LMFDB - Embedded newform 299.2.i.b.231.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(231,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("299.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.i (of order $6$, 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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			231.11
Character	$\chi$	$=$	299.231
Dual form			299.2.i.b.277.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09124 - 0.630030i) q^{2} +(0.0678705 + 0.117555i) q^{3} +(-0.206124 + 0.357017i) q^{4} -3.87251i q^{5} +(0.148127 + 0.0855209i) q^{6} +(-0.798718 - 0.461140i) q^{7} +3.03958i q^{8} +(1.49079 - 2.58212i) q^{9} +O(q^{10})$	\(q+(1.09124 - 0.630030i) q^{2} +(0.0678705 + 0.117555i) q^{3} +(-0.206124 + 0.357017i) q^{4} -3.87251i q^{5} +(0.148127 + 0.0855209i) q^{6} +(-0.798718 - 0.461140i) q^{7} +3.03958i q^{8} +(1.49079 - 2.58212i) q^{9} +(-2.43980 - 4.22586i) q^{10} +(2.06349 - 1.19136i) q^{11} -0.0559589 q^{12} +(0.937975 - 3.48141i) q^{13} -1.16213 q^{14} +(0.455234 - 0.262830i) q^{15} +(1.50278 + 2.60289i) q^{16} +(-2.44813 + 4.24028i) q^{17} -3.75696i q^{18} +(2.28593 + 1.31978i) q^{19} +(1.38255 + 0.798218i) q^{20} -0.125191i q^{21} +(1.50118 - 2.60012i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.357318 + 0.206298i) q^{24} -9.99637 q^{25} +(-1.16983 - 4.39002i) q^{26} +0.811945 q^{27} +(0.329270 - 0.190104i) q^{28} +(2.56524 + 4.44312i) q^{29} +(0.331181 - 0.573622i) q^{30} +7.64997i q^{31} +(-1.98491 - 1.14599i) q^{32} +(0.280100 + 0.161716i) q^{33} +6.16958i q^{34} +(-1.78577 + 3.09305i) q^{35} +(0.614574 + 1.06447i) q^{36} +(8.84784 - 5.10830i) q^{37} +3.32601 q^{38} +(0.472918 - 0.126021i) q^{39} +11.7708 q^{40} +(-7.90240 + 4.56245i) q^{41} +(-0.0788743 - 0.136614i) q^{42} +(1.60647 - 2.78249i) q^{43} +0.982268i q^{44} +(-9.99929 - 5.77309i) q^{45} +(-1.09124 - 0.630030i) q^{46} +12.9831i q^{47} +(-0.203989 + 0.353319i) q^{48} +(-3.07470 - 5.32554i) q^{49} +(-10.9085 + 6.29801i) q^{50} -0.664623 q^{51} +(1.04958 + 1.05247i) q^{52} -1.47076 q^{53} +(0.886030 - 0.511550i) q^{54} +(-4.61355 - 7.99090i) q^{55} +(1.40167 - 2.42777i) q^{56} +0.358297i q^{57} +(5.59860 + 3.23235i) q^{58} +(-1.76608 - 1.01965i) q^{59} +0.216702i q^{60} +(-5.00414 + 8.66743i) q^{61} +(4.81971 + 8.34798i) q^{62} +(-2.38144 + 1.37492i) q^{63} -8.89914 q^{64} +(-13.4818 - 3.63232i) q^{65} +0.407544 q^{66} +(8.69516 - 5.02015i) q^{67} +(-1.00924 - 1.74805i) q^{68} +(0.0678705 - 0.117555i) q^{69} +4.50036i q^{70} +(6.93734 + 4.00528i) q^{71} +(7.84855 + 4.53136i) q^{72} -4.74277i q^{73} +(6.43677 - 11.1488i) q^{74} +(-0.678459 - 1.17512i) q^{75} +(-0.942368 + 0.544077i) q^{76} -2.19753 q^{77} +(0.436672 - 0.435473i) q^{78} +13.5774 q^{79} +(10.0797 - 5.81953i) q^{80} +(-4.41725 - 7.65091i) q^{81} +(-5.74897 + 9.95750i) q^{82} +9.82073i q^{83} +(0.0446954 + 0.0258049i) q^{84} +(16.4206 + 9.48041i) q^{85} -4.04850i q^{86} +(-0.348208 + 0.603114i) q^{87} +(3.62122 + 6.27214i) q^{88} +(4.60459 - 2.65846i) q^{89} -14.5489 q^{90} +(-2.35460 + 2.34813i) q^{91} +0.412248 q^{92} +(-0.899293 + 0.519207i) q^{93} +(8.17972 + 14.1677i) q^{94} +(5.11087 - 8.85228i) q^{95} -0.311115i q^{96} +(6.06178 + 3.49977i) q^{97} +(-6.71050 - 3.87431i) q^{98} -7.10424i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/299\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.09124	−	0.630030i	0.771626	−	0.445499i	−0.0618282	−	0.998087i	$-0.519693\pi$
$2$	1.09124	−	0.630030i	0.771626	−	0.445499i	0.833454	+	0.552588i	$0.186360\pi$
$3$	0.0678705	+	0.117555i	0.0391851	+	0.0678705i	0.884953	−	0.465681i	$-0.154190\pi$
$3$	0.0678705	+	0.117555i	0.0391851	+	0.0678705i	−0.845768	+	0.533551i	$0.820857\pi$
$4$	−0.206124	+	0.357017i	−0.103062	+	0.178509i
$5$		−	3.87251i		−	1.73184i	−0.500182	−	0.865921i	$-0.666733\pi$
$5$		−	3.87251i		−	1.73184i	0.500182	−	0.865921i	$-0.333267\pi$
$6$	0.148127	+	0.0855209i	0.0604724	+	0.0349138i
$7$	−0.798718	−	0.461140i	−0.301887	−	0.174295i	0.341403	−	0.939917i	$-0.389098\pi$
$7$	−0.798718	−	0.461140i	−0.301887	−	0.174295i	−0.643290	+	0.765622i	$0.722431\pi$
$8$			3.03958i			1.07465i
$9$	1.49079	−	2.58212i	0.496929	−	0.860706i
$10$	−2.43980	−	4.22586i	−0.771533	−	1.33633i
$11$	2.06349	−	1.19136i	0.622166	−	0.359208i	−0.155546	−	0.987829i	$-0.549714\pi$
$11$	2.06349	−	1.19136i	0.622166	−	0.359208i	0.777712	+	0.628621i	$0.216380\pi$
$12$	−0.0559589			−0.0161540
$13$	0.937975	−	3.48141i	0.260147	−	0.965569i
$13$	0.937975	−	3.48141i	0.260147	−	0.965569i
$14$	−1.16213			−0.310592
$15$	0.455234	−	0.262830i	0.117541	−	0.0678623i
$16$	1.50278	+	2.60289i	0.375695	+	0.650722i
$17$	−2.44813	+	4.24028i	−0.593759	+	1.02842i	0.399962	+	0.916532i	$0.369023\pi$
$17$	−2.44813	+	4.24028i	−0.593759	+	1.02842i	−0.993721	+	0.111888i	$0.964310\pi$
$18$		−	3.75696i		−	0.885525i
$19$	2.28593	+	1.31978i	0.524427	+	0.302778i	0.738744	−	0.673986i	$-0.235419\pi$
$19$	2.28593	+	1.31978i	0.524427	+	0.302778i	−0.214317	+	0.976764i	$0.568752\pi$
$20$	1.38255	+	0.798218i	0.309148	+	0.178487i
$21$		−	0.125191i		−	0.0273190i
$22$	1.50118	−	2.60012i	0.320053	−	0.554348i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.357318	+	0.206298i	−0.0729373	+	0.0421103i
$25$	−9.99637			−1.99927
$26$	−1.16983	−	4.39002i	−0.229423	−	0.860954i
$27$	0.811945			0.156259
$28$	0.329270	−	0.190104i	0.0622262	−	0.0359263i
$29$	2.56524	+	4.44312i	0.476353	+	0.825067i	0.999633	−	0.0270937i	$-0.00862526\pi$
$29$	2.56524	+	4.44312i	0.476353	+	0.825067i	−0.523280	+	0.852161i	$0.675292\pi$
$30$	0.331181	−	0.573622i	0.0604651	−	0.104729i
$31$			7.64997i			1.37397i	0.726670	+	0.686987i	$0.241067\pi$
$31$			7.64997i			1.37397i	−0.726670	+	0.686987i	$0.758933\pi$
$32$	−1.98491	−	1.14599i	−0.350885	−	0.202584i
$33$	0.280100	+	0.161716i	0.0487592	+	0.0281511i
$34$			6.16958i			1.05807i
$35$	−1.78577	+	3.09305i	−0.301851	+	0.522821i
$36$	0.614574	+	1.06447i	0.102429	+	0.177412i
$37$	8.84784	−	5.10830i	1.45458	−	0.839800i	0.455839	−	0.890062i	$-0.349339\pi$
$37$	8.84784	−	5.10830i	1.45458	−	0.839800i	0.998736	+	0.0502624i	$0.0160058\pi$
$38$	3.32601			0.539549
$39$	0.472918	−	0.126021i	0.0757275	−	0.0201795i
$40$	11.7708			1.86113
$41$	−7.90240	+	4.56245i	−1.23415	+	0.712536i	−0.967892	−	0.251367i	$-0.919120\pi$
$41$	−7.90240	+	4.56245i	−1.23415	+	0.712536i	−0.266256	+	0.963902i	$0.585787\pi$
$42$	−0.0788743	−	0.136614i	−0.0121706	−	0.0210800i
$43$	1.60647	−	2.78249i	0.244985	−	0.424326i	−0.717143	−	0.696926i	$-0.754550\pi$
$43$	1.60647	−	2.78249i	0.244985	−	0.424326i	0.962127	+	0.272601i	$0.0878838\pi$
$44$			0.982268i			0.148083i
$45$	−9.99929	−	5.77309i	−1.49061	−	0.860602i
$46$	−1.09124	−	0.630030i	−0.160895	−	0.0928929i
$47$			12.9831i			1.89377i	0.321566	+	0.946887i	$0.395791\pi$
$47$			12.9831i			1.89377i	−0.321566	+	0.946887i	$0.604209\pi$
$48$	−0.203989	+	0.353319i	−0.0294432	+	0.0509972i
$49$	−3.07470	−	5.32554i	−0.439243	−	0.760791i
$50$	−10.9085	+	6.29801i	−1.54269	+	0.890674i
$51$	−0.664623			−0.0930658
$52$	1.04958	+	1.05247i	0.145551	+	0.145952i
$53$	−1.47076			−0.202025			−0.101012	−	0.994885i	$-0.532208\pi$
$53$	−1.47076			−0.202025			−0.101012	+	0.994885i	$0.532208\pi$
$54$	0.886030	−	0.511550i	0.120573	−	0.0696131i
$55$	−4.61355	−	7.99090i	−0.622090	−	1.07749i
$56$	1.40167	−	2.42777i	0.187306	−	0.324424i
$57$			0.358297i			0.0474575i
$58$	5.59860	+	3.23235i	0.735132	+	0.424429i
$59$	−1.76608	−	1.01965i	−0.229924	−	0.132747i	0.380613	−	0.924735i	$-0.375713\pi$
$59$	−1.76608	−	1.01965i	−0.229924	−	0.132747i	−0.610537	+	0.791988i	$0.709046\pi$
$60$			0.216702i			0.0279761i
$61$	−5.00414	+	8.66743i	−0.640715	+	1.10975i	0.344559	+	0.938765i	$0.388029\pi$
$61$	−5.00414	+	8.66743i	−0.640715	+	1.10975i	−0.985274	+	0.170986i	$0.945305\pi$
$62$	4.81971	+	8.34798i	0.612104	+	1.06019i
$63$	−2.38144	+	1.37492i	−0.300033	+	0.173224i
$64$	−8.89914			−1.11239
$65$	−13.4818	−	3.63232i	−1.67221	−	0.450534i
$66$	0.407544			0.0501652
$67$	8.69516	−	5.02015i	1.06228	−	0.613310i	0.136220	−	0.990679i	$-0.456504\pi$
$67$	8.69516	−	5.02015i	1.06228	−	0.613310i	0.926063	+	0.377369i	$0.123171\pi$
$68$	−1.00924	−	1.74805i	−0.122388	−	0.211982i
$69$	0.0678705	−	0.117555i	0.00817065	−	0.0141520i
$70$			4.50036i			0.537896i
$71$	6.93734	+	4.00528i	0.823311	+	0.475339i	0.851557	−	0.524262i	$-0.175659\pi$
$71$	6.93734	+	4.00528i	0.823311	+	0.475339i	−0.0282458	+	0.999601i	$0.508992\pi$
$72$	7.84855	+	4.53136i	0.924961	+	0.534026i
$73$		−	4.74277i		−	0.555099i	−0.960711	−	0.277550i	$-0.910478\pi$
