LMFDB - Embedded newform 546.2.bb.a.269.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.6
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.926039 + 1.46371i) q^{3} -1.00000 q^{4} +(-2.14723 - 3.71911i) q^{5} +(1.46371 + 0.926039i) q^{6} +(-0.786623 + 2.52611i) q^{7} +1.00000i q^{8} +(-1.28490 - 2.71091i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.926039 + 1.46371i) q^{3} -1.00000 q^{4} +(-2.14723 - 3.71911i) q^{5} +(1.46371 + 0.926039i) q^{6} +(-0.786623 + 2.52611i) q^{7} +1.00000i q^{8} +(-1.28490 - 2.71091i) q^{9} +(-3.71911 + 2.14723i) q^{10} +(-0.940488 + 0.542991i) q^{11} +(0.926039 - 1.46371i) q^{12} +(2.47541 + 2.62151i) q^{13} +(2.52611 + 0.786623i) q^{14} +(7.43212 + 0.301118i) q^{15} +1.00000 q^{16} +3.91616 q^{17} +(-2.71091 + 1.28490i) q^{18} +(3.51361 + 2.02858i) q^{19} +(2.14723 + 3.71911i) q^{20} +(-2.96905 - 3.49067i) q^{21} +(0.542991 + 0.940488i) q^{22} +7.63945i q^{23} +(-1.46371 - 0.926039i) q^{24} +(-6.72118 + 11.6414i) q^{25} +(2.62151 - 2.47541i) q^{26} +(5.15786 + 0.629682i) q^{27} +(0.786623 - 2.52611i) q^{28} +(-1.84864 - 1.06731i) q^{29} +(0.301118 - 7.43212i) q^{30} +(-1.04968 - 0.606034i) q^{31} -1.00000i q^{32} +(0.0761468 - 1.87943i) q^{33} -3.91616i q^{34} +(11.0839 - 2.49860i) q^{35} +(1.28490 + 2.71091i) q^{36} -6.07856 q^{37} +(2.02858 - 3.51361i) q^{38} +(-6.12947 + 1.19566i) q^{39} +(3.71911 - 2.14723i) q^{40} +(1.00855 - 1.74686i) q^{41} +(-3.49067 + 2.96905i) q^{42} +(1.69618 + 2.93788i) q^{43} +(0.940488 - 0.542991i) q^{44} +(-7.32319 + 10.5996i) q^{45} +7.63945 q^{46} +(4.97996 + 8.62555i) q^{47} +(-0.926039 + 1.46371i) q^{48} +(-5.76245 - 3.97419i) q^{49} +(11.6414 + 6.72118i) q^{50} +(-3.62652 + 5.73213i) q^{51} +(-2.47541 - 2.62151i) q^{52} +(2.81574 + 1.62567i) q^{53} +(0.629682 - 5.15786i) q^{54} +(4.03889 + 2.33185i) q^{55} +(-2.52611 - 0.786623i) q^{56} +(-6.22300 + 3.26436i) q^{57} +(-1.06731 + 1.84864i) q^{58} -1.64474 q^{59} +(-7.43212 - 0.301118i) q^{60} +(12.0708 + 6.96907i) q^{61} +(-0.606034 + 1.04968i) q^{62} +(7.85878 - 1.11334i) q^{63} -1.00000 q^{64} +(4.43442 - 14.8353i) q^{65} +(-1.87943 - 0.0761468i) q^{66} +(-4.01884 - 6.96084i) q^{67} -3.91616 q^{68} +(-11.1819 - 7.07443i) q^{69} +(-2.49860 - 11.0839i) q^{70} +(-2.68997 + 1.55305i) q^{71} +(2.71091 - 1.28490i) q^{72} +(3.86528 + 2.23162i) q^{73} +6.07856i q^{74} +(-10.8156 - 20.6183i) q^{75} +(-3.51361 - 2.02858i) q^{76} +(-0.631845 - 2.80290i) q^{77} +(1.19566 + 6.12947i) q^{78} +(2.33626 + 4.04652i) q^{79} +(-2.14723 - 3.71911i) q^{80} +(-5.69805 + 6.96651i) q^{81} +(-1.74686 - 1.00855i) q^{82} -4.52632 q^{83} +(2.96905 + 3.49067i) q^{84} +(-8.40889 - 14.5646i) q^{85} +(2.93788 - 1.69618i) q^{86} +(3.27414 - 1.71750i) q^{87} +(-0.542991 - 0.940488i) q^{88} -16.9794 q^{89} +(10.5996 + 7.32319i) q^{90} +(-8.56944 + 4.19102i) q^{91} -7.63945i q^{92} +(1.85910 - 0.975219i) q^{93} +(8.62555 - 4.97996i) q^{94} -17.4233i q^{95} +(1.46371 + 0.926039i) q^{96} +(10.7814 - 6.22463i) q^{97} +(-3.97419 + 5.76245i) q^{98} +(2.68043 + 1.85189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.926039	+	1.46371i	−0.534649	+	0.845074i
$3$	−0.926039	+	1.46371i	−0.534649	+	0.845074i
$4$	−1.00000			−0.500000
$5$	−2.14723	−	3.71911i	−0.960270	−	1.66324i	−0.721819	−	0.692082i	$-0.756694\pi$
$5$	−2.14723	−	3.71911i	−0.960270	−	1.66324i	−0.238451	−	0.971155i	$-0.576639\pi$
$6$	1.46371	+	0.926039i	0.597558	+	0.378054i
$7$	−0.786623	+	2.52611i	−0.297316	+	0.954779i
$7$	−0.786623	+	2.52611i	−0.297316	+	0.954779i
$8$			1.00000i			0.353553i
$9$	−1.28490	−	2.71091i	−0.428301	−	0.903636i
$10$	−3.71911	+	2.14723i	−1.17609	+	0.679013i
$11$	−0.940488	+	0.542991i	−0.283568	+	0.163718i	−0.635038	−	0.772481i	$-0.719015\pi$
$11$	−0.940488	+	0.542991i	−0.283568	+	0.163718i	0.351470	+	0.936199i	$0.385682\pi$
$12$	0.926039	−	1.46371i	0.267325	−	0.422537i
$13$	2.47541	+	2.62151i	0.686556	+	0.727077i
$13$	2.47541	+	2.62151i	0.686556	+	0.727077i
$14$	2.52611	+	0.786623i	0.675131	+	0.210234i
$15$	7.43212	+	0.301118i	1.91897	+	0.0777484i
$16$	1.00000			0.250000
$17$	3.91616			0.949808			0.474904	−	0.880038i	$-0.342483\pi$
$17$	3.91616			0.949808			0.474904	+	0.880038i	$0.342483\pi$
$18$	−2.71091	+	1.28490i	−0.638967	+	0.302854i
$19$	3.51361	+	2.02858i	0.806078	+	0.465389i	0.845592	−	0.533830i	$-0.179248\pi$
$19$	3.51361	+	2.02858i	0.806078	+	0.465389i	−0.0395143	+	0.999219i	$0.512581\pi$
$20$	2.14723	+	3.71911i	0.480135	+	0.831618i
$21$	−2.96905	−	3.49067i	−0.647900	−	0.761726i
$22$	0.542991	+	0.940488i	0.115766	+	0.200513i
$23$			7.63945i			1.59293i	0.604682	+	0.796467i	$0.293300\pi$
$23$			7.63945i			1.59293i	−0.604682	+	0.796467i	$0.706700\pi$
$24$	−1.46371	−	0.926039i	−0.298779	−	0.189027i
$25$	−6.72118	+	11.6414i	−1.34424	+	2.32829i
$26$	2.62151	−	2.47541i	0.514121	−	0.485468i
$27$	5.15786	+	0.629682i	0.992630	+	0.121182i
$28$	0.786623	−	2.52611i	0.148658	−	0.477390i
$29$	−1.84864	−	1.06731i	−0.343283	−	0.198195i	0.318440	−	0.947943i	$-0.396841\pi$
$29$	−1.84864	−	1.06731i	−0.343283	−	0.198195i	−0.661723	+	0.749748i	$0.730174\pi$
$30$	0.301118	−	7.43212i	0.0549764	−	1.35691i
$31$	−1.04968	−	0.606034i	−0.188528	−	0.108847i	0.402765	−	0.915303i	$-0.368049\pi$
$31$	−1.04968	−	0.606034i	−0.188528	−	0.108847i	−0.591293	+	0.806457i	$0.701382\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.0761468	−	1.87943i	0.0132555	−	0.327168i
$34$		−	3.91616i		−	0.671616i
$35$	11.0839	−	2.49860i	1.87353	−	0.422340i
$36$	1.28490	+	2.71091i	0.214150	+	0.451818i
$37$	−6.07856			−0.999309			−0.499654	−	0.866225i	$-0.666540\pi$
$37$	−6.07856			−0.999309			−0.499654	+	0.866225i	$0.666540\pi$
$38$	2.02858	−	3.51361i	0.329080	−	0.569983i
$39$	−6.12947	+	1.19566i	−0.981500	+	0.191460i
$40$	3.71911	−	2.14723i	0.588043	−	0.339507i
$41$	1.00855	−	1.74686i	0.157509	−	0.272814i	−0.776461	−	0.630166i	$-0.782987\pi$
$41$	1.00855	−	1.74686i	0.157509	−	0.272814i	0.933970	+	0.357352i	$0.116320\pi$
$42$	−3.49067	+	2.96905i	−0.538621	+	0.458134i
$43$	1.69618	+	2.93788i	0.258666	+	0.448022i	0.965885	−	0.258972i	$-0.0833838\pi$
$43$	1.69618	+	2.93788i	0.258666	+	0.448022i	−0.707219	+	0.706995i	$0.750051\pi$
$44$	0.940488	−	0.542991i	0.141784	−	0.0818590i
$45$	−7.32319	+	10.5996i	−1.09168	+	1.58010i
$46$	7.63945			1.12637
$47$	4.97996	+	8.62555i	0.726402	+	1.25817i	0.958394	+	0.285448i	$0.0921424\pi$
$47$	4.97996	+	8.62555i	0.726402	+	1.25817i	−0.231992	+	0.972718i	$0.574524\pi$
$48$	−0.926039	+	1.46371i	−0.133662	+	0.211269i
$49$	−5.76245	−	3.97419i	−0.823207	−	0.567742i
$50$	11.6414	+	6.72118i	1.64635	+	0.950519i
$51$	−3.62652	+	5.73213i	−0.507814	+	0.802658i
$52$	−2.47541	−	2.62151i	−0.343278	−	0.363539i
