
$976$	−2.11645			−0.0677460
$977$	−8.65200	+	14.9857i	−0.276802	+	0.479435i	−0.970588	−	0.240746i	$-0.922608\pi$
$977$	−8.65200	+	14.9857i	−0.276802	+	0.479435i	0.693786	+	0.720181i	$0.255941\pi$
$978$	−14.6261			−0.467692
$979$	−0.0828006			−0.00264632
$980$	−7.05727	+	12.2236i	−0.225436	+	0.390467i
$981$	6.71496	−	11.6307i	0.214392	−	0.371338i
$982$	0.121473	−	0.210398i	0.00387637	−	0.00671407i
$983$	14.8702	−	25.7559i	0.474285	−	0.821485i	−0.525282	−	0.850928i	$-0.676040\pi$
$983$	14.8702	−	25.7559i	0.474285	−	0.821485i	0.999566	+	0.0294431i	$0.00937339\pi$
$984$	−3.22355			−0.102763
$985$	−34.1028			−1.08661
$986$	−7.99426	+	13.8465i	−0.254589	+	0.440962i
$987$	−0.504671			−0.0160639
$988$	−15.2707	−	26.4496i	−0.485825	−	0.841473i
$989$	−20.2324			−0.643351
$990$	−0.0477730			−0.00151833
$991$	12.9984	−	22.5139i	0.412908	−	0.715177i	−0.582298	−	0.812975i	$-0.697846\pi$
$991$	12.9984	−	22.5139i	0.412908	−	0.715177i	0.995206	+	0.0977977i	$0.0311798\pi$
$992$	−34.5523			−1.09704
$993$	−13.1797			−0.418244
$994$	0.328578	+	0.569114i	0.0104219	+	0.0180512i
$995$	−5.22949	+	9.05774i	−0.165786	+	0.287150i
$996$	11.1208	−	19.2618i	0.352376	−	0.610332i
$997$	−19.5211			−0.618240			−0.309120	−	0.951023i	$-0.600035\pi$
$997$	−19.5211			−0.618240			−0.309120	+	0.951023i	$0.600035\pi$
$998$	14.4397			0.457082
$999$	28.5751	+	49.4935i	0.904077	+	1.56591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.c.a.32.5	✓	12
151.118	even	3	inner	151.2.c.a.118.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.c.a.32.5	✓	12	1.1	even	1	trivial
151.2.c.a.118.5	yes	12	151.118	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.368036 + 0.637457i) q^{2} +1.32785 q^{3} +(0.729099 - 1.26284i) q^{4} +(-0.697137 - 1.20748i) q^{5} +(0.488697 + 0.846448i) q^{6} +(-0.120119 - 0.208053i) q^{7} +2.54548 q^{8} -1.23681 q^{9} +O(q^{10})\)	\(q+(0.368036 + 0.637457i) q^{2} +1.32785 q^{3} +(0.729099 - 1.26284i) q^{4} +(-0.697137 - 1.20748i) q^{5} +(0.488697 + 0.846448i) q^{6} +(-0.120119 - 0.208053i) q^{7} +2.54548 q^{8} -1.23681 q^{9} +(0.513143 - 0.888790i) q^{10} +(0.0188183 + 0.0325942i) q^{11} +(0.968134 - 1.67686i) q^{12} +(-3.10511 + 5.37821i) q^{13} +(0.0884165 - 0.153142i) q^{14} +(-0.925694 - 1.60335i) q^{15} +(-0.521367 - 0.903034i) q^{16} +(2.51569 + 4.35731i) q^{17} +(-0.455192 - 0.788415i) q^{18} -3.37259 q^{19} -2.03313 q^{20} +(-0.159500 - 0.276263i) q^{21} +(-0.0138516 + 0.0239917i) q^{22} +(3.23165 + 5.59738i) q^{23} +3.38002 q^{24} +(1.52800 - 2.64657i) q^{25} -4.57118 q^{26} -5.62585 q^{27} -0.350315 q^{28} +4.31718 q^{29} +(0.681378 - 1.18018i) q^{30} +(-2.94890 - 5.10765i) q^{31} +(2.92925 - 5.07361i) q^{32} +(0.0249879 + 0.0432803i) q^{33} +(-1.85173 + 3.20729i) q^{34} +(-0.167479 + 0.290082i) q^{35} +(-0.901758 + 1.56189i) q^{36} +(-5.07925 - 8.79752i) q^{37} +(-1.24124 - 2.14989i) q^{38} +(-4.12313 + 7.14147i) q^{39} +(-1.77455 - 3.07361i) q^{40} -0.953705 q^{41} +(0.117404 - 0.203350i) q^{42} +(-1.56517 + 2.71096i) q^{43} +0.0548815 q^{44} +(0.862228 + 1.49342i) q^{45} +(-2.37873 + 4.12008i) q^{46} +(0.791018 - 1.37008i) q^{47} +(-0.692298 - 1.19909i) q^{48} +(3.47114 - 6.01220i) q^{49} +2.24944 q^{50} +(3.34046 + 5.78585i) q^{51} +(4.52787 + 7.84250i) q^{52} -9.65415 q^{53} +(-2.07052 - 3.58624i) q^{54} +(0.0262378 - 0.0454453i) q^{55} +(-0.305762 - 0.529595i) q^{56} -4.47830 q^{57} +(1.58888 + 2.75202i) q^{58} +6.45322 q^{59} -2.69969 q^{60} +(1.01486 - 