$73$		−	4.74277i		−	0.555099i	0.960711	−	0.277550i	$-0.0895223\pi$
$74$	6.43677	−	11.1488i	0.748259	−	1.29602i
$75$	−0.678459	−	1.17512i	−0.0783416	−	0.135692i
$76$	−0.942368	+	0.544077i	−0.108097	+	0.0624099i
$77$	−2.19753			−0.250432
$78$	0.436672	−	0.435473i	0.0494434	−	0.0493076i
$79$	13.5774			1.52757			0.763786	−	0.645470i	$-0.223338\pi$
$79$	13.5774			1.52757			0.763786	+	0.645470i	$0.223338\pi$
$80$	10.0797	−	5.81953i	1.12695	−	0.650643i
$81$	−4.41725	−	7.65091i	−0.490806	−	0.850101i
$82$	−5.74897	+	9.95750i	−0.634867	+	1.09962i
$83$			9.82073i			1.07797i	0.842317	+	0.538983i	$0.181191\pi$
$83$			9.82073i			1.07797i	−0.842317	+	0.538983i	$0.818809\pi$
$84$	0.0446954	+	0.0258049i	0.00487667	+	0.00281555i
$85$	16.4206	+	9.48041i	1.78106	+	1.02830i
$86$		−	4.04850i		−	0.436561i
$87$	−0.348208	+	0.603114i	−0.0373318	+	0.0646606i
$88$	3.62122	+	6.27214i	0.386024	+	0.668612i
$89$	4.60459	−	2.65846i	0.488086	−	0.281797i	−0.235694	−	0.971827i	$-0.575736\pi$
$89$	4.60459	−	2.65846i	0.488086	−	0.281797i	0.723780	+	0.690031i	$0.242403\pi$
$90$	−14.5489			−1.53359
$91$	−2.35460	+	2.34813i	−0.246829	+	0.246151i
$92$	0.412248			0.0429798
$93$	−0.899293	+	0.519207i	−0.0932523	+	0.0538393i
$94$	8.17972	+	14.1677i	0.843674	+	1.46129i
$95$	5.11087	−	8.85228i	0.524364	−	0.908225i
$96$		−	0.311115i		−	0.0317530i
$97$	6.06178	+	3.49977i	0.615480	+	0.355348i	0.775107	−	0.631830i	$-0.217696\pi$
$97$	6.06178	+	3.49977i	0.615480	+	0.355348i	−0.159627	+	0.987177i	$0.551029\pi$
$98$	−6.71050	−	3.87431i	−0.677863	−	0.391364i
$99$		−	7.10424i		−	0.714003i
$100$	2.06049	−	3.56887i	0.206049	−	0.356887i
$101$	1.61517	+	2.79756i	0.160715	+	0.278367i	0.935125	−	0.354317i	$-0.115287\pi$
$101$	1.61517	+	2.79756i	0.160715	+	0.278367i	−0.774410	+	0.632684i	$0.781953\pi$
$102$	−0.725266	+	0.418733i	−0.0718120	+	0.0414607i
$103$	−7.72003			−0.760677			−0.380338	−	0.924847i	$-0.624192\pi$
$103$	−7.72003			−0.760677			−0.380338	+	0.924847i	$0.624192\pi$
$104$	10.5820	+	2.85105i	1.03765	+	0.279568i
$105$	−0.484805			−0.0473121
$106$	−1.60496	+	0.926624i	−0.155888	+	0.0900017i
$107$	−9.46380	−	16.3918i	−0.914900	−	1.58465i	−0.807048	−	0.590486i	$-0.798936\pi$
$107$	−9.46380	−	16.3918i	−0.914900	−	1.58465i	−0.107852	−	0.994167i	$-0.534397\pi$
$108$	−0.167361	+	0.289878i	−0.0161043	+	0.0278935i
$109$			1.54474i			0.147959i	0.997260	+	0.0739797i	$0.0235700\pi$
$109$			1.54474i			0.147959i	−0.997260	+	0.0739797i	$0.976430\pi$
$110$	−10.0690	−	5.81335i	−0.960043	−	0.554281i
$111$	1.20101	+	0.693406i	0.113995	+	0.0658152i
$112$		−	2.77197i		−	0.261926i
$113$	4.60244	−	7.97166i	0.432961	−	0.749910i	−0.564166	−	0.825662i	$-0.690802\pi$
$113$	4.60244	−	7.97166i	0.432961	−	0.749910i	0.997127	+	0.0757511i	$0.0241354\pi$
$114$	0.225738	+	0.390989i	0.0211423	+	0.0366195i
$115$	−3.35370	+	1.93626i	−0.312734	+	0.180557i
$116$	−2.11503			−0.196375
$117$	−7.59109	−	7.61200i	−0.701796	−	0.703730i
$118$	−2.56964			−0.236554
$119$	3.91073	−	2.25786i	0.358496	−	0.206978i
$120$	0.798891	+	1.38372i	0.0729284	+	0.126316i
$121$	−2.66134	+	4.60957i	−0.241940	+	0.419052i
$122$			12.6110i			1.14175i
$123$	−1.07268	−	0.619312i	−0.0967203	−	0.0558415i
$124$	−2.73117	−	1.57684i	−0.245266	−	0.141604i
$125$			19.3485i			1.73058i
$126$	−1.73249	+	3.00076i	−0.154342	+	0.267329i
$127$	−5.90953	−	10.2356i	−0.524386	−	0.908264i	−0.999597	−	0.0283915i	$-0.990961\pi$
$127$	−5.90953	−	10.2356i	−0.524386	−	0.908264i	0.475211	−	0.879872i	$-0.342372\pi$
$128$	−5.74132	+	3.31475i	−0.507466	+	0.292985i
$129$	0.436128			0.0383989
$130$	−17.0004	+	4.53019i	−1.49103	+	0.397324i
$131$	−2.85603			−0.249533			−0.124766	−	0.992186i	$-0.539818\pi$
$131$	−2.85603			−0.249533			−0.124766	+	0.992186i	$0.539818\pi$
$132$	−0.115471	+	0.0666671i	−0.0100504	+	0.00580262i
$133$	−1.21721	−	2.10827i	−0.105545	−	0.182810i
$134$	6.32570	−	10.9564i	0.546457	−	0.946491i
$135$		−	3.14427i		−	0.270616i
$136$	−12.8887	−	7.44128i	−1.10519	−	0.638084i
$137$	−8.29315	−	4.78805i	−0.708532	−	0.409071i	0.101985	−	0.994786i	$-0.467480\pi$
$137$	−8.29315	−	4.78805i	−0.708532	−	0.409071i	−0.810517	+	0.585715i	$0.800814\pi$
$138$		−	0.171042i		−	0.0145601i
$139$	2.42161	−	4.19435i	0.205398	−	0.355760i	−0.744861	−	0.667219i	$-0.767484\pi$
$139$	2.42161	−	4.19435i	0.205398	−	0.355760i	0.950259	+	0.311459i	$0.100818\pi$
$140$	−0.736181	−	1.27510i	−0.0622186	−	0.107766i
$141$	−1.52623	+	0.881167i	−0.128531	+	0.0742077i
$142$	10.0938			0.847051
$143$	−2.21210	−	8.30132i	−0.184985	−	0.694191i
$144$	8.96129			0.746774
$145$	17.2061	−	9.93392i	1.42888	−	0.824967i
$146$	−2.98809	−	5.17552i	−0.247296	−	0.428329i
$147$	0.417363	−	0.722894i	0.0344235	−	0.0596233i
$148$			4.21177i			0.346206i
$149$	3.24744	+	1.87491i	0.266041	+	0.153599i	0.627087	−	0.778949i	$-0.284247\pi$
$149$	3.24744	+	1.87491i	0.266041	+	0.153599i	−0.361046	+	0.932548i	$0.617580\pi$
$150$	−1.48073	−	0.854899i	−0.120901	−	0.0698022i
$151$			7.05010i			0.573729i	0.957971	+	0.286864i	$0.0926129\pi$
$151$			7.05010i			0.573729i	−0.957971	+	0.286864i	$0.907387\pi$
$152$	−4.01157	+	6.94825i	−0.325382	+	0.563578i
$153$	7.29928	+	12.6427i	0.590112	+	1.02210i
$154$	−2.39804	+	1.38451i	−0.193240	+	0.111567i
$155$	29.6246			2.37951
$156$	−0.0524881	+	0.194816i	−0.00420241	+	0.0155978i
$157$	−9.02819			−0.720528			−0.360264	−	0.932850i	$-0.617313\pi$
$157$	−9.02819			−0.720528			−0.360264	+	0.932850i	$0.617313\pi$
$158$	14.8162	−	8.55414i	1.17871	−	0.680531i
$159$	−0.0998214	−	0.172896i	−0.00791635	−	0.0137115i
$160$	−4.43785	+	7.68658i	−0.350843	+	0.607678i
$161$			0.922280i			0.0726859i
$162$	−9.64061	−	5.56601i	−0.757438	−	0.437307i
$163$	−17.0775	−	9.85969i	−1.33761	−	0.772270i	−0.351159	−	0.936316i	$-0.614212\pi$
$163$	−17.0775	−	9.85969i	−1.33761	−	0.772270i	−0.986453	+	0.164046i	$0.947546\pi$
$164$		−	3.76172i		−	0.293741i
$165$	0.626247	−	1.08469i	0.0487533	−	0.0844432i
$166$	6.18736	+	10.7168i	0.480232	+	0.831786i
$167$	6.16908	−	3.56172i	0.477377	−	0.275614i	−0.241946	−	0.970290i	$-0.577786\pi$
$167$	6.16908	−	3.56172i	0.477377	−	0.275614i	0.719323	+	0.694676i	$0.244452\pi$
$168$	0.380529			0.0293584
$169$	−11.2404	−	6.53095i	−0.864647	−	0.502381i
$170$	23.8918			1.83242
$171$	6.81566	−	3.93502i	0.521207	−	0.300919i
$172$	0.662264	+	1.14708i	0.0504972	+	0.0874637i
$173$	−2.91271	+	5.04495i	−0.221449	+	0.383561i	−0.955248	−	0.295806i	$-0.904412\pi$
$173$	−2.91271	+	5.04495i	−0.221449	+	0.383561i	0.733799	+	0.679366i	$0.237745\pi$
$174$			0.877526i			0.0665251i
$175$	7.98428	+	4.60973i	0.603555	+	0.348463i
$176$	6.20194	+	3.58069i	0.467489	+	0.269905i
$177$		−	0.276816i		−	0.0208068i
$178$	3.34982	−	5.80207i	0.251080	−	0.434883i
$179$	−5.84435	−	10.1227i	−0.436827	−	0.756607i	0.560616	−	0.828076i	$-0.310564\pi$
$179$	−5.84435	−	10.1227i	−0.436827	−	0.756607i	−0.997443	+	0.0714694i	$0.977231\pi$
$180$	4.12219	−	2.37995i	0.307250	−	0.177391i
$181$	6.93508			0.515480			0.257740	−	0.966214i	$-0.417022\pi$
$181$	6.93508			0.515480			0.257740	+	0.966214i	$0.417022\pi$
$182$	−1.09005	+	4.04585i	−0.0807997	+	0.299898i
$183$	−1.35853			−0.100426
$184$	2.63235	−	1.51979i	0.194060	−	0.112040i
$185$	−19.7820	−	34.2634i	−1.45440	−	2.51909i
$186$	−0.654232	+	1.13316i	−0.0479706	+	0.0830876i
$187$			11.6664i			0.853130i
$188$	−4.63518	−	2.67612i	−0.338055	−	0.195176i
$189$	−0.648515	−	0.374421i	−0.0471726	−	0.0272351i
$190$		−	12.8800i		−	0.934414i
$191$	−5.80052	+	10.0468i	−0.419711	+	0.726961i	−0.995910	−	0.0903485i	$-0.971202\pi$
$191$	−5.80052	+	10.0468i	−0.419711	+	0.726961i	0.576199	+	0.817309i	$0.304535\pi$
$192$	−0.603989	−	1.04614i	−0.0435892	−	0.0754986i
$193$	−3.54637	+	2.04749i	−0.255273	+	0.147382i	−0.622176	−	0.782877i	$-0.713751\pi$
$193$	−3.54637	+	2.04749i	−0.255273	+	0.147382i	0.366903	+	0.930259i	$0.380418\pi$
$194$	8.81984			0.633227
$195$	−0.488019	−	1.83138i	−0.0349477	−	0.131148i
$196$	2.53508			0.181077
$197$	−18.4376	+	10.6450i	−1.31362	+	0.758422i	−0.982695	−	0.185234i	$-0.940696\pi$
$197$	−18.4376	+	10.6450i	−1.31362	+	0.758422i	−0.330930	+	0.943655i	$0.607362\pi$
$198$	−4.47588	−	7.75246i	−0.318087	−	0.550943i
$199$	−1.12814	+	1.95399i	−0.0799716	+	0.138515i	−0.903237	−	0.429141i	$-0.858816\pi$
$199$	−1.12814	+	1.95399i	−0.0799716	+	0.138515i	0.823266	+	0.567656i	$0.192150\pi$
$200$		−	30.3847i		−	2.14853i
$201$	1.18029	+	0.681441i	0.0832513	+	0.0480651i
$202$	3.52509	+	2.03521i	0.248024	+	0.143197i
$203$		−	4.73174i		−	0.332103i
$204$	0.136995	−	0.237282i	0.00959155	−	0.0166130i