$53$	2.81574	+	1.62567i	0.386772	+	0.223303i	0.680761	−	0.732506i	$-0.261649\pi$
$53$	2.81574	+	1.62567i	0.386772	+	0.223303i	−0.293989	+	0.955809i	$0.594983\pi$
$54$	0.629682	−	5.15786i	0.0856889	−	0.701896i
$55$	4.03889	+	2.33185i	0.544603	+	0.314427i
$56$	−2.52611	−	0.786623i	−0.337565	−	0.105117i
$57$	−6.22300	+	3.26436i	−0.824257	+	0.432375i
$58$	−1.06731	+	1.84864i	−0.140145	+	0.242738i
$59$	−1.64474			−0.214127			−0.107064	−	0.994252i	$-0.534145\pi$
$59$	−1.64474			−0.214127			−0.107064	+	0.994252i	$0.534145\pi$
$60$	−7.43212	−	0.301118i	−0.959483	−	0.0388742i
$61$	12.0708	+	6.96907i	1.54551	+	0.892298i	0.998476	+	0.0551850i	$0.0175749\pi$
$61$	12.0708	+	6.96907i	1.54551	+	0.892298i	0.547030	+	0.837113i	$0.315758\pi$
$62$	−0.606034	+	1.04968i	−0.0769664	+	0.133310i
$63$	7.85878	−	1.11334i	0.990114	−	0.140267i
$64$	−1.00000			−0.125000
$65$	4.43442	−	14.8353i	0.550022	−	1.84009i
$66$	−1.87943	−	0.0761468i	−0.231342	−	0.00937302i
$67$	−4.01884	−	6.96084i	−0.490980	−	0.850402i	0.508966	−	0.860787i	$-0.330028\pi$
$67$	−4.01884	−	6.96084i	−0.490980	−	0.850402i	−0.999946	+	0.0103844i	$0.996694\pi$
$68$	−3.91616			−0.474904
$69$	−11.1819	−	7.07443i	−1.34615	−	0.851661i
$70$	−2.49860	−	11.0839i	−0.298639	−	1.32478i
$71$	−2.68997	+	1.55305i	−0.319241	+	0.184314i	−0.651054	−	0.759031i	$-0.725673\pi$
$71$	−2.68997	+	1.55305i	−0.319241	+	0.184314i	0.331813	+	0.943345i	$0.392340\pi$
$72$	2.71091	−	1.28490i	0.319484	−	0.151427i
$73$	3.86528	+	2.23162i	0.452397	+	0.261191i	0.708842	−	0.705367i	$-0.249218\pi$
$73$	3.86528	+	2.23162i	0.452397	+	0.261191i	−0.256445	+	0.966559i	$0.582551\pi$
$74$			6.07856i			0.706618i
$75$	−10.8156	−	20.6183i	−1.24888	−	2.38080i
$76$	−3.51361	−	2.02858i	−0.403039	−	0.232695i
$77$	−0.631845	−	2.80290i	−0.0720054	−	0.319421i
$78$	1.19566	+	6.12947i	0.135382	+	0.694026i
$79$	2.33626	+	4.04652i	0.262850	+	0.455269i	0.966998	−	0.254784i	$-0.0820043\pi$
$79$	2.33626	+	4.04652i	0.262850	+	0.455269i	−0.704148	+	0.710053i	$0.748671\pi$
$80$	−2.14723	−	3.71911i	−0.240067	−	0.415809i
$81$	−5.69805	+	6.96651i	−0.633117	+	0.774056i
$82$	−1.74686	−	1.00855i	−0.192908	−	0.111376i
$83$	−4.52632			−0.496828			−0.248414	−	0.968654i	$-0.579909\pi$
$83$	−4.52632			−0.496828			−0.248414	+	0.968654i	$0.579909\pi$
$84$	2.96905	+	3.49067i	0.323950	+	0.380863i
$85$	−8.40889	−	14.5646i	−0.912072	−	1.57976i
$86$	2.93788	−	1.69618i	0.316800	−	0.182904i
$87$	3.27414	−	1.71750i	0.351025	−	0.184135i
$88$	−0.542991	−	0.940488i	−0.0578831	−	0.100256i
$89$	−16.9794			−1.79981			−0.899905	−	0.436086i	$-0.856364\pi$
$89$	−16.9794			−1.79981			−0.899905	+	0.436086i	$0.856364\pi$
$90$	10.5996	+	7.32319i	1.11730	+	0.771932i
$91$	−8.56944	+	4.19102i	−0.898322	+	0.439338i
$92$		−	7.63945i		−	0.796467i
$93$	1.85910	−	0.975219i	0.192780	−	0.101126i
$94$	8.62555	−	4.97996i	0.889658	−	0.513644i
$95$		−	17.4233i		−	1.78760i
$96$	1.46371	+	0.926039i	0.149389	+	0.0945135i
$97$	10.7814	−	6.22463i	1.09468	−	0.632015i	0.159863	−	0.987139i	$-0.448895\pi$
$97$	10.7814	−	6.22463i	1.09468	−	0.632015i	0.934819	+	0.355124i	$0.115561\pi$
$98$	−3.97419	+	5.76245i	−0.401454	+	0.582095i
$99$	2.68043	+	1.85189i	0.269394	+	0.186122i
$100$	6.72118	−	11.6414i	0.672118	−	1.16414i
$101$	2.60428	+	4.51075i	0.259136	+	0.448837i	0.966011	−	0.258502i	$-0.0832289\pi$
$101$	2.60428	+	4.51075i	0.259136	+	0.448837i	−0.706875	+	0.707339i	$0.749896\pi$
$102$	5.73213	+	3.62652i	0.567565	+	0.359079i
$103$	−5.74356	+	3.31605i	−0.565930	+	0.326740i	−0.755522	−	0.655123i	$-0.772617\pi$
$103$	−5.74356	+	3.31605i	−0.565930	+	0.326740i	0.189592	+	0.981863i	$0.439283\pi$
$104$	−2.62151	+	2.47541i	−0.257061	+	0.242734i
$105$	−6.60694	+	18.5375i	−0.644771	+	1.80907i
$106$	1.62567	−	2.81574i	0.157899	−	0.273489i
$107$		−	5.60143i		−	0.541511i	−0.962648	−	0.270755i	$-0.912727\pi$
$107$		−	5.60143i		−	0.541511i	0.962648	−	0.270755i	$-0.0872734\pi$
$108$	−5.15786	−	0.629682i	−0.496315	−	0.0605912i
$109$	6.04035	−	10.4622i	0.578561	−	1.00210i	−0.417084	−	0.908868i	$-0.636948\pi$
$109$	6.04035	−	10.4622i	0.578561	−	1.00210i	0.995645	−	0.0932289i	$-0.0297188\pi$
$110$	2.33185	−	4.03889i	0.222333	−	0.385093i
$111$	5.62898	−	8.89726i	0.534280	−	0.844490i
$112$	−0.786623	+	2.52611i	−0.0743289	+	0.238695i
$113$	−11.8295	+	6.82976i	−1.11283	+	0.642490i	−0.939560	−	0.342385i	$-0.888765\pi$
$113$	−11.8295	+	6.82976i	−1.11283	+	0.642490i	−0.173266	+	0.984875i	$0.555432\pi$
$114$	3.26436	+	6.22300i	0.305736	+	0.582838i
$115$	28.4119	−	16.4036i	2.64943	−	1.52965i
$116$	1.84864	+	1.06731i	0.171642	+	0.0990973i
$117$	3.92602	−	10.0790i	0.362961	−	0.931804i
$118$			1.64474i			0.151411i
$119$	−3.08054	+	9.89264i	−0.282393	+	0.906857i
$120$	−0.301118	+	7.43212i	−0.0274882	+	0.678457i
$121$	−4.91032	+	8.50493i	−0.446393	+	0.773175i
$122$	6.96907	−	12.0708i	0.630950	−	1.09284i
$123$	1.62294	+	3.09389i	0.146336	+	0.278966i
$124$	1.04968	+	0.606034i	0.0942642	+	0.0544234i
$125$	36.2554			3.24278
$126$	−1.11334	−	7.85878i	−0.0991841	−	0.700116i
$127$	−8.72940	+	15.1198i	−0.774609	+	1.34166i	0.160405	+	0.987051i	$0.448720\pi$
$127$	−8.72940	+	15.1198i	−0.774609	+	1.34166i	−0.935014	+	0.354611i	$0.884613\pi$
$128$			1.00000i			0.0883883i
$129$	−5.87094	−	0.237866i	−0.516907	−	0.0209429i
$130$	−14.8353	−	4.43442i	−1.30114	−	0.388924i
$131$	−4.80013	−	8.31407i	−0.419389	−	0.726404i	0.576489	−	0.817105i	$-0.304422\pi$
$131$	−4.80013	−	8.31407i	−0.419389	−	0.726404i	−0.995878	+	0.0907014i	$0.971089\pi$
$132$	−0.0761468	+	1.87943i	−0.00662773	+	0.163584i
$133$	−7.88831	+	7.28003i	−0.684003	+	0.631259i
$134$	−6.96084	+	4.01884i	−0.601325	+	0.347175i
$135$	−8.73324	−	20.5347i	−0.751638	−	1.76735i
$136$			3.91616i			0.335808i
$137$			0.976331i			0.0834136i	0.999130	+	0.0417068i	$0.0132795\pi$
$137$			0.976331i			0.0834136i	−0.999130	+	0.0417068i	$0.986720\pi$
$138$	−7.07443	+	11.1819i	−0.602215	+	0.951870i
$139$	−4.16317	+	2.40361i	−0.353116	+	0.203871i	−0.666057	−	0.745901i	$-0.732019\pi$
$139$	−4.16317	+	2.40361i	−0.353116	+	0.203871i	0.312941	+	0.949773i	$0.398686\pi$
$140$	−11.0839	+	2.49860i	−0.936763	+	0.211170i
$141$	−17.2370	−	0.698369i	−1.45161	−	0.0588133i
$142$	1.55305	+	2.68997i	0.130329	+	0.225737i
$143$	−3.75156	−	1.12138i	−0.313721	−	0.0937741i
$144$	−1.28490	−	2.71091i	−0.107075	−	0.225909i
$145$			9.16704i			0.761281i
$146$	2.23162	−	3.86528i	0.184690	−	0.319893i
$147$	11.1533	−	4.75430i	0.919911	−	0.392128i
$148$	6.07856			0.499654
$149$	3.63236	+	2.09714i	0.297574	+	0.171805i	0.641353	−	0.767246i	$-0.278374\pi$
$149$	3.63236	+	2.09714i	0.297574	+	0.171805i	−0.343778	+	0.939051i	$0.611707\pi$
$150$	−20.6183	+	10.8156i	−1.68348	+	0.883091i
$151$	−4.52705	+	7.84109i	−0.368406	+	0.638099i	−0.989317	−	0.145783i	$-0.953430\pi$
