LMFDB - Embedded newform 637.2.bl.a.53.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.9
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15236 - 0.785668i) q^{2} +(1.86576 + 1.73118i) q^{3} +(-0.0200159 - 0.0509996i) q^{4} +(-1.72793 + 0.532996i) q^{5} +(-0.789908 - 3.46081i) q^{6} +(-0.964248 - 2.46378i) q^{7} +(-0.637707 + 2.79398i) q^{8} +(0.259914 + 3.46832i) q^{9} +O(q^{10})$	\(q+(-1.15236 - 0.785668i) q^{2} +(1.86576 + 1.73118i) q^{3} +(-0.0200159 - 0.0509996i) q^{4} +(-1.72793 + 0.532996i) q^{5} +(-0.789908 - 3.46081i) q^{6} +(-0.964248 - 2.46378i) q^{7} +(-0.637707 + 2.79398i) q^{8} +(0.259914 + 3.46832i) q^{9} +(2.40996 + 0.743375i) q^{10} +(0.185892 - 2.48055i) q^{11} +(0.0509444 - 0.129804i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-0.824550 + 3.59675i) q^{14} +(-4.14662 - 1.99691i) q^{15} +(2.84968 - 2.64412i) q^{16} +(7.11388 - 1.07224i) q^{17} +(2.42543 - 4.20096i) q^{18} +(-1.55764 - 2.69791i) q^{19} +(0.0617687 + 0.0774555i) q^{20} +(2.46618 - 6.26612i) q^{21} +(-2.16310 + 2.71245i) q^{22} +(8.21367 + 1.23801i) q^{23} +(-6.02668 + 4.10892i) q^{24} +(-1.42953 + 0.974638i) q^{25} +(-1.37913 - 0.207871i) q^{26} +(-0.758605 + 0.951261i) q^{27} +(-0.106352 + 0.0984911i) q^{28} +(-5.32693 - 6.67976i) q^{29} +(3.20951 + 5.55903i) q^{30} +(4.83641 - 8.37692i) q^{31} +(0.306373 - 0.0461782i) q^{32} +(4.64110 - 4.30631i) q^{33} +(-9.04020 - 4.35353i) q^{34} +(2.97934 + 3.74331i) q^{35} +(0.171680 - 0.0826769i) q^{36} +(-0.590165 + 1.50372i) q^{37} +(-0.324695 + 4.33276i) q^{38} +(2.43212 + 0.750211i) q^{39} +(-0.387265 - 5.16770i) q^{40} +(-0.591849 + 2.59306i) q^{41} +(-7.76502 + 5.28324i) q^{42} +(1.01510 + 4.44745i) q^{43} +(-0.130228 + 0.0401700i) q^{44} +(-2.29771 - 5.85448i) q^{45} +(-8.49246 - 7.87985i) q^{46} +(6.50246 + 4.43330i) q^{47} +9.89427 q^{48} +(-5.14045 + 4.75140i) q^{49} +2.41308 q^{50} +(15.1291 + 10.3148i) q^{51} +(-0.0401616 - 0.0372645i) q^{52} +(-1.64788 - 4.19873i) q^{53} +(1.62156 - 0.500186i) q^{54} +(1.00092 + 4.38530i) q^{55} +(7.49866 - 1.12292i) q^{56} +(1.76437 - 7.73021i) q^{57} +(0.890485 + 11.8827i) q^{58} +(9.86934 + 3.04429i) q^{59} +(-0.0188433 + 0.251446i) q^{60} +(2.14718 - 5.47093i) q^{61} +(-12.1548 + 5.85343i) q^{62} +(8.29455 - 3.98469i) q^{63} +(-7.39423 - 3.56087i) q^{64} +(-1.32555 + 1.22993i) q^{65} +(-8.73156 + 1.31607i) q^{66} +(1.07641 - 1.86439i) q^{67} +(-0.197075 - 0.341343i) q^{68} +(13.1815 + 16.5291i) q^{69} +(-0.492288 - 6.65442i) q^{70} +(-0.825710 + 1.03541i) q^{71} +(-9.85614 - 1.48557i) q^{72} +(-6.46159 + 4.40544i) q^{73} +(1.86150 - 1.26915i) q^{74} +(-4.35444 - 0.656326i) q^{75} +(-0.106415 + 0.133440i) q^{76} +(-6.29079 + 1.93387i) q^{77} +(-2.21327 - 2.77536i) q^{78} +(-5.70950 - 9.88914i) q^{79} +(-3.51475 + 6.08773i) q^{80} +(7.25540 - 1.09358i) q^{81} +(2.71931 - 2.52315i) q^{82} +(-14.3242 - 6.89819i) q^{83} +(-0.368933 - 0.000352414i) q^{84} +(-11.7208 + 5.64444i) q^{85} +(2.32445 - 5.92261i) q^{86} +(1.62504 - 21.6847i) q^{87} +(6.81206 + 2.10124i) q^{88} +(-0.638431 - 8.51927i) q^{89} +(-1.95187 + 8.55172i) q^{90} +(-1.93775 - 1.80142i) q^{91} +(-0.101266 - 0.443674i) q^{92} +(23.5255 - 7.25666i) q^{93} +(-4.01009 - 10.2175i) q^{94} +(4.12947 + 3.83159i) q^{95} +(0.651561 + 0.444227i) q^{96} -14.7327 q^{97} +(9.65668 - 1.43665i) q^{98} +8.65165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−1.15236	−	0.785668i	−0.814843	−	0.555551i	0.0826500	−	0.996579i	$-0.473662\pi$
$2$	−1.15236	−	0.785668i	−0.814843	−	0.555551i	−0.897493	+	0.441028i	$0.854614\pi$
$3$	1.86576	+	1.73118i	1.07720	+	0.999495i	0.999997	+	0.00247905i	$0.000789108\pi$
$3$	1.86576	+	1.73118i	1.07720	+	0.999495i	0.0772020	+	0.997015i	$0.475401\pi$
$4$	−0.0200159	−	0.0509996i	−0.0100079	−	0.0254998i
$5$	−1.72793	+	0.532996i	−0.772754	+	0.238363i	−0.655963	−	0.754793i	$-0.727737\pi$
$5$	−1.72793	+	0.532996i	−0.772754	+	0.238363i	−0.116792	+	0.993156i	$0.537261\pi$
$6$	−0.789908	−	3.46081i	−0.322478	−	1.41287i
$7$	−0.964248	−	2.46378i	−0.364452	−	0.931222i
$7$	−0.964248	−	2.46378i	−0.364452	−	0.931222i
$8$	−0.637707	+	2.79398i	−0.225464	+	0.987820i
$9$	0.259914	+	3.46832i	0.0866381	+	1.15611i
$10$	2.40996	+	0.743375i	0.762097	+	0.235076i
$11$	0.185892	−	2.48055i	0.0560485	−	0.747915i	−0.896406	−	0.443234i	$-0.853831\pi$
$11$	0.185892	−	2.48055i	0.0560485	−	0.747915i	0.952455	−	0.304681i	$-0.0985498\pi$
$12$	0.0509444	−	0.129804i	0.0147064	−	0.0374713i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	−0.824550	+	3.59675i	−0.220370	+	0.961272i
$15$	−4.14662	−	1.99691i	−1.07065	−	0.515599i
$16$	2.84968	−	2.64412i	0.712421	−	0.661030i
$17$	7.11388	−	1.07224i	1.72537	−	0.260058i	0.789842	−	0.613311i	$-0.210163\pi$
$17$	7.11388	−	1.07224i	1.72537	−	0.260058i	0.935528	+	0.353253i	$0.114925\pi$
$18$	2.42543	−	4.20096i	0.571679	−	0.990176i
$19$	−1.55764	−	2.69791i	−0.357347	−	0.618943i	0.630170	−	0.776457i	$-0.282985\pi$
$19$	−1.55764	−	2.69791i	−0.357347	−	0.618943i	−0.987517	+	0.157514i	$0.949652\pi$
$20$	0.0617687	+	0.0774555i	0.0138119	+	0.0173196i
$21$	2.46618	−	6.26612i	0.538165	−	1.36738i
$22$	−2.16310	+	2.71245i	−0.461175	+	0.578296i
$23$	8.21367	+	1.23801i	1.71267	+	0.258143i	0.930860	−	0.365376i	$-0.119060\pi$
$23$	8.21367	+	1.23801i	1.71267	+	0.258143i	0.781808	+	0.623520i	$0.214298\pi$
$24$	−6.02668	+	4.10892i	−1.23019	+	0.838729i
$25$	−1.42953	+	0.974638i	−0.285906	+	0.194928i
$26$	−1.37913	−	0.207871i	−0.270470	−	0.0407668i
$27$	−0.758605	+	0.951261i	−0.145994	+	0.183070i
$28$	−0.106352	+	0.0984911i	−0.0200986	+	0.0186131i
$29$	−5.32693	−	6.67976i	−0.989186	−	1.24040i	−0.970631	−	0.240572i	$-0.922665\pi$
$29$	−5.32693	−	6.67976i	−0.989186	−	1.24040i	−0.0185541	−	0.999828i	$-0.505906\pi$
$30$	3.20951	+	5.55903i	0.585973	+	1.01493i
$31$	4.83641	−	8.37692i	0.868646	−	1.50454i	0.00526445	−	0.999986i	$-0.498324\pi$
$31$	4.83641	−	8.37692i	0.868646	−	1.50454i	0.863381	−	0.504552i	$-0.168342\pi$
$32$	0.306373	−	0.0461782i	0.0541595	−	0.00816324i
$33$	4.64110	−	4.30631i	0.807912	−	0.749633i
$34$	−9.04020	−	4.35353i	−1.55038	−	0.746624i
$35$	2.97934	+	3.74331i	0.503601	+	0.632734i
$36$	0.171680	−	0.0826769i	0.0286134	−	0.0137795i
$37$	−0.590165	+	1.50372i	−0.0970225	+	0.247209i	−0.971142	−	0.238501i	$-0.923344\pi$
$37$	−0.590165	+	1.50372i	−0.0970225	+	0.247209i	0.874120	+	0.485711i	$0.161439\pi$
$38$	−0.324695	+	4.33276i	−0.0526725	+	0.702866i
$39$	2.43212	+	0.750211i	0.389451	+	0.120130i
$40$	−0.387265	−	5.16770i	−0.0612320	−	0.817085i
$41$	−0.591849	+	2.59306i	−0.0924314	+	0.404968i	−0.999885	−	0.0151846i	$-0.995166\pi$
$41$	−0.591849	+	2.59306i	−0.0924314	+	0.404968i	0.907453	+	0.420153i	$0.138024\pi$
$42$	−7.76502	+	5.28324i	−1.19817	+	0.815222i
$43$	1.01510	+	4.44745i	0.154802	+	0.678230i	0.991450	+	0.130489i	$0.0416548\pi$
$43$	1.01510	+	4.44745i	0.154802	+	0.678230i	−0.836648	+	0.547741i	$0.815488\pi$
$44$	−0.130228	+	0.0401700i	−0.0196326	+	0.00605586i
$45$	−2.29771	−	5.85448i	−0.342523	−	0.872734i
$46$	−8.49246	−	7.87985i	−1.25214	−	1.16182i
$47$	6.50246	+	4.43330i	0.948481	+	0.646663i	0.935528	−	0.353253i	$-0.114924\pi$
$47$	6.50246	+	4.43330i	0.948481	+	0.646663i	0.0129531	+	0.999916i	$0.495877\pi$
$48$	9.89427			1.42812
$49$	−5.14045	+	4.75140i	−0.734350	+	0.678771i
$50$	2.41308			0.341261
$51$	15.1291	+	10.3148i	2.11849	+	1.44436i
$52$	−0.0401616	−	0.0372645i	−0.00556941	−	0.00516766i
$53$	−1.64788	−	4.19873i	−0.226353	−	0.576739i	0.771905	−	0.635738i	$-0.219304\pi$
$53$	−1.64788	−	4.19873i	−0.226353	−	0.576739i	−0.998258	+	0.0589992i	$0.981209\pi$
$54$	1.62156	−	0.500186i	0.220667	−	0.0680667i
$55$	1.00092	+	4.38530i	0.134964	+	0.591314i
$56$	7.49866	−	1.12292i	1.00205	−	0.150056i
$57$	1.76437	−	7.73021i	0.233696	−	1.02389i
$58$	0.890485	+	11.8827i	0.116926	+	1.56027i
$59$	9.86934	+	3.04429i	1.28488	+	0.396332i	0.860638	−	0.509217i	$-0.170065\pi$
$59$	9.86934	+	3.04429i	1.28488	+	0.396332i	0.424240	+	0.905550i	$0.360541\pi$
$60$	−0.0188433	+	0.251446i	−0.00243266	+	0.0324615i
$61$	2.14718	−	5.47093i	0.274918	−	0.700480i	−0.725013	−	0.688735i	$-0.758166\pi$
$61$	2.14718	−	5.47093i	0.274918	−	0.700480i	0.999931	−	0.0117448i	$-0.00373858\pi$
$62$	−12.1548	+	5.85343i	−1.54366	+	0.743386i
$63$	8.29455	−	3.98469i	1.04502	−	0.502024i
$64$	−7.39423	−	3.56087i	−0.924279	−	0.445109i
$65$	−1.32555	+	1.22993i	−0.164415	+	0.152555i
$66$	−8.73156	+	1.31607i	−1.07478	+	0.161997i
$67$	1.07641	−	1.86439i	0.131504	−	0.227772i	−0.792752	−	0.609544i	$-0.791353\pi$
$67$	1.07641	−	1.86439i	0.131504	−	0.227772i	0.924257	+	0.381772i	$0.124686\pi$
$68$	−0.197075	−	0.341343i	−0.0238988	−	0.0413940i
$69$	13.1815	+	16.5291i	1.58687	+	1.98987i
$70$	−0.492288	−	6.65442i	−0.0588397	−	0.795355i
$71$	−0.825710	+	1.03541i	−0.0979938	+	0.122880i	−0.828410	−	0.560121i	$-0.810754\pi$
$71$	−0.825710	+	1.03541i	−0.0979938	+	0.122880i	0.730417	+	0.683002i	$0.239326\pi$
$72$	−9.85614	−	1.48557i	−1.16156	−	0.175077i
$73$	−6.46159	+	4.40544i	−0.756272	+	0.515618i	−0.878999	−	0.476823i	$-0.841788\pi$
$73$	−6.46159	+	4.40544i	−0.756272	+	0.515618i	0.122727	+	0.992440i	$0.460836\pi$
$74$	1.86150	−	1.26915i	0.216396	−	0.147536i
$75$	−4.35444	−	0.656326i	−0.502807	−	0.0757860i
$76$	−0.106415	+	0.133440i	−0.0122066	+	0.0153066i
$77$	−6.29079	+	1.93387i	−0.716902	+	0.220385i