$205$	17.6682	+	30.6022i	1.23400	+	2.13735i
$206$	−8.42443	+	4.86385i	−0.586958	+	0.338880i
$207$	−2.98157			−0.207234
$208$	10.4713	−	2.79034i	0.726053	−	0.193475i
$209$	6.28932			0.435041
$210$	−0.529041	+	0.305442i	−0.0365073	+	0.0210775i
$211$	11.9166	+	20.6402i	0.820376	+	1.42093i	0.905403	+	0.424554i	$0.139569\pi$
$211$	11.9166	+	20.6402i	0.820376	+	1.42093i	−0.0850272	+	0.996379i	$0.527098\pi$
$212$	0.303159	−	0.525087i	0.0208211	−	0.0360631i
$213$			1.08736i			0.0745047i
$214$	−20.6546	−	11.9250i	−1.41192	−	0.815173i
$215$	−10.7752	−	6.22108i	−0.734865	−	0.424274i
$216$			2.46797i			0.167924i
$217$	3.52771	−	6.11017i	0.239476	−	0.414785i
$218$	0.973233	+	1.68569i	0.0659157	+	0.114169i
$219$	0.557537	−	0.321894i	0.0376749	−	0.0217516i
$220$	3.80385			0.256455
$221$	12.4659	+	12.5002i	0.838546	+	0.840856i
$222$	1.74747			0.117282
$223$	22.1727	−	12.8014i	1.48479	−	0.857246i	0.484943	−	0.874546i	$-0.338840\pi$
$223$	22.1727	−	12.8014i	1.48479	−	0.857246i	0.999850	+	0.0172998i	$0.00550697\pi$
$224$	1.05692	+	1.83064i	0.0706185	+	0.122315i
$225$	−14.9025	+	25.8118i	−0.993497	+	1.72079i
$226$		−	11.5987i		−	0.771534i
$227$	−10.2930	−	5.94268i	−0.683172	−	0.394430i	0.117877	−	0.993028i	$-0.462391\pi$
$227$	−10.2930	−	5.94268i	−0.683172	−	0.394430i	−0.801049	+	0.598599i	$0.795724\pi$
$228$	−0.127918	−	0.0738535i	−0.00847158	−	0.00489107i
$229$			7.72269i			0.510330i	0.966898	+	0.255165i	$0.0821297\pi$
$229$			7.72269i			0.510330i	−0.966898	+	0.255165i	$0.917870\pi$
$230$	−2.43980	+	4.22586i	−0.160876	+	0.278645i
$231$	−0.149147	−	0.258331i	−0.00981318	−	0.0169969i
$232$	−13.5052	+	7.79724i	−0.886661	+	0.511914i
$233$	5.89048			0.385898			0.192949	−	0.981209i	$-0.438195\pi$
$233$	5.89048			0.385898			0.192949	+	0.981209i	$0.438195\pi$
$234$	−13.0795	−	3.52394i	−0.855035	−	0.230367i
$235$	50.2771			3.27972
$236$	0.728064	−	0.420348i	0.0473929	−	0.0273623i
$237$	0.921502	+	1.59609i	0.0598580	+	0.103677i
$238$	2.84504	−	4.92776i	0.184417	−	0.319419i
$239$			0.698721i			0.0451965i	0.999745	+	0.0225983i	$0.00719386\pi$
$239$			0.698721i			0.0451965i	−0.999745	+	0.0225983i	$0.992806\pi$
$240$	1.36823	+	0.789949i	0.0883190	+	0.0509910i
$241$	−15.0568	−	8.69308i	−0.969897	−	0.559970i	−0.0706921	−	0.997498i	$-0.522521\pi$
$241$	−15.0568	−	8.69308i	−0.969897	−	0.559970i	−0.899205	+	0.437528i	$0.855854\pi$
$242$			6.70689i			0.431135i
$243$	1.81752	−	3.14804i	0.116594	−	0.201947i
$244$	−2.06295	−	3.57313i	−0.132067	−	0.228746i
$245$	−20.6232	+	11.9068i	−1.31757	+	0.760699i
$246$	−1.56074			−0.0995092
$247$	6.73884	−	6.72032i	0.428782	−	0.427604i
$248$	−23.2527			−1.47655
$249$	−1.15448	+	0.666538i	−0.0731621	+	0.0422401i
$250$	12.1901	+	21.1139i	0.770972	+	1.33536i
$251$	4.97321	−	8.61386i	0.313906	−	0.543702i	−0.665298	−	0.746578i	$-0.731696\pi$
$251$	4.97321	−	8.61386i	0.313906	−	0.543702i	0.979204	+	0.202876i	$0.0650288\pi$
$252$		−	1.13362i		−	0.0714113i
$253$	−2.06349	−	1.19136i	−0.129731	−	0.0749000i
$254$	−12.8975	−	7.44637i	−0.809260	−	0.467227i
$255$			2.57376i			0.161175i
$256$	4.72235	−	8.17935i	0.295147	−	0.511209i
$257$	−2.63134	−	4.55761i	−0.164138	−	0.284296i	0.772211	−	0.635367i	$-0.219151\pi$
$257$	−2.63134	−	4.55761i	−0.164138	−	0.284296i	−0.936349	+	0.351071i	$0.885818\pi$
$258$	0.475922	−	0.274774i	0.0296296	−	0.0171067i
$259$	−9.42257			−0.585490
$260$	4.07572	−	4.06453i	0.252766	−	0.252071i
$261$	15.2969			0.946854
$262$	−3.11663	+	1.79939i	−0.192546	+	0.111166i
$263$	3.10200	+	5.37283i	0.191278	+	0.331303i	0.945674	−	0.325117i	$-0.105404\pi$
$263$	3.10200	+	5.37283i	0.191278	+	0.331303i	−0.754396	+	0.656419i	$0.772070\pi$
$264$	−0.491548	+	0.851387i	−0.0302527	+	0.0523992i
$265$			5.69555i			0.349875i
$266$	−2.65654	−	1.53376i	−0.162883	−	0.0940406i
$267$	0.625032	+	0.360862i	0.0382513	+	0.0220844i
$268$			4.13910i			0.252836i
$269$	−0.638524	+	1.10596i	−0.0389315	+	0.0674313i	−0.884835	−	0.465905i	$-0.845729\pi$
$269$	−0.638524	+	1.10596i	−0.0389315	+	0.0674313i	0.845903	+	0.533337i	$0.179062\pi$
$270$	−1.98098	−	3.43117i	−0.120559	−	0.208814i
$271$	−5.25337	+	3.03303i	−0.319119	+	0.184244i	−0.651000	−	0.759078i	$-0.725650\pi$
$271$	−5.25337	+	3.03303i	−0.319119	+	0.184244i	0.331881	+	0.943321i	$0.392317\pi$
$272$	−14.7160			−0.892287
$273$	−0.435842	−	0.117426i	−0.0263784	−	0.00710696i
$274$	−12.0665			−0.728962
$275$	−20.6274	+	11.9092i	−1.24388	+	0.718154i
$276$	0.0279795	+	0.0484619i	0.00168417	+	0.00291706i
$277$	4.75973	−	8.24410i	0.285985	−	0.495340i	−0.686863	−	0.726787i	$-0.741013\pi$
$277$	4.75973	−	8.24410i	0.285985	−	0.495340i	0.972847	+	0.231447i	$0.0743460\pi$
$278$		−	6.10274i		−	0.366018i
$279$	19.7531	+	11.4045i	1.18259	+	0.682768i
$280$	−9.40156	−	5.42799i	−0.561851	−	0.324385i
$281$			27.7657i			1.65637i	0.560458	+	0.828183i	$0.310625\pi$
$281$			27.7657i			1.65637i	−0.560458	+	0.828183i	$0.689375\pi$
$282$	−1.11032	+	1.92314i	−0.0661188	+	0.114521i
$283$	3.46614	+	6.00353i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$283$	3.46614	+	6.00353i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$284$	−2.85990	+	1.65117i	−0.169704	+	0.0979787i
$285$	1.38751			0.0821889
$286$	−7.64402	−	7.66508i	−0.452000	−	0.453245i
$287$	8.41572			0.496764
$288$	−5.91815	+	3.41684i	−0.348730	+	0.201340i
$289$	−3.48667	−	6.03909i	−0.205098	−	0.355241i
$290$	12.5173	−	21.6807i	0.735043	−	1.27313i
$291$			0.950124i			0.0556973i
$292$	1.69325	+	0.977598i	0.0990899	+	0.0572096i
$293$	−7.71012	−	4.45144i	−0.450430	−	0.260056i	0.257582	−	0.966256i	$-0.417074\pi$
$293$	−7.71012	−	4.45144i	−0.450430	−	0.260056i	−0.708012	+	0.706201i	$0.750408\pi$
$294$		−	1.05180i		−	0.0613425i
$295$	−3.94860	+	6.83918i	−0.229897	+	0.398193i
$296$	15.5271	+	26.8937i	0.902493	+	1.56316i
$297$	1.67544	−	0.967316i	0.0972189	−	0.0561294i
$298$	4.72500			0.273712
$299$	−3.48398	+	0.928394i	−0.201484	+	0.0536904i
$300$	0.559386			0.0322962
$301$	−2.56624	+	1.48162i	−0.147915	+	0.0853990i
$302$	4.44177	+	7.69338i	0.255595	+	0.442704i
$303$	−0.219245	+	0.379743i	−0.0125953	+	0.0218157i
$304$			7.93335i			0.455009i
$305$	33.5647	+	19.3786i	1.92191	+	1.10962i
$306$	15.9306	+	9.19753i	0.910691	+	0.525788i
$307$			32.6896i			1.86569i	0.360273	+	0.932847i	$0.382684\pi$
$307$			32.6896i			1.86569i	−0.360273	+	0.932847i	$0.617316\pi$
$308$	0.452964	−	0.784556i	0.0258100	−	0.0447042i
$309$	−0.523962	−	0.907529i	−0.0298072	−	0.0516275i
$310$	32.3277	−	18.6644i	1.83609	−	1.06007i
$311$	−16.0164			−0.908207			−0.454103	−	0.890949i	$-0.650040\pi$
$311$	−16.0164			−0.908207			−0.454103	+	0.890949i	$0.650040\pi$
$312$	0.383051	+	1.43747i	0.0216860	+	0.0813808i
$313$	−2.82564			−0.159714			−0.0798572	−	0.996806i	$-0.525446\pi$
$313$	−2.82564			−0.159714			−0.0798572	+	0.996806i	$0.525446\pi$
$314$	−9.85196	+	5.68803i	−0.555978	+	0.320994i
$315$	5.32441	+	9.22215i	0.299997	+	0.519609i
$316$	−2.79862	+	4.84735i	−0.157435	+	0.272685i
$317$			2.92273i			0.164157i	0.996626	+	0.0820784i	$0.0261558\pi$
$317$			2.92273i			0.164157i	−0.996626	+	0.0820784i	$0.973844\pi$
$318$	−0.217859	−	0.125781i	−0.0122169	−	0.00705344i
$319$	10.5867	+	6.11223i	0.592741	+	0.342219i
$320$			34.4620i			1.92649i
$321$	1.28463	−	2.22504i	0.0717008	−	0.124189i
$322$	0.581065	+	1.00643i	0.0323815	+	0.0560863i
$323$	−11.1925	+	6.46198i	−0.622767	+	0.359554i
$324$	3.64201			0.202334
$325$	−9.37634	+	34.8014i	−0.520106	+	1.93044i
$326$	−24.8476			−1.37618
$327$	−0.181592	+	0.104842i	−0.0100421	+	0.00579779i
$328$	−13.8679	−	24.0200i	−0.765729	−	1.32628i
$329$	5.98701	−	10.3698i	0.330075	−	0.571706i
$330$		−	1.57822i		−	0.0868781i
$331$	9.60827	+	5.54734i	0.528118	+	0.304909i	0.740250	−	0.672332i	$-0.234707\pi$
$331$	9.60827	+	5.54734i	0.528118	+	0.304909i	−0.212131	+	0.977241i	$0.568041\pi$
$332$	−3.50617	−	2.02429i	−0.192426	−	0.111097i
$333$		−	30.4616i		−	1.66928i
$334$	4.48798	−	7.77341i	0.245571	−	0.425342i
$335$	−19.4406	−	33.6721i	−1.06215	−	1.83971i
$336$	0.325859	−	0.188135i	0.0177771	−	0.0102636i
$337$	−32.2552			−1.75705			−0.878526	−	0.477695i	$-0.841472\pi$
$337$	−32.2552			−1.75705			−0.878526	+	0.477695i	$0.841472\pi$
$338$	−16.3807	−	0.0450642i	−0.890994	−	0.00245117i
$339$	1.24948			0.0678624
$340$	−6.76934	+	3.90828i	−0.367119	+	0.211956i
$341$	9.11384	+	15.7856i	0.493542	+	0.854840i
$342$	4.95837	−	8.58814i	0.268118	−	0.464394i
$343$			12.1274i			0.654820i
$344$	8.45759	+	4.88299i	0.456003	+	0.263273i
$345$	−0.455234	−	0.262830i	−0.0245090	−	0.0141503i
$346$			7.34037i			0.394621i