$151$	−4.52705	+	7.84109i	−0.368406	+	0.638099i	0.620910	+	0.783882i	$0.286763\pi$
$152$	−2.02858	+	3.51361i	−0.164540	+	0.284991i
$153$	−5.03188	−	10.6163i	−0.406803	−	0.858281i
$154$	−2.80290	+	0.631845i	−0.225865	+	0.0509155i
$155$			5.20517i			0.418089i
$156$	6.12947	−	1.19566i	0.490750	−	0.0957298i
$157$	5.51607	+	3.18471i	0.440230	+	0.254167i	0.703695	−	0.710502i	$-0.251532\pi$
$157$	5.51607	+	3.18471i	0.440230	+	0.254167i	−0.263465	+	0.964669i	$0.584865\pi$
$158$	4.04652	−	2.33626i	0.321924	−	0.185863i
$159$	−4.98700	+	2.61600i	−0.395495	+	0.207462i
$160$	−3.71911	+	2.14723i	−0.294021	+	0.169753i
$161$	−19.2981	−	6.00936i	−1.52090	−	0.473604i
$162$	6.96651	+	5.69805i	0.547340	+	0.447681i
$163$	1.32733	−	2.29900i	0.103964	−	0.180072i	−0.809350	−	0.587326i	$-0.800181\pi$
$163$	1.32733	−	2.29900i	0.103964	−	0.180072i	0.913315	+	0.407255i	$0.133514\pi$
$164$	−1.00855	+	1.74686i	−0.0787545	+	0.136407i
$165$	−7.15333	+	3.75238i	−0.556886	+	0.292122i
$166$			4.52632i			0.351310i
$167$	12.3076	−	21.3175i	0.952394	−	1.64959i	0.212172	−	0.977232i	$-0.431946\pi$
$167$	12.3076	−	21.3175i	0.952394	−	1.64959i	0.740222	−	0.672363i	$-0.234720\pi$
$168$	3.49067	−	2.96905i	0.269311	−	0.229067i
$169$	−0.744666	+	12.9787i	−0.0572820	+	0.998358i
$170$	−14.5646	+	8.40889i	−1.11706	+	0.644932i
$171$	0.984660	−	12.1316i	0.0752989	−	0.927727i
$172$	−1.69618	−	2.93788i	−0.129333	−	0.224011i
$173$	−5.66350	+	9.80947i	−0.430588	+	0.745800i	−0.996924	−	0.0783743i	$-0.975027\pi$
$173$	−5.66350	+	9.80947i	−0.430588	+	0.745800i	0.566336	+	0.824174i	$0.308360\pi$
$174$	−1.71750	−	3.27414i	−0.130203	−	0.248212i
$175$	−24.1205	−	26.1359i	−1.82334	−	1.97568i
$176$	−0.940488	+	0.542991i	−0.0708920	+	0.0409295i
$177$	1.52310	−	2.40743i	0.114483	−	0.180953i
$178$			16.9794i			1.27266i
$179$	−3.60503	+	2.08136i	−0.269453	+	0.155569i	−0.628639	−	0.777697i	$-0.716388\pi$
$179$	−3.60503	+	2.08136i	−0.269453	+	0.155569i	0.359186	+	0.933266i	$0.383054\pi$
$180$	7.32319	−	10.5996i	0.545838	−	0.790050i
$181$			15.2174i			1.13110i	0.824715	+	0.565549i	$0.191336\pi$
$181$			15.2174i			1.13110i	−0.824715	+	0.565549i	$0.808664\pi$
$182$	4.19102	+	8.56944i	0.310659	+	0.635209i
$183$	−21.3787	+	11.2145i	−1.58036	+	0.829001i
$184$	−7.63945			−0.563187
$185$	13.0521	+	22.6068i	0.959606	+	1.66209i
$186$	−0.975219	−	1.85910i	−0.0715065	−	0.136316i
$187$	−3.68310	+	2.12644i	−0.269335	+	0.155501i
$188$	−4.97996	−	8.62555i	−0.363201	−	0.629083i
$189$	−5.64794	+	12.5340i	−0.410827	+	0.911713i
$190$	−17.4233			−1.26402
$191$	2.54594	+	1.46990i	0.184218	+	0.106358i	0.589273	−	0.807934i	$-0.299414\pi$
$191$	2.54594	+	1.46990i	0.184218	+	0.106358i	−0.405055	+	0.914292i	$0.632748\pi$
$192$	0.926039	−	1.46371i	0.0668311	−	0.105634i
$193$	0.237608	+	0.411549i	0.0171034	+	0.0296240i	0.874450	−	0.485115i	$-0.161222\pi$
$193$	0.237608	+	0.411549i	0.0171034	+	0.0296240i	−0.857347	+	0.514739i	$0.827889\pi$
$194$	−6.22463	−	10.7814i	−0.446902	−	0.774057i
$195$	17.6082	+	20.2288i	1.26095	+	1.44861i
$196$	5.76245	+	3.97419i	0.411603	+	0.283871i
$197$	15.1888	+	8.76926i	1.08216	+	0.624784i	0.931478	−	0.363799i	$-0.118520\pi$
$197$	15.1888	+	8.76926i	1.08216	+	0.624784i	0.150680	+	0.988583i	$0.451854\pi$
$198$	1.85189	−	2.68043i	0.131608	−	0.190490i
$199$		−	0.745911i		−	0.0528762i	−0.999650	−	0.0264381i	$-0.991584\pi$
$199$		−	0.745911i		−	0.0528762i	0.999650	−	0.0264381i	$-0.00841649\pi$
$200$	−11.6414	−	6.72118i	−0.823173	−	0.475259i
$201$	13.9103	+	0.563586i	0.981155	+	0.0397523i
$202$	4.51075	−	2.60428i	0.317375	−	0.183237i
$203$	4.15032	−	3.83028i	0.291296	−	0.268833i
$204$	3.62652	−	5.73213i	0.253907	−	0.401329i
$205$	−8.66235			−0.605005
$206$	3.31605	+	5.74356i	0.231040	+	0.400173i
$207$	20.7098	−	9.81594i	1.43943	−	0.682255i
$208$	2.47541	+	2.62151i	0.171639	+	0.181769i
$209$	−4.40601			−0.304770
$210$	18.5375	+	6.60694i	1.27921	+	0.455922i
$211$	8.40841	−	14.5638i	0.578859	−	1.00261i	−0.416751	−	0.909020i	$-0.636831\pi$
$211$	8.40841	−	14.5638i	0.578859	−	1.00261i	0.995611	−	0.0935929i	$-0.0298352\pi$
$212$	−2.81574	−	1.62567i	−0.193386	−	0.111651i
$213$	0.217794	−	5.37553i	0.0149230	−	0.368325i
$214$	−5.60143			−0.382906
$215$	7.28419	−	12.6166i	0.496778	−	0.860444i
$216$	−0.629682	+	5.15786i	−0.0428445	+	0.350948i
$217$	2.35661	−	2.17489i	0.159977	−	0.147641i
$218$	−10.4622	−	6.04035i	−0.708590	−	0.409104i
$219$	−6.84585	+	3.59109i	−0.462600	+	0.242663i
$220$	−4.03889	−	2.33185i	−0.272302	−	0.157213i
$221$	9.69411	+	10.2663i	0.652096	+	0.690584i
$222$	−8.89726	−	5.62898i	−0.597145	−	0.377793i
$223$	19.8957	+	11.4868i	1.33232	+	0.769213i	0.985654	−	0.168777i	$-0.0539819\pi$
$223$	19.8957	+	11.4868i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$224$	2.52611	+	0.786623i	0.168783	+	0.0525585i
$225$	40.1949	+	3.26241i	2.67966	+	0.217494i
$226$	6.82976	+	11.8295i	0.454309	+	0.786886i
$227$	−9.58859			−0.636417			−0.318208	−	0.948021i	$-0.603081\pi$
$227$	−9.58859			−0.636417			−0.318208	+	0.948021i	$0.603081\pi$
$228$	6.22300	−	3.26436i	0.412128	−	0.216188i
$229$	5.98689	−	3.45653i	0.395625	−	0.228414i	−0.288970	−	0.957338i	$-0.593313\pi$
$229$	5.98689	−	3.45653i	0.395625	−	0.228414i	0.684594	+	0.728924i	$0.259979\pi$
$230$	−16.4036	−	28.4119i	−1.08162	−	1.87343i
$231$	4.68776	+	1.67076i	0.308432	+	0.109928i
$232$	1.06731	−	1.84864i	0.0700724	−	0.121369i
$233$	13.8432	−	7.99238i	0.906899	−	0.523599i	0.0274670	−	0.999623i	$-0.491256\pi$
$233$	13.8432	−	7.99238i	0.906899	−	0.523599i	0.879432	+	0.476024i	$0.157923\pi$
$234$	−10.0790	−	3.92602i	−0.658885	−	0.256652i
$235$	21.3862	−	37.0421i	1.39508	−	2.41636i
$236$	1.64474			0.107064
$237$	−8.08641	−	0.327627i	−0.525268	−	0.0212817i
$238$	9.89264	+	3.08054i	0.641245	+	0.199682i
$239$			15.7358i			1.01786i	0.860807	+	0.508931i	$0.169959\pi$
$239$			15.7358i			1.01786i	−0.860807	+	0.508931i	$0.830041\pi$
$240$	7.43212	+	0.301118i	0.479741	+	0.0194371i
$241$		−	18.3268i		−	1.18054i	−0.807208	−	0.590268i	$-0.799022\pi$
$241$		−	18.3268i		−	1.18054i	0.807208	−	0.590268i	$-0.200978\pi$
$242$	8.50493	+	4.91032i	0.546717	+	0.315647i
$243$	−4.92033	−	14.7916i	−0.315639	−	0.948879i
$244$	−12.0708	−	6.96907i	−0.772753	−	0.446149i
$245$	−2.40716	+	29.9647i	−0.153788	+	1.91437i
$246$	3.09389	−	1.62294i	0.197259	−	0.103475i
$247$	3.37968	+	14.2326i	0.215044	+	0.905596i
$248$	0.606034	−	1.04968i	0.0384832	−	0.0666548i
$249$	4.19155	−	6.62522i	0.265629	−	0.419857i
$250$		−	36.2554i		−	2.29299i
$251$	4.55211	+	7.88449i	0.287327	+	0.497665i	0.973171	−	0.230084i	$-0.0739001\pi$
$251$	4.55211	+	7.88449i	0.287327	+	0.497665i	−0.685844	+	0.727749i	$0.740567\pi$
$252$	−7.85878	+	1.11334i	−0.495057	+	0.0701337i
$253$	−4.14815	−	7.18481i	−0.260792	−	0.451705i