$78$	−2.21327	−	2.77536i	−0.250604	−	0.314247i
$79$	−5.70950	−	9.88914i	−0.642369	−	1.11261i	−0.984903	−	0.173110i	$-0.944619\pi$
$79$	−5.70950	−	9.88914i	−0.642369	−	1.11261i	0.342534	−	0.939505i	$-0.388715\pi$
$80$	−3.51475	+	6.08773i	−0.392961	+	0.680629i
$81$	7.25540	−	1.09358i	0.806156	−	0.121508i
$82$	2.71931	−	2.52315i	0.300298	−	0.278635i
$83$	−14.3242	−	6.89819i	−1.57229	−	0.757175i	−0.574185	−	0.818725i	$-0.694681\pi$
$83$	−14.3242	−	6.89819i	−1.57229	−	0.757175i	−0.998104	+	0.0615508i	$0.980395\pi$
$84$	−0.368933		0.000352414i	−0.0402538		3.84516e-5i
$85$	−11.7208	+	5.64444i	−1.27130	+	0.612225i
$86$	2.32445	−	5.92261i	0.250652	−	0.638651i
$87$	1.62504	−	21.6847i	0.174223	−	2.32484i
$88$	6.81206	+	2.10124i	0.726168	+	0.223993i
$89$	−0.638431	−	8.51927i	−0.0676735	−	0.903041i	−0.922963	−	0.384890i	$-0.874240\pi$
$89$	−0.638431	−	8.51927i	−0.0676735	−	0.903041i	0.855289	−	0.518151i	$-0.173380\pi$
$90$	−1.95187	+	8.55172i	−0.205746	+	0.901430i
$91$	−1.93775	−	1.80142i	−0.203132	−	0.188840i
$92$	−0.101266	−	0.443674i	−0.0105577	−	0.0462562i
$93$	23.5255	−	7.25666i	2.43948	−	0.752481i
$94$	−4.01009	−	10.2175i	−0.413609	−	1.05386i
$95$	4.12947	+	3.83159i	0.423675	+	0.393113i
$96$	0.651561	+	0.444227i	0.0664997	+	0.0453387i
$97$	−14.7327			−1.49588			−0.747940	−	0.663767i	$-0.768957\pi$
$97$	−14.7327			−1.49588			−0.747940	+	0.663767i	$0.768957\pi$
$98$	9.65668	−	1.43665i	0.975472	−	0.145123i
$99$	8.65165			0.869524
$100$	0.0783196	+	0.0533974i	0.00783196	+	0.00533974i
$101$	−1.54802	−	1.43635i	−0.154033	−	0.142922i	0.599392	−	0.800456i	$-0.295409\pi$
$101$	−1.54802	−	1.43635i	−0.154033	−	0.142922i	−0.753425	+	0.657534i	$0.771600\pi$
$102$	−9.33015	−	23.7728i	−0.923822	−	2.35386i
$103$	5.18509	−	1.59939i	0.510902	−	0.157593i	−0.0285766	−	0.999592i	$-0.509097\pi$
$103$	5.18509	−	1.59939i	0.510902	−	0.157593i	0.539479	+	0.841999i	$0.318621\pi$
$104$	0.637707	+	2.79398i	0.0625323	+	0.273972i
$105$	−0.921573	+	12.1419i	−0.0899363	+	1.18493i
$106$	−1.39985	+	6.13314i	−0.135965	+	0.595703i
$107$	0.301180	+	4.01896i	0.0291161	+	0.388528i	0.992657	+	0.120966i	$0.0385991\pi$
$107$	0.301180	+	4.01896i	0.0291161	+	0.388528i	−0.963541	+	0.267562i	$0.913782\pi$
$108$	0.0636981	+	0.0196483i	0.00612935	+	0.00189066i
$109$	−0.320803	+	4.28081i	−0.0307273	+	0.410028i	0.960538	+	0.278148i	$0.0897204\pi$
$109$	−0.320803	+	4.28081i	−0.0307273	+	0.410028i	−0.991266	+	0.131880i	$0.957899\pi$
$110$	2.29197	−	5.83985i	0.218531	−	0.556808i
$111$	−3.70430	+	1.78390i	−0.351597	+	0.169320i
$112$	−9.26234	−	4.47141i	−0.875209	−	0.422509i
$113$	15.5431	+	7.48515i	1.46217	+	0.704144i	0.984660	−	0.174483i	$-0.0558255\pi$
$113$	15.5431	+	7.48515i	1.46217	+	0.704144i	0.477509	+	0.878627i	$0.341540\pi$
$114$	−8.10657	+	7.52179i	−0.759249	+	0.704481i
$115$	−14.8525	+	2.23865i	−1.38500	+	0.208756i
$116$	−0.234042	+	0.405373i	−0.0217303	+	0.0376379i
$117$	1.73902	+	3.01207i	0.160772	+	0.278466i
$118$	−8.98126	−	11.2621i	−0.826792	−	1.03676i
$119$	−9.50133	−	16.4931i	−0.870985	−	1.51192i
$120$	8.22364	−	10.3121i	0.750713	−	0.941364i
$121$	4.75856	+	0.717237i	0.432596	+	0.0652034i
$122$	−6.77266	+	4.61752i	−0.613168	+	0.418051i
$123$	−5.59330	+	3.81344i	−0.504330	+	0.343847i
$124$	−0.524025	−	0.0789840i	−0.0470588	−	0.00709297i
$125$	7.58784	−	9.51485i	0.678677	−	0.851034i
$126$	−12.6890	−	1.92495i	−1.13042	−	0.171488i
$127$	−4.60677	−	5.77671i	−0.408785	−	0.512600i	0.534235	−	0.845336i	$-0.320600\pi$
$127$	−4.60677	−	5.77671i	−0.408785	−	0.512600i	−0.943020	+	0.332736i	$0.892028\pi$
$128$	5.41334	+	9.37618i	0.478476	+	0.828745i
$129$	−5.80538	+	10.0552i	−0.511135	+	0.885312i
$130$	2.49384	−	0.375886i	0.218724	−	0.0329674i
$131$	−12.4170	+	11.5213i	−1.08488	+	1.00662i	−0.0849277	+	0.996387i	$0.527066\pi$
$131$	−12.4170	+	11.5213i	−1.08488	+	1.00662i	−0.999948	+	0.0102302i	$0.996744\pi$
$132$	−0.312516	−	0.150500i	−0.0272010	−	0.0130993i
$133$	−5.14511	+	6.43914i	−0.446138	+	0.558344i
$134$	−2.70521	+	1.30276i	−0.233694	+	0.112541i
$135$	0.803799	−	2.04805i	0.0691800	−	0.176268i
$136$	−1.54074	+	20.5598i	−0.132118	+	1.76299i
$137$	1.36767	+	0.421872i	0.116848	+	0.0360429i	0.352628	−	0.935764i	$-0.385288\pi$
$137$	1.36767	+	0.421872i	0.116848	+	0.0360429i	−0.235780	+	0.971807i	$0.575764\pi$
$138$	−2.20351	−	29.4039i	−0.187576	−	2.50302i
$139$	−3.51349	+	15.3936i	−0.298010	+	1.30567i	0.575074	+	0.818101i	$0.304973\pi$
$139$	−3.51349	+	15.3936i	−0.298010	+	1.30567i	−0.873085	+	0.487568i	$0.837884\pi$
$140$	0.131273	−	0.226871i	0.0110946	−	0.0191741i
$141$	4.45723	+	19.5284i	0.375366	+	1.64459i
$142$	1.76500	−	0.544432i	0.148116	−	0.0456877i
$143$	−0.908789	−	2.31556i	−0.0759967	−	0.193636i
$144$	9.91132	+	9.19636i	0.825943	+	0.766363i
$145$	12.7648	+	8.70293i	1.06006	+	0.722739i
$146$	10.9073			0.902695
$147$	−17.8164	−	0.0340374i	−1.46947	−	0.00280736i
$148$	0.0885016			0.00727479
$149$	4.66134	+	3.17805i	0.381872	+	0.260356i	0.739008	−	0.673697i	$-0.235295\pi$
$149$	4.66134	+	3.17805i	0.381872	+	0.260356i	−0.357136	+	0.934052i	$0.616247\pi$
$150$	4.50224	+	4.17747i	0.367606	+	0.341089i
$151$	8.39720	+	21.3957i	0.683354	+	1.74116i	0.671249	+	0.741232i	$0.265758\pi$
$151$	8.39720	+	21.3957i	0.683354	+	1.74116i	0.0121054	+	0.999927i	$0.496147\pi$
$152$	8.53122	−	2.63153i	0.691973	−	0.213445i
$153$	5.56788	+	24.3945i	0.450137	+	1.97218i
$154$	8.76865	+	2.71395i	0.706598	+	0.218696i
$155$	−3.89213	+	17.0525i	−0.312623	+	1.36969i
$156$	−0.0104206	−	0.139054i	−0.000834318	−	0.0111332i
$157$	−9.15594	−	2.82423i	−0.730724	−	0.225398i	−0.0930026	−	0.995666i	$-0.529646\pi$
$157$	−9.15594	−	2.82423i	−0.730724	−	0.225398i	−0.637721	+	0.770268i	$0.720123\pi$
$158$	−1.19016	+	15.8816i	−0.0946844	+	1.26348i
$159$	4.19418	−	10.6866i	0.332620	−	0.847502i
$160$	−0.504778	+	0.243088i	−0.0399062	+	0.0192178i
$161$	−4.86982	−	21.4304i	−0.383796	−	1.68895i
$162$	−9.22004	−	4.44014i	−0.724395	−	0.348850i
$163$	8.02804	−	7.44893i	0.628805	−	0.583445i	−0.300035	−	0.953928i	$-0.596998\pi$
$163$	8.02804	−	7.44893i	0.628805	−	0.583445i	0.928839	+	0.370483i	$0.120808\pi$
$164$	0.144092	−	0.0217183i	0.0112517	−	0.00169592i
$165$	−5.72426	+	9.91470i	−0.445633	+	0.771858i
$166$	11.0870	+	19.2033i	0.860521	+	1.49047i
$167$	−3.58213	−	4.49185i	−0.277194	−	0.347590i	0.623673	−	0.781685i	$-0.285640\pi$
$167$	−3.58213	−	4.49185i	−0.277194	−	0.347590i	−0.900867	+	0.434095i	$0.857068\pi$
$168$	15.9347	+	10.8864i	1.22939	+	0.839904i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	17.9413	+	2.70421i	1.37603	+	0.207403i
$171$	8.95235	−	6.10361i	0.684603	−	0.466755i
$172$	0.206500	−	0.140789i	0.0157455	−	0.0107351i
$173$	−5.86780	−	0.884429i	−0.446121	−	0.0672419i	−0.0778597	−	0.996964i	$-0.524809\pi$
$173$	−5.86780	−	0.884429i	−0.446121	−	0.0672419i	−0.368261	+	0.929722i	$0.620047\pi$
$174$	−18.9096	+	23.7119i	−1.43353	+	1.79759i
$175$	3.77972	+	2.58226i	0.285720	+	0.195201i
$176$	−6.02915	−	7.56031i	−0.454464	−	0.569880i
$177$	13.1436	+	22.7655i	0.987937	+	1.71116i
$178$	−5.95761	+	10.3189i	−0.446542	+	0.773433i
$179$	21.6979	−	3.27043i	1.62178	−	0.244444i	0.725592	−	0.688125i	$-0.241566\pi$
$179$	21.6979	−	3.27043i	1.62178	−	0.244444i	0.896185	+	0.443682i	$0.146328\pi$
$180$	−0.252585	+	0.234365i	−0.0188266	+	0.0174685i
$181$	−8.69298	−	4.18632i	−0.646144	−	0.311167i	0.0819576	−	0.996636i	$-0.473883\pi$
$181$	−8.69298	−	4.18632i	−0.646144	−	0.311167i	−0.728102	+	0.685469i	$0.759597\pi$
$182$	0.817677	+	3.59832i	0.0606103	+	0.266725i
$183$	13.4773	−	6.49031i	0.996268	−	0.479777i
$184$	−8.69689	+	22.1593i	−0.641143	+	1.63361i
$185$	0.218290	−	2.91287i	0.0160490	−	0.214159i
$186$	−32.8112	−	10.1209i	−2.40584	−	0.742102i
$187$	−1.33735	−	17.8457i	−0.0977966	−	1.30500i
$188$	0.0959443	−	0.420359i	0.00699746	−	0.0306579i
$189$	3.07518	+	0.951786i	0.223687	+	0.0692323i
$190$	−1.74829	−	7.65977i	−0.126834	−	0.555698i
$191$	−20.7585	+	6.40315i	−1.50203	+	0.463316i	−0.933267	−	0.359184i	$-0.883055\pi$
$191$	−20.7585	+	6.40315i	−1.50203	+	0.463316i	−0.568766	+	0.822500i	$0.692579\pi$
$192$	−7.63139	−	19.4445i	−0.550748	−	1.40328i
$193$	1.27697	+	1.18485i	0.0919182	+	0.0852876i	0.724794	−	0.688966i	$-0.241935\pi$
$193$	1.27697	+	1.18485i	0.0919182	+	0.0852876i	−0.632876	+	0.774254i	$0.718126\pi$
$194$	16.9774	+	11.5750i	1.21891	+	0.831037i
$195$	−4.60240			−0.329585
$196$	0.345210	+	0.167058i	0.0246579	+	0.0119327i
$197$	20.2583			1.44335			0.721674	−	0.692233i	$-0.243373\pi$
$197$	20.2583			1.44335			0.721674	+	0.692233i	$0.243373\pi$
$198$	−9.96984	−	6.79732i	−0.708526	−	0.483065i
$199$	7.87394	+	7.30595i	0.558169	+	0.517905i	0.908035	−	0.418895i	$-0.137582\pi$
$199$	7.87394	+	7.30595i	0.558169	+	0.517905i	−0.349866	+	0.936800i	$0.613773\pi$
$200$	−1.81149	−	4.61561i	−0.128092	−	0.326373i
$201$	5.23591	−	1.61507i	0.369313	−	0.113918i
$202$	0.655383	+	2.87142i	0.0461126	+	0.202032i
$203$	−11.3210	+	19.5653i	−0.794577	+	1.37322i
$204$	0.223231	−	0.978037i	0.0156293	−	0.0684763i
$205$	−0.359417	−	4.79609i	−0.0251028	−	0.334973i
$206$	−7.23170	−	2.23068i	−0.503856	−	0.155419i
$207$	−2.15896	+	28.8094i	−0.150058	+	2.00239i
$208$	1.42024	−	3.61870i	0.0984756	−	0.250912i
$209$	−6.98186	+	3.36229i	−0.482945	+	0.232574i
$210$	10.6015	−	13.2678i	0.731571	−	0.915566i