$347$	−15.2493	+	26.4126i	−0.818626	+	1.41790i	0.0880689	+	0.996114i	$0.471930\pi$
$347$	−15.2493	+	26.4126i	−0.818626	+	1.41790i	−0.906695	+	0.421787i	$0.861403\pi$
$348$	−0.143548	−	0.248632i	−0.00769498	−	0.0133281i
$349$	19.3112	−	11.1493i	1.03371	−	0.596810i	0.115662	−	0.993289i	$-0.463101\pi$
$349$	19.3112	−	11.1493i	1.03371	−	0.596810i	0.918044	+	0.396479i	$0.129768\pi$
$350$	11.6171			0.620958
$351$	0.761584	−	2.82671i	0.0406504	−	0.150879i
$352$	−5.46112			−0.291078
$353$	−3.03836	+	1.75420i	−0.161715	+	0.0933664i	−0.578674	−	0.815559i	$-0.696429\pi$
$353$	−3.03836	+	1.75420i	−0.161715	+	0.0933664i	0.416958	+	0.908926i	$0.363096\pi$
$354$	−0.174403	−	0.302074i	−0.00926939	−	0.0160551i
$355$	15.5105	−	26.8650i	0.823212	−	1.42584i
$356$			2.19189i			0.116170i
$357$	0.530847	+	0.306484i	0.0280954	+	0.0162209i
$358$	−12.7552	−	7.36423i	−0.674134	−	0.389212i
$359$		−	24.9476i		−	1.31669i	−0.752718	−	0.658343i	$-0.771258\pi$
$359$		−	24.9476i		−	1.31669i	0.752718	−	0.658343i	$-0.228742\pi$
$360$	17.5478	−	30.3936i	0.924849	−	1.60189i
$361$	−6.01636	−	10.4206i	−0.316651	−	0.548455i
$362$	7.56786	−	4.36931i	0.397758	−	0.229646i
$363$	−0.722505			−0.0379217
$364$	−0.352983	−	1.32464i	−0.0185013	−	0.0694298i
$365$	−18.3664			−0.961343
$366$	−1.48249	+	0.855918i	−0.0774912	+	0.0447395i
$367$	6.78074	+	11.7446i	0.353952	+	0.613062i	0.986938	−	0.161101i	$-0.0515044\pi$
$367$	6.78074	+	11.7446i	0.353952	+	0.613062i	−0.632986	+	0.774163i	$0.718171\pi$
$368$	1.50278	−	2.60289i	0.0783377	−	0.135685i
$369$			27.2066i			1.41632i
$370$	−43.1739	−	24.9265i	−2.24451	−	1.29587i
$371$	1.17472	+	0.678227i	0.0609887	+	0.0352118i
$372$		−	0.428084i		−	0.0221951i
$373$	7.24378	−	12.5466i	0.375069	−	0.649638i	−0.615269	−	0.788317i	$-0.710952\pi$
$373$	7.24378	−	12.5466i	0.375069	−	0.649638i	0.990337	+	0.138680i	$0.0442858\pi$
$374$	7.35017	+	12.7309i	0.380068	+	0.658298i
$375$	−2.27452	+	1.31319i	−0.117456	+	0.0678130i
$376$	−39.4630			−2.03515
$377$	17.8744	−	4.76310i	0.920581	−	0.245312i
$378$	−0.943585			−0.0485328
$379$	−6.93007	+	4.00108i	−0.355974	+	0.205522i	−0.667313	−	0.744777i	$-0.732556\pi$
$379$	−6.93007	+	4.00108i	−0.355974	+	0.205522i	0.311339	+	0.950299i	$0.399222\pi$
$380$	2.10694	+	3.64933i	0.108084	+	0.187207i
$381$	0.802166	−	1.38939i	0.0410962	−	0.0711807i
$382$			14.6180i			0.747923i
$383$	0.474623	+	0.274023i	0.0242521	+	0.0140019i	0.512077	−	0.858940i	$-0.328876\pi$
$383$	0.474623	+	0.274023i	0.0242521	+	0.0140019i	−0.487825	+	0.872941i	$0.662210\pi$
$384$	−0.779332	−	0.449948i	−0.0397701	−	0.0229613i
$385$			8.50997i			0.433708i
$386$	−2.57997	+	4.46863i	−0.131317	+	0.227447i
$387$	−4.78981	−	8.29620i	−0.243480	−	0.421720i
$388$	−2.49895	+	1.44277i	−0.126865	+	0.0732456i
$389$	−1.80203			−0.0913663			−0.0456832	−	0.998956i	$-0.514546\pi$
$389$	−1.80203			−0.0913663			−0.0456832	+	0.998956i	$0.514546\pi$
$390$	−1.68637	−	1.69102i	−0.0853929	−	0.0856281i
$391$	4.89626			0.247614
$392$	16.1874	−	9.34579i	0.817586	−	0.472034i
$393$	−0.193840	−	0.335741i	−0.00977795	−	0.0169359i
$394$	−13.4133	+	23.2325i	−0.675752	+	1.17044i
$395$		−	52.5785i		−	2.64551i
$396$	2.53633	+	1.46435i	0.127456	+	0.0735865i
$397$	−12.8410	−	7.41376i	−0.644472	−	0.372086i	0.141863	−	0.989886i	$-0.454691\pi$
$397$	−12.8410	−	7.41376i	−0.644472	−	0.372086i	−0.786335	+	0.617800i	$0.788024\pi$
$398$			2.84305i			0.142509i
$399$	0.165225	−	0.286178i	0.00827160	−	0.0143268i
$400$	−15.0223	−	26.0194i	−0.751116	−	1.30097i
$401$	−32.9086	+	18.9998i	−1.64338	+	0.948804i	−0.663755	+	0.747950i	$0.731038\pi$
$401$	−32.9086	+	18.9998i	−1.64338	+	0.948804i	−0.979621	+	0.200854i	$0.935628\pi$
$402$	1.71731			0.0856518
$403$	26.6327	+	7.17548i	1.32667	+	0.357436i
$404$	−1.33170			−0.0662546
$405$	−29.6283	+	17.1059i	−1.47224	+	0.849998i
$406$	−2.98114	−	5.16348i	−0.147951	−	0.256259i
$407$	12.1716	−	21.0819i	0.603325	−	1.04499i
$408$		−	2.02017i		−	0.100013i
$409$	10.9350	+	6.31335i	0.540703	+	0.312175i	0.745364	−	0.666658i	$-0.232276\pi$
$409$	10.9350	+	6.31335i	0.540703	+	0.312175i	−0.204661	+	0.978833i	$0.565609\pi$
$410$	38.5606	+	22.2630i	1.90437	+	1.09949i
$411$		−	1.29987i		−	0.0641179i
$412$	1.59128	−	2.75618i	0.0783968	−	0.135787i
$413$	0.940402	+	1.62882i	0.0462742	+	0.0801492i
$414$	−3.25363	+	1.87848i	−0.159907	+	0.0923223i
$415$	38.0309			1.86686
$416$	−5.85144	+	5.83537i	−0.286891	+	0.286102i
$417$	0.657423			0.0321941
$418$	6.86318	−	3.96246i	0.335689	−	0.193810i
$419$	−16.3678	−	28.3499i	−0.799620	−	1.38498i	−0.919864	−	0.392238i	$-0.871701\pi$
$419$	−16.3678	−	28.3499i	−0.799620	−	1.38498i	0.120244	−	0.992744i	$-0.461632\pi$
$420$	0.0999299	−	0.173084i	0.00487608	−	0.00844562i
$421$		−	26.8365i		−	1.30793i	−0.756524	−	0.653966i	$-0.773104\pi$
$421$		−	26.8365i		−	1.30793i	0.756524	−	0.653966i	$-0.226896\pi$
$422$	26.0079	+	15.0157i	1.26605	+	0.730952i
$423$	33.5238	+	19.3550i	1.62998	+	0.941072i
$424$		−	4.47050i		−	0.217106i
$425$	24.4724	−	42.3874i	1.18709	−	2.05609i
$426$	0.685070	+	1.18658i	0.0331918	+	0.0574898i
$427$	7.99380	−	4.61522i	0.386847	−	0.223346i
$428$	7.80286			0.377166
$429$	0.825726	−	0.823458i	0.0398664	−	0.0397569i
$430$	−15.6779			−0.756055
$431$	−11.9441	+	6.89591i	−0.575325	+	0.332164i	−0.759273	−	0.650772i	$-0.774445\pi$
$431$	−11.9441	+	6.89591i	−0.575325	+	0.332164i	0.183948	+	0.982936i	$0.441112\pi$
$432$	1.22017	+	2.11340i	0.0587056	+	0.101681i
$433$	16.6513	−	28.8409i	0.800210	−	1.38600i	−0.119268	−	0.992862i	$-0.538055\pi$
$433$	16.6513	−	28.8409i	0.800210	−	1.38600i	0.919478	−	0.393142i	$-0.128612\pi$
$434$		−	8.89025i		−	0.426746i
$435$	2.33557	+	1.34844i	0.111982	+	0.0646528i
$436$	−0.551499	−	0.318408i	−0.0264120	−	0.0152490i
$437$		−	2.63956i		−	0.126267i
$438$	0.405606	−	0.702530i	0.0193806	−	0.0335682i
$439$	10.9167	+	18.9082i	0.521023	+	0.902439i	0.999701	+	0.0244482i	$0.00778287\pi$
$439$	10.9167	+	18.9082i	0.521023	+	0.902439i	−0.478678	+	0.877991i	$0.658884\pi$
$440$	24.2890	−	14.0232i	1.15793	−	0.668531i
$441$	−18.3349			−0.873090
$442$	21.4788	+	5.78691i	1.02164	+	0.275255i
$443$	15.0705			0.716019			0.358009	−	0.933718i	$-0.383456\pi$
$443$	15.0705			0.716019			0.358009	+	0.933718i	$0.383456\pi$
$444$	−0.495116	+	0.285855i	−0.0234971	+	0.0135661i
$445$	−10.2949	−	17.8314i	−0.488027	−	0.845287i
$446$	16.1306	−	27.9389i	0.763804	−	1.32295i
$447$			0.509005i			0.0240751i
$448$	7.10790	+	4.10375i	0.335817	+	0.193884i
$449$	9.51576	+	5.49393i	0.449076	+	0.259274i	0.707440	−	0.706773i	$-0.249850\pi$
$449$	9.51576	+	5.49393i	0.449076	+	0.259274i	−0.258364	+	0.966048i	$0.583183\pi$
$450$			37.5560i			1.77041i
$451$	−10.8710	+	18.8292i	−0.511896	+	0.886631i
$452$	1.89735	+	3.28630i	0.0892436	+	0.154574i
$453$	−0.828775	+	0.478494i	−0.0389393	+	0.0224816i
$454$	−14.9763			−0.702871
$455$	9.09315	+	9.11820i	0.426294	+	0.427468i
$456$	−1.08907			−0.0510004
$457$	14.1758	−	8.18443i	0.663118	−	0.382851i	−0.130346	−	0.991469i	$-0.541609\pi$
$457$	14.1758	−	8.18443i	0.663118	−	0.382851i	0.793464	+	0.608617i	$0.208276\pi$
$458$	4.86553	+	8.42734i	0.227351	+	0.393784i
$459$	−1.98775	+	3.44288i	−0.0927800	+	0.160700i
$460$		−	1.59644i		−	0.0744342i
$461$	7.50586	+	4.33351i	0.349583	+	0.201832i	0.664502	−	0.747287i	$-0.268644\pi$
$461$	7.50586	+	4.33351i	0.349583	+	0.201832i	−0.314919	+	0.949119i	$0.601977\pi$
$462$	−0.325513	−	0.187935i	−0.0151442	−	0.00874352i
$463$		−	39.7706i		−	1.84830i	−0.382035	−	0.924148i	$-0.624777\pi$
$463$		−	39.7706i		−	1.84830i	0.382035	−	0.924148i	$-0.375223\pi$
$464$	−7.70996	+	13.3541i	−0.357926	+	0.619946i
$465$	2.01064	+	3.48252i	0.0932410	+	0.161498i
$466$	6.42795	−	3.71118i	0.297769	−	0.171917i
$467$	22.3907			1.03612			0.518058	−	0.855345i	$-0.326655\pi$
$467$	22.3907			1.03612			0.518058	+	0.855345i	$0.326655\pi$
$468$	4.28232	−	1.14113i	0.197950	−	0.0527489i
$469$	−9.25998			−0.427586
$470$	54.8646	−	31.6761i	2.53072	−	1.46111i
$471$	−0.612748	−	1.06131i	−0.0282339	−	0.0489026i
$472$	3.09930	−	5.36815i	0.142657	−	0.247089i
$473$		−	7.65552i		−	0.352001i
$474$	2.01117	+	1.16115i	0.0923760	+	0.0533333i
$475$	−22.8510	−	13.1930i	−1.04847	−	0.605337i
$476$			1.86160i			0.0853262i
$477$	−2.19259	+	3.79768i	−0.100392	+	0.173884i
$478$	0.440216	+	0.762476i	0.0201350	+	0.0348748i
$479$	−18.5373	+	10.7025i	−0.846991	+	0.489010i	−0.859634	−	0.510910i	$-0.829309\pi$
$479$	−18.5373	+	10.7025i	−0.846991	+	0.489010i	0.0126438	+	0.999920i	$0.495975\pi$
$480$	−1.20480			−0.0549912
$481$	−9.48503	−	35.5944i	−0.432480	−	1.62296i
$482$	−21.9076			−0.997864