$254$	15.1198	+	8.72940i	0.948698	+	0.547731i
$255$	29.1054	+	1.17923i	1.82265	+	0.0738461i
$256$	1.00000			0.0625000
$257$	−8.94770			−0.558142			−0.279071	−	0.960270i	$-0.590027\pi$
$257$	−8.94770			−0.558142			−0.279071	+	0.960270i	$0.590027\pi$
$258$	−0.237866	+	5.87094i	−0.0148089	+	0.365509i
$259$	4.78153	−	15.3551i	0.297110	−	0.954119i
$260$	−4.43442	+	14.8353i	−0.275011	+	0.920047i
$261$	−0.518065	+	6.38287i	−0.0320674	+	0.395090i
$262$	−8.31407	+	4.80013i	−0.513645	+	0.296553i
$263$	−18.4030	+	10.6250i	−1.13478	+	0.655164i	−0.945132	−	0.326689i	$-0.894067\pi$
$263$	−18.4030	+	10.6250i	−1.13478	+	0.655164i	−0.189645	+	0.981853i	$0.560734\pi$
$264$	1.87943	+	0.0761468i	0.115671	+	0.00468651i
$265$		−	13.9627i		−	0.857724i
$266$	7.28003	+	7.88831i	0.446367	+	0.483663i
$267$	15.7236	−	24.8529i	0.962267	−	1.52097i
$268$	4.01884	+	6.96084i	0.245490	+	0.425201i
$269$	9.11399			0.555690			0.277845	−	0.960626i	$-0.410380\pi$
$269$	9.11399			0.555690			0.277845	+	0.960626i	$0.410380\pi$
$270$	−20.5347	+	8.73324i	−1.24970	+	0.531488i
$271$			23.7919i			1.44525i	0.691238	+	0.722627i	$0.257066\pi$
$271$			23.7919i			1.44525i	−0.691238	+	0.722627i	$0.742934\pi$
$272$	3.91616			0.237452
$273$	1.80120	−	16.4242i	0.109014	−	0.994040i
$274$	0.976331			0.0589823
$275$		−	14.5982i		−	0.880303i
$276$	11.1819	+	7.07443i	0.673074	+	0.425830i
$277$	16.0852			0.966468			0.483234	−	0.875491i	$-0.339462\pi$
$277$	16.0852			0.966468			0.483234	+	0.875491i	$0.339462\pi$
$278$	2.40361	+	4.16317i	0.144159	+	0.249690i
$279$	−0.294164	+	3.62428i	−0.0176112	+	0.216980i
$280$	2.49860	+	11.0839i	0.149320	+	0.662392i
$281$			4.07708i			0.243218i	0.992578	+	0.121609i	$0.0388055\pi$
$281$			4.07708i			0.243218i	−0.992578	+	0.121609i	$0.961195\pi$
$282$	−0.698369	+	17.2370i	−0.0415873	+	1.02645i
$283$	8.06035	−	4.65364i	0.479138	−	0.276630i	−0.240919	−	0.970545i	$-0.577449\pi$
$283$	8.06035	−	4.65364i	0.479138	−	0.276630i	0.720057	+	0.693915i	$0.244116\pi$
$284$	2.68997	−	1.55305i	0.159620	−	0.0921568i
$285$	25.5027	+	16.1347i	1.51065	+	0.955737i
$286$	−1.12138	+	3.75156i	−0.0663083	+	0.221834i
$287$	3.61941	+	3.92183i	0.213647	+	0.231498i
$288$	−2.71091	+	1.28490i	−0.159742	+	0.0757136i
$289$	−1.66370			−0.0978647
$290$	9.16704			0.538307
$291$	−0.872916	+	21.5451i	−0.0511712	+	1.26299i
$292$	−3.86528	−	2.23162i	−0.226198	−	0.130596i
$293$	−5.17715	−	8.96708i	−0.302452	−	0.523862i	0.674239	−	0.738513i	$-0.264472\pi$
$293$	−5.17715	−	8.96708i	−0.302452	−	0.523862i	−0.976691	+	0.214651i	$0.931139\pi$
$294$	−4.75430	−	11.1533i	−0.277277	−	0.650475i
$295$	3.53164	+	6.11698i	0.205620	+	0.356144i
$296$		−	6.07856i		−	0.353309i
$297$	−5.19282	+	2.20846i	−0.301318	+	0.128148i
$298$	2.09714	−	3.63236i	0.121484	−	0.210417i
$299$	−20.0269	+	18.9108i	−1.15819	+	1.09364i
$300$	10.8156	+	20.6183i	0.624440	+	1.19040i
$301$	−8.75566	+	1.97374i	−0.504668	+	0.113765i
$302$	7.84109	+	4.52705i	0.451204	+	0.260503i
$303$	−9.01411	−	0.365214i	−0.517847	−	0.0209810i
$304$	3.51361	+	2.02858i	0.201519	+	0.116347i
$305$		−	59.8568i		−	3.42739i
$306$	−10.6163	+	5.03188i	−0.606896	+	0.287653i
$307$		−	3.63183i		−	0.207280i	−0.994615	−	0.103640i	$-0.966951\pi$
$307$		−	3.63183i		−	0.207280i	0.994615	−	0.103640i	$-0.0330489\pi$
$308$	0.631845	+	2.80290i	0.0360027	+	0.159710i
$309$	0.465029	−	11.4777i	0.0264546	−	0.652944i
$310$	5.20517			0.295634
$311$	7.55359	−	13.0832i	0.428325	−	0.741881i	−0.568400	−	0.822753i	$-0.692437\pi$
$311$	7.55359	−	13.0832i	0.428325	−	0.741881i	0.996724	+	0.0808721i	$0.0257705\pi$
$312$	−1.19566	−	6.12947i	−0.0676912	−	0.347013i
$313$	−21.7519	+	12.5585i	−1.22949	+	0.709848i	−0.966924	−	0.255066i	$-0.917903\pi$
$313$	−21.7519	+	12.5585i	−1.22949	+	0.709848i	−0.262568	+	0.964913i	$0.584569\pi$
$314$	3.18471	−	5.51607i	0.179723	−	0.311290i
$315$	−21.0152	−	26.8371i	−1.18407	−	1.51210i
$316$	−2.33626	−	4.04652i	−0.131425	−	0.227635i
$317$	−9.48911	+	5.47854i	−0.532962	+	0.307706i	−0.742222	−	0.670154i	$-0.766228\pi$
$317$	−9.48911	+	5.47854i	−0.532962	+	0.307706i	0.209260	+	0.977860i	$0.432895\pi$
$318$	2.61600	+	4.98700i	0.146698	+	0.279657i
$319$	2.31816			0.129792
$320$	2.14723	+	3.71911i	0.120034	+	0.207905i
$321$	8.19887	+	5.18714i	0.457617	+	0.289518i
$322$	−6.00936	+	19.2981i	−0.334889	+	1.07544i
$323$	13.7599	+	7.94426i	0.765619	+	0.442030i
$324$	5.69805	−	6.96651i	0.316558	−	0.387028i
$325$	−47.1559	+	11.1977i	−2.61574	+	0.621135i
$326$	−2.29900	−	1.32733i	−0.127330	−	0.0735140i
$327$	9.72004	+	18.5297i	0.537519	+	1.02470i
$328$	1.74686	+	1.00855i	0.0964542	+	0.0556879i
$329$	−25.7064	+	5.79487i	−1.41724	+	0.319482i
$330$	3.75238	+	7.15333i	0.206562	+	0.393778i
$331$	−2.50688	+	4.34205i	−0.137791	+	0.238660i	−0.926660	−	0.375900i	$-0.877333\pi$
$331$	−2.50688	+	4.34205i	−0.137791	+	0.238660i	0.788869	+	0.614561i	$0.210667\pi$
$332$	4.52632			0.248414
$333$	7.81035	+	16.4784i	0.428005	+	0.903012i
$334$	−21.3175	−	12.3076i	−1.16644	−	0.673444i
$335$	−17.2588	+	29.8930i	−0.942946	+	1.63323i
$336$	−2.96905	−	3.49067i	−0.161975	−	0.190431i
$337$	27.4419			1.49486			0.747428	−	0.664343i	$-0.231288\pi$
$337$	27.4419			1.49486			0.747428	+	0.664343i	$0.231288\pi$
$338$	12.9787	+	0.744666i	0.705946	+	0.0405045i
$339$	0.957777	−	23.6396i	0.0520193	−	1.28393i
$340$	8.40889	+	14.5646i	0.456036	+	0.789878i
$341$	1.31628			0.0712808
$342$	−12.1316	−	0.984660i	−0.656002	−	0.0532443i
$343$	14.5721	−	11.4304i	0.786820	−	0.617182i
$344$	−2.93788	+	1.69618i	−0.158400	+	0.0914522i
$345$	−2.30038	+	56.7773i	−0.123848	+	3.05679i
$346$	9.80947	+	5.66350i	0.527360	+	0.304472i
$347$		−	29.3039i		−	1.57312i	−0.617517	−	0.786558i	$-0.711861\pi$
$347$		−	29.3039i		−	1.57312i	0.617517	−	0.786558i	$-0.288139\pi$
$348$	−3.27414	+	1.71750i	−0.175513	+	0.0920676i
$349$	−20.5600	−	11.8703i	−1.10055	−	0.635402i	−0.164184	−	0.986430i	$-0.552499\pi$
$349$	−20.5600	−	11.8703i	−1.10055	−	0.635402i	−0.936365	+	0.351027i	$0.885832\pi$
$350$	−26.1359	+	24.1205i	−1.39702	+	1.28929i
$351$	11.1171	+	15.0801i	0.593387	+	0.804917i
$352$	0.542991	+	0.940488i	0.0289415	+	0.0501282i
$353$	−3.80125	−	6.58396i	−0.202320	−	0.350429i	0.746955	−	0.664874i	$-0.231515\pi$
$353$	−3.80125	−	6.58396i	−0.202320	−	0.350429i	−0.949276	+	0.314445i	$0.898181\pi$
$354$	−2.40743	−	1.52310i	−0.127953	−	0.0809517i
$355$	11.5520	+	6.66953i	0.613114	+	0.353982i
$356$	16.9794			0.899905
$357$	−11.6273	−	13.6700i	−0.615380	−	0.723493i
$358$	2.08136	+	3.60503i	0.110004	+	0.190532i
$359$	−19.1204	+	11.0392i	−1.00914	+	0.582626i	−0.910939	−	0.412541i	$-0.864641\pi$
$359$	−19.1204	+	11.0392i	−1.00914	+	0.582626i	−0.0981985	+	0.995167i	$0.531308\pi$
$360$	−10.5996	−	7.32319i	−0.558650	−	0.385966i