$211$	−17.6973	−	8.52256i	−1.21833	−	0.586717i	−0.289485	−	0.957183i	$-0.593484\pi$
$211$	−17.6973	−	8.52256i	−1.21833	−	0.586717i	−0.928846	+	0.370465i	$0.879198\pi$
$212$	−0.181150	+	0.168082i	−0.0124414	+	0.0115439i
$213$	−3.33305	+	0.502377i	−0.228377	+	0.0344223i
$214$	2.81050	−	4.86793i	0.192122	−	0.332765i
$215$	−4.12450	−	7.14384i	−0.281289	−	0.487206i
$216$	−2.17403	−	2.72615i	−0.147924	−	0.185491i
$217$	−25.3024	−	3.83845i	−1.71764	−	0.260571i
$218$	3.73298	−	4.68101i	0.252829	−	0.317038i
$219$	−19.6824	−	2.96664i	−1.33001	−	0.200467i
$220$	0.203615	−	0.138822i	0.0137277	−	0.00935939i
$221$	5.94416	−	4.05266i	0.399847	−	0.272611i
$222$	5.67025	+	0.854653i	0.380562	+	0.0573606i
$223$	−1.45015	+	1.81844i	−0.0971095	+	0.121771i	−0.828012	−	0.560711i	$-0.810528\pi$
$223$	−1.45015	+	1.81844i	−0.0971095	+	0.121771i	0.730902	+	0.682482i	$0.239099\pi$
$224$	−0.409192	−	0.710308i	−0.0273403	−	0.0474595i
$225$	−3.75191	−	4.70474i	−0.250127	−	0.313650i
$226$	−12.0304	−	20.8373i	−0.800251	−	1.38608i
$227$	−9.17542	+	15.8923i	−0.608994	+	1.05481i	0.382412	+	0.923992i	$0.375093\pi$
$227$	−9.17542	+	15.8923i	−0.608994	+	1.05481i	−0.991407	+	0.130817i	$0.958240\pi$
$228$	−0.429553	+	0.0647447i	−0.0284479	+	0.00428782i
$229$	−0.495378	+	0.459644i	−0.0327355	+	0.0303741i	−0.696371	−	0.717682i	$-0.745203\pi$
$229$	−0.495378	+	0.459644i	−0.0327355	+	0.0303741i	0.663635	+	0.748056i	$0.269013\pi$
$230$	18.8743	+	9.08939i	1.24454	+	0.599337i
$231$	−15.0850	−	7.28231i	−0.992520	−	0.479141i
$232$	22.0601	−	10.6236i	1.44832	−	0.697473i
$233$	−5.70807	+	14.5439i	−0.373948	+	0.952803i	0.612756	+	0.790272i	$0.290061\pi$
$233$	−5.70807	+	14.5439i	−0.373948	+	0.952803i	−0.986703	+	0.162531i	$0.948034\pi$
$234$	0.362505	−	4.83729i	0.0236977	−	0.316224i
$235$	−13.5987	−	4.19465i	−0.887084	−	0.273629i
$236$	−0.0422859	−	0.564267i	−0.00275258	−	0.0367306i
$237$	6.46726	−	28.3349i	0.420094	−	1.84055i
$238$	−2.00915	+	26.4710i	−0.130234	+	1.71586i
$239$	1.10253	+	4.83050i	0.0713167	+	0.312459i	0.997987	−	0.0634158i	$-0.0201994\pi$
$239$	1.10253	+	4.83050i	0.0713167	+	0.312459i	−0.926670	+	0.375875i	$0.877342\pi$
$240$	−17.0966	+	5.27361i	−1.10358	+	0.340410i
$241$	2.64117	+	6.72958i	0.170132	+	0.433490i	0.990355	−	0.138554i	$-0.0442456\pi$
$241$	2.64117	+	6.72958i	0.170132	+	0.433490i	−0.820222	+	0.572045i	$0.806150\pi$
$242$	−4.92007	−	4.56516i	−0.316274	−	0.293460i
$243$	18.4459	+	12.5762i	1.18331	+	0.806764i
$244$	−0.321993			−0.0206135
$245$	6.34987	−	10.9499i	0.405678	−	0.699565i
$246$	9.44160			0.601975
$247$	−2.57396	−	1.75490i	−0.163777	−	0.111662i
$248$	20.3207	+	18.8548i	1.29037	+	1.19728i
$249$	−14.7837	−	37.6682i	−0.936876	−	2.38712i
$250$	−16.2194	+	5.00304i	−1.02581	+	0.316420i
$251$	1.57010	+	6.87904i	0.0991036	+	0.434201i	1.00000		0.000166985i	$5.31529e-5\pi$
$251$	1.57010	+	6.87904i	0.0991036	+	0.434201i	−0.900896	+	0.434034i	$0.857090\pi$
$252$	−0.369241	−	0.343262i	−0.0232600	−	0.0216235i
$253$	4.59780	−	20.1443i	0.289061	−	1.26646i
$254$	0.770099	+	10.2763i	0.0483203	+	0.644790i
$255$	−31.6397	−	9.75957i	−1.98136	−	0.611168i
$256$	−0.0981870	+	1.31021i	−0.00613669	+	0.0818884i
$257$	−7.26238	+	18.5042i	−0.453015	+	1.15426i	0.503866	+	0.863782i	$0.331910\pi$
$257$	−7.26238	+	18.5042i	−0.453015	+	1.15426i	−0.956881	+	0.290481i	$0.906185\pi$
$258$	14.5899	−	7.02615i	0.908330	−	0.437429i
$259$	4.27389	+	0.00408254i	0.265567	+	0.000253677i
$260$	0.0892583	+	0.0429846i	0.00553557	+	0.00266579i
$261$	21.7830	−	20.2116i	1.34833	−	1.25107i
$262$	23.3607	−	3.52106i	1.44323	−	0.217532i
$263$	−2.56577	+	4.44405i	−0.158212	+	0.274032i	−0.934224	−	0.356687i	$-0.883906\pi$
$263$	−2.56577	+	4.44405i	−0.158212	+	0.274032i	0.776012	+	0.630718i	$0.217240\pi$
$264$	9.07208	+	15.7133i	0.558348	+	0.967086i
$265$	5.08533	+	6.37680i	0.312389	+	0.391723i
$266$	10.9881	−	3.37788i	0.673721	−	0.207111i
$267$	13.5572	−	17.0002i	0.829686	−	1.04039i
$268$	−0.116629	−	0.0175789i	−0.00712423	−	0.00107380i
$269$	−10.4134	+	7.09971i	−0.634914	+	0.432877i	−0.837538	−	0.546380i	$-0.816006\pi$
$269$	−10.4134	+	7.09971i	−0.634914	+	0.432877i	0.202624	+	0.979257i	$0.435053\pi$
$270$	−2.53535	+	1.72857i	−0.154297	+	0.105198i
$271$	−14.9743	−	2.25701i	−0.909622	−	0.137103i	−0.322469	−	0.946580i	$-0.604513\pi$
$271$	−14.9743	−	2.25701i	−0.909622	−	0.137103i	−0.587152	+	0.809477i	$0.699751\pi$
$272$	17.4372	−	21.8655i	1.05728	−	1.32579i
$273$	−0.496815	−	6.71561i	−0.0300686	−	0.406447i
$274$	−1.24461	−	1.56069i	−0.0751894	−	0.0942845i
$275$	2.15190	+	3.72721i	0.129765	+	0.224759i
$276$	0.579139	−	1.00310i	0.0348601	−	0.0603795i
$277$	−2.58689	+	0.389911i	−0.155431	+	0.0234275i	−0.226297	−	0.974058i	$-0.572662\pi$
$277$	−2.58689	+	0.389911i	−0.155431	+	0.0234275i	0.0708656	+	0.997486i	$0.477424\pi$
$278$	16.1431	−	14.9786i	0.968198	−	0.898356i
$279$	30.3108	+	14.5969i	1.81466	+	0.873895i
$280$	−12.3587	+	5.93708i	−0.738571	+	0.354808i
$281$	13.0075	−	6.26408i	0.775962	−	0.373684i	−0.00361211	−	0.999993i	$-0.501150\pi$
$281$	13.0075	−	6.26408i	0.775962	−	0.373684i	0.779574	+	0.626310i	$0.215435\pi$
$282$	10.2065	−	26.0057i	0.607787	−	1.54862i
$283$	1.50852	−	20.1298i	0.0896720	−	1.19659i	−0.752948	−	0.658080i	$-0.771369\pi$
$283$	1.50852	−	20.1298i	0.0896720	−	1.19659i	0.842620	−	0.538509i	$-0.181012\pi$
$284$	0.0693327	+	0.0213863i	0.00411414	+	0.00126904i
$285$	1.07146	+	14.2977i	0.0634679	+	0.846921i
$286$	−0.772003	+	3.38237i	−0.0456495	+	0.200003i
$287$	6.95943	−	1.04217i	0.410802	−	0.0615172i
$288$	0.239791	+	1.05059i	0.0141298	+	0.0619069i
$289$	33.2128	−	10.2448i	1.95370	−	0.602636i
$290$	−7.87213	−	20.0579i	−0.462267	−	1.17784i
$291$	−27.4877	−	25.5049i	−1.61136	−	1.49512i
$292$	0.354010	+	0.241360i	0.0207169	+	0.0141245i
$293$	29.7001			1.73510			0.867550	−	0.497350i	$-0.165693\pi$
$293$	29.7001			1.73510			0.867550	+	0.497350i	$0.165693\pi$
$294$	20.5042	+	14.0370i	1.19583	+	0.818652i
$295$	−18.6761			−1.08737
$296$	−3.82500	−	2.60784i	−0.222323	−	0.151577i
$297$	2.21863	+	2.05859i	0.128738	+	0.119452i
$298$	−2.87466	−	7.32452i	−0.166525	−	0.424298i
$299$	7.93741	−	2.44837i	0.459032	−	0.141593i
$300$	0.0536855	+	0.235212i	0.00309954	+	0.0135800i
$301$	9.97874	−	6.78944i	0.575165	−	0.391337i
$302$	7.13330	−	31.2530i	0.410475	−	1.79841i
$303$	−0.401659	−	5.35977i	−0.0230747	−	0.307911i
$304$	−11.5724	−	3.56961i	−0.663721	−	0.204731i
$305$	−0.794197	+	10.5978i	−0.0454756	+	0.606830i
$306$	12.7497	−	32.4858i	0.728854	−	1.85709i
$307$	−2.12162	+	1.02172i	−0.121087	+	0.0583126i	−0.493447	−	0.869776i	$-0.664263\pi$
$307$	−2.12162	+	1.02172i	−0.121087	+	0.0583126i	0.372359	+	0.928089i	$0.378549\pi$
$308$	0.224542	+	0.282120i	0.0127945	+	0.0160753i
$309$	12.4430	+	5.99222i	0.707856	+	0.340886i
$310$	17.8828	−	16.5928i	1.01567	−	0.942406i
$311$	10.1963	−	1.53685i	0.578180	−	0.0871466i	0.146560	−	0.989202i	$-0.453180\pi$
$311$	10.1963	−	1.53685i	0.578180	−	0.0871466i	0.431621	+	0.902055i	$0.357942\pi$
$312$	−3.64705	+	6.31688i	−0.206474	+	0.357623i
$313$	−4.06330	−	7.03784i	−0.229671	−	0.397802i	0.728039	−	0.685535i	$-0.240432\pi$
$313$	−4.06330	−	7.03784i	−0.229671	−	0.397802i	−0.957711	+	0.287733i	$0.907098\pi$
$314$	8.33205	+	10.4481i	0.470205	+	0.589618i
$315$	−12.2086	+	11.3062i	−0.687876	+	0.637034i
$316$	−0.390062	+	0.489122i	−0.0219427	+	0.0275153i
$317$	17.2251	+	2.59627i	0.967458	+	0.145821i	0.613720	−	0.789524i	$-0.289672\pi$
$317$	17.2251	+	2.59627i	0.967458	+	0.145821i	0.353738	+	0.935345i	$0.384910\pi$
$318$	−13.2293	+	9.01960i	−0.741864	+	0.505794i
$319$	−17.5597	+	11.9720i	−0.983155	+	0.670304i
$320$	14.6747	+	2.21185i	0.820338	+	0.123646i
$321$	−6.39560	+	8.01983i	−0.356968	+	0.447623i
$322$	−11.2254	+	28.5217i	−0.625567	+	1.58945i
$323$	−13.9737	−	17.5224i	−0.777516	−	0.974974i
$324$	−0.200995	−	0.348134i	−0.0111664	−	0.0193408i
$325$	−0.865084	+	1.49837i	−0.0479862	+	0.0831146i
$326$	−15.1036	+	2.27650i	−0.836511	+	0.126084i
$327$	−8.00938	+	7.43162i	−0.442920	+	0.410970i
$328$	−6.86753	−	3.30723i	−0.379196	−	0.182611i
$329$	4.65270	−	20.2954i	0.256512	−	1.11892i
$330$	14.3861	−	6.92797i	0.791927	−	0.381372i
$331$	0.884242	−	2.25301i	0.0486023	−	0.123837i	−0.904511	−	0.426450i	$-0.859764\pi$
$331$	0.884242	−	2.25301i	0.0486023	−	0.123837i	0.953113	+	0.302614i	$0.0978592\pi$
$332$	−0.0650929	+	0.868604i	−0.00357244	+	0.0476709i
$333$	−5.36875	−	1.65604i	−0.294206	−	0.0907505i
$334$	0.598813	+	7.99061i	0.0327656	+	0.437227i
$335$	−0.866245	+	3.79527i	−0.0473280	+	0.207358i
$336$	−9.54054	−	24.3773i	−0.520479	−	1.32989i
$337$	0.264506	+	1.15888i	0.0144086	+	0.0631281i	0.981621	−	0.190840i	$-0.0611212\pi$
$337$	0.264506	+	1.15888i	0.0144086	+	0.0631281i	−0.967213	+	0.253968i	$0.918264\pi$
$338$	−1.33275	+	0.411098i	−0.0724918	+	0.0223608i
$339$	16.0416	+	40.8733i	0.871259	+	2.21993i
$340$	0.522466	+	0.484778i	0.0283347	+	0.0262908i
$341$	−19.8803	−	13.5542i	−1.07658	−	0.734000i
$342$	−15.1118			−0.817150
$343$	16.6631	+	8.08342i	0.899722	+	0.436464i
$344$	−13.0734			−0.704871
$345$	−31.5868	−	21.5355i	−1.70057	−	1.15943i
$346$	6.06697	+	5.62932i	0.326162	+	0.302634i
$347$	−4.58075	−	11.6716i	−0.245908	−	0.626562i	0.753620	−	0.657311i	$-0.228306\pi$
$347$	−4.58075	−	11.6716i	−0.245908	−	0.626562i	−0.999527	+	0.0307485i	$0.990211\pi$
$348$	−1.13844	+	0.351162i	−0.0610267	+	0.0188242i