$483$	−0.108419	+	0.0625956i	−0.00493323	+	0.00284820i
$484$	−1.09713	−	1.90029i	−0.0498696	−	0.0863766i
$485$	13.5529	−	23.4743i	0.615406	−	1.06591i
$486$		−	4.58037i		−	0.207770i
$487$	13.2464	+	7.64780i	0.600251	+	0.346555i	0.769140	−	0.639080i	$-0.220685\pi$
$487$	13.2464	+	7.64780i	0.600251	+	0.346555i	−0.168890	+	0.985635i	$0.554018\pi$
$488$	−26.3453	−	15.2105i	−1.19260	−	0.688546i
$489$		−	2.67673i		−	0.121046i
$490$	−15.0033	+	25.9865i	−0.677780	+	1.17395i
$491$	1.82376	+	3.15884i	0.0823051	+	0.142557i	0.904240	−	0.427025i	$-0.140438\pi$
$491$	1.82376	+	3.15884i	0.0823051	+	0.142557i	−0.821935	+	0.569582i	$0.807105\pi$
$492$	0.442210	−	0.255310i	0.0199364	−	0.0115103i
$493$	−25.1201			−1.13135
$494$	3.11971	−	11.5792i	0.140362	−	0.520972i
$495$	−27.5113			−1.23654
$496$	−19.9120	+	11.4962i	−0.894075	+	0.516195i
$497$	−3.69399	−	6.39818i	−0.165698	−	0.286997i
$498$	−0.839878	+	1.45471i	−0.0376358	+	0.0651872i
$499$			20.1550i			0.902264i	0.892457	+	0.451132i	$0.148980\pi$
$499$			20.1550i			0.902264i	−0.892457	+	0.451132i	$0.851020\pi$
$500$	−6.90775	−	3.98819i	−0.308924	−	0.178357i
$501$	0.837397	+	0.483471i	0.0374121	+	0.0215999i
$502$		−	12.5331i		−	0.559379i
$503$	8.39736	−	14.5447i	0.374420	−	0.648514i	−0.615820	−	0.787887i	$-0.711175\pi$
$503$	8.39736	−	14.5447i	0.374420	−	0.648514i	0.990240	+	0.139373i	$0.0445086\pi$
$504$	−4.17919	−	7.23857i	−0.186156	−	0.322431i
$505$	10.8336	−	6.25477i	0.482088	−	0.278333i
$506$	−3.00236			−0.133471
$507$	0.00485458	−	1.76463i	0.000215599	−	0.0783698i
$508$	4.87238			0.216177
$509$	0.253326	−	0.146258i	0.0112285	−	0.00648276i	−0.494375	−	0.869249i	$-0.664603\pi$
$509$	0.253326	−	0.146258i	0.0112285	−	0.00648276i	0.505604	+	0.862766i	$0.331270\pi$
$510$	1.62155	+	2.80860i	0.0718034	+	0.124367i
$511$	−2.18708	+	3.78814i	−0.0967508	+	0.167577i
$512$		−	25.1599i		−	1.11192i
$513$	1.85605	+	1.07159i	0.0819465	+	0.0473118i
$514$	−5.74286	−	3.31564i	−0.253307	−	0.146247i
$515$			29.8959i			1.31737i
$516$	−0.0898964	+	0.155705i	−0.00395747	+	0.00685454i
$517$	15.4675	+	26.7904i	0.680258	+	1.17824i
$518$	−10.2823	+	5.93651i	−0.451780	+	0.260835i
$519$	−0.790747			−0.0347100
$520$	11.0407	−	40.9790i	0.484168	−	1.79705i
$521$	−11.1662			−0.489200			−0.244600	−	0.969624i	$-0.578657\pi$
$521$	−11.1662			−0.489200			−0.244600	+	0.969624i	$0.578657\pi$
$522$	16.6926	−	9.63750i	0.730617	−	0.421822i
$523$	−5.98371	−	10.3641i	−0.261650	−	0.453190i	0.705031	−	0.709177i	$-0.250933\pi$
$523$	−5.98371	−	10.3641i	−0.261650	−	0.453190i	−0.966680	+	0.255986i	$0.917600\pi$
$524$	0.588696	−	1.01965i	0.0257173	−	0.0445437i
$525$			1.25146i			0.0546181i
$526$	6.77009	+	3.90871i	0.295190	+	0.170428i
$527$	−32.4380	−	18.7281i	−1.41302	−	0.815809i
$528$			0.972093i			0.0423049i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.58837	+	6.21523i	0.155869	+	0.269972i
$531$	−5.26571	+	3.04016i	−0.228512	+	0.131932i
$532$	1.00358			0.0435108
$533$	8.47151	+	31.7910i	0.366942	+	1.37702i
$534$	0.909417			0.0393543
$535$	−63.4774	+	36.6487i	−2.74437	+	1.58446i
$536$	15.2592	+	26.4296i	0.659095	+	1.14159i
$537$	0.793318	−	1.37407i	0.0342342	−	0.0592953i
$538$			1.60916i			0.0693757i
$539$	−12.6892	−	7.32613i	−0.546564	−	0.315559i
$540$	1.12256	+	0.648109i	0.0483072	+	0.0278902i
$541$		−	17.9501i		−	0.771734i	−0.922554	−	0.385867i	$-0.873902\pi$
$541$		−	17.9501i		−	0.771734i	0.922554	−	0.385867i	$-0.126098\pi$
$542$	−3.82180	+	6.61956i	−0.164161	+	0.284334i
$543$	0.470687	+	0.815254i	0.0201991	+	0.0349859i
$544$	9.71862	−	5.61105i	0.416682	−	0.240572i
$545$	5.98203			0.256242
$546$	−0.549592	+	0.146453i	−0.0235204	+	0.00626760i
$547$	−36.7259			−1.57029			−0.785143	−	0.619314i	$-0.787411\pi$
$547$	−36.7259			−1.57029			−0.785143	+	0.619314i	$0.787411\pi$
$548$	3.41883	−	1.97386i	0.146045	−	0.0843193i
$549$	14.9202	+	25.8426i	0.636779	+	1.10293i
$550$	−15.0064	+	25.9918i	−0.639873	+	1.10829i
$551$			13.5422i			0.576917i
$552$	0.357318	+	0.206298i	0.0152085	+	0.00878061i
$553$	−10.8445	−	6.26107i	−0.461154	−	0.266248i
$554$		−	11.9951i		−	0.509623i
$555$	2.68522	−	4.65095i	0.113981	−	0.197422i
$556$	0.998302	+	1.72911i	0.0423374	+	0.0733306i
$557$	16.3969	−	9.46673i	0.694757	−	0.401118i	−0.110634	−	0.993861i	$-0.535288\pi$
$557$	16.3969	−	9.46673i	0.694757	−	0.401118i	0.805392	+	0.592743i	$0.201955\pi$
$558$	28.7406			1.21669
$559$	−8.18015	−	8.20269i	−0.345984	−	0.346937i
$560$	−10.7345			−0.453614
$561$	−1.37144	+	0.791803i	−0.0579024	+	0.0334300i
$562$	17.4933	+	30.2992i	0.737908	+	1.27809i
$563$	−23.2122	+	40.2046i	−0.978276	+	1.69442i	−0.309606	+	0.950865i	$0.600197\pi$
$563$	−23.2122	+	40.2046i	−0.978276	+	1.69442i	−0.668671	+	0.743559i	$0.733136\pi$
$564$		−	0.726518i		−	0.0305919i
$565$	−30.8704	−	17.8230i	−1.29873	−	0.749820i
$566$	7.56481	+	4.36754i	0.317973	+	0.183582i
$567$			8.14790i			0.342179i
$568$	−12.1744	+	21.0866i	−0.510824	+	0.884774i
$569$	−6.39571	−	11.0777i	−0.268122	−	0.464401i	0.700255	−	0.713893i	$-0.253070\pi$
$569$	−6.39571	−	11.0777i	−0.268122	−	0.464401i	−0.968377	+	0.249492i	$0.919736\pi$
$570$	1.51411	−	0.874172i	0.0634191	−	0.0366151i
$571$	16.2579			0.680374			0.340187	−	0.940358i	$-0.389510\pi$
$571$	16.2579			0.680374			0.340187	+	0.940358i	$0.389510\pi$
$572$	3.41968	+	0.921343i	0.142984	+	0.0385233i
$573$	−1.57474			−0.0657856
$574$	9.18361	−	5.30216i	0.383317	−	0.221308i
$575$	4.99818	+	8.65711i	0.208439	+	0.361026i
$576$	−13.2667	+	22.9786i	−0.552780	+	0.957443i
$577$		−	17.5085i		−	0.728887i	−0.931226	−	0.364443i	$-0.881259\pi$
$577$		−	17.5085i		−	0.728887i	0.931226	−	0.364443i	$-0.118741\pi$
$578$	−7.60962	−	4.39342i	−0.316519	−	0.182742i
$579$	−0.481387	−	0.277929i	−0.0200058	−	0.0115503i
$580$			8.19047i			0.340091i
$581$	4.52873	−	7.84400i	0.187884	−	0.325424i
$582$	0.598607	+	1.03682i	0.0248131	+	0.0429775i
$583$	−3.03490	+	1.75220i	−0.125693	+	0.0725688i
$584$	14.4160			0.596539
$585$	−29.4776	+	29.3966i	−1.21875	+	1.21540i
$586$	−11.2182			−0.463418
$587$	−2.87766	+	1.66142i	−0.118774	+	0.0685741i	−0.558210	−	0.829700i	$-0.688512\pi$
$587$	−2.87766	+	1.66142i	−0.118774	+	0.0685741i	0.439436	+	0.898274i	$0.355178\pi$
$588$	0.172057	+	0.298011i	0.00709551	+	0.0122898i
$589$	−10.0963	+	17.4873i	−0.416010	+	0.720550i
$590$			9.95096i			0.409674i
$591$	−2.50274	−	1.44496i	−0.102949	−	0.0594376i
$592$	26.5927	+	15.3533i	1.09295	+	0.631016i
$593$		−	39.7177i		−	1.63101i	−0.578750	−	0.815505i	$-0.696459\pi$
$593$		−	39.7177i		−	1.63101i	0.578750	−	0.815505i	$-0.303541\pi$
$594$	1.21888	−	2.11116i	0.0500111	−	0.0866218i
$595$	−8.74360	−	15.1444i	−0.358453	−	0.620858i
$596$	−1.33875	+	0.772928i	−0.0548374	+	0.0316604i
$597$	−0.306269			−0.0125348
$598$	−3.21695	+	3.20811i	−0.131551	+	0.131190i
$599$	16.2995			0.665980			0.332990	−	0.942930i	$-0.391942\pi$
$599$	16.2995			0.665980			0.332990	+	0.942930i	$0.391942\pi$
$600$	3.57188	−	2.06223i	0.145822	−	0.0841901i
$601$	−10.1399	−	17.5628i	−0.413614	−	0.716400i	0.581668	−	0.813426i	$-0.302400\pi$
$601$	−10.1399	−	17.5628i	−0.413614	−	0.716400i	−0.995282	+	0.0970263i	$0.969067\pi$
$602$	−1.86693	+	3.23361i	−0.0760903	+	0.131792i
$603$		−	29.9359i		−	1.21909i
$604$	−2.51700	−	1.45319i	−0.102415	−	0.0591296i
$605$	17.8506	+	10.3061i	0.725732	+	0.419001i
$606$			0.552523i			0.0224447i
$607$	1.58653	−	2.74794i	0.0643951	−	0.111536i	−0.832030	−	0.554730i	$-0.812822\pi$
$607$	1.58653	−	2.74794i	0.0643951	−	0.111536i	0.896425	+	0.443194i	$0.146155\pi$
$608$	−3.02490	−	5.23928i	−0.122676	−	0.212481i
$609$	0.556240	−	0.321145i	0.0225400	−	0.0130135i
$610$	48.8364			1.97733
$611$	45.1993	+	12.1778i	1.82857	+	0.492661i
$612$	−6.01822			−0.243272
$613$	−6.26671	+	3.61809i	−0.253110	+	0.146133i	−0.621188	−	0.783662i	$-0.713349\pi$
$613$	−6.26671	+	3.61809i	−0.253110	+	0.146133i	0.368077	+	0.929795i	$0.380016\pi$
$614$	20.5954	+	35.6723i	0.831164	+	1.43962i
$615$	−2.39830	+	4.15397i	−0.0967086	+	0.167504i
$616$		−	6.67956i		−	0.269127i
$617$	6.43788	+	3.71691i	0.259179	+	0.149637i	0.623960	−	0.781456i	$-0.285523\pi$
$617$	6.43788	+	3.71691i	0.259179	+	0.149637i	−0.364781	+	0.931093i	$0.618856\pi$
$618$	−1.14354	−	0.660224i	−0.0460000	−	0.0265581i
$619$		−	25.2143i		−	1.01345i	−0.862108	−	0.506724i	$-0.830856\pi$
$619$		−	25.2143i		−	1.01345i	0.862108	−	0.506724i	$-0.169144\pi$
$620$	−6.10634	+	10.5765i	−0.245236	+	0.424762i
$621$	−0.405973	−	0.703165i	−0.0162911	−	0.0282170i
$622$	−17.4778	+	10.0908i	−0.700796	+	0.404605i
$623$	−4.90370			−0.196462