$361$	−1.26969	−	2.19917i	−0.0668259	−	0.115746i
$362$	15.2174			0.799806
$363$	−7.90161	−	15.0632i	−0.414727	−	0.790612i
$364$	8.56944	−	4.19102i	0.449161	−	0.219669i
$365$		−	19.1672i		−	1.00326i
$366$	11.2145	+	21.3787i	0.586192	+	1.11748i
$367$	−6.23889	+	3.60202i	−0.325667	+	0.188024i	−0.653916	−	0.756567i	$-0.726875\pi$
$367$	−6.23889	+	3.60202i	−0.325667	+	0.188024i	0.328249	+	0.944591i	$0.393542\pi$
$368$			7.63945i			0.398234i
$369$	−6.03147	−	0.489543i	−0.313986	−	0.0254846i
$370$	22.6068	−	13.0521i	1.17527	−	0.678544i
$371$	−6.32155	+	5.83408i	−0.328198	+	0.302890i
$372$	−1.85910	+	0.975219i	−0.0963901	+	0.0505628i
$373$	13.3345	−	23.0960i	0.690432	−	1.19586i	−0.281264	−	0.959630i	$-0.590754\pi$
$373$	13.3345	−	23.0960i	0.690432	−	1.19586i	0.971696	−	0.236233i	$-0.0759130\pi$
$374$	2.12644	+	3.68310i	0.109956	+	0.190449i
$375$	−33.5739	+	53.0674i	−1.73375	+	2.74039i
$376$	−8.62555	+	4.97996i	−0.444829	+	0.256822i
$377$	−1.77817	−	7.48826i	−0.0915803	−	0.385665i
$378$	12.5340	+	5.64794i	0.644679	+	0.290498i
$379$	−9.47287	+	16.4075i	−0.486589	+	0.842796i	−0.999881	−	0.0154174i	$-0.995092\pi$
$379$	−9.47287	+	16.4075i	−0.486589	+	0.842796i	0.513292	+	0.858214i	$0.328426\pi$
$380$			17.4233i			0.893798i
$381$	−14.0472	−	26.7788i	−0.719660	−	1.37192i
$382$	1.46990	−	2.54594i	0.0752067	−	0.130262i
$383$	14.9555	−	25.9036i	0.764188	−	1.32361i	−0.176487	−	0.984303i	$-0.556473\pi$
$383$	14.9555	−	25.9036i	0.764188	−	1.32361i	0.940675	−	0.339309i	$-0.110193\pi$
$384$	−1.46371	−	0.926039i	−0.0746947	−	0.0472567i
$385$	−9.06759	+	8.36838i	−0.462127	+	0.426492i
$386$	0.411549	−	0.237608i	0.0209473	−	0.0120939i
$387$	5.78489	−	8.37309i	0.294062	−	0.425628i
$388$	−10.7814	+	6.22463i	−0.547341	+	0.316008i
$389$	0.821075	+	0.474048i	0.0416301	+	0.0240352i	0.520671	−	0.853758i	$-0.325682\pi$
$389$	0.821075	+	0.474048i	0.0416301	+	0.0240352i	−0.479040	+	0.877793i	$0.659015\pi$
$390$	20.2288	−	17.6082i	1.02432	−	0.891625i
$391$			29.9173i			1.51298i
$392$	3.97419	−	5.76245i	0.200727	−	0.291048i
$393$	16.6145	+	0.673150i	0.838091	+	0.0339559i
$394$	8.76926	−	15.1888i	0.441789	−	0.765201i
$395$	10.0330	−	17.3776i	0.504813	−	0.874362i
$396$	−2.68043	−	1.85189i	−0.134697	−	0.0930608i
$397$	−12.1023	−	6.98728i	−0.607399	−	0.350682i	0.164548	−	0.986369i	$-0.447383\pi$
$397$	−12.1023	−	6.98728i	−0.607399	−	0.350682i	−0.771947	+	0.635687i	$0.780717\pi$
$398$	−0.745911			−0.0373891
$399$	−3.35098	−	18.2878i	−0.167759	−	0.915535i
$400$	−6.72118	+	11.6414i	−0.336059	+	0.582071i
$401$		−	37.3418i		−	1.86476i	−0.361476	−	0.932381i	$-0.617727\pi$
$401$		−	37.3418i		−	1.86476i	0.361476	−	0.932381i	$-0.382273\pi$
$402$	0.563586	−	13.9103i	0.0281091	−	0.693781i
$403$	−1.00967	−	4.25194i	−0.0502952	−	0.211804i
$404$	−2.60428	−	4.51075i	−0.129568	−	0.224418i
$405$	38.1442	+	6.23300i	1.89540	+	0.309720i
$406$	−3.83028	−	4.15032i	−0.190094	−	0.205977i
$407$	5.71681	−	3.30060i	0.283372	−	0.163605i
$408$	−5.73213	−	3.62652i	−0.283783	−	0.179539i
$409$		−	8.10672i		−	0.400852i	−0.979709	−	0.200426i	$-0.935767\pi$
$409$		−	8.10672i		−	0.400852i	0.979709	−	0.200426i	$-0.0642326\pi$
$410$			8.66235i			0.427803i
$411$	−1.42907	−	0.904121i	−0.0704907	−	0.0445970i
$412$	5.74356	−	3.31605i	0.282965	−	0.163370i
$413$	1.29379	−	4.15480i	0.0636634	−	0.204444i
$414$	−9.81594	−	20.7098i	−0.482427	−	1.01783i
$415$	9.71904	+	16.8339i	0.477089	+	0.826342i
$416$	2.62151	−	2.47541i	0.128530	−	0.121367i
$417$	0.337072	−	8.31952i	0.0165065	−	0.407409i
$418$			4.40601i			0.215505i
$419$	−6.79325	+	11.7663i	−0.331872	+	0.574819i	−0.982879	−	0.184253i	$-0.941014\pi$
$419$	−6.79325	+	11.7663i	−0.331872	+	0.574819i	0.651007	+	0.759072i	$0.274347\pi$
$420$	6.60694	−	18.5375i	0.322385	−	0.904536i
$421$	28.4439			1.38627			0.693136	−	0.720807i	$-0.256229\pi$
$421$	28.4439			1.38627			0.693136	+	0.720807i	$0.256229\pi$
$422$	−14.5638	−	8.40841i	−0.708955	−	0.409315i
$423$	16.9843	−	24.5832i	0.825806	−	1.19528i
$424$	−1.62567	+	2.81574i	−0.0789495	+	0.136745i
$425$	−26.3212	+	45.5897i	−1.27677	+	2.21142i
$426$	−5.37553	−	0.217794i	−0.260445	−	0.0105521i
$427$	−27.0998	+	25.0101i	−1.31145	+	1.21032i
$428$			5.60143i			0.270755i
$429$	5.11546	−	4.45276i	0.246977	−	0.214981i
$430$	−12.6166	−	7.28419i	−0.608426	−	0.351275i
$431$	−10.4947	+	6.05914i	−0.505514	+	0.291859i	−0.730988	−	0.682391i	$-0.760940\pi$
$431$	−10.4947	+	6.05914i	−0.505514	+	0.291859i	0.225474	+	0.974249i	$0.427607\pi$
$432$	5.15786	+	0.629682i	0.248158	+	0.0302956i
$433$	−5.42399	+	3.13154i	−0.260661	+	0.150492i	−0.624636	−	0.780916i	$-0.714753\pi$
$433$	−5.42399	+	3.13154i	−0.260661	+	0.150492i	0.363975	+	0.931409i	$0.381419\pi$
$434$	−2.17489	−	2.35661i	−0.104398	−	0.113121i
$435$	−13.4179	−	8.48904i	−0.643339	−	0.407018i
$436$	−6.04035	+	10.4622i	−0.289280	+	0.501049i
$437$	−15.4973	+	26.8420i	−0.741334	+	1.28403i
$438$	3.59109	+	6.84585i	0.171589	+	0.327107i
$439$		−	32.8000i		−	1.56546i	−0.622363	−	0.782729i	$-0.713827\pi$
$439$		−	32.8000i		−	1.56546i	0.622363	−	0.782729i	$-0.286173\pi$
$440$	−2.33185	+	4.03889i	−0.111167	+	0.192546i
$441$	−3.36949	+	20.7279i	−0.160452	+	0.987044i
$442$	10.2663	−	9.69411i	0.488316	−	0.461102i
$443$	−15.8838	+	9.17053i	−0.754663	+	0.435705i	−0.827376	−	0.561648i	$-0.810168\pi$
$443$	−15.8838	+	9.17053i	−0.754663	+	0.435705i	0.0727133	+	0.997353i	$0.476834\pi$
$444$	−5.62898	+	8.89726i	−0.267140	+	0.422245i
$445$	36.4586	+	63.1481i	1.72830	+	2.99351i
$446$	11.4868	−	19.8957i	0.543916	−	0.942090i
$447$	−6.43332	+	3.37469i	−0.304285	+	0.159617i
$448$	0.786623	−	2.52611i	0.0371645	−	0.119347i
$449$	−14.5674	+	8.41050i	−0.687478	+	0.396916i	−0.802667	−	0.596428i	$-0.796586\pi$
$449$	−14.5674	+	8.41050i	−0.687478	+	0.396916i	0.115188	+	0.993344i	$0.463253\pi$
$450$	3.26241	−	40.1949i	0.153792	−	1.89481i
$451$			2.19054i			0.103148i
$452$	11.8295	−	6.82976i	0.556413	−	0.321245i
$453$	−7.28486	−	13.8875i	−0.342272	−	0.652490i
$454$			9.58859i			0.450015i
$455$	33.9874	+	22.8716i	1.59335	+	1.07224i
$456$	−3.26436	−	6.22300i	−0.152868	−	0.291419i
$457$	36.7626			1.71968			0.859840	−	0.510564i	$-0.170563\pi$
$457$	36.7626			1.71968			0.859840	+	0.510564i	$0.170563\pi$
$458$	−3.45653	−	5.98689i	−0.161513	−	0.279749i
$459$	20.1990	+	2.46594i	0.942808	+	0.115100i
$460$	−28.4119	+	16.4036i	−1.32471	+	0.764824i
$461$	7.08949	+	12.2793i	0.330190	+	0.571906i	0.982549	−	0.186004i	$-0.0595538\pi$
$461$	7.08949	+	12.2793i	0.330190	+	0.571906i	−0.652359	+	0.757910i	$0.726220\pi$
$462$	1.67076	−	4.68776i	0.0777309	−	0.218094i
$463$	−23.7992			−1.10604			−0.553022	−	0.833167i	$-0.686525\pi$
$463$	−23.7992			−1.10604			−0.553022	+	0.833167i	$0.686525\pi$