$349$	−4.82660	−	21.1467i	−0.258362	−	1.13196i	−0.923002	−	0.384794i	$-0.874272\pi$
$349$	−4.82660	−	21.1467i	−0.258362	−	1.13196i	0.664640	−	0.747163i	$-0.268585\pi$
$350$	−2.32681	−	5.94531i	−0.124373	−	0.317790i
$351$	−0.270743	+	1.18620i	−0.0144512	+	0.0633148i
$352$	−0.0575954	−	0.768557i	−0.00306985	−	0.0409642i
$353$	−11.1383	−	3.43572i	−0.592834	−	0.182865i	−0.0162017	−	0.999869i	$-0.505157\pi$
$353$	−11.1383	−	3.43572i	−0.592834	−	0.182865i	−0.576633	+	0.817004i	$0.695634\pi$
$354$	2.73984	−	36.5606i	0.145621	−	1.94317i
$355$	0.874902	−	2.22921i	0.0464350	−	0.118314i
$356$	−0.421701	+	0.203080i	−0.0223501	+	0.0107632i
$357$	10.8253	−	47.2208i	0.572936	−	2.49919i
$358$	−27.5733	−	13.2786i	−1.45729	−	0.701796i
$359$	−3.70582	+	3.43850i	−0.195586	+	0.181477i	−0.771886	−	0.635761i	$-0.780686\pi$
$359$	−3.70582	+	3.43850i	−0.195586	+	0.181477i	0.576300	+	0.817238i	$0.304496\pi$
$360$	17.8225	−	2.68632i	0.939331	−	0.141581i
$361$	4.64752	−	8.04974i	0.244606	−	0.423671i
$362$	6.72841	+	11.6539i	0.353637	+	0.612518i
$363$	7.63668	+	9.57609i	0.400822	+	0.502614i
$364$	−0.0530859	+	0.134882i	−0.00278246	+	0.00706972i
$365$	8.81710	−	11.0563i	0.461508	−	0.578713i
$366$	−20.6299	−	3.10946i	−1.07834	−	0.162534i
$367$	14.9762	−	10.2106i	0.781750	−	0.532988i	−0.105422	−	0.994428i	$-0.533619\pi$
$367$	14.9762	−	10.2106i	0.781750	−	0.532988i	0.887172	+	0.461439i	$0.152667\pi$
$368$	26.6798	−	18.1900i	1.39078	−	0.948218i
$369$	−9.14739	−	1.37875i	−0.476194	−	0.0717747i
$370$	−2.54010	+	3.18518i	−0.132053	+	0.165590i
$371$	−8.75578	+	8.10863i	−0.454578	+	0.420979i
$372$	−0.840971	−	1.05454i	−0.0436023	−	0.0546756i
$373$	−7.96440	−	13.7947i	−0.412381	−	0.714265i	0.582769	−	0.812638i	$-0.301969\pi$
$373$	−7.96440	−	13.7947i	−0.412381	−	0.714265i	−0.995150	+	0.0983733i	$0.968636\pi$
$374$	−12.4797	+	21.6154i	−0.645308	+	1.11771i
$375$	30.6290	−	4.61658i	1.58167	−	0.238399i
$376$	−16.5332	+	15.3406i	−0.852635	+	0.791130i
$377$	−7.69763	−	3.70698i	−0.396448	−	0.190919i
$378$	−2.79594	−	3.51288i	−0.143808	−	0.180683i
$379$	−18.2585	+	8.79284i	−0.937878	+	0.451658i	−0.839420	−	0.543483i	$-0.817105\pi$
$379$	−18.2585	+	8.79284i	−0.937878	+	0.451658i	−0.0984576	+	0.995141i	$0.531391\pi$
$380$	0.112755	−	0.287294i	0.00578419	−	0.0147379i
$381$	1.40535	−	18.7531i	0.0719983	−	0.960751i
$382$	28.9521	+	8.93053i	1.48132	+	0.456926i
$383$	1.22893	+	16.3989i	0.0627954	+	0.837946i	0.936316	+	0.351159i	$0.114212\pi$
$383$	1.22893	+	16.3989i	0.0627954	+	0.837946i	−0.873521	+	0.486787i	$0.838169\pi$
$384$	−6.13180	+	26.8652i	−0.312912	+	1.37096i
$385$	9.83930	−	6.69456i	0.501457	−	0.341187i
$386$	−0.540630	−	2.36865i	−0.0275173	−	0.120561i
$387$	−15.1613	+	4.67665i	−0.770693	+	0.237727i
$388$	0.294888	+	0.751363i	0.0149707	+	0.0381447i
$389$	−4.73573	−	4.39412i	−0.240111	−	0.222791i	0.550933	−	0.834549i	$-0.314272\pi$
$389$	−4.73573	−	4.39412i	−0.240111	−	0.222791i	−0.791044	+	0.611759i	$0.790462\pi$
$390$	5.30364	+	3.61596i	0.268560	+	0.183101i
$391$	59.7585			3.02212
$392$	−9.99719	−	17.3923i	−0.504935	−	0.878444i
$393$	−43.1124			−2.17474
$394$	−23.3450	−	15.9163i	−1.17610	−	0.801853i
$395$	15.1365	+	14.0446i	0.761600	+	0.706661i
$396$	−0.173170	−	0.441231i	−0.00870214	−	0.0221727i
$397$	9.21167	−	2.84142i	0.462321	−	0.142607i	−0.0548405	−	0.998495i	$-0.517465\pi$
$397$	9.21167	−	2.84142i	0.462321	−	0.142607i	0.517161	+	0.855888i	$0.326989\pi$
$398$	−3.33359	−	14.6054i	−0.167098	−	0.732102i
$399$	−20.7468	+	3.10682i	−1.03864	+	0.155535i
$400$	−1.49665	+	6.55727i	−0.0748327	+	0.327863i
$401$	2.46428	+	32.8835i	0.123060	+	1.64212i	0.627457	+	0.778651i	$0.284096\pi$
$401$	2.46428	+	32.8835i	0.123060	+	1.64212i	−0.504397	+	0.863472i	$0.668285\pi$
$402$	−7.30258	−	2.25255i	−0.364219	−	0.112347i
$403$	0.722851	−	9.64578i	0.0360078	−	0.480491i
$404$	−0.0422684	+	0.107698i	−0.00210293	+	0.00535818i
$405$	−11.9540	+	5.75673i	−0.593997	+	0.286054i
$406$	28.4177	−	13.6518i	1.41035	−	0.677529i
$407$	3.62034	+	1.74346i	0.179454	+	0.0864203i
$408$	−38.4673	+	35.6924i	−1.90441	+	1.76704i
$409$	22.7801	−	3.43355i	1.12640	−	0.169778i	0.440697	−	0.897656i	$-0.354731\pi$
$409$	22.7801	−	3.43355i	1.12640	−	0.169778i	0.685707	+	0.727878i	$0.259493\pi$
$410$	−3.35395	+	5.80921i	−0.165640	+	0.286897i
$411$	1.82142	+	3.15480i	0.0898442	+	0.155615i
$412$	−0.185353	−	0.232425i	−0.00913166	−	0.0114507i
$413$	−2.01603	−	27.2513i	−0.0992024	−	1.34095i
$414$	25.1225	−	31.5026i	1.23470	−	1.54827i
$415$	28.4280	+	4.28483i	1.39548	+	0.210334i
$416$	0.255996	−	0.174535i	0.0125512	−	0.00855730i
$417$	−33.2044	+	22.6384i	−1.62603	+	1.10861i
$418$	10.6873	+	1.61085i	0.522731	+	0.0787891i
$419$	−3.16588	+	3.96988i	−0.154663	+	0.193942i	−0.853126	−	0.521705i	$-0.825296\pi$
$419$	−3.16588	+	3.96988i	−0.154663	+	0.193942i	0.698463	+	0.715646i	$0.253868\pi$
$420$	0.637678	−	0.196031i	0.0311155	−	0.00956532i
$421$	−1.01397	−	1.27148i	−0.0494178	−	0.0619679i	0.756508	−	0.653984i	$-0.226904\pi$
$421$	−1.01397	−	1.27148i	−0.0494178	−	0.0619679i	−0.805926	+	0.592016i	$0.798332\pi$
$422$	13.6978	+	23.7253i	0.666798	+	1.15493i
$423$	−13.6860	+	23.7049i	−0.665436	+	1.15257i
$424$	12.7820	−	1.92658i	0.620749	−	0.0935629i
$425$	−9.12447	+	8.46627i	−0.442602	+	0.410674i
$426$	4.23559	+	2.03975i	0.205215	+	0.0988262i
$427$	−15.5496	−	0.0148534i	−0.752497	−	0.000718806i
$428$	0.198937	−	0.0958031i	0.00961600	−	0.00463082i
$429$	2.31305	−	5.89355i	0.111675	−	0.284543i
$430$	−0.859766	+	11.4728i	−0.0414616	+	0.553267i
$431$	−18.5234	−	5.71371i	−0.892241	−	0.275220i	−0.185459	−	0.982652i	$-0.559377\pi$
$431$	−18.5234	−	5.71371i	−0.892241	−	0.275220i	−0.706781	+	0.707432i	$0.749853\pi$
$432$	0.353463	+	4.71664i	0.0170060	+	0.226929i
$433$	4.88556	−	21.4050i	0.234785	−	1.02866i	−0.710828	−	0.703366i	$-0.751680\pi$
$433$	4.88556	−	21.4050i	0.234785	−	1.02866i	0.945613	−	0.325294i	$-0.105463\pi$
$434$	26.1418	+	24.3026i	1.25485	+	1.16656i
$435$	8.74989	+	38.3358i	0.419525	+	1.83806i
$436$	0.224741	−	0.0693235i	0.0107631	−	0.00331999i
$437$	−9.45388	−	24.0881i	−0.452241	−	1.15229i
$438$	20.3505	+	18.8825i	0.972382	+	0.902239i
$439$	22.8171	+	15.5564i	1.08900	+	0.742469i	0.968192	−	0.250207i	$-0.0804987\pi$
$439$	22.8171	+	15.5564i	1.08900	+	0.742469i	0.120809	+	0.992676i	$0.461451\pi$
$440$	−12.8907			−0.614541
$441$	−17.8154	−	16.5937i	−0.848353	−	0.790178i
$442$	−10.0339			−0.477262
$443$	27.6198	+	18.8309i	1.31226	+	0.894683i	0.998496	−	0.0548188i	$-0.0174581\pi$
$443$	27.6198	+	18.8309i	1.31226	+	0.894683i	0.313762	+	0.949502i	$0.398411\pi$
$444$	0.165123	+	0.153212i	0.00783640	+	0.00727111i
$445$	5.64390	+	14.3804i	0.267547	+	0.681698i
$446$	3.09979	−	0.956159i	0.146779	−	0.0452754i
$447$	3.19520	+	13.9991i	0.151128	+	0.662133i
$448$	−1.64334	+	21.6513i	−0.0776407	+	1.02293i
$449$	−8.37286	+	36.6839i	−0.395140	+	1.73122i	0.250986	+	0.967991i	$0.419245\pi$
$449$	−8.37286	+	36.6839i	−0.395140	+	1.73122i	−0.646126	+	0.763230i	$0.723612\pi$
$450$	0.627194	+	8.36933i	0.0295662	+	0.394534i
$451$	6.32221	+	1.95014i	0.297701	+	0.0918286i
$452$	0.0706316	−	0.942513i	0.00332223	−	0.0443321i
$453$	−21.3725	+	54.4564i	−1.00417	+	2.55858i
$454$	23.0595	−	11.1049i	1.08224	−	0.521177i
$455$	4.30845	+	2.07991i	0.201983	+	0.0975079i
$456$	20.4729	+	9.85922i	0.958730	+	0.461700i
$457$	9.96315	−	9.24445i	0.466057	−	0.432437i	−0.411863	−	0.911246i	$-0.635122\pi$
$457$	9.96315	−	9.24445i	0.466057	−	0.432437i	0.877919	+	0.478809i	$0.158931\pi$
$458$	0.931983	−	0.140474i	0.0435487	−	0.00656391i
$459$	−4.37664	+	7.58057i	−0.204284	+	0.353831i
$460$	0.411457	+	0.712664i	0.0191843	+	0.0332281i
$461$	−10.0273	−	12.5738i	−0.467017	−	0.585621i	0.491421	−	0.870922i	$-0.336478\pi$
$461$	−10.0273	−	12.5738i	−0.467017	−	0.585621i	−0.958438	+	0.285302i	$0.907906\pi$
$462$	11.6619	+	20.2436i	0.542561	+	0.941820i
$463$	10.4346	−	13.0846i	0.484937	−	0.608092i	−0.477820	−	0.878458i	$-0.658573\pi$
$463$	10.4346	−	13.0846i	0.484937	−	0.608092i	0.962758	+	0.270365i	$0.0871445\pi$
$464$	−32.8421	−	4.95016i	−1.52466	−	0.229805i
$465$	−36.7827	+	25.0780i	−1.70576	+	1.16297i
$466$	18.0044	−	12.2752i	0.834040	−	0.568639i
$467$	−14.1316	−	2.12999i	−0.653931	−	0.0985643i	−0.186307	−	0.982492i	$-0.559652\pi$
$467$	−14.1316	−	2.12999i	−0.653931	−	0.0985643i	−0.467624	+	0.883927i	$0.654890\pi$
$468$	0.118807	−	0.148979i	0.00549183	−	0.00688654i
$469$	−5.63139	−	0.854297i	−0.260033	−	0.0394478i
$470$	12.3751	+	15.5178i	0.570819	+	0.715785i
$471$	−12.1936	−	21.1199i	−0.561850	−	0.973153i
$472$	−14.7994	+	25.6333i	−0.681198	+	1.17987i
$473$	11.2208	−	1.69127i	0.515934	−	0.0777646i
$474$	−29.7145	+	27.5710i	−1.36483	+	1.26638i
$475$	4.85618	+	2.33861i	0.222817	+	0.107303i
$476$	−0.650967	+	0.814689i	−0.0298370	+	0.0373412i
$477$	14.1342	−	6.80667i	0.647160	−	0.311656i
$478$	2.52465	−	6.43271i	0.115475	−	0.294225i
$479$	−0.875738	+	11.6859i	−0.0400135	+	0.533943i	0.940796	+	0.338974i	$0.110080\pi$
$479$	−0.875738	+	11.6859i	−0.0400135	+	0.533943i	−0.980809	+	0.194969i	$0.937539\pi$
$480$	−1.36262	−	0.420314i	−0.0621950	−	0.0191846i
$481$	0.120718	+	1.61086i	0.00550425	+	0.0734491i
$482$	2.24363	−	9.82999i	0.102195	−	0.447744i
$483$	28.0139	−	48.4146i	1.27468	−	2.20294i
$484$	−0.0586679	−	0.257041i	−0.00266672	−	0.0116837i
$485$	25.4571	−	7.85248i	1.15595	−	0.356563i