$624$	1.03871	+	1.04157i	0.0415817	+	0.0416962i
$625$	24.9455			0.997821
$626$	−3.08346	+	1.78024i	−0.123240	+	0.0711525i
$627$	0.426859	+	0.739342i	0.0170471	+	0.0295265i
$628$	1.86093	−	3.22322i	0.0742590	−	0.128620i
$629$			50.0231i			1.99455i
$630$	11.6205	+	6.70908i	0.462971	+	0.267296i
$631$	14.4152	+	8.32262i	0.573860	+	0.331318i	0.758690	−	0.651452i	$-0.225840\pi$
$631$	14.4152	+	8.32262i	0.573860	+	0.331318i	−0.184829	+	0.982771i	$0.559173\pi$
$632$			41.2694i			1.64161i
$633$	−1.61758	+	2.80173i	−0.0642929	+	0.111359i
$634$	1.84141	+	3.18941i	0.0731316	+	0.126668i
$635$	−39.6375	+	22.8847i	−1.57297	+	0.908154i
$636$	0.0823023			0.00326350
$637$	−21.4244	+	5.70906i	−0.848864	+	0.226201i
$638$	15.4035			0.609832
$639$	20.6842	−	11.9420i	0.818255	−	0.472419i
$640$	12.8364	+	22.2333i	0.507404	+	0.878850i
$641$	7.47596	−	12.9487i	0.295283	−	0.511444i	−0.679768	−	0.733427i	$-0.737920\pi$
$641$	7.47596	−	12.9487i	0.295283	−	0.511444i	0.975051	+	0.221983i	$0.0712529\pi$
$642$		−	3.23741i		−	0.127770i
$643$	−8.94962	−	5.16706i	−0.352938	−	0.203769i	0.313040	−	0.949740i	$-0.398653\pi$
$643$	−8.94962	−	5.16706i	−0.352938	−	0.203769i	−0.665979	+	0.745971i	$0.731986\pi$
$644$	−0.329270	−	0.190104i	−0.0129751	−	0.00749115i
$645$		−	1.68891i		−	0.0665009i
$646$	−8.14249	+	14.1032i	−0.320362	+	0.554883i
$647$	−12.5518	−	21.7403i	−0.493462	−	0.854701i	0.506510	−	0.862234i	$-0.330935\pi$
$647$	−12.5518	−	21.7403i	−0.493462	−	0.854701i	−0.999972	+	0.00753303i	$0.997602\pi$
$648$	23.2555	−	13.4266i	0.913564	−	0.527446i
$649$	−4.85906			−0.190735
$650$	11.6941	+	43.8842i	0.458679	+	1.72128i
$651$	0.957709			0.0375356
$652$	7.04015	−	4.06463i	0.275714	−	0.159183i
$653$	0.257668	+	0.446294i	0.0100833	+	0.0174648i	0.871023	−	0.491242i	$-0.163457\pi$
$653$	0.257668	+	0.446294i	0.0100833	+	0.0174648i	−0.860940	+	0.508707i	$0.830124\pi$
$654$	−0.132108	+	0.228817i	−0.00516582	+	0.00894746i
$655$			11.0600i			0.432151i
$656$	−23.7511	−	13.7127i	−0.927325	−	0.535391i
$657$	−12.2464	−	7.07046i	−0.477777	−	0.275845i
$658$		−	15.0880i		−	0.588191i
$659$	3.82338	−	6.62229i	0.148938	−	0.257968i	−0.781897	−	0.623407i	$-0.785748\pi$
$659$	3.82338	−	6.62229i	0.148938	−	0.257968i	0.930835	+	0.365439i	$0.119081\pi$
$660$	0.258169	+	0.447162i	0.0100492	+	0.0174058i
$661$	41.9705	−	24.2317i	1.63246	−	0.942503i	0.649133	−	0.760675i	$-0.275132\pi$
$661$	41.9705	−	24.2317i	1.63246	−	0.942503i	0.983330	−	0.181828i	$-0.0582015\pi$
$662$	13.9800			0.543347
$663$	−0.623400	+	2.31382i	−0.0242108	+	0.0898615i
$664$	−29.8509			−1.15844
$665$	−8.16429	+	4.71365i	−0.316597	+	0.182788i
$666$	−19.1917	−	33.2410i	−0.743663	−	1.28806i
$667$	2.56524	−	4.44312i	0.0993264	−	0.172038i
$668$			2.93662i			0.113621i
$669$	3.00974	+	1.73768i	0.116363	+	0.0671825i
$670$	−42.4289	−	24.4964i	−1.63917	−	0.946377i
$671$			23.8469i			0.920598i
$672$	−0.143468	+	0.248493i	−0.00553438	+	0.00958583i
$673$	−6.44794	−	11.1682i	−0.248550	−	0.430501i	0.714574	−	0.699560i	$-0.246621\pi$
$673$	−6.44794	−	11.1682i	−0.248550	−	0.430501i	−0.963124	+	0.269059i	$0.913287\pi$
$674$	−35.1983	+	20.3217i	−1.35579	+	0.782764i
$675$	−8.11650			−0.312404
$676$	4.64858	−	2.66683i	0.178791	−	0.102570i
$677$	−18.7565			−0.720872			−0.360436	−	0.932784i	$-0.617372\pi$
$677$	−18.7565			−0.720872			−0.360436	+	0.932784i	$0.617372\pi$
$678$	1.36349	−	0.787210i	0.0523644	−	0.0302326i
$679$	−3.22777	−	5.59066i	−0.123870	−	0.214550i
$680$	−28.8165	+	49.9116i	−1.10506	+	1.91402i
$681$		−	1.61333i		−	0.0618230i
$682$	19.8908	+	11.4840i	0.761660	+	0.439745i
$683$	19.7295	+	11.3908i	0.754927	+	0.435857i	0.827471	−	0.561508i	$-0.189779\pi$
$683$	19.7295	+	11.3908i	0.754927	+	0.435857i	−0.0725446	+	0.997365i	$0.523112\pi$
$684$			3.24441i			0.124053i
$685$	−18.5418	+	32.1153i	−0.708446	+	1.22706i
$686$	7.64065	+	13.2340i	0.291721	+	0.505276i
$687$	−0.907842	+	0.524143i	−0.0346363	+	0.0199973i
$688$	9.65668			0.368157
$689$	−1.37954	+	5.12032i	−0.0525562	+	0.195069i
$690$	−0.662362			−0.0252157
$691$	−12.1068	+	6.98989i	−0.460566	+	0.265908i	−0.712282	−	0.701893i	$-0.752338\pi$
$691$	−12.1068	+	6.98989i	−0.460566	+	0.265908i	0.251716	+	0.967801i	$0.419005\pi$
$692$	−1.20076	−	2.07977i	−0.0456459	−	0.0790610i
$693$	−3.27605	+	5.67428i	−0.124447	+	0.215548i
$694$			38.4301i			1.45879i
$695$	−16.2427	−	9.37771i	−0.616119	−	0.355717i
$696$	−1.83321	−	1.05841i	−0.0694877	−	0.0401187i
$697$		−	44.6779i		−	1.69230i
$698$	14.0488	−	24.3333i	0.531756	−	0.921029i
$699$	0.399790	+	0.692456i	0.0151214	+	0.0261911i
$700$	−3.29150	+	1.90035i	−0.124407	+	0.0718265i
$701$	25.0149			0.944798			0.472399	−	0.881385i	$-0.343388\pi$
$701$	25.0149			0.944798			0.472399	+	0.881385i	$0.343388\pi$
$702$	−0.949840	−	3.56445i	−0.0358494	−	0.134532i
$703$	26.9673			1.01709
$704$	−18.3633	+	10.6020i	−0.692092	+	0.399580i
$705$	3.41233	+	5.91033i	0.128516	+	0.222596i
$706$	−2.21039	+	3.82851i	−0.0831892	+	0.144088i
$707$		−	2.97928i		−	0.112047i
$708$	0.0988281	+	0.0570584i	0.00371419	+	0.00214439i
$709$	6.43588	+	3.71576i	0.241705	+	0.139548i	0.615960	−	0.787777i	$-0.288768\pi$
$709$	6.43588	+	3.71576i	0.241705	+	0.139548i	−0.374255	+	0.927326i	$0.622102\pi$
$710$		−	39.0883i		−	1.46696i
$711$	20.2409	−	35.0584i	0.759095	−	1.31479i
$712$	8.08061	+	13.9960i	0.302833	+	0.524523i
$713$	6.62506	−	3.82498i	0.248111	−	0.143247i
$714$	0.772378			0.0289055
$715$	−32.1470	+	8.56638i	−1.20223	+	0.320364i
$716$	4.81864			0.180081
$717$	−0.0821383	+	0.0474226i	−0.00306751	+	0.00177103i
$718$	−15.7178	−	27.2240i	−0.586582	−	1.01599i
$719$	−7.33870	+	12.7110i	−0.273687	+	0.474041i	−0.969803	−	0.243889i	$-0.921577\pi$
$719$	−7.33870	+	12.7110i	−0.273687	+	0.474041i	0.696116	+	0.717930i	$0.254910\pi$
$720$		−	34.7027i		−	1.29329i
$721$	6.16613	+	3.56001i	0.229639	+	0.132582i
$722$	−13.1306	−	7.58098i	−0.488672	−	0.282135i
$723$		−	2.36001i		−	0.0877699i
$724$	−1.42948	+	2.47594i	−0.0531264	+	0.0920176i
$725$	−25.6431	−	44.4151i	−0.952359	−	1.64953i
$726$	−0.788430	+	0.455200i	−0.0292614	+	0.0168941i
$727$	−11.9828			−0.444419			−0.222209	−	0.974999i	$-0.571327\pi$
$727$	−11.9828			−0.444419			−0.222209	+	0.974999i	$0.571327\pi$
$728$	−7.13731	−	7.15698i	−0.264526	−	0.265255i
$729$	−26.0101			−0.963337
$730$	−20.0423	+	11.5714i	−0.741798	+	0.428277i
$731$	7.86570	+	13.6238i	0.290923	+	0.503894i
$732$	0.280026	−	0.485020i	0.0103501	−	0.0179269i
$733$		−	38.1951i		−	1.41077i	−0.708825	−	0.705385i	$-0.750774\pi$
$733$		−	38.1951i		−	1.41077i	0.708825	−	0.705385i	$-0.249226\pi$
$734$	14.7989	+	8.54414i	0.546237	+	0.315370i
$735$	−2.79942	−	1.61624i	−0.103258	−	0.0596160i
$736$			2.29197i			0.0844833i
$737$	11.9616	−	20.7181i	0.440611	−	0.763160i
$738$	17.1410	+	29.6890i	0.630968	+	1.09287i
$739$	0.443952	−	0.256316i	0.0163310	−	0.00942873i	−0.491812	−	0.870701i	$-0.663665\pi$
$739$	0.443952	−	0.256316i	0.0163310	−	0.00942873i	0.508143	+	0.861273i	$0.330332\pi$
$740$	16.3101			0.599573
$741$	1.24738	+	0.336073i	0.0458235	+	0.0123460i
$742$	1.70922			0.0627473
$743$	11.3941	−	6.57836i	0.418007	−	0.241337i	−0.276217	−	0.961095i	$-0.589081\pi$
$743$	11.3941	−	6.57836i	0.418007	−	0.241337i	0.694224	+	0.719759i	$0.255748\pi$
$744$	−1.57817	−	2.73347i	−0.0578585	−	0.100214i
$745$	7.26062	−	12.5758i	0.266009	−	0.460741i
$746$		−	18.2552i		−	0.668370i
$747$	25.3583	+	14.6406i	0.927812	+	0.535672i
$748$	−4.16510	−	2.40472i	−0.152291	−	0.0879253i
$749$			17.4566i			0.637849i
$750$	−1.65470	+	2.86603i	−0.0604212	+	0.104653i
$751$	14.2258	+	24.6398i	0.519106	+	0.899118i	0.999753	+	0.0222040i	$0.00706833\pi$
$751$	14.2258	+	24.6398i	0.519106	+	0.899118i	−0.480648	+	0.876914i	$0.659598\pi$
$752$	−33.7935	+	19.5107i	−1.23232	+	0.711481i
$753$	1.35014			0.0492018
$754$	16.5045	−	16.4591i	0.601058	−	0.599407i
$755$	27.3016			0.993607
$756$	0.267349	−	0.154354i	0.00972339	−	0.00561380i
$757$	−19.3976	−	33.5975i	−0.705016	−	1.22112i	−0.966686	−	0.255966i	$-0.917606\pi$
$757$	−19.3976	−	33.5975i	−0.705016	−	1.22112i	0.261670	−	0.965157i	$-0.415727\pi$
$758$	−5.04160	+	8.73231i	−0.183119	+	0.317172i
$759$		−	0.323432i		−	0.0117398i
$760$	26.9072	+	15.5349i	0.976027	+	0.563509i
$761$	46.5358	+	26.8675i	1.68692	+	0.973945i	0.956853	+	0.290573i	$0.0938459\pi$
$761$	46.5358	+	26.8675i	1.68692	+	0.973945i	0.730070	+	0.683372i	$0.239487\pi$
$762$		−	2.02156i		−	0.0732332i
$763$	0.712342	−	1.23381i	0.0257885	−	0.0446670i
$764$	−2.39125	−	4.14177i	−0.0865125	−	0.149844i
$765$	48.9591	−	28.2666i	1.77012	−	1.02198i
$766$	0.690572			0.0249514