1.75778i) q^{61} +(2.17061 - 3.75960i) q^{62} +(0.148565 + 0.257322i) q^{63} +2.22681 q^{64} +8.65876 q^{65} +(-0.0183929 + 0.0318574i) q^{66} +9.75088 q^{67} +7.33675 q^{68} +(4.29115 + 7.43248i) q^{69} -0.246554 q^{70} +(-1.85813 + 3.21837i) q^{71} -3.14829 q^{72} -0.595531 q^{73} +(3.73869 - 6.47561i) q^{74} +(2.02896 - 3.51425i) q^{75} +(-2.45895 + 4.25903i) q^{76} +(0.00452088 - 0.00783039i) q^{77} -6.06984 q^{78} -4.91715 q^{79} +(-0.726929 + 1.25908i) q^{80} -3.75986 q^{81} +(-0.350998 - 0.607947i) q^{82} +11.4868 q^{83} -0.465166 q^{84} +(3.50756 - 6.07528i) q^{85} -2.30416 q^{86} +5.73257 q^{87} +(0.0479016 + 0.0829681i) q^{88} +(-1.10000 + 1.90526i) q^{89} +(-0.634662 + 1.09927i) q^{90} +1.49194 q^{91} +9.42476 q^{92} +(-3.91570 - 6.78219i) q^{93} +1.16449 q^{94} +(2.35116 + 4.07233i) q^{95} +(3.88960 - 6.73699i) q^{96} +(0.973937 + 1.68691i) q^{97} +5.11003 q^{98} +(-0.0232747 - 0.0403129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 2 q^{3} - 10 q^{4} - 7 q^{5} - 5 q^{6} - 6 q^{7} + 22 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 2 * q^3 - 10 * q^4 - 7 * q^5 - 5 * q^6 - 6 * q^7 + 22 * q^9	\( 12 q - 4 q^{2} - 2 q^{3} - 10 q^{4} - 7 q^{5} - 5 q^{6} - 6 q^{7} + 22 q^{9} - 17 q^{10} + 6 q^{11} + 24 q^{12} - 3 q^{13} + q^{14} + 2 q^{15} - 10 q^{16} + 5 q^{17} - 5 q^{18} - 12 q^{19} - 4 q^{20} + 11 q^{21} - 9 q^{22} + 18 q^{23} + 2 q^{24} - 5 q^{25} - 60 q^{26} - 56 q^{27} + 80 q^{28} + 34 q^{29} + 44 q^{30} + 8 q^{31} + 11 q^{32} - 19 q^{33} - 2 q^{34} + 18 q^{35} - 55 q^{36} + 2 q^{37} + 18 q^{38} + 6 q^{39} - 24 q^{40} + 18 q^{41} - 31 q^{42} - 9 q^{43} - 32 q^{44} - 3 q^{45} + 6 q^{46} + 7 q^{47} + 47 q^{48} - 6 q^{49} + 24 q^{50} + 13 q^{51} - 4 q^{52} - 40 q^{53} + 18 q^{54} + 6 q^{55} - 6 q^{56} + 12 q^{57} + 17 q^{58} - 46 q^{59} - 46 q^{60} + 12 q^{61} + 37 q^{62} - 19 q^{63} - 12 q^{64} - 44 q^{65} + 11 q^{66} + 20 q^{67} - 20 q^{68} - 8 q^{69} + 30 q^{70} + 29 q^{71} - 18 q^{72} - 18 q^{73} + 47 q^{74} + 44 q^{75} + 28 q^{76} - q^{77} + 50 q^{78} - 4 q^{79} - 2 q^{80} + 68 q^{81} - q^{82} + 2 q^{83} - 88 q^{84} - 15 q^{85} - 2 q^{86} - 74 q^{87} - 31 q^{88} - 39 q^{89} - 89 q^{90} + 10 q^{91} - 48 q^{92} - 3 q^{93} + 64 q^{94} + 8 q^{95} + 6 q^{96} - 4 q^{97} - 6 q^{98} + 42 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 - 10 * q^4 - 7 * q^5 - 5 * q^6 - 6 * q^7 + 22 * q^9 - 17 * q^10 + 6 * q^11 + 24 * q^12 - 3 * q^13 + q^14 + 2 * q^15 - 10 * q^16 + 5 * q^17 - 5 * q^18 - 12 * q^19 - 4 * q^20 + 11 * q^21 - 9 * q^22 + 18 * q^23 + 2 * q^24 - 5 * q^25 - 60 * q^26 - 56 * q^27 + 80 * q^28 + 34 * q^29 + 44 * q^30 + 8 * q^31 + 11 * q^32 - 19 * q^33 - 2 * q^34 + 18 * q^35 - 55 * q^36 + 2 * q^37 + 18 * q^38 + 6 * q^39 - 24 * q^40 + 18 * q^41 - 31 * q^42 - 9 * q^43 - 32 * q^44 - 3 * q^45 + 6 * q^46 + 7 * q^47 + 47 * q^48 - 6 * q^49 + 24 * q^50 + 13 * q^51 - 4 * q^52 - 40 * q^53 + 18 * q^54 + 6 * q^55 - 6 * q^56 + 12 * q^57 + 17 * q^58 - 46 * q^59 - 46 * q^60 + 12 * q^61 + 37 * q^62 - 19 * q^63 - 12 * q^64 - 44 * q^65 + 11 * q^66 + 20 * q^67 - 20 * q^68 - 8 * q^69 + 30 * q^70 + 29 * q^71 - 18 * q^72 - 18 * q^73 + 47 * q^74 + 44 * q^75 + 28 * q^76 - q^77 + 50 * q^78 - 4 * q^79 - 2 * q^80 + 68 * q^81 - q^82 + 2 * q^83 - 88 * q^84 - 15 * q^85 - 2 * q^86 - 74 * q^87 - 31 * q^88 - 39 * q^89 - 89 * q^90 + 10 * q^91 - 48 * q^92 - 3 * q^93 + 64 * q^94 + 8 * q^95 + 6 * q^96 - 4 * q^97 - 6 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more