$486$	−11.3757	−	28.9847i	−0.516010	−	1.31477i
$487$	5.97717	+	5.54600i	0.270851	+	0.251313i	0.803891	−	0.594777i	$-0.202760\pi$
$487$	5.97717	+	5.54600i	0.270851	+	0.251313i	−0.533039	+	0.846091i	$0.678950\pi$
$488$	13.9164	+	9.48802i	0.629964	+	0.429502i
$489$	27.8738			1.26050
$490$	−15.9204	+	7.62940i	−0.719208	+	0.344661i
$491$	−3.30470			−0.149139			−0.0745695	−	0.997216i	$-0.523758\pi$
$491$	−3.30470			−0.149139			−0.0745695	+	0.997216i	$0.523758\pi$
$492$	0.306439	+	0.208927i	0.0138153	+	0.00941914i
$493$	−45.0575	−	41.8072i	−2.02929	−	1.88290i
$494$	1.58737	+	4.04456i	0.0714193	+	0.181973i
$495$	−14.9495	+	4.61130i	−0.671928	+	0.207262i
$496$	−8.36732	−	36.6596i	−0.375704	−	1.64607i
$497$	3.34721	+	1.03598i	0.150143	+	0.0464700i
$498$	−12.5585	+	55.0224i	−0.562760	+	2.46561i
$499$	1.04997	+	14.0108i	0.0470029	+	0.627211i	0.970110	+	0.242667i	$0.0780222\pi$
$499$	1.04997	+	14.0108i	0.0470029	+	0.627211i	−0.923107	+	0.384544i	$0.874359\pi$
$500$	−0.637131	−	0.196529i	−0.0284934	−	0.00878904i
$501$	1.09277	−	14.5820i	0.0488215	−	0.651477i
$502$	3.59532	−	9.16072i	0.160467	−	0.408863i
$503$	−14.7915	+	7.12322i	−0.659521	+	0.317609i	−0.733538	−	0.679648i	$-0.762132\pi$
$503$	−14.7915	+	7.12322i	−0.659521	+	0.317609i	0.0740169	+	0.997257i	$0.476418\pi$
$504$	5.84364	+	25.7159i	0.260296	+	1.14548i
$505$	3.44043	+	1.65682i	0.153097	+	0.0737277i
$506$	−21.1251	+	19.6012i	−0.939123	+	0.871379i
$507$	2.51677	−	0.379342i	0.111774	−	0.0168472i
$508$	−0.202402	+	0.350570i	−0.00898012	+	0.0155540i
$509$	0.987166	+	1.70982i	0.0437553	+	0.0757865i	0.887074	−	0.461628i	$-0.152734\pi$
$509$	0.987166	+	1.70982i	0.0437553	+	0.0757865i	−0.843318	+	0.537414i	$0.819401\pi$
$510$	28.7927	+	36.1049i	1.27496	+	1.59875i
$511$	17.0846	+	11.6720i	0.755779	+	0.516340i
$512$	14.6432	−	18.3620i	0.647144	−	0.811492i
$513$	3.74805	+	0.564927i	0.165480	+	0.0249422i
$514$	22.9071	−	15.6178i	1.01039	−	0.688871i
$515$	−8.10702	+	5.52727i	−0.357238	+	0.243561i
$516$	0.629012	+	0.0948083i	0.0276907	+	0.00417370i
$517$	12.2058	−	15.3056i	0.536810	−	0.673138i
$518$	−4.92187	−	3.36256i	−0.216254	−	0.147743i
$519$	−9.41683	−	11.8083i	−0.413353	−	0.518328i
$520$	−2.59109	−	4.48791i	−0.113627	−	0.196808i
$521$	−20.4418	+	35.4063i	−0.895573	+	1.55118i	−0.0624781	+	0.998046i	$0.519900\pi$
$521$	−20.4418	+	35.4063i	−0.895573	+	1.55118i	−0.833094	+	0.553131i	$0.813433\pi$
$522$	−40.9815	+	6.17696i	−1.79371	+	0.270358i
$523$	5.39988	−	5.01035i	0.236120	−	0.219087i	−0.553234	−	0.833026i	$-0.686606\pi$
$523$	5.39988	−	5.01035i	0.236120	−	0.219087i	0.789354	+	0.613939i	$0.210416\pi$
$524$	0.836117	+	0.402653i	0.0365259	+	0.0175900i
$525$	2.58172	+	11.3613i	0.112675	+	0.495846i
$526$	6.44824	−	3.10531i	0.281157	−	0.135398i
$527$	25.4236	−	64.7782i	1.10747	−	2.82178i
$528$	1.83926	−	24.5433i	0.0800436	−	1.06811i
$529$	43.9535	+	13.5578i	1.91102	+	0.589471i
$530$	−0.850097	−	11.3438i	−0.0369259	−	0.492741i
$531$	−7.99336	+	35.0212i	−0.346882	+	1.51979i
$532$	0.431378	+	0.133514i	0.0187026	+	0.00578856i
$533$	0.591849	+	2.59306i	0.0256358	+	0.112318i
$534$	−28.9793	+	8.93892i	−1.25406	+	0.386825i
$535$	−2.66251	−	6.78396i	−0.115110	−	0.293296i
$536$	4.52264	+	4.19640i	0.195348	+	0.181257i
$537$	46.1448	+	31.4610i	1.99130	+	1.35764i
$538$	17.5780			0.757841
$539$	10.8305	+	13.6344i	0.466504	+	0.587275i
$540$	−0.120538			−0.00518715
$541$	4.30769	+	2.93693i	0.185202	+	0.126269i	0.652372	−	0.757899i	$-0.273774\pi$
$541$	4.30769	+	2.93693i	0.185202	+	0.126269i	−0.467170	+	0.884168i	$0.654726\pi$
$542$	15.4825	+	14.3657i	0.665031	+	0.617059i
$543$	−8.97179	−	22.8597i	−0.385016	−	0.981006i
$544$	2.12998	−	0.657013i	0.0913223	−	0.0281692i
$545$	−1.72733	−	7.56794i	−0.0739908	−	0.324175i
$546$	−4.70373	+	8.12915i	−0.201301	+	0.347896i
$547$	−4.81392	+	21.0912i	−0.205828	+	0.901792i	0.761480	+	0.648189i	$0.224473\pi$
$547$	−4.81392	+	21.0912i	−0.205828	+	0.901792i	−0.967308	+	0.253604i	$0.918384\pi$
$548$	−0.00585991	−	0.0781950i	−0.000250323	−	0.00334033i
$549$	19.5330	+	6.02513i	0.833647	+	0.257146i
$550$	0.448572	−	5.98577i	0.0191272	−	0.255234i
$551$	−9.72395	+	24.7762i	−0.414254	+	1.05550i
$552$	−54.5880	+	26.2882i	−2.32342	+	1.11890i
$553$	−18.8593	+	23.6025i	−0.801980	+	1.00368i
$554$	3.28738	+	1.58312i	0.139667	+	0.0672602i
$555$	5.44997	−	5.05683i	0.231338	−	0.214651i
$556$	0.855394	−	0.128930i	0.0362768	−	0.00546785i
$557$	17.0484	−	29.5288i	0.722366	−	1.25117i	−0.237683	−	0.971343i	$-0.576388\pi$
$557$	17.0484	−	29.5288i	0.722366	−	1.25117i	0.960049	−	0.279832i	$-0.0902786\pi$
$558$	−23.4607	−	40.6352i	−0.993172	−	1.72022i
$559$	2.84425	+	3.56658i	0.120299	+	0.150850i
$560$	18.3879	+	2.78950i	0.777032	+	0.117878i
$561$	28.3988	−	35.6110i	1.19900	−	1.50350i
$562$	−19.9108	−	3.00108i	−0.839888	−	0.126593i
$563$	19.6134	−	13.3722i	0.826606	−	0.563570i	−0.0744744	−	0.997223i	$-0.523728\pi$
$563$	19.6134	−	13.3722i	0.826606	−	0.563570i	0.901080	+	0.433653i	$0.142776\pi$
$564$	0.906725	−	0.618195i	0.0381800	−	0.0260307i
$565$	−30.8469	−	4.64942i	−1.29774	−	0.195603i
$566$	−17.5537	+	22.0116i	−0.737835	+	0.925216i
$567$	−9.69035	−	16.8213i	−0.406956	−	0.706426i
$568$	−2.36634	−	2.96730i	−0.0992896	−	0.124505i
$569$	1.11216	+	1.92632i	0.0466242	+	0.0807555i	0.888396	−	0.459078i	$-0.151820\pi$
$569$	1.11216	+	1.92632i	0.0466242	+	0.0807555i	−0.841771	+	0.539834i	$0.818487\pi$
$570$	9.99850	−	17.3179i	0.418791	−	0.725368i
$571$	−7.15127	+	1.07788i	−0.299271	+	0.0451079i	−0.296962	−	0.954889i	$-0.595973\pi$
$571$	−7.15127	+	1.07788i	−0.299271	+	0.0451079i	−0.00230973	+	0.999997i	$0.500735\pi$
$572$	−0.0999023	+	0.0926958i	−0.00417713	+	0.00387581i
$573$	−49.8154	−	23.9898i	−2.08107	−	1.00219i
$574$	−8.83859	−	4.26684i	−0.368915	−	0.178095i
$575$	−12.9483	+	6.23558i	−0.539982	+	0.260042i
$576$	10.4284	−	26.5710i	0.434515	−	1.10713i
$577$	−3.38046	+	45.1091i	−0.140730	+	1.87792i	0.265452	+	0.964124i	$0.414479\pi$
$577$	−3.38046	+	45.1091i	−0.140730	+	1.87792i	−0.406182	+	0.913792i	$0.633140\pi$
$578$	−46.3223	−	14.2885i	−1.92675	−	0.594324i
$579$	0.331331	+	4.42131i	0.0137697	+	0.183743i
$580$	0.188346	−	0.825199i	0.00782066	−	0.0342645i
$581$	−3.18351	+	41.9434i	−0.132074	+	1.74010i
$582$	11.6375	+	50.9871i	0.482389	+	2.11348i
$583$	−10.7215	+	3.30714i	−0.444038	+	0.136968i
$584$	−8.18809	−	20.8629i	−0.338826	−	0.863314i
$585$	−4.61033	−	4.27776i	−0.190614	−	0.176864i
$586$	−34.2253	−	23.3344i	−1.41384	−	0.963936i
$587$	−42.6622			−1.76086			−0.880429	−	0.474178i	$-0.842745\pi$
$587$	−42.6622			−1.76086			−0.880429	+	0.474178i	$0.842745\pi$
$588$	0.354874	+	0.909309i	0.0146348	+	0.0374993i
$589$	−30.1335			−1.24163
$590$	21.5217	+	14.6732i	0.886033	+	0.604087i
$591$	37.7973	+	35.0708i	1.55477	+	1.44262i
$592$	2.29422	+	5.84558i	0.0942919	+	0.240252i
$593$	−33.0110	+	10.1825i	−1.35560	+	0.418147i	−0.885571	−	0.464504i	$-0.846233\pi$
$593$	−33.0110	+	10.1825i	−1.35560	+	0.418147i	−0.470028	+	0.882651i	$0.655756\pi$
$594$	−0.939302	−	4.11535i	−0.0385400	−	0.168855i
$595$	25.2084	+	23.4349i	1.03344	+	0.960735i
$596$	0.0687784	−	0.301338i	0.00281727	−	0.0123433i
$597$	2.04303	+	27.2623i	0.0836156	+	1.11577i
$598$	−11.0704	−	3.41476i	−0.452701	−	0.139640i
$599$	1.37181	−	18.3055i	0.0560506	−	0.747943i	−0.896399	−	0.443248i	$-0.853826\pi$
$599$	1.37181	−	18.3055i	0.0560506	−	0.747943i	0.952450	−	0.304696i	$-0.0985547\pi$
$600$	4.61062	−	11.7477i	0.188228	−	0.479596i
$601$	37.6422	−	18.1275i	1.53546	−	0.739437i	0.540653	−	0.841245i	$-0.318177\pi$
$601$	37.6422	−	18.1275i	1.53546	−	0.739437i	0.994804	+	0.101808i	$0.0324628\pi$
$602$	−16.8334	−	0.0160797i	−0.686077	−	0.000655359i
$603$	6.74608	+	3.24874i	0.274722	+	0.132299i
$604$	0.923096	−	0.856508i	0.0375603	−	0.0348508i
$605$	−8.60474	+	1.29696i	−0.349833	+	0.0527288i
$606$	−3.74814	+	6.49197i	−0.152258	+	0.263718i
$607$	−2.48131	−	4.29775i	−0.100713	−	0.174440i	0.811266	−	0.584678i	$-0.198779\pi$
$607$	−2.48131	−	4.29775i	−0.100713	−	0.174440i	−0.911979	+	0.410238i	$0.865446\pi$
$608$	−0.601803	−	0.754637i	−0.0244063	−	0.0306046i
$609$	−54.9933	+	16.9057i	−2.22844	+	0.685052i
$610$	9.24157	−	11.5886i	0.374180	−	0.469207i
$611$	7.78205	+	1.17296i	0.314828	+	0.0474527i
$612$	1.13266	−	0.772237i	0.0457852	−	0.0312158i
$613$	8.59763	−	5.86176i	0.347255	−	0.236754i	−0.377114	−	0.926167i	$-0.623084\pi$
$613$	8.59763	−	5.86176i	0.347255	−	0.236754i	0.724369	+	0.689412i	$0.242131\pi$
$614$	3.24761	+	0.489499i	0.131063	+	0.0197546i
$615$	7.63228	−	9.57058i	0.307763	−	0.385923i
$616$	−1.39151	−	18.8096i	−0.0560657	−	0.757859i
$617$	−1.73528	−	2.17598i	−0.0698599	−	0.0876016i	0.745674	−	0.666311i	$-0.232128\pi$
$617$	−1.73528	−	2.17598i	−0.0698599	−	0.0876016i	−0.815534	+	0.578710i	$0.803556\pi$
$618$	−9.63093	−	16.6813i	−0.387413	−	0.671019i
$619$	1.46999	−	2.54610i	0.0590840	−	0.102336i	−0.834970	−	0.550295i	$-0.814515\pi$
$619$	1.46999	−	2.54610i	0.0590840	−	0.102336i	0.894054	+	0.447958i	$0.147849\pi$
$620$	0.947577	−	0.142824i	0.0380556	−	0.00573596i
$621$	−7.40860	+	6.87418i	−0.297297	+	0.275851i
$622$	−12.9573	−	6.23991i	−0.519541	−	0.250198i
$623$	−20.3740	+	9.78765i	−0.816268	+	0.392134i
$624$	8.91443	−	4.29296i	0.356863	−	0.171856i
$625$	−4.87938	+	12.4325i	−0.195175	+	0.497298i