$767$	−5.20635	+	5.19205i	−0.187991	+	0.187474i
$768$	1.28203			0.0462614
$769$	28.1859	−	16.2731i	1.01641	−	0.586824i	0.103347	−	0.994645i	$-0.467045\pi$
$769$	28.1859	−	16.2731i	1.01641	−	0.586824i	0.913062	+	0.407822i	$0.133712\pi$
$770$	5.36154	+	9.28645i	0.193216	+	0.334661i
$771$	0.357180	−	0.618654i	0.0128635	−	0.0222803i
$772$		−	1.68815i		−	0.0607579i
$773$	3.49771	+	2.01941i	0.125804	+	0.0726330i	0.561581	−	0.827422i	$-0.310193\pi$
$773$	3.49771	+	2.01941i	0.125804	+	0.0726330i	−0.435777	+	0.900055i	$0.643526\pi$
$774$	−10.4537	−	6.03545i	−0.375751	−	0.216940i
$775$		−	76.4719i		−	2.74695i
$776$	−10.6378	+	18.4252i	−0.381875	+	0.661428i
$777$	−0.639515	−	1.10767i	−0.0229425	−	0.0397375i
$778$	−1.96645	+	1.13533i	−0.0705007	+	0.0407036i
$779$	−24.0857			−0.862961
$780$	0.754427	+	0.203261i	0.0270128	+	0.00727791i
$781$	19.0869			0.682981
$782$	5.34301	−	3.08479i	0.191066	−	0.110312i
$783$	2.08283	+	3.60757i	0.0744343	+	0.128924i
$784$	9.24118	−	16.0062i	0.330042	−	0.571650i
$785$			34.9618i			1.24784i
$786$	−0.423054	−	0.244250i	−0.0150898	−	0.00871212i
$787$	9.16909	+	5.29378i	0.326843	+	0.188703i	0.654438	−	0.756115i	$-0.272905\pi$
$787$	9.16909	+	5.29378i	0.326843	+	0.188703i	−0.327596	+	0.944818i	$0.606238\pi$
$788$		−	8.77672i		−	0.312658i
$789$	−0.421069	+	0.729313i	−0.0149905	+	0.0259642i
$790$	−33.1260	−	57.3760i	−1.17857	−	2.04135i
$791$	−7.35210	+	4.24474i	−0.261411	+	0.150926i
$792$	21.5939			0.767305
$793$	25.4811	+	25.5513i	0.904860	+	0.907353i
$794$	−18.6836			−0.663055
$795$	−0.669541	+	0.386560i	−0.0237462	+	0.0137099i
$796$	−0.465073	−	0.805529i	−0.0164841	−	0.0285512i
$797$	−19.5370	+	33.8391i	−0.692037	+	1.19864i	0.279132	+	0.960253i	$0.409953\pi$
$797$	−19.5370	+	33.8391i	−0.692037	+	1.19864i	−0.971169	+	0.238391i	$0.923380\pi$
$798$		−	0.416387i		−	0.0147399i
$799$	−55.0519	−	31.7842i	−1.94760	−	1.12444i
$800$	19.8419	+	11.4557i	0.701516	+	0.405020i
$801$		−	15.8528i		−	0.560132i
$802$	−23.9409	+	41.4668i	−0.845382	+	1.46424i
$803$	−5.65033	−	9.78666i	−0.199396	−	0.345364i
$804$	−0.486572	+	0.280923i	−0.0171601	+	0.00990737i
$805$	3.57154			0.125880
$806$	33.5835	−	8.94918i	1.18293	−	0.315221i
$807$	−0.173348			−0.00610213
$808$	−8.50339	+	4.90943i	−0.299148	+	0.172713i
$809$	11.4312	+	19.7995i	0.401900	+	0.696112i	0.993955	−	0.109786i	$-0.0350165\pi$
$809$	11.4312	+	19.7995i	0.401900	+	0.696112i	−0.592055	+	0.805898i	$0.701683\pi$
$810$	−21.5544	+	37.3334i	−0.757346	+	1.31176i
$811$			40.9858i			1.43920i	0.694387	+	0.719602i	$0.255676\pi$
$811$			40.9858i			1.43920i	−0.694387	+	0.719602i	$0.744324\pi$
$812$	1.68931	+	0.975324i	0.0592832	+	0.0342272i
$813$	−0.713097	−	0.411707i	−0.0250094	−	0.0144392i
$814$		−	30.6740i		−	1.07512i
$815$	−38.1818	+	66.1328i	−1.33745	+	2.31653i
$816$	−0.998781	−	1.72994i	−0.0349643	−	0.0605600i
$817$	7.34455	−	4.24038i	0.256953	−	0.148352i
$818$	15.9104			0.556294
$819$	2.55294	+	9.58040i	0.0892070	+	0.334766i
$820$	−14.5673			−0.508713
$821$	−31.9324	+	18.4362i	−1.11445	+	0.643427i	−0.939978	−	0.341235i	$-0.889155\pi$
$821$	−31.9324	+	18.4362i	−1.11445	+	0.643427i	−0.174471	+	0.984662i	$0.555821\pi$
$822$	−0.818958	−	1.41848i	−0.0285644	−	0.0494750i
$823$	14.2789	−	24.7318i	0.497731	−	0.862095i	−0.502266	−	0.864713i	$-0.667500\pi$
$823$	14.2789	−	24.7318i	0.497731	−	0.862095i	0.999997	+	0.00261827i	$0.000833422\pi$
$824$		−	23.4656i		−	0.817464i
$825$	−2.79999	−	1.61657i	−0.0974830	−	0.0562818i
$826$	2.05242	+	1.18496i	0.0714127	+	0.0412301i
$827$		−	48.0891i		−	1.67222i	−0.548561	−	0.836111i	$-0.684824\pi$
$827$		−	48.0891i		−	1.67222i	0.548561	−	0.836111i	$-0.315176\pi$
$828$	0.614574	−	1.06447i	0.0213579	−	0.0369930i
$829$	12.2797	+	21.2690i	0.426490	+	0.738703i	0.996558	−	0.0828948i	$-0.0264165\pi$
$829$	12.2797	+	21.2690i	0.426490	+	0.738703i	−0.570068	+	0.821597i	$0.693083\pi$
$830$	41.5010	−	23.9606i	1.44052	−	0.831686i
$831$	1.29218			0.0448253
$832$	−8.34717	+	30.9815i	−0.289386	+	1.07409i
$833$	30.1090			1.04322
$834$	0.717409	−	0.414196i	0.0248418	−	0.0143424i
$835$	−13.7928	−	23.8898i	−0.477320	−	0.826742i
$836$	−1.29638	+	2.24539i	−0.0448362	+	0.0776586i
$837$			6.21135i			0.214696i
$838$	−35.7226	−	20.6244i	−1.23402	−	0.712459i
$839$	2.20497	+	1.27304i	0.0761239	+	0.0439502i	0.537579	−	0.843214i	$-0.319339\pi$
$839$	2.20497	+	1.27304i	0.0761239	+	0.0439502i	−0.461455	+	0.887164i	$0.652672\pi$
$840$		−	1.47360i		−	0.0508441i
$841$	1.33912	−	2.31942i	0.0461764	−	0.0799799i
$842$	−16.9078	−	29.2852i	−0.582682	−	1.00923i
$843$	−3.26401	+	1.88447i	−0.112418	+	0.0649048i
$844$	−9.82522			−0.338198
$845$	−25.2912	+	43.5286i	−0.870043	+	1.49743i
$846$	48.7769			1.67698
$847$	4.25132	−	2.45450i	0.146077	−	0.0843376i
$848$	−2.21023	−	3.82823i	−0.0758996	−	0.131462i
$849$	−0.470497	+	0.814925i	−0.0161474	+	0.0279682i
$850$		−	61.6734i		−	2.11538i
$851$	−8.84784	−	5.10830i	−0.303300	−	0.175110i
$852$	−0.388206	−	0.224131i	−0.0132997	−	0.00767860i
$853$			16.3902i			0.561189i	0.959826	+	0.280595i	$0.0905316\pi$
$853$			16.3902i			0.561189i	−0.959826	+	0.280595i	$0.909468\pi$
$854$	5.81546	−	10.0727i	0.199001	−	0.344680i
$855$	−15.2384	−	26.3937i	−0.521143	−	0.902647i
$856$	49.8241	−	28.7660i	1.70295	−	0.983200i
$857$	−14.2344			−0.486237			−0.243118	−	0.969997i	$-0.578170\pi$
$857$	−14.2344			−0.486237			−0.243118	+	0.969997i	$0.578170\pi$
$858$	0.382266	−	1.41883i	0.0130503	−	0.0484379i
$859$	25.7914			0.879992			0.439996	−	0.898000i	$-0.354980\pi$
$859$	25.7914			0.879992			0.439996	+	0.898000i	$0.354980\pi$
$860$	4.44207	−	2.56463i	0.151473	−	0.0874531i
$861$	0.571179	+	0.989312i	0.0194657	+	0.0337157i
$862$	−8.68926	+	15.0502i	−0.295957	+	0.512613i
$863$			41.2129i			1.40290i	0.712717	+	0.701452i	$0.247464\pi$
$863$			41.2129i			1.40290i	−0.712717	+	0.701452i	$0.752536\pi$
$864$	−1.61164	−	0.930478i	−0.0548290	−	0.0316555i
$865$	19.5367	+	11.2795i	0.664266	+	0.383514i
$866$		−	41.9632i		−	1.42597i
$867$	0.473284	−	0.819753i	0.0160736	−	0.0278403i
$868$	1.45429	+	2.51890i	0.0493618	+	0.0854971i
$869$	28.0167	−	16.1755i	0.950403	−	0.548715i
$870$	3.39823			0.115211
$871$	−9.32136	−	34.9802i	−0.315842	−	1.18526i
$872$	−4.69536			−0.159005
$873$	18.0736	−	10.4348i	0.611700	−	0.353165i
$874$	−1.66300	−	2.88041i	−0.0562519	−	0.0974312i
$875$	8.92237	−	15.4540i	0.301631	−	0.522441i
$876$			0.265400i			0.00896704i
$877$	33.9932	+	19.6260i	1.14787	+	0.662722i	0.948367	−	0.317175i	$-0.102734\pi$
$877$	33.9932	+	19.6260i	1.14787	+	0.662722i	0.199502	+	0.979897i	$0.436068\pi$
$878$	23.8255	+	13.7556i	0.804070	+	0.464230i
$879$		−	1.20849i		−	0.0407612i
$880$	13.8663	−	24.0171i	0.467432	−	0.809616i
$881$	7.44716	+	12.8989i	0.250901	+	0.434574i	0.963774	−	0.266720i	$-0.0859398\pi$
$881$	7.44716	+	12.8989i	0.250901	+	0.434574i	−0.712873	+	0.701293i	$0.752606\pi$
$882$	−20.0078	+	11.5515i	−0.673699	+	0.388960i
$883$	12.0969			0.407094			0.203547	−	0.979065i	$-0.434753\pi$
$883$	12.0969			0.407094			0.203547	+	0.979065i	$0.434753\pi$
$884$	−7.03231	+	1.87394i	−0.236522	+	0.0630273i
$885$	−1.07197			−0.0360340
$886$	16.4455	−	9.49484i	0.552499	−	0.318985i
$887$	−24.2733	−	42.0425i	−0.815017	−	1.41165i	−0.909316	−	0.416107i	$-0.863394\pi$
$887$	−24.2733	−	42.0425i	−0.815017	−	1.41165i	0.0942989	−	0.995544i	$-0.469939\pi$
$888$	−2.10766	+	3.65058i	−0.0707285	+	0.122505i
$889$			10.9005i			0.365591i
$890$	−22.4686	−	12.9722i	−0.753149	−	0.434831i
$891$	−18.2299	−	10.5251i	−0.610725	−	0.352603i
$892$			10.5547i			0.353398i
$893$	−17.1348	+	29.6783i	−0.573394	+	0.993147i
$894$	0.320688	+	0.555449i	0.0107254	+	0.0185770i
$895$	−39.2003	+	22.6323i	−1.31032	+	0.756515i
$896$	6.11426			0.204263
$897$	−0.345597	−	0.346549i	−0.0115391	−	0.0115709i
$898$	13.8454			0.462026
$899$	−33.9897	+	19.6240i	−1.13362	+	0.654496i
$900$	−6.14351	−	10.6409i	−0.204784	−	0.354695i
$901$	3.60061	−	6.23645i	0.119954	−	0.207766i
$902$			27.3963i			0.912197i
$903$	−0.348344	−	0.201116i	−0.0115921	−	0.00669273i
$904$	24.2305	+	13.9895i	0.805894	+	0.465283i
$905$		−	26.8562i		−	0.892730i
$906$	−0.602931	+	1.04431i	−0.0200310	+	0.0346948i
$907$	−11.3143	−	19.5970i	−0.375686	−	0.650708i	0.614743	−	0.788727i	$-0.289260\pi$
$907$	−11.3143	−	19.5970i	−0.375686	−	0.650708i	−0.990430	+	0.138019i	$0.955926\pi$
$908$	4.24328	−	2.44986i	0.140818	−	0.0813014i
$909$	9.63150			0.319457
$910$	15.6676	+	4.22123i	0.519376	+	0.139932i
$911$	−44.1396			−1.46241			−0.731205	−	0.682158i	$-0.761042\pi$
$911$	−44.1396			−1.46241			−0.731205	+	0.682158i	$0.761042\pi$