$464$	−1.84864	−	1.06731i	−0.0858208	−	0.0495487i
$465$	−7.61887	−	4.82019i	−0.353317	−	0.223531i
$466$	−7.99238	−	13.8432i	−0.370240	−	0.641275i
$467$	2.73830	+	4.74288i	0.126713	+	0.219474i	0.922401	−	0.386233i	$-0.126224\pi$
$467$	2.73830	+	4.74288i	0.126713	+	0.219474i	−0.795688	+	0.605707i	$0.792890\pi$
$468$	−3.92602	+	10.0790i	−0.181480	+	0.465902i
$469$	20.7452	−	4.67648i	0.957922	−	0.215940i
$470$	−37.0421	−	21.3862i	−1.70862	−	0.986474i
$471$	−9.76959	+	5.12477i	−0.450159	+	0.236137i
$472$		−	1.64474i		−	0.0757054i
$473$	−3.19048	−	1.84203i	−0.146699	−	0.0846965i
$474$	−0.327627	+	8.08641i	−0.0150484	+	0.371421i
$475$	−47.2312	+	27.2690i	−2.16712	+	1.25119i
$476$	3.08054	−	9.89264i	0.141196	−	0.453429i
$477$	0.789089	−	9.72205i	0.0361299	−	0.445142i
$478$	15.7358			0.719737
$479$	6.46693	+	11.2010i	0.295482	+	0.511789i	0.975097	−	0.221780i	$-0.0711866\pi$
$479$	6.46693	+	11.2010i	0.295482	+	0.511789i	−0.679615	+	0.733569i	$0.737853\pi$
$480$	0.301118	−	7.43212i	0.0137441	−	0.339228i
$481$	−15.0469	−	15.9350i	−0.686081	−	0.726575i
$482$	−18.3268			−0.834765
$483$	26.6667	−	22.6819i	1.21338	−	1.03206i
$484$	4.91032	−	8.50493i	0.223196	−	0.386588i
$485$	−46.3001	−	26.7314i	−2.10238	−	1.21381i
$486$	−14.7916	+	4.92033i	−0.670959	+	0.223191i
$487$	−11.5525			−0.523494			−0.261747	−	0.965137i	$-0.584299\pi$
$487$	−11.5525			−0.523494			−0.261747	+	0.965137i	$0.584299\pi$
$488$	−6.96907	+	12.0708i	−0.315475	+	0.546419i
$489$	2.13592	+	4.07179i	0.0965895	+	0.184133i
$490$	29.9647	+	2.40716i	1.35367	+	0.108744i
$491$	18.2188	+	10.5186i	0.822202	+	0.474698i	0.851175	−	0.524882i	$-0.175890\pi$
$491$	18.2188	+	10.5186i	0.822202	+	0.474698i	−0.0289733	+	0.999580i	$0.509224\pi$
$492$	−1.62294	−	3.09389i	−0.0731679	−	0.139483i
$493$	−7.23955	−	4.17976i	−0.326053	−	0.188247i
$494$	14.2326	−	3.37968i	0.640353	−	0.152059i
$495$	1.13186	−	13.9453i	0.0508735	−	0.626793i
$496$	−1.04968	−	0.606034i	−0.0471321	−	0.0272117i
$497$	−1.80719	−	8.01682i	−0.0810636	−	0.359604i
$498$	−6.62522	−	4.19155i	−0.296883	−	0.187828i
$499$	12.4392	+	21.5453i	0.556855	+	0.964502i	0.997757	+	0.0669462i	$0.0213256\pi$
$499$	12.4392	+	21.5453i	0.556855	+	0.964502i	−0.440901	+	0.897556i	$0.645341\pi$
$500$	−36.2554			−1.62139
$501$	19.8053	+	37.7556i	0.884833	+	1.68680i
$502$	7.88449	−	4.55211i	0.351902	−	0.203171i
$503$	0.553605	+	0.958873i	0.0246840	+	0.0427540i	0.878104	−	0.478471i	$-0.158809\pi$
$503$	0.553605	+	0.958873i	0.0246840	+	0.0427540i	−0.853420	+	0.521225i	$0.825475\pi$
$504$	1.11334	+	7.85878i	0.0495920	+	0.350058i
$505$	11.1840	−	19.3712i	0.497681	−	0.862008i
$506$	−7.18481	+	4.14815i	−0.319404	+	0.184408i
$507$	−18.3074	−	13.1087i	−0.813061	−	0.582179i
$508$	8.72940	−	15.1198i	0.387304	−	0.670831i
$509$	−9.31159			−0.412729			−0.206365	−	0.978475i	$-0.566163\pi$
$509$	−9.31159			−0.412729			−0.206365	+	0.978475i	$0.566163\pi$
$510$	1.17923	−	29.1054i	0.0522171	−	1.28881i
$511$	−8.67784	+	8.00867i	−0.383885	+	0.354283i
$512$		−	1.00000i		−	0.0441942i
$513$	16.8453	+	12.6756i	0.743740	+	0.559642i
$514$			8.94770i			0.394666i
$515$	24.6655	+	14.2406i	1.08689	+	0.627517i
$516$	5.87094	+	0.237866i	0.258454	+	0.0104715i
$517$	−9.36720	−	5.40815i	−0.411969	−	0.237850i
$518$	−15.3551	−	4.78153i	−0.674664	−	0.210089i
$519$	−9.11361	−	17.3737i	−0.400043	−	0.762620i
$520$	14.8353	+	4.43442i	0.650572	+	0.194462i
$521$	1.07206	−	1.85687i	0.0469680	−	0.0813510i	−0.841586	−	0.540124i	$-0.818377\pi$
$521$	1.07206	−	1.85687i	0.0469680	−	0.0813510i	0.888554	+	0.458773i	$0.151711\pi$
$522$	6.38287	+	0.518065i	0.279371	+	0.0226751i
$523$		−	22.7351i		−	0.994138i	−0.867711	−	0.497069i	$-0.834410\pi$
$523$		−	22.7351i		−	0.994138i	0.867711	−	0.497069i	$-0.165590\pi$
$524$	4.80013	+	8.31407i	0.209695	+	0.363202i
$525$	60.5919	−	11.1026i	2.64445	−	0.484557i
$526$	10.6250	+	18.4030i	0.463271	+	0.802409i
$527$	−4.11072	−	2.37332i	−0.179066	−	0.103384i
$528$	0.0761468	−	1.87943i	0.00331386	−	0.0817919i
$529$	−35.3611			−1.53744
$530$	−13.9627			−0.606503
$531$	2.11333	+	4.45875i	0.0917109	+	0.193493i
$532$	7.88831	−	7.28003i	0.342002	−	0.315629i
$533$	7.07600	−	1.68027i	0.306495	−	0.0727806i
$534$	−24.8529	−	15.7236i	−1.07549	−	0.680425i
$535$	−20.8323	+	12.0275i	−0.900660	+	0.519996i
$536$	6.96084	−	4.01884i	0.300663	−	0.173588i
$537$	0.291882	−	7.20415i	0.0125956	−	0.310882i
$538$		−	9.11399i		−	0.392932i
$539$	7.57747	+	0.608722i	0.326385	+	0.0262195i
$540$	8.73324	+	20.5347i	0.375819	+	0.883673i
$541$	−12.4149	−	21.5032i	−0.533756	−	0.924493i	−0.999222	−	0.0394274i	$-0.987447\pi$
$541$	−12.4149	−	21.5032i	−0.533756	−	0.924493i	0.465466	−	0.885066i	$-0.345887\pi$
$542$	23.7919			1.02195
$543$	−22.2738	−	14.0919i	−0.955861	−	0.604740i
$544$		−	3.91616i		−	0.167904i
$545$	−51.8801			−2.22230
$546$	−16.4242	−	1.80120i	−0.702893	−	0.0770844i
$547$	12.4908			0.534066			0.267033	−	0.963687i	$-0.413957\pi$
$547$	12.4908			0.534066			0.267033	+	0.963687i	$0.413957\pi$
$548$		−	0.976331i		−	0.0417068i
$549$	3.38274	−	41.6774i	0.144372	−	1.77875i
$550$	−14.5982			−0.622468
$551$	−4.33026	−	7.50023i	−0.184475	−	0.319520i
$552$	7.07443	−	11.1819i	0.301108	−	0.475935i
$553$	−12.0597	+	2.71856i	−0.512831	+	0.115605i
$554$		−	16.0852i		−	0.683396i
$555$	−45.1766	−	1.83037i	−1.91764	−	0.0776947i
$556$	4.16317	−	2.40361i	0.176558	−	0.101936i
$557$	6.08704	−	3.51435i	0.257916	−	0.148908i	−0.365467	−	0.930824i	$-0.619091\pi$
$557$	6.08704	−	3.51435i	0.257916	−	0.148908i	0.623384	+	0.781916i	$0.285758\pi$
$558$	3.62428	+	0.294164i	0.153428	+	0.0124530i
$559$	−3.50293	+	11.7190i	−0.148158	+	0.495662i
$560$	11.0839	−	2.49860i	0.468382	−	0.105585i
$561$	0.298203	−	7.36016i	0.0125901	−	0.310746i
$562$	4.07708			0.171981
$563$	1.77556			0.0748309			0.0374155	−	0.999300i	$-0.488088\pi$
$563$	1.77556			0.0748309			0.0374155	+	0.999300i	$0.488088\pi$
$564$	17.2370	+	0.698369i	0.725807	+	0.0294067i
$565$	50.8013	+	29.3301i	2.13722	+	1.23393i
$566$	−4.65364	−	8.06035i	−0.195607	−	0.338802i
$567$	−13.1159	−	19.8739i	−0.550817	−	0.834626i
$568$	−1.55305	−	2.68997i	−0.0651647	−	0.112869i
$569$		−	5.15704i		−	0.216194i	−0.994140	−	0.108097i	$-0.965524\pi$
$569$		−	5.15704i		−	0.216194i	0.994140	−	0.108097i	$-0.0344758\pi$
$570$	16.1347	−	25.5027i	0.675808	−	1.06819i
$571$	12.8678	−	22.2876i	0.538499	−	0.932707i	−0.460486	−	0.887667i	$-0.652325\pi$
$571$	12.8678	−	22.2876i	0.538499	−	0.932707i	0.998985	−	0.0450405i	$-0.0143417\pi$
$572$	3.75156	+	1.12138i	0.156860	+	0.0468871i
$573$	−4.50916	+	2.36534i	−0.188373	+	0.0988136i
$574$	3.92183	−	3.61941i	0.163694	−	0.151071i
$575$	−88.9341	−	51.3461i	−3.70881	−	2.14128i
$576$	1.28490	+	2.71091i	0.0535376	+	0.112955i
$577$	−5.09936	−	2.94412i	−0.212289	−	0.122565i	0.390086	−	0.920779i	$-0.372445\pi$