$626$	−0.847009	+	11.3025i	−0.0338533	+	0.451741i
$627$	−18.8472	−	5.81359i	−0.752685	−	0.232172i
$628$	0.0392293	+	0.523479i	0.00156542	+	0.0208891i
$629$	−2.58601	+	11.3301i	−0.103111	+	0.451759i
$630$	22.9517	−	3.43699i	0.914416	−	0.136933i
$631$	5.48888	+	24.0484i	0.218509	+	0.957350i	0.958580	+	0.284822i	$0.0919344\pi$
$631$	5.48888	+	24.0484i	0.218509	+	0.957350i	−0.740072	+	0.672528i	$0.765208\pi$
$632$	31.2710	−	9.64583i	1.24389	−	0.383691i
$633$	−18.2649	−	46.5382i	−0.725964	−	1.84973i
$634$	−17.8098	−	16.5250i	−0.707316	−	0.656293i
$635$	11.0392	+	7.52637i	0.438076	+	0.298675i
$636$	−0.628963			−0.0249400
$637$	−2.56983	+	6.51122i	−0.101820	+	0.257984i
$638$	29.6412			1.17351
$639$	−3.80573	−	2.59471i	−0.150553	−	0.102645i
$640$	−14.3513	−	13.3161i	−0.567287	−	0.526365i
$641$	−1.18335	−	3.01513i	−0.0467395	−	0.119090i	0.905598	−	0.424138i	$-0.139423\pi$
$641$	−1.18335	−	3.01513i	−0.0467395	−	0.119090i	−0.952337	+	0.305048i	$0.901328\pi$
$642$	13.6710	−	4.21694i	0.539550	−	0.166429i
$643$	−2.91073	−	12.7528i	−0.114788	−	0.502920i	−0.999335	−	0.0364681i	$-0.988389\pi$
$643$	−2.91073	−	12.7528i	−0.114788	−	0.502920i	0.884547	−	0.466452i	$-0.154468\pi$
$644$	−0.995471	+	0.677308i	−0.0392270	+	0.0266897i
$645$	4.67190	−	20.4690i	0.183956	−	0.805964i
$646$	2.33593	+	31.1709i	0.0919061	+	1.22640i
$647$	33.5169	+	10.3386i	1.31768	+	0.406452i	0.872337	−	0.488905i	$-0.162604\pi$
$647$	33.5169	+	10.3386i	1.31768	+	0.406452i	0.445348	+	0.895357i	$0.353080\pi$
$648$	−1.57140	+	20.9688i	−0.0617302	+	0.823733i
$649$	9.38614	−	23.9155i	0.368438	−	0.938765i
$650$	2.17411	−	1.04700i	0.0852756	−	0.0410666i
$651$	−40.5633	−	50.9645i	−1.58980	−	1.99746i
$652$	−0.540581	−	0.260330i	−0.0211708	−	0.0101953i
$653$	3.37874	−	3.13501i	0.132220	−	0.122683i	−0.611291	−	0.791406i	$-0.709349\pi$
$653$	3.37874	−	3.13501i	0.132220	−	0.122683i	0.743511	+	0.668723i	$0.233159\pi$
$654$	15.0685	−	2.27121i	0.589225	−	0.0888113i
$655$	15.3149	−	26.5261i	0.598402	−	1.03646i
$656$	5.16978	+	8.95433i	0.201846	+	0.349608i
$657$	−16.9589	−	21.2658i	−0.661630	−	0.829658i
$658$	−21.3071	+	19.7322i	−0.830636	+	0.769243i
$659$	1.08134	−	1.35595i	0.0421229	−	0.0528204i	−0.760324	−	0.649544i	$-0.774960\pi$
$659$	1.08134	−	1.35595i	0.0421229	−	0.0528204i	0.802447	+	0.596724i	$0.203531\pi$
$660$	0.620222	+	0.0934835i	0.0241421	+	0.00363884i
$661$	−11.1259	+	7.58549i	−0.432746	+	0.295042i	−0.760034	−	0.649883i	$-0.774818\pi$
$661$	−11.1259	+	7.58549i	−0.432746	+	0.295042i	0.327288	+	0.944925i	$0.393865\pi$
$662$	−2.78909	+	1.90157i	−0.108401	+	0.0739065i
$663$	18.1062	+	2.72908i	0.703188	+	0.105989i
$664$	28.4081	−	35.6226i	1.10245	−	1.38242i
$665$	5.45836	−	13.8687i	0.211666	−	0.537806i
$666$	4.88565	+	6.12641i	0.189315	+	0.237394i
$667$	−35.4840	−	61.4601i	−1.37395	−	2.37974i
$668$	−0.157383	+	0.272596i	−0.00608934	+	0.0105471i
$669$	−5.85368	+	0.882300i	−0.226316	+	0.0341117i
$670$	3.98005	−	3.69294i	0.153763	−	0.142671i
$671$	−13.1718	−	6.34319i	−0.508491	−	0.244876i
$672$	0.466212	−	2.03365i	0.0179845	−	0.0784498i
$673$	7.21091	−	3.47259i	0.277960	−	0.133859i	−0.289710	−	0.957114i	$-0.593559\pi$
$673$	7.21091	−	3.47259i	0.277960	−	0.133859i	0.567671	+	0.823256i	$0.307845\pi$
$674$	0.605686	−	1.54326i	0.0233301	−	0.0594442i
$675$	0.157315	−	2.09922i	0.00605506	−	0.0807991i
$676$	−0.0523528	−	0.0161487i	−0.00201357	−	0.000621104i
$677$	−2.81231	−	37.5276i	−0.108086	−	1.44230i	−0.742777	−	0.669539i	$-0.766492\pi$
$677$	−2.81231	−	37.5276i	−0.108086	−	1.44230i	0.634691	−	0.772766i	$-0.281127\pi$
$678$	13.6271	−	59.7042i	0.523345	−	2.29293i
$679$	14.2060	+	36.2982i	0.545176	+	1.39300i
$680$	−8.29600	−	36.3471i	−0.318137	−	1.39385i
$681$	−44.6315	+	13.7670i	−1.71028	+	0.527553i
$682$	12.2603	+	31.2387i	0.469470	+	1.19619i
$683$	15.4768	+	14.3604i	0.592203	+	0.549484i	0.918317	−	0.395847i	$-0.129549\pi$
$683$	15.4768	+	14.3604i	0.592203	+	0.549484i	−0.326114	+	0.945330i	$0.605739\pi$
$684$	−0.490471	−	0.334397i	−0.0187536	−	0.0127860i
$685$	−2.58810			−0.0988863
$686$	−12.8510	−	22.4067i	−0.490655	−	0.855491i
$687$	−1.71998			−0.0656214
$688$	14.6523	+	9.98978i	0.558614	+	0.380857i
$689$	−3.30645	−	3.06793i	−0.125966	−	0.116879i
$690$	19.4797	+	49.6334i	0.741578	+	1.88951i
$691$	−1.19968	+	0.370053i	−0.0456381	+	0.0140775i	−0.317490	−	0.948262i	$-0.602840\pi$
$691$	−1.19968	+	0.370053i	−0.0456381	+	0.0140775i	0.271852	+	0.962339i	$0.412364\pi$
$692$	0.0723437	+	0.316958i	0.00275009	+	0.0120489i
$693$	−8.34234	−	21.3158i	−0.316899	−	0.809720i
$694$	−3.89128	+	17.0488i	−0.147711	+	0.647164i
$695$	−2.13367	−	28.4718i	−0.0809345	−	1.08000i
$696$	59.5502	+	18.3688i	2.25725	+	0.696268i
$697$	−1.42995	+	19.0813i	−0.0541632	+	0.722757i
$698$	−11.0523	+	28.1608i	−0.418335	+	1.06590i
$699$	−35.8280	+	17.2538i	−1.35514	+	0.652600i
$700$	0.0560400	−	0.244451i	0.00211811	−	0.00923937i
$701$	−11.3027	−	5.44310i	−0.426898	−	0.205583i	0.208083	−	0.978111i	$-0.433278\pi$
$701$	−11.3027	−	5.44310i	−0.426898	−	0.205583i	−0.634981	+	0.772528i	$0.718992\pi$
$702$	1.24396	−	1.15422i	0.0469501	−	0.0435633i
$703$	4.97615	−	0.750034i	0.187679	−	0.0282881i
$704$	−10.2075	+	17.6798i	−0.384708	+	0.666334i
$705$	−18.1103	−	31.3680i	−0.682075	−	1.18139i
$706$	10.1361	+	12.7102i	0.381476	+	0.478356i
$707$	−2.04618	+	5.19897i	−0.0769545	+	0.195527i
$708$	0.897949	−	1.12599i	0.0337470	−	0.0423174i
$709$	−0.524305	−	0.0790262i	−0.0196907	−	0.00296789i	0.139190	−	0.990266i	$-0.455550\pi$
$709$	−0.524305	−	0.0790262i	−0.0196907	−	0.00296789i	−0.158880	+	0.987298i	$0.550788\pi$
$710$	−2.75963	+	1.88148i	−0.103567	+	0.0706107i
$711$	32.8147	−	22.3727i	1.23065	−	0.839040i
$712$	24.2098	+	3.64904i	0.907300	+	0.136753i
$713$	50.0954	−	62.8176i	1.87609	−	2.35254i
$714$	−49.5745	+	45.9104i	−1.85528	+	1.71815i
$715$	2.80451	+	3.51674i	0.104883	+	0.131519i
$716$	−0.601093	−	1.04112i	−0.0224639	−	0.0389086i
$717$	−6.30538	+	10.9212i	−0.235479	+	0.407861i
$718$	6.97197	−	1.05086i	0.260192	−	0.0392176i
$719$	24.7317	−	22.9476i	0.922336	−	0.855803i	−0.0675430	−	0.997716i	$-0.521516\pi$
$719$	24.7317	−	22.9476i	0.922336	−	0.855803i	0.989879	+	0.141914i	$0.0453255\pi$
$720$	−22.0277	−	10.6080i	−0.820924	−	0.395336i
$721$	−8.94027	−	11.2327i	−0.332953	−	0.418329i
$722$	−11.6801	+	5.62482i	−0.434687	+	0.209334i
$723$	−6.72229	+	17.1281i	−0.250005	+	0.637002i
$724$	−0.0395031	+	0.527132i	−0.00146812	+	0.0195907i
$725$	14.1254	+	4.35710i	0.524603	+	0.161818i
$726$	−1.27660	−	17.0350i	−0.0473790	−	0.632229i
$727$	−4.92378	+	21.5725i	−0.182613	+	0.800079i	0.797768	+	0.602965i	$0.206014\pi$
$727$	−4.92378	+	21.5725i	−0.182613	+	0.800079i	−0.980381	+	0.197114i	$0.936843\pi$
$728$	6.26884	−	4.26526i	0.232339	−	0.158081i
$729$	7.74594	+	33.9372i	0.286886	+	1.25693i
$730$	−18.8471	+	5.81355i	−0.697562	+	0.215169i
$731$	11.9901	+	30.5502i	0.443469	+	1.12994i
$732$	−0.600763	−	0.557426i	−0.0222048	−	0.0206031i
$733$	−29.0410	−	19.7998i	−1.07265	−	0.731323i	−0.107817	−	0.994171i	$-0.534386\pi$
$733$	−29.0410	−	19.7998i	−1.07265	−	0.731323i	−0.964837	+	0.262848i	$0.915338\pi$
$734$	−25.2801			−0.933106
$735$	30.8036	−	9.43724i	1.13621	−	0.348098i
$736$	2.57361			0.0948646
$737$	−4.42463	−	3.01666i	−0.162983	−	0.111120i
$738$	9.45787	+	8.77562i	0.348149	+	0.323035i
$739$	13.8450	+	35.2765i	0.509296	+	1.29767i	0.922137	+	0.386863i	$0.126441\pi$
$739$	13.8450	+	35.2765i	0.509296	+	1.29767i	−0.412841	+	0.910803i	$0.635464\pi$
$740$	−0.152925	+	0.0471710i	−0.00562163	+	0.00173404i
$741$	−1.76437	−	7.73021i	−0.0648157	−	0.283976i
$742$	16.4605	−	2.46495i	0.604285	−	0.0904910i
$743$	−9.81442	+	42.9998i	−0.360056	+	1.57751i	0.392991	+	0.919542i	$0.371440\pi$
$743$	−9.81442	+	42.9998i	−0.360056	+	1.57751i	−0.753047	+	0.657967i	$0.771417\pi$
$744$	5.27256	+	70.3574i	0.193301	+	2.57943i
$745$	−9.74836	−	3.00697i	−0.357152	−	0.110167i
$746$	−1.66021	+	22.1539i	−0.0607845	+	0.811113i
$747$	20.2020	−	51.4739i	0.739153	−	1.88333i
$748$	−0.883355	+	0.425401i	−0.0322986	+	0.0155542i
$749$	9.61144	−	4.61732i	0.351194	−	0.168713i
$750$	−38.9228	−	18.7442i	−1.42126	−	0.684442i
$751$	−33.7144	+	31.2824i	−1.23025	+	1.14151i	−0.245162	+	0.969482i	$0.578841\pi$
$751$	−33.7144	+	31.2824i	−1.23025	+	1.14151i	−0.985092	+	0.172027i	$0.944968\pi$
$752$	30.2521	−	4.55978i	1.10318	−	0.166278i
$753$	−8.97940	+	15.5528i	−0.327227	+	0.566775i
$754$	5.95801	+	10.3196i	0.216978	+	0.375817i
$755$	−25.9136	−	32.4947i	−0.943093	−	1.18260i
$756$	−0.0130118	−	0.175884i	−0.000473233	−	0.00639684i
$757$	7.90525	−	9.91287i	0.287321	−	0.360289i	−0.617134	−	0.786858i	$-0.711706\pi$
$757$	7.90525	−	9.91287i	0.287321	−	0.360289i	0.904455	+	0.426569i	$0.140278\pi$
$758$	27.9487	+	4.21259i	1.01514	+	0.153008i
$759$	43.4517	−	29.6249i	1.57720	−	1.07531i
$760$	−13.3388	+	9.09421i	−0.483848	+	0.329882i
$761$	29.4755	+	4.44271i	1.06849	+	0.161048i	0.659660	−	0.751564i	$-0.270700\pi$
$761$	29.4755	+	4.44271i	1.06849	+	0.161048i	0.408825	+	0.912613i	$0.365938\pi$
$762$	−16.3532	+	20.5062i	−0.592413	+	0.742863i
$763$	10.8563	−	3.33738i	0.393025	−	0.120821i
$764$	0.742058	+	0.930511i	0.0268467	+	0.0336647i
$765$	−22.6231	−	39.1843i	−0.817940	−	1.41671i
$766$	11.4679	−	19.8630i	0.414353	−	0.717681i
$767$	10.2128	−	1.53934i	0.368764	−	0.0555822i
$768$	−2.45141	+	2.27457i	−0.0884575	+	0.0820765i