$912$	−0.932606	+	0.538440i	−0.0308817	+	0.0178295i
$913$	11.7000	+	20.2650i	0.387213	+	0.670673i
$914$	10.3129	−	17.8624i	0.341119	−	0.590836i
$915$			5.26094i			0.173921i
$916$	−2.75713	−	1.59183i	−0.0910982	−	0.0525956i
$917$	2.28116	+	1.31703i	0.0753307	+	0.0434922i
$918$			5.00936i			0.165334i
$919$	7.08264	−	12.2675i	0.233635	−	0.404667i	−0.725240	−	0.688496i	$-0.758271\pi$
$919$	7.08264	−	12.2675i	0.233635	−	0.404667i	0.958875	+	0.283828i	$0.0916046\pi$
$920$	−5.88540	−	10.1938i	−0.194036	−	0.336080i
$921$	−3.84283	+	2.21866i	−0.126626	+	0.0731073i
$922$	10.9210			0.359663
$923$	20.4511	−	20.3949i	0.673155	−	0.671305i
$924$	0.122971			0.00404546
$925$	−88.4462	+	51.0645i	−2.90809	+	1.67899i
$926$	−25.0567	−	43.3994i	−0.823413	−	1.42619i
$927$	−11.5089	+	19.9340i	−0.378002	+	0.654719i
$928$		−	11.7589i		−	0.386005i
$929$	−15.8779	−	9.16710i	−0.520937	−	0.300763i	0.216381	−	0.976309i	$-0.430575\pi$
$929$	−15.8779	−	9.16710i	−0.520937	−	0.300763i	−0.737318	+	0.675546i	$0.763908\pi$
$930$	4.38819	+	2.53352i	0.143894	+	0.0830775i
$931$		−	16.2317i		−	0.531973i
$932$	−1.21417	+	2.10300i	−0.0397714	+	0.0688861i
$933$	−1.08704	−	1.88281i	−0.0355881	−	0.0616404i
$934$	24.4337	−	14.1068i	0.799495	−	0.461589i
$935$	45.1782			1.47749
$936$	23.1373	−	23.0737i	0.756265	−	0.754188i
$937$	2.56271			0.0837200			0.0418600	−	0.999123i	$-0.486672\pi$
$937$	2.56271			0.0837200			0.0418600	+	0.999123i	$0.486672\pi$
$938$	−10.1049	+	5.83407i	−0.329937	+	0.190489i
$939$	−0.191777	−	0.332168i	−0.00625842	−	0.0108399i
$940$	−10.3633	+	17.9498i	−0.338014	+	0.585457i
$941$		−	4.69726i		−	0.153126i	−0.997065	−	0.0765631i	$-0.975605\pi$
$941$		−	4.69726i		−	0.153126i	0.997065	−	0.0765631i	$-0.0243947\pi$
$942$	−1.33731	−	0.772099i	−0.0435721	−	0.0251564i
$943$	7.90240	+	4.56245i	0.257338	+	0.148574i
$944$		−	6.12922i		−	0.199489i
$945$	−1.44995	+	2.51139i	−0.0471668	+	0.0816954i
$946$	−4.82321	−	8.35404i	−0.156816	−	0.271613i
$947$	1.33046	−	0.768141i	0.0432341	−	0.0249612i	−0.478227	−	0.878236i	$-0.658720\pi$
$947$	1.33046	−	0.768141i	0.0432341	−	0.0249612i	0.521461	+	0.853275i	$0.325387\pi$
$948$	−0.759774			−0.0246763
$949$	−16.5115	−	4.44860i	−0.535986	−	0.144408i
$950$	−33.2480			−1.07871
$951$	−0.343582	+	0.198367i	−0.0111414	+	0.00643249i
$952$	6.86295	+	11.8870i	0.222429	+	0.385259i
$953$	16.7039	−	28.9320i	0.541092	−	0.937199i	−0.457749	−	0.889081i	$-0.651344\pi$
$953$	16.7039	−	28.9320i	0.541092	−	0.937199i	0.998842	−	0.0481182i	$-0.0153224\pi$
$954$			5.52560i			0.178898i
$955$	38.9064	+	22.4626i	1.25898	+	0.726873i
$956$	−0.249455	−	0.144023i	−0.00806797	−	0.00465804i
$957$			1.65936i			0.0536395i
$958$	−13.4858	+	23.3581i	−0.435707	+	0.754666i
$959$	4.41593	+	7.64861i	0.142598	+	0.246987i
$960$	−4.05119	+	2.33896i	−0.130752	+	0.0754895i
$961$	−27.5220			−0.887805
$962$	−32.7760	−	32.8663i	−1.05674	−	1.05965i
$963$	−56.4340			−1.81856
$964$	6.20715	−	3.58370i	0.199919	−	0.115423i
$965$	7.92895	+	13.7333i	0.255242	+	0.442092i
$966$	−0.0788743	+	0.136614i	−0.00253774	+	0.00439549i
$967$			31.7847i			1.02213i	0.859543	+	0.511063i	$0.170748\pi$
$967$			31.7847i			1.02213i	−0.859543	+	0.511063i	$0.829252\pi$
$968$	−14.0112	−	8.08934i	−0.450336	−	0.260001i
$969$	−1.51928	−	0.877156i	−0.0488063	−	0.0281783i
$970$		−	34.1550i		−	1.09665i
$971$	−9.94868	+	17.2316i	−0.319268	+	0.552989i	−0.980336	−	0.197338i	$-0.936770\pi$
$971$	−9.94868	+	17.2316i	−0.319268	+	0.552989i	0.661067	+	0.750327i	$0.270104\pi$
$972$	0.749269	+	1.29777i	0.0240328	+	0.0416260i
$973$	−3.86836	+	2.23340i	−0.124014	+	0.0715995i
$974$	19.2734			0.617559
$975$	−4.72747	+	1.25975i	−0.151400	+	0.0403444i
$976$	−30.0805			−0.962852
$977$	41.0977	−	23.7278i	1.31483	−	0.759118i	0.331939	−	0.943301i	$-0.392297\pi$
$977$	41.0977	−	23.7278i	1.31483	−	0.759118i	0.982892	+	0.184182i	$0.0589637\pi$
$978$	−1.68642	−	2.92096i	−0.0539257	−	0.0934021i
$979$	6.33436	−	10.9714i	0.202447	−	0.350648i
$980$		−	9.81712i		−	0.313596i
$981$	3.98870	+	2.30288i	0.127350	+	0.0735253i
$982$	3.98033	+	2.29805i	0.127018	+	0.0733336i
$983$			5.93213i			0.189206i	0.995515	+	0.0946028i	$0.0301581\pi$
$983$			5.93213i			0.189206i	−0.995515	+	0.0946028i	$0.969842\pi$
$984$	1.88245	−	3.26049i	0.0600102	−	0.103941i
$985$	41.2227	+	71.3999i	1.31347	+	2.27499i
$986$	−27.4122	+	15.8264i	−0.872982	+	0.504016i
$987$	1.62537			0.0517360
$988$	1.01023	+	3.79110i	0.0321398	+	0.120611i
$989$	−3.21294			−0.102166
$990$	−30.0215	+	17.3329i	−0.954146	+	0.550877i
$991$	30.6426	+	53.0745i	0.973393	+	1.68597i	0.685139	+	0.728413i	$0.259742\pi$
$991$	30.6426	+	53.0745i	0.973393	+	1.68597i	0.288254	+	0.957554i	$0.406925\pi$
$992$	8.76676	−	15.1845i	0.278345	−	0.482107i
$993$			1.50600i			0.0477916i
$994$	−8.06209	−	4.65465i	−0.255714	−	0.147637i
$995$	7.56687	+	4.36873i	0.239886	+	0.138498i
$996$		−	0.549558i		−	0.0174134i
$997$	−1.59007	+	2.75409i	−0.0503581	+	0.0872228i	−0.890106	−	0.455754i	$-0.849370\pi$
$997$	−1.59007	+	2.75409i	−0.0503581	+	0.0872228i	0.839748	+	0.542977i	$0.182703\pi$
$998$	12.6983	+	21.9941i	0.401957	+	0.696210i
$999$	7.18396	−	4.14766i	0.227290	−	0.131226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.i.b.231.11	✓	30
13.2	odd	12		3887.2.a.u.1.22		30
13.4	even	6	inner	299.2.i.b.277.11	yes	30
13.11	odd	12		3887.2.a.u.1.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.i.b.231.11	✓	30	1.1	even	1	trivial
299.2.i.b.277.11	yes	30	13.4	even	6	inner
3887.2.a.u.1.9		30	13.11	odd	12
3887.2.a.u.1.22		30	13.2	odd	12

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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09124 - 0.630030i) q^{2} +(0.0678705 + 0.117555i) q^{3} +(-0.206124 + 0.357017i) q^{4} -3.87251i q^{5} +(0.148127 + 0.0855209i) q^{6} +(-0.798718 - 0.461140i) q^{7} +3.03958i q^{8} +(1.49079 - 2.58212i) q^{9} +O(q^{10})\)	\(q+(1.09124 - 0.630030i) q^{2} +(0.0678705 + 0.117555i) q^{3} +(-0.206124 + 0.357017i) q^{4} -3.87251i q^{5} +(0.148127 + 0.0855209i) q^{6} +(-0.798718 - 0.461140i) q^{7} +3.03958i q^{8} +(1.49079 - 2.58212i) q^{9} +(-2.43980 - 4.22586i) q^{10} +(2.06349 - 1.19136i) q^{11} -0.0559589 q^{12} +(0.937975 - 3.48141i) q^{13} -1.16213 q^{14} +(0.455234 - 0.262830i) q^{15} +(1.50278 + 2.60289i) q^{16} +(-2.44813 + 4.24028i) q^{17} -3.75696i q^{18} +(2.28593 + 1.31978i) q^{19} +(1.38255 + 0.798218i) q^{20} -0.125191i q^{21} +(1.50118 - 2.60012i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.357318 + 0.206298i) q^{24} -9.99637 q^{25} +(-1.16983 - 4.39002i) q^{26} +0.811945 q^{27} +(0.329270 - 0.190104i) q^{28} +(2.56524 + 4.44312i) q^{29} +(0.331181 - 0.573622i) q^{30} +7.64997i q^{31} +(-1.98491 - 1.14599i) q^{32} +(0.280100 + 0.161716i) q^{33} +6.16958i q^{34} +(-1.78577 + 3.09305i) q^{35} +(0.614574 + 1.06447i) q^{36} +(8.84784 - 5.10830i) q^{37} +3.32601 q^{38} +(0.472918 - 0.126021i) q^{39} +11.7708 q^{40} +(-7.90240 + 4.56245i) q^{41} +(-0.0788743 - 0.136614i) q^{42} +(1.60647 - 2.78249i) q^{43} +0.982268i q^{44} +(-9.99929 - 5.77309i) q^{45} +(-1.09124 - 0.630030i) q^{46} +12.9831i q^{47} +(-0.203989 + 0.353319i) q^{48} +(-3.07470 - 5.32554i) q^{49} +(-10.9085 + 6.29801i) q^{50} -0.664623 q^{51} +(1.04958 + 1.05247i) q^{52} -1.47076 q^{53} +(0.886030 - 0.511550i) q^{54} +(-4.61355 - 7.99090i) q^{55} +(1.40167 - 2.42777i) q^{56} +0.358297i q^{57} +(5.59860 + 3.23235i) q^{58} +(-1.76608 - 1.01965i) q^{59} +0.216702i q^{60} +(-5.00414 + 8.66743i) q^{61} +(4.81971 + 8.34798i) q^{62} +(-2.38144 + 1.37492i) q^{63} -8.89914 q^{64} +(-13.4818 - 3.63232i) q^{65} +0.407544 q^{66} +(8.69516 - 5.02015i) q^{67} +(-1.00924 - 1.74805i) q^{68} +(0.0678705 - 0.117555i) q^{69} +4.50036i q^{70} +(6.93734 + 4.00528i) q^{71} +(7.84855 + 4.53136i) q^{72} -4.74277i q^{73} +(6.43677 - 11.1488i) q^{74} +(-0.678459 - 1.17512i) q^{75} +(-0.942368 + 0.544077i) q^{76} -2.19753 q^{77} +(0.436672 - 0.435473i) q^{78} +13.5774 q^{79} +(10.0797 - 5.81953i) q^{80} +(-4.41725 - 7.65091i) q^{81} +(-5.74897 + 9.95750i) q^{82} +9.82073i q^{83} +(0.0446954 + 0.0258049i) q^{84} +(16.4206 + 9.48041i) q^{85} -4.04850i q^{86} +(-0.348208 + 0.603114i) q^{87} +(3.62122 + 6.27214i) q^{88} +(4.60459 - 2.65846i) q^{89} -14.5489 q^{90} +(-2.35460 + 2.34813i) q^{91} +0.412248 q^{92} +(-0.899293 + 0.519207i) q^{93} +(8.17972 + 14.1677i) q^{94} +(5.11087 - 8.85228i) q^{95} -0.311115i q^{96} +(6.06178 + 3.49977i) q^{97} +(-6.71050 - 3.87431i) q^{98} -7.10424i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more