$577$	−5.09936	−	2.94412i	−0.212289	−	0.122565i	−0.602375	+	0.798213i	$0.705779\pi$
$578$			1.66370i			0.0692008i
$579$	−0.822424	−	0.0333212i	−0.0341788	−	0.00138478i
$580$		−	9.16704i		−	0.380641i
$581$	3.56051	−	11.4340i	0.147715	−	0.474361i
$582$	21.5451	+	0.872916i	0.893072	+	0.0361835i
$583$	−3.53090			−0.146235
$584$	−2.23162	+	3.86528i	−0.0923451	+	0.159946i
$585$	−45.9150	+	7.04063i	−1.89835	+	0.291094i
$586$	−8.96708	+	5.17715i	−0.370427	+	0.213866i
$587$	19.3999	−	33.6017i	0.800721	−	1.38689i	−0.118421	−	0.992963i	$-0.537783\pi$
$587$	19.3999	−	33.6017i	0.800721	−	1.38689i	0.919142	−	0.393926i	$-0.128883\pi$
$588$	−11.1533	+	4.75430i	−0.459955	+	0.196064i
$589$	−2.45878	−	4.25873i	−0.101312	−	0.175478i
$590$	6.11698	−	3.53164i	0.251832	−	0.145395i
$591$	−26.9011	+	14.1113i	−1.10656	+	0.580463i
$592$	−6.07856			−0.249827
$593$	8.45753	+	14.6489i	0.347309	+	0.601557i	0.985770	−	0.168097i	$-0.0537621\pi$
$593$	8.45753	+	14.6489i	0.347309	+	0.601557i	−0.638461	+	0.769654i	$0.720429\pi$
$594$	2.20846	+	5.19282i	0.0906143	+	0.213064i
$595$	43.4064	−	9.78490i	1.77949	−	0.401142i
$596$	−3.63236	−	2.09714i	−0.148787	−	0.0859023i
$597$	1.09180	+	0.690743i	0.0446843	+	0.0282702i
$598$	18.9108	+	20.0269i	0.773319	+	0.818961i
$599$	27.3660	+	15.7998i	1.11814	+	0.645561i	0.940926	−	0.338611i	$-0.109957\pi$
$599$	27.3660	+	15.7998i	1.11814	+	0.645561i	0.177217	+	0.984172i	$0.443290\pi$
$600$	20.6183	−	10.8156i	0.841738	−	0.441546i
$601$	−5.98901	−	3.45775i	−0.244297	−	0.141045i	0.372853	−	0.927890i	$-0.378379\pi$
$601$	−5.98901	−	3.45775i	−0.244297	−	0.141045i	−0.617150	+	0.786846i	$0.711713\pi$
$602$	1.97374	+	8.75566i	0.0804438	+	0.356854i
$603$	−13.7064	+	19.8387i	−0.558167	+	0.807895i
$604$	4.52705	−	7.84109i	0.184203	−	0.319049i
$605$	42.1743			1.71463
$606$	−0.365214	+	9.01411i	−0.0148358	+	0.366173i
$607$	24.3700	+	14.0701i	0.989150	+	0.571086i	0.905020	−	0.425369i	$-0.139856\pi$
$607$	24.3700	+	14.0701i	0.989150	+	0.571086i	0.0841297	+	0.996455i	$0.473189\pi$
$608$	2.02858	−	3.51361i	0.0822699	−	0.142496i
$609$	1.76307	+	9.62187i	0.0714432	+	0.389898i
$610$	−59.8568			−2.42353
$611$	−10.2845	+	34.4068i	−0.416068	+	1.39195i
$612$	5.03188	+	10.6163i	0.203402	+	0.429140i
$613$	−22.9440	−	39.7401i	−0.926698	−	1.60509i	−0.788807	−	0.614641i	$-0.789301\pi$
$613$	−22.9440	−	39.7401i	−0.926698	−	1.60509i	−0.137891	−	0.990447i	$-0.544032\pi$
$614$	−3.63183			−0.146569
$615$	8.02168	−	12.6792i	0.323465	−	0.511274i
$616$	2.80290	−	0.631845i	0.112932	−	0.0254577i
$617$	−13.1635	+	7.59995i	−0.529942	+	0.305962i	−0.740993	−	0.671513i	$-0.765645\pi$
$617$	−13.1635	+	7.59995i	−0.529942	+	0.305962i	0.211051	+	0.977475i	$0.432312\pi$
$618$	−11.4777	−	0.465029i	−0.461701	−	0.0187062i
$619$	42.0050	+	24.2516i	1.68832	+	0.974753i	0.955804	+	0.294005i	$0.0949882\pi$
$619$	42.0050	+	24.2516i	1.68832	+	0.974753i	0.732518	+	0.680748i	$0.238345\pi$
$620$		−	5.20517i		−	0.209045i
$621$	−4.81042	+	39.4032i	−0.193036	+	1.58119i
$622$	−13.0832	−	7.55359i	−0.524589	−	0.302871i
$623$	13.3564	−	42.8917i	0.535111	−	1.71842i
$624$	−6.12947	+	1.19566i	−0.245375	+	0.0478649i
$625$	−44.2427	−	76.6305i	−1.76971	−	3.06522i
$626$	12.5585	+	21.7519i	0.501938	+	0.869382i
$627$	4.08014	−	6.44913i	0.162945	−	0.257554i
$628$	−5.51607	−	3.18471i	−0.220115	−	0.127084i
$629$	−23.8046			−0.949152
$630$	−26.8371	+	21.0152i	−1.06921	+	0.837267i
$631$	−6.26200	−	10.8461i	−0.249286	−	0.431776i	0.714042	−	0.700103i	$-0.246863\pi$
$631$	−6.26200	−	10.8461i	−0.249286	−	0.431776i	−0.963328	+	0.268327i	$0.913529\pi$
$632$	−4.04652	+	2.33626i	−0.160962	+	0.0929314i
$633$	13.5307	+	25.7941i	0.537796	+	1.02523i
$634$	5.47854	+	9.48911i	0.217581	+	0.376861i
$635$	74.9761			2.97533
$636$	4.98700	−	2.61600i	0.197747	−	0.103731i
$637$	−3.84604	−	24.9441i	−0.152386	−	0.988321i
$638$		−	2.31816i		−	0.0917769i
$639$	7.66654	+	5.29674i	0.303284	+	0.209536i
$640$	3.71911	−	2.14723i	0.147011	−	0.0848767i
$641$			0.723607i			0.0285808i	0.999898	+	0.0142904i	$0.00454892\pi$
$641$			0.723607i			0.0285808i	−0.999898	+	0.0142904i	$0.995451\pi$
$642$	5.18714	−	8.19887i	0.204720	−	0.323584i
$643$	32.0601	−	18.5099i	1.26433	−	0.729959i	0.290418	−	0.956900i	$-0.406206\pi$
$643$	32.0601	−	18.5099i	1.26433	−	0.729959i	0.973909	+	0.226940i	$0.0728722\pi$
$644$	19.2981	+	6.00936i	0.760450	+	0.236802i
$645$	11.7216	+	22.3454i	0.461538	+	0.879850i
$646$	7.94426	−	13.7599i	0.312563	−	0.541374i
$647$	14.2809	+	24.7352i	0.561439	+	0.972440i	0.997371	+	0.0724610i	$0.0230853\pi$
$647$	14.2809	+	24.7352i	0.561439	+	0.972440i	−0.435933	+	0.899979i	$0.643581\pi$
$648$	−6.96651	−	5.69805i	−0.273670	−	0.223841i
$649$	1.54686	−	0.893081i	0.0607196	−	0.0350565i
$650$	11.1977	+	47.1559i	0.439209	+	1.84961i
$651$	1.00109	+	5.46343i	0.0392360	+	0.214129i
$652$	−1.32733	+	2.29900i	−0.0519822	+	0.0900359i
$653$			14.4837i			0.566792i	0.959003	+	0.283396i	$0.0914611\pi$
$653$			14.4837i			0.566792i	−0.959003	+	0.283396i	$0.908539\pi$
$654$	18.5297	−	9.72004i	0.724570	−	0.380083i
$655$	−20.6140	+	35.7044i	−0.805454	+	1.39509i
$656$	1.00855	−	1.74686i	0.0393773	−	0.0682034i
$657$	1.08321	−	13.3458i	0.0422602	−	0.520671i
$658$	5.79487	+	25.7064i	0.225908	+	1.00214i
$659$	−10.1298	+	5.84845i	−0.394601	+	0.227823i	−0.684152	−	0.729340i	$-0.739827\pi$
$659$	−10.1298	+	5.84845i	−0.394601	+	0.227823i	0.289551	+	0.957163i	$0.406494\pi$
$660$	7.15333	−	3.75238i	0.278443	−	0.146061i
$661$	9.73224	−	5.61891i	0.378540	−	0.218550i	−0.298643	−	0.954365i	$-0.596534\pi$
$661$	9.73224	−	5.61891i	0.378540	−	0.218550i	0.677183	+	0.735815i	$0.263201\pi$
$662$	4.34205	+	2.50688i	0.168758	+	0.0974327i
$663$	−24.0040	+	4.68241i	−0.932237	+	0.181850i
$664$		−	4.52632i		−	0.175655i
$665$	44.0132	+	13.7056i	1.70676	+	0.531480i
$666$	16.4784	−	7.81035i	0.638526	−	0.302645i
$667$	8.15366	−	14.1226i	0.315711	−	0.546828i
$668$	−12.3076	+	21.3175i	−0.476197	+	0.824797i
$669$	−35.2376	+	18.4844i	−1.36236	+	0.714647i
$670$	29.8930	+	17.2588i	1.15487	+	0.666764i
$671$	−15.1366			−0.584341
$672$	−3.49067	+	2.96905i	−0.134655	+	0.114534i
$673$	10.0141	−	17.3450i	0.386016	−	0.668600i	−0.605893	−	0.795546i	$-0.707184\pi$
$673$	10.0141	−	17.3450i	0.386016	−	0.668600i	0.991910	+	0.126946i	$0.0405176\pi$
$674$		−	27.4419i		−	1.05702i
$675$	−41.9973	+	55.8126i	−1.61648	+	2.14823i
$676$	0.744666	−	12.9787i	0.0286410	−	0.499179i
$677$	−21.3263	−	36.9382i	−0.819635	−	1.41965i	−0.905952	−	0.423381i	$-0.860843\pi$
$677$	−21.3263	−	36.9382i	−0.819635	−	1.41965i	0.0863170	−	0.996268i	$-0.472490\pi$
$678$	−23.6396	−	0.957777i	−0.907873	−	0.0367832i
$679$	7.24321	+	32.1314i	0.277969	+	1.23309i