$769$	−19.1675	−	9.23057i	−0.691197	−	0.332863i	0.0550955	−	0.998481i	$-0.482454\pi$
$769$	−19.1675	−	9.23057i	−0.691197	−	0.332863i	−0.746292	+	0.665618i	$0.768168\pi$
$770$	−16.5981	−	0.0158550i	−0.598156	−	0.000571374i
$771$	−45.5840	+	21.9521i	−1.64167	+	0.790585i
$772$	0.0348674	−	0.0888408i	0.00125491	−	0.00319745i
$773$	0.0637234	−	0.850330i	0.00229197	−	0.0305842i	−0.995941	−	0.0900134i	$-0.971309\pi$
$773$	0.0637234	−	0.850330i	0.00229197	−	0.0305842i	0.998233	+	0.0594292i	$0.0189281\pi$
$774$	21.1456	+	6.52256i	0.760064	+	0.234449i
$775$	1.25065	+	16.6888i	0.0449248	+	0.599480i
$776$	9.39515	−	41.1628i	0.337266	−	1.47766i
$777$	7.96701	+	7.40648i	0.285815	+	0.265706i
$778$	2.00497	+	8.78433i	0.0718815	+	0.314934i
$779$	7.91773	−	2.44230i	0.283682	−	0.0875044i
$780$	0.0921211	+	0.234721i	0.00329847	+	0.00840435i
$781$	2.41489	+	2.24069i	0.0864116	+	0.0801782i
$782$	−68.8634	−	46.9503i	−2.46255	−	1.67894i
$783$	10.3952			0.371495
$784$	−2.08539	+	27.1319i	−0.0744783	+	0.968998i
$785$	17.3261			0.618397
$786$	49.6812	+	33.8720i	1.77207	+	1.20818i
$787$	−1.59440	−	1.47939i	−0.0568342	−	0.0527345i	0.651244	−	0.758868i	$-0.274247\pi$
$787$	−1.59440	−	1.47939i	−0.0568342	−	0.0527345i	−0.708079	+	0.706134i	$0.750438\pi$
$788$	−0.405489	−	1.03317i	−0.0144449	−	0.0368051i
$789$	−12.4805	+	3.84974i	−0.444319	+	0.137054i
$790$	−6.40833	−	28.0767i	−0.227998	−	0.998925i
$791$	3.45440	−	45.5123i	0.122824	−	1.61823i
$792$	−5.51722	+	24.1725i	−0.196046	+	0.858933i
$793$	−0.439203	−	5.86076i	−0.0155966	−	0.208122i
$794$	−12.8476	−	3.96296i	−0.455944	−	0.140640i
$795$	−1.55134	+	20.7012i	−0.0550203	+	0.734195i
$796$	0.214997	−	0.547803i	0.00762036	−	0.0194164i
$797$	−37.0231	+	17.8294i	−1.31143	+	0.631550i	−0.953272	−	0.302113i	$-0.902308\pi$
$797$	−37.0231	+	17.8294i	−1.31143	+	0.631550i	−0.358154	+	0.933662i	$0.616594\pi$
$798$	26.3488	+	12.7199i	0.932738	+	0.450281i
$799$	51.0113	+	24.5657i	1.80465	+	0.869074i
$800$	−0.392962	+	0.364616i	−0.0138933	+	0.0128911i
$801$	29.3816	−	4.42856i	1.03815	−	0.156475i
$802$	22.9958	−	39.8298i	0.812008	−	1.40644i
$803$	9.72676	+	16.8472i	0.343250	+	0.594527i
$804$	−0.187169	−	0.234703i	−0.00660095	−	0.00827733i
$805$	19.8371	+	34.4347i	0.699165	+	1.21366i
$806$	−8.41136	+	10.5475i	−0.296278	+	0.371520i
$807$	−31.7197	−	4.78098i	−1.11659	−	0.168298i
$808$	5.00030	−	3.40915i	0.175910	−	0.119933i
$809$	10.6859	−	7.28551i	0.375695	−	0.256145i	−0.360720	−	0.932674i	$-0.617469\pi$
$809$	10.6859	−	7.28551i	0.375695	−	0.256145i	0.736416	+	0.676529i	$0.236517\pi$
$810$	18.2982	+	2.75801i	0.642933	+	0.0969065i
$811$	−11.3992	+	14.2942i	−0.400282	+	0.501937i	−0.940597	−	0.339525i	$-0.889734\pi$
$811$	−11.3992	+	14.2942i	−0.400282	+	0.501937i	0.540315	+	0.841463i	$0.318305\pi$
$812$	1.22442	+	0.185749i	0.0429689	+	0.00651850i
$813$	−24.0312	−	30.1341i	−0.842809	−	1.05685i
$814$	−2.80216	−	4.85348i	−0.0982157	−	0.170115i
$815$	−9.90165	+	17.1502i	−0.346840	+	0.600744i
$816$	70.3867	−	10.6091i	2.46403	−	0.371392i
$817$	10.4177	−	9.66617i	0.364468	−	0.338177i
$818$	−28.9486	−	13.9409i	−1.01216	−	0.487432i
$819$	5.74424	−	7.18895i	0.200720	−	0.251202i
$820$	−0.237405	+	0.114328i	−0.00829053	+	0.00399251i
$821$	−2.69430	+	6.86497i	−0.0940318	+	0.239589i	−0.970149	−	0.242509i	$-0.922030\pi$
$821$	−2.69430	+	6.86497i	−0.0940318	+	0.239589i	0.876117	+	0.482098i	$0.160125\pi$
$822$	0.379682	−	5.06650i	0.0132429	−	0.176715i
$823$	−2.33427	−	0.720028i	−0.0813677	−	0.0250986i	0.253804	−	0.967256i	$-0.418318\pi$
$823$	−2.33427	−	0.720028i	−0.0813677	−	0.0250986i	−0.335172	+	0.942157i	$0.608794\pi$
$824$	1.16209	+	15.5070i	0.0404832	+	0.540211i
$825$	−2.43750	+	10.6794i	−0.0848630	+	0.371809i
$826$	−19.0873	+	32.9874i	−0.664132	+	1.14778i
$827$	−0.476013	−	2.08555i	−0.0165526	−	0.0725217i	0.965977	−	0.258628i	$-0.0832703\pi$
$827$	−0.476013	−	2.08555i	−0.0165526	−	0.0725217i	−0.982530	+	0.186106i	$0.940413\pi$
$828$	1.51248	−	0.466538i	0.0525623	−	0.0162133i
$829$	−13.1524	−	33.5117i	−0.456800	−	1.16391i	−0.954937	−	0.296810i	$-0.904077\pi$
$829$	−13.1524	−	33.5117i	−0.456800	−	1.16391i	0.498136	−	0.867099i	$-0.334018\pi$
$830$	−29.3929	−	27.2726i	−1.02024	−	0.946647i
$831$	−5.50153	−	3.75088i	−0.190846	−	0.130117i
$832$	−8.20698			−0.284526
$833$	−31.4739	+	39.3127i	−1.09051	+	1.36210i
$834$	56.0497			1.94084
$835$	8.58382	+	5.85235i	0.297055	+	0.202529i
$836$	0.311223	+	0.288773i	0.0107639	+	0.00998743i
$837$	4.29970	+	10.9555i	0.148619	+	0.378676i
$838$	6.76725	−	2.08742i	0.233771	−	0.0721087i
$839$	2.58937	+	11.3448i	0.0893951	+	0.391666i	0.999755	−	0.0221528i	$-0.00705203\pi$
$839$	2.58937	+	11.3448i	0.0893951	+	0.391666i	−0.910359	+	0.413818i	$0.864195\pi$
$840$	−33.3365	−	10.3178i	−1.15022	−	0.355999i
$841$	−9.78987	+	42.8922i	−0.337582	+	1.47904i
$842$	0.169502	+	2.26184i	0.00584141	+	0.0779482i
$843$	35.1131	+	10.8310i	1.20936	+	0.373038i
$844$	−0.0804208	+	1.07314i	−0.00276820	+	0.0369391i
$845$	−0.660634	+	1.68327i	−0.0227265	+	0.0579062i
$846$	34.3954	−	16.5639i	1.18254	−	0.569480i
$847$	−2.82131	−	12.4156i	−0.0969415	−	0.426606i
$848$	−15.7979	−	7.60785i	−0.542501	−	0.261255i
$849$	37.6627	−	34.9458i	1.29258	−	1.19934i
$850$	17.1664	−	2.58741i	0.588802	−	0.0887476i
$851$	−6.70903	+	11.6204i	−0.229983	+	0.398342i
$852$	0.0923350	+	0.159929i	0.00316335	+	0.00547907i
$853$	0.281035	+	0.352407i	0.00962247	+	0.0120662i	0.786619	−	0.617438i	$-0.211829\pi$
$853$	0.281035	+	0.352407i	0.00962247	+	0.0120662i	−0.776997	+	0.629504i	$0.783258\pi$
$854$	17.9071	+	12.2339i	0.612768	+	0.418636i
$855$	−12.2158	+	15.3182i	−0.417773	+	0.523871i
$856$	−11.4210	−	1.72143i	−0.390360	−	0.0588373i
$857$	21.3210	−	14.5364i	0.728313	−	0.496555i	−0.141499	−	0.989938i	$-0.545192\pi$
$857$	21.3210	−	14.5364i	0.728313	−	0.496555i	0.869812	+	0.493383i	$0.164240\pi$
$858$	−7.29584	+	4.97422i	−0.249076	+	0.169817i
$859$	20.2802	+	3.05675i	0.691953	+	0.104295i	0.485598	−	0.874182i	$-0.338602\pi$
$859$	20.2802	+	3.05675i	0.691953	+	0.104295i	0.206355	+	0.978477i	$0.433840\pi$
$860$	−0.281778	+	0.353338i	−0.00960855	+	0.0120487i
$861$	14.7888	+	10.1036i	0.504002	+	0.344328i
$862$	16.8566	+	21.1375i	0.574138	+	0.719946i
$863$	−8.91755	−	15.4456i	−0.303557	−	0.525776i	0.673382	−	0.739295i	$-0.264841\pi$
$863$	−8.91755	−	15.4456i	−0.303557	−	0.525776i	−0.976939	+	0.213519i	$0.931508\pi$
$864$	−0.188488	+	0.326471i	−0.00641250	+	0.0111068i
$865$	10.6106	−	1.59928i	0.360770	−	0.0543773i
$866$	−22.4472	+	20.8279i	−0.762786	+	0.707762i
$867$	79.7029	+	38.3829i	2.70685	+	1.30355i
$868$	0.310691	+	1.36724i	0.0105455	+	0.0464073i
$869$	−25.5919	+	12.3244i	−0.868145	+	0.418076i
$870$	20.0361	−	51.0512i	0.679289	−	1.73080i
$871$	0.160880	−	2.14680i	0.00545122	−	0.0727414i
$872$	−11.7559	−	3.62622i	−0.398106	−	0.122799i
$873$	−3.82924	−	51.0977i	−0.129600	−	1.72939i
$874$	−8.03094	+	35.1858i	−0.271651	+	1.19018i
$875$	−30.7591	−	9.52010i	−1.03985	−	0.321838i
$876$	0.242663	+	1.06317i	0.00819881	+	0.0359213i
$877$	−20.2083	+	6.23344i	−0.682387	+	0.210488i	−0.616519	−	0.787340i	$-0.711458\pi$
$877$	−20.2083	+	6.23344i	−0.682387	+	0.210488i	−0.0658677	+	0.997828i	$0.520982\pi$
$878$	−14.0714	−	35.8533i	−0.474887	−	1.20999i
$879$	55.4134	+	51.4161i	1.86905	+	1.73422i
$880$	14.4476	+	9.85018i	0.487027	+	0.332050i
$881$	1.44407			0.0486519			0.0243259	−	0.999704i	$-0.492256\pi$
$881$	1.44407			0.0486519			0.0243259	+	0.999704i	$0.492256\pi$
$882$	7.49266	+	33.1190i	0.252291	+	1.11517i
$883$	−19.3689			−0.651815			−0.325908	−	0.945402i	$-0.605670\pi$
$883$	−19.3689			−0.651815			−0.325908	+	0.945402i	$0.605670\pi$
$884$	−0.325662	−	0.222032i	−0.0109532	−	0.00746775i
$885$	−34.8452	−	32.3317i	−1.17131	−	1.08682i
$886$	−17.0333	−	43.4000i	−0.572244	−	1.45805i
$887$	−46.6412	+	14.3869i	−1.56606	+	0.483065i	−0.951975	−	0.306177i	$-0.900950\pi$
$887$	−46.6412	+	14.3869i	−1.56606	+	0.483065i	−0.614083	+	0.789241i	$0.710474\pi$
$888$	−2.62191	−	11.4873i	−0.0879856	−	0.385490i
$889$	−9.79049	+	16.9203i	−0.328362	+	0.567488i
$890$	4.79441	−	21.0057i	0.160709	−	0.704113i
$891$	−1.36395	−	18.2007i	−0.0456942	−	0.609746i
$892$	0.121766	+	0.0375597i	0.00407702	+	0.00125759i
$893$	1.83216	−	24.4485i	0.0613110	−	0.818139i
$894$	7.31659	−	18.6424i	0.244703	−	0.623494i
$895$	−35.7493	+	17.2160i	−1.19497	+	0.575467i
$896$	17.8811	−	22.3783i	0.597364	−	0.747605i
$897$	19.0479	+	9.17297i	0.635990	+	0.306277i
$898$	38.4699	−	35.6949i	1.28376	−	1.19115i
$899$	−81.7190	+	12.3172i	−2.72548	+	0.410800i
$900$	−0.164843	+	0.285516i	−0.00549475	+	0.00951719i
$901$	−16.2249	−	28.1023i	−0.540529	−	0.936223i
$902$	−5.75331	−	7.21442i	−0.191564	−	0.240214i
$903$	30.3717	+	4.60747i	1.01071	+	0.153327i
$904$	−30.8253	+	38.6537i	−1.02523	+	1.28560i
$905$	17.2522	+	2.60034i	0.573481	+	0.0864384i
$906$	67.4135	−	45.9618i	2.23966	−	1.52698i
$907$	−42.8565	+	29.2191i	−1.42303	+	0.970203i	−0.425146	+	0.905125i	$0.639777\pi$
$907$	−42.8565	+	29.2191i	−1.42303	+	0.970203i	−0.997880	+	0.0650784i	$0.979270\pi$
$908$	0.994156	+	0.149845i	0.0329922	+	0.00497278i
$909$	4.57936	−	5.74233i	0.151888	−	0.190461i
$910$	−3.33078	−	5.78183i	−0.110414	−	0.191666i
$911$	16.0372	+	20.1101i	0.531338	+	0.666276i	0.972973	−	0.230918i	$-0.0741730\pi$
$911$	16.0372	+	20.1101i	0.531338	+	0.666276i	−0.441635	+	0.897195i	$0.645602\pi$
$912$	−15.4117	−	26.6939i	−0.510332	−	0.883922i
$913$	−19.7741	+	34.2497i	−0.654426	+	1.13350i
$914$	−18.7442	+	2.82524i	−0.620004	+	0.0934506i
$915$	−19.8285	+	18.3981i	−0.655509	+	0.608224i
$916$	0.0333571	+	0.0160639i	0.00110215	+	0.000530767i
$917$	40.3589	+	19.4833i	1.33277	+	0.643397i
$918$	10.9993	−	5.29698i	0.363030	−	0.174826i
$919$	−3.53836	+	9.01561i	−0.116720	+	0.297397i	−0.977280	−	0.211951i	$-0.932018\pi$
$919$	−3.53836	+	9.01561i	−0.116720	+	0.297397i	0.860560	+	0.509348i	$0.170114\pi$
$920$	3.21680	−	42.9252i	0.106055	−	1.41520i
$921$	−5.72722	−	1.76661i	−0.188718	−	0.0582119i
$922$	1.67623	+	22.3677i	0.0552036	+	0.736641i
$923$	−0.294693	+	1.29113i	−0.00969992	+	0.0424981i
$924$	−0.0694557	+	0.915091i	−0.00228492	+	0.0301043i
$925$	−0.621919	−	2.72481i	−0.0204486	−	0.0895911i
$926$	−22.3046	+	6.88005i	−0.732974	+	0.226093i
$927$	6.89487	+	17.5678i	0.226457	+	0.577003i
$928$	−1.94048	−	1.80051i	−0.0636995	−	0.0591045i
$929$	−13.7822	−	9.39651i	−0.452178	−	0.308290i	0.315731	−	0.948849i	$-0.397750\pi$
$929$	−13.7822	−	9.39651i	−0.452178	−	0.308290i	−0.767909	+	0.640559i	$0.778703\pi$
$930$	62.0900			2.03601
$931$	20.8258	+	6.46751i	0.682538	+	0.211964i
$932$	0.855986			0.0280388
$933$	21.6845	+	14.7842i	0.709918	+	0.484014i
$934$	14.6112	+	13.5572i	0.478094	+	0.443606i
$935$	11.8225	+	30.1233i	0.386638	+	0.985137i
$936$	−9.52464	+	2.93796i	−0.311323	+	0.0960304i
$937$	−6.22103	−	27.2561i	−0.203232	−	0.890419i	−0.968953	−	0.247245i	$-0.920475\pi$
$937$	−6.22103	−	27.2561i	−0.203232	−	0.890419i	0.765721	−	0.643173i	$-0.222383\pi$
$938$	5.81820	+	5.40886i	0.189971	+	0.176605i
$939$	4.60258	−	20.1652i	0.150200	−	0.658067i
$940$	0.0582648	+	0.777490i	0.00190039	+	0.0253589i
$941$	28.6083	+	8.82449i	0.932604	+	0.287670i	0.723580	−	0.690240i	$-0.242495\pi$
$941$	28.6083	+	8.82449i	0.932604	+	0.287670i	0.209024	+	0.977911i	$0.432971\pi$
$942$	−2.54179	+	33.9179i	−0.0828161	+	1.10510i
$943$	−8.07149	+	20.5658i	−0.262844	+	0.669715i
$944$	36.1739	−	17.4205i	1.17736	−	0.566987i
$945$	−5.82101	−	0.00556038i	−0.189357	−	0.000180879i
$946$	−14.2592	−	6.86689i	−0.463608	−	0.223262i
$947$	−22.0227	+	20.4341i	−0.715641	+	0.664018i	−0.951458	−	0.307780i	$-0.900414\pi$
$947$	−22.0227	+	20.4341i	−0.715641	+	0.664018i	0.235816	+	0.971798i	$0.424224\pi$
$948$	−1.57452	+	0.237321i	−0.0511380	+	0.00770781i
$949$	−3.91024	+	6.77274i	−0.126932	+	0.219853i
$950$	−3.75871	−	6.51027i	−0.121949	−	0.211221i
$951$	27.6434	+	34.6637i	0.896398	+	1.12405i
$952$	52.1405	−	16.0287i	1.68988	−	0.519493i
$953$	−7.98729	+	10.0157i	−0.258734	+	0.324442i	−0.894184	−	0.447700i	$-0.852243\pi$
$953$	−7.98729	+	10.0157i	−0.258734	+	0.324442i	0.635450	+	0.772142i	$0.280815\pi$
$954$	−21.6355	−	3.26103i	−0.700475	−	0.105580i
$955$	32.4564	−	22.1284i	1.05026	−	0.716058i
$956$	0.224286	−	0.152915i	0.00725391	−	0.00494563i
$957$	−53.4879	−	8.06201i	−1.72902	−	0.260608i
$958$	10.1904	−	12.7784i	0.329237	−	0.412850i
$959$	−0.279378	−	3.77644i	−0.00902158	−	0.121948i
$960$	23.5503	+	29.5312i	0.760084	+	0.953115i
$961$	−31.2818	−	54.1817i	−1.00909	−	1.74780i
$962$	1.12649	−	1.95114i	0.0363196	−	0.0629074i
$963$	−13.8607	+	2.08917i	−0.446656	+	0.0673226i
$964$	0.290341	−	0.269397i	0.00935125	−	0.00867669i
$965$	−2.83804	−	1.36673i	−0.0913596	−	0.0439965i
$966$	−70.3200	+	33.7816i	−2.26251	+	1.08691i
$967$	−26.5739	+	12.7973i	−0.854558	+	0.411533i	−0.809267	−	0.587441i	$-0.800136\pi$
$967$	−26.5739	+	12.7973i	−0.854558	+	0.411533i	−0.0452905	+	0.998974i	$0.514421\pi$
$968$	−5.03851	+	12.8379i	−0.161944	+	0.412626i
$969$	4.26284	−	56.8836i	0.136942	−	1.82736i
$970$	−35.5052	−	10.9519i	−1.14000	−	0.351645i
$971$	−0.812775	−	10.8457i	−0.0260832	−	0.348056i	−0.994943	−	0.100445i	$-0.967973\pi$
$971$	−0.812775	−	10.8457i	−0.0260832	−	0.348056i	0.968859	−	0.247611i	$-0.0796456\pi$
$972$	0.272171	−	1.19246i	0.00872989	−	0.0382481i
$973$	41.3144	−	6.18679i	1.32448	−	0.198339i
$974$	−2.53055	−	11.0871i	−0.0810842	−	0.355253i
$975$	−4.20798	+	1.29799i	−0.134763	+	0.0415690i
$976$	−8.34700	−	21.2678i	−0.267181	−	0.680766i
$977$	30.5118	+	28.3108i	0.976158	+	0.905742i	0.995566	−	0.0940692i	$-0.0299875\pi$
$977$	30.5118	+	28.3108i	0.976158	+	0.905742i	−0.0194075	+	0.999812i	$0.506178\pi$
$978$	−32.1208	−	21.8996i	−1.02711	−	0.700271i
$979$	−21.2512			−0.679190
$980$	−0.685541	−	0.104668i	−0.0218988	−	0.00334351i
$981$	−14.9306			−0.476697
$982$	3.80821	+	2.59639i	0.121525	+	0.0828543i
$983$	−4.10226	−	3.80634i	−0.130842	−	0.121403i	0.612038	−	0.790828i	$-0.290350\pi$
$983$	−4.10226	−	3.80634i	−0.130842	−	0.121403i	−0.742879	+	0.669425i	$0.766540\pi$
$984$	−7.08779	−	18.0594i	−0.225951	−	0.575713i
$985$	−35.0050	+	10.7976i	−1.11535	+	0.344041i
$986$	19.0760	+	83.5772i	0.607502	+	2.66164i
$987$	43.8158	−	29.8119i	1.39467	−	0.948922i
$988$	−0.0379790	+	0.166397i	−0.00120827	+	0.00529380i
$989$	2.83171	+	37.7866i	0.0900432	+	1.20154i
$990$	20.8501	+	6.43142i	0.662661	+	0.204404i
$991$	3.50736	−	46.8025i	0.111415	−	1.48673i	−0.608990	−	0.793178i	$-0.708425\pi$
$991$	3.50736	−	46.8025i	0.111415	−	1.48673i	0.720405	−	0.693553i	$-0.243956\pi$
$992$	1.09491	−	2.78979i	0.0347635	−	0.0885761i
$993$	5.55014	−	2.67281i	0.176128	−	0.0848190i
$994$	−3.04326	−	3.82362i	−0.0965264	−	0.121278i
$995$	−17.4997	−	8.42740i	−0.554777	−	0.267166i
$996$	−1.62515	+	1.50792i	−0.0514950	+	0.0477804i
$997$	−29.5679	+	4.45664i	−0.936425	+	0.141143i	−0.599488	−	0.800384i	$-0.704629\pi$
$997$	−29.5679	+	4.45664i	−0.936425	+	0.141143i	−0.336937	+	0.941527i	$0.609391\pi$
$998$	9.79791	−	16.9705i	0.310147	−	0.537191i
$999$	−0.982724	−	1.70213i	−0.0310920	−	0.0538529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.9	✓	324
49.37	even	21	inner	637.2.bl.a.625.9	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.9	✓	324	1.1	even	1	trivial
637.2.bl.a.625.9	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15236 - 0.785668i) q^{2} +(1.86576 + 1.73118i) q^{3} +(-0.0200159 - 0.0509996i) q^{4} +(-1.72793 + 0.532996i) q^{5} +(-0.789908 - 3.46081i) q^{6} +(-0.964248 - 2.46378i) q^{7} +(-0.637707 + 2.79398i) q^{8} +(0.259914 + 3.46832i) q^{9} +O(q^{10})\)	\(q+(-1.15236 - 0.785668i) q^{2} +(1.86576 + 1.73118i) q^{3} +(-0.0200159 - 0.0509996i) q^{4} +(-1.72793 + 0.532996i) q^{5} +(-0.789908 - 3.46081i) q^{6} +(-0.964248 - 2.46378i) q^{7} +(-0.637707 + 2.79398i) q^{8} +(0.259914 + 3.46832i) q^{9} +(2.40996 + 0.743375i) q^{10} +(0.185892 - 2.48055i) q^{11} +(0.0509444 - 0.129804i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-0.824550 + 3.59675i) q^{14} +(-4.14662 - 1.99691i) q^{15} +(2.84968 - 2.64412i) q^{16} +(7.11388 - 1.07224i) q^{17} +(2.42543 - 4.20096i) q^{18} +(-1.55764 - 2.69791i) q^{19} +(0.0617687 + 0.0774555i) q^{20} +(2.46618 - 6.26612i) q^{21} +(-2.16310 + 2.71245i) q^{22} +(8.21367 + 1.23801i) q^{23} +(-6.02668 + 4.10892i) q^{24} +(-1.42953 + 0.974638i) q^{25} +(-1.37913 - 0.207871i) q^{26} +(-0.758605 + 0.951261i) q^{27} +(-0.106352 + 0.0984911i) q^{28} +(-5.32693 - 6.67976i) q^{29} +(3.20951 + 5.55903i) q^{30} +(4.83641 - 8.37692i) q^{31} +(0.306373 - 0.0461782i) q^{32} +(4.64110 - 4.30631i) q^{33} +(-9.04020 - 4.35353i) q^{34} +(2.97934 + 3.74331i) q^{35} +(0.171680 - 0.0826769i) q^{36} +(-0.590165 + 1.50372i) q^{37} +(-0.324695 + 4.33276i) q^{38} +(2.43212 + 0.750211i) q^{39} +(-0.387265 - 5.16770i) q^{40} +(-0.591849 + 2.59306i) q^{41} +(-7.76502 + 5.28324i) q^{42} +(1.01510 + 4.44745i) q^{43} +(-0.130228 + 0.0401700i) q^{44} +(-2.29771 - 5.85448i) q^{45} +(-8.49246 - 7.87985i) q^{46} +(6.50246 + 4.43330i) q^{47} +9.89427 q^{48} +(-5.14045 + 4.75140i) q^{49} +2.41308 q^{50} +(15.1291 + 10.3148i) q^{51} +(-0.0401616 - 0.0372645i) q^{52} +(-1.64788 - 4.19873i) q^{53} +(1.62156 - 0.500186i) q^{54} +(1.00092 + 4.38530i) q^{55} +(7.49866 - 1.12292i) q^{56} +(1.76437 - 7.73021i) q^{57} +(0.890485 + 11.8827i) q^{58} +(9.86934 + 3.04429i) q^{59} +(-0.0188433 + 0.251446i) q^{60} +(2.14718 - 5.47093i) q^{61} +(-12.1548 + 5.85343i) q^{62} +(8.29455 - 3.98469i) q^{63} +(-7.39423 - 3.56087i) q^{64} +(-1.32555 + 1.22993i) q^{65} +(-8.73156 + 1.31607i) q^{66} +(1.07641 - 1.86439i) q^{67} +(-0.197075 - 0.341343i) q^{68} +(13.1815 + 16.5291i) q^{69} +(-0.492288 - 6.65442i) q^{70} +(-0.825710 + 1.03541i) q^{71} +(-9.85614 - 1.48557i) q^{72} +(-6.46159 + 4.40544i) q^{73} +(1.86150 - 1.26915i) q^{74} +(-4.35444 - 0.656326i) q^{75} +(-0.106415 + 0.133440i) q^{76} +(-6.29079 + 1.93387i) q^{77} +(-2.21327 - 2.77536i) q^{78} +(-5.70950 - 9.88914i) q^{79} +(-3.51475 + 6.08773i) q^{80} +(7.25540 - 1.09358i) q^{81} +(2.71931 - 2.52315i) q^{82} +(-14.3242 - 6.89819i) q^{83} +(-0.368933 - 0.000352414i) q^{84} +(-11.7208 + 5.64444i) q^{85} +(2.32445 - 5.92261i) q^{86} +(1.62504 - 21.6847i) q^{87} +(6.81206 + 2.10124i) q^{88} +(-0.638431 - 8.51927i) q^{89} +(-1.95187 + 8.55172i) q^{90} +(-1.93775 - 1.80142i) q^{91} +(-0.101266 - 0.443674i) q^{92} +(23.5255 - 7.25666i) q^{93} +(-4.01009 - 10.2175i) q^{94} +(4.12947 + 3.83159i) q^{95} +(0.651561 + 0.444227i) q^{96} -14.7327 q^{97} +(9.65668 - 1.43665i) q^{98} +8.65165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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Database

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