$680$	14.5646	−	8.40889i	0.558528	−	0.322466i
$681$	8.87941	−	14.0349i	0.340260	−	0.537819i
$682$		−	1.31628i		−	0.0504031i
$683$			13.9553i			0.533985i	0.963699	+	0.266993i	$0.0860299\pi$
$683$			13.9553i			0.533985i	−0.963699	+	0.266993i	$0.913970\pi$
$684$	−0.984660	+	12.1316i	−0.0376494	+	0.463864i
$685$	3.63108	−	2.09641i	0.138736	−	0.0800996i
$686$	−11.4304	−	14.5721i	−0.436414	−	0.556366i
$687$	−0.484730	+	11.9640i	−0.0184936	+	0.456454i
$688$	1.69618	+	2.93788i	0.0646664	+	0.112006i
$689$	2.70841	+	11.4057i	0.103182	+	0.434523i
$690$	56.7773	+	2.30038i	2.16147	+	0.0875739i
$691$		−	37.4384i		−	1.42422i	−0.702066	−	0.712112i	$-0.747739\pi$
$691$		−	37.4384i		−	1.42422i	0.702066	−	0.712112i	$-0.252261\pi$
$692$	5.66350	−	9.80947i	0.215294	−	0.372900i
$693$	−6.78656	+	5.31433i	−0.257800	+	0.201875i
$694$	−29.3039			−1.11236
$695$	17.8786	+	10.3222i	0.678173	+	0.391543i
$696$	1.71750	+	3.27414i	0.0651016	+	0.124106i
$697$	3.94964	−	6.84098i	0.149603	−	0.259121i
$698$	−11.8703	+	20.5600i	−0.449297	+	0.778206i
$699$	−1.12082	+	27.6637i	−0.0423933	+	1.04634i
$700$	24.1205	+	26.1359i	0.911668	+	0.987842i
$701$		−	20.0942i		−	0.758948i	−0.925202	−	0.379474i	$-0.876105\pi$
$701$		−	20.0942i		−	0.758948i	0.925202	−	0.379474i	$-0.123895\pi$
$702$	15.0801	−	11.1171i	0.569162	−	0.419588i
$703$	−21.3577	−	12.3309i	−0.805520	−	0.465067i
$704$	0.940488	−	0.542991i	0.0354460	−	0.0204647i
$705$	34.4144	+	65.6057i	1.29612	+	2.47085i
$706$	−6.58396	+	3.80125i	−0.247791	+	0.143062i
$707$	−13.4432	+	3.03044i	−0.505585	+	0.113971i
$708$	−1.52310	+	2.40743i	−0.0572415	+	0.0904767i
$709$	8.34291	−	14.4503i	0.313325	−	0.542694i	−0.665755	−	0.746170i	$-0.731891\pi$
$709$	8.34291	−	14.4503i	0.313325	−	0.542694i	0.979080	+	0.203476i	$0.0652239\pi$
$710$	6.66953	−	11.5520i	0.250303	−	0.433537i
$711$	7.96788	−	11.5328i	0.298819	−	0.432513i
$712$		−	16.9794i		−	0.636329i
$713$	4.62976	−	8.01898i	0.173386	−	0.300313i
$714$	−13.6700	+	11.6273i	−0.511587	+	0.435140i
$715$	3.88493	+	16.3603i	0.145288	+	0.611840i
$716$	3.60503	−	2.08136i	0.134726	−	0.0777843i
$717$	−23.0326	−	14.5719i	−0.860169	−	0.544199i
$718$	11.0392	+	19.1204i	0.411979	+	0.713568i
$719$	−8.17299	+	14.1560i	−0.304801	+	0.527931i	−0.977217	−	0.212243i	$-0.931923\pi$
$719$	−8.17299	+	14.1560i	−0.304801	+	0.527931i	0.672416	+	0.740173i	$0.265257\pi$
$720$	−7.32319	+	10.5996i	−0.272919	+	0.395025i
$721$	−3.85868	−	17.1173i	−0.143705	−	0.637483i
$722$	−2.19917	+	1.26969i	−0.0818447	+	0.0472531i
$723$	26.8252	+	16.9714i	0.997640	+	0.631172i
$724$		−	15.2174i		−	0.565549i
$725$	24.8500	−	14.3472i	0.922907	−	0.532841i
$726$	−15.0632	+	7.90161i	−0.559047	+	0.293256i
$727$		−	20.7212i		−	0.768508i	−0.923227	−	0.384254i	$-0.874459\pi$
$727$		−	20.7212i		−	0.768508i	0.923227	−	0.384254i	$-0.125541\pi$
$728$	−4.19102	−	8.56944i	−0.155329	−	0.317605i
$729$	26.2070	+	6.49562i	0.970630	+	0.240579i
$730$	−19.1672			−0.709410
$731$	6.64253	+	11.5052i	0.245683	+	0.425535i
$732$	21.3787	−	11.2145i	0.790181	−	0.414500i
$733$	−34.6007	+	19.9767i	−1.27801	+	0.737857i	−0.976482	−	0.215601i	$-0.930829\pi$
$733$	−34.6007	+	19.9767i	−1.27801	+	0.737857i	−0.301525	+	0.953458i	$0.597496\pi$
$734$	3.60202	+	6.23889i	0.132953	+	0.230281i
$735$	−41.6305	−	31.2718i	−1.53556	−	1.15348i
$736$	7.63945			0.281594
$737$	7.55935	+	4.36439i	0.278452	+	0.160764i
$738$	−0.489543	+	6.03147i	−0.0180203	+	0.222021i
$739$	−19.9743	−	34.5965i	−0.734766	−	1.27265i	−0.954826	−	0.297166i	$-0.903959\pi$
$739$	−19.9743	−	34.5965i	−0.734766	−	1.27265i	0.220060	−	0.975486i	$-0.429375\pi$
$740$	−13.0521	−	22.6068i	−0.479803	−	0.831043i
$741$	−23.9621	−	8.23304i	−0.880269	−	0.302448i
$742$	5.83408	+	6.32155i	0.214176	+	0.232071i
$743$	−25.4018	−	14.6657i	−0.931900	−	0.538033i	−0.0444880	−	0.999010i	$-0.514166\pi$
$743$	−25.4018	−	14.6657i	−0.931900	−	0.538033i	−0.887412	+	0.460977i	$0.847499\pi$
$744$	0.975219	+	1.85910i	0.0357533	+	0.0681581i
$745$		−	18.0122i		−	0.659915i
$746$	−23.0960	−	13.3345i	−0.845603	−	0.488209i
$747$	5.81588	+	12.2704i	0.212792	+	0.448952i
$748$	3.68310	−	2.12644i	0.134668	−	0.0777503i
$749$	14.1498	+	4.40621i	0.517023	+	0.161000i
$750$	53.0674	+	33.5739i	1.93775	+	1.22595i
$751$	4.32605			0.157860			0.0789299	−	0.996880i	$-0.474850\pi$
$751$	4.32605			0.157860			0.0789299	+	0.996880i	$0.474850\pi$
$752$	4.97996	+	8.62555i	0.181601	+	0.314541i
$753$	−15.7561	−	0.638369i	−0.574183	−	0.0232635i
$754$	−7.48826	+	1.77817i	−0.272706	+	0.0647571i
$755$	38.8825			1.41508
$756$	5.64794	−	12.5340i	0.205413	−	0.455857i
$757$	−22.0785	+	38.2410i	−0.802456	+	1.38989i	0.115540	+	0.993303i	$0.463140\pi$
$757$	−22.0785	+	38.2410i	−0.802456	+	1.38989i	−0.917995	+	0.396591i	$0.870193\pi$
$758$	16.4075	+	9.47287i	0.595947	+	0.344070i
$759$	14.3578	+	0.581719i	0.521157	+	0.0211151i
$760$	17.4233			0.632011
$761$	−12.6054	+	21.8333i	−0.456947	+	0.791455i	−0.998798	−	0.0490196i	$-0.984390\pi$
$761$	−12.6054	+	21.8333i	−0.456947	+	0.791455i	0.541851	+	0.840474i	$0.317724\pi$
$762$	−26.7788	+	14.0472i	−0.970094	+	0.508876i
$763$	21.6772	+	23.4884i	0.784766	+	0.850337i
$764$	−2.54594	−	1.46990i	−0.0921090	−	0.0531792i
$765$	−28.6788	+	41.5098i	−1.03688	+	1.50079i
$766$	−25.9036	−	14.9555i	−0.935935	−	0.540362i
$767$	−4.07142	−	4.31172i	−0.147010	−	0.155687i
$768$	−0.926039	+	1.46371i	−0.0334156	+	0.0528171i
$769$	−34.7089	−	20.0392i	−1.25164	−	0.722633i	−0.280202	−	0.959941i	$-0.590401\pi$
$769$	−34.7089	−	20.0392i	−1.25164	−	0.722633i	−0.971434	+	0.237308i	$0.923735\pi$
$770$	8.36838	+	9.06759i	0.301575	+	0.326773i
$771$	8.28592	−	13.0968i	0.298410	−	0.471671i
$772$	−0.237608	−	0.411549i	−0.00855171	−	0.0148120i
$773$	43.6203			1.56891			0.784456	−	0.620184i	$-0.212942\pi$
$773$	43.6203			1.56891			0.784456	+	0.620184i	$0.212942\pi$
$774$	−8.37309	−	5.78489i	−0.300964	−	0.207934i
$775$	14.1102	−	8.14653i	0.506853	−	0.292632i
$776$	6.22463	+	10.7814i	0.223451	+	0.387029i
$777$	18.0475	+	21.2182i	0.647452	+	0.761199i
$778$	0.474048	−	0.821075i	0.0169954	−	0.0294369i
$779$	7.08731	−	4.09186i	0.253929	−	0.146606i
$780$	−17.6082	−	20.2288i	−0.630474	−	0.724307i
$781$	1.68659	−	2.92126i	0.0603509	−	0.104531i
$782$	29.9173			1.06984
$783$	−8.86294	−	6.66909i	−0.316736	−	0.238334i
$784$	−5.76245	−	3.97419i	−0.205802	−	0.141935i
$785$		−	27.3532i		−	0.976276i
$786$	0.673150	−	16.6145i	0.0240105	−	0.592620i
$787$			24.3619i			0.868408i	0.900815	+	0.434204i	$0.142970\pi$
$787$			24.3619i			0.868408i	−0.900815	+	0.434204i	$0.857030\pi$
$788$	−15.1888	−	8.76926i	−0.541079	−	0.312392i
$789$	1.49000	−	36.7758i	0.0530455	−	1.30925i
$790$	−17.3776	−	10.0330i	−0.618268	−	0.356957i
$791$	−7.94736	−	35.2550i	−0.282576	−	1.25352i
$792$	−1.85189	+	2.68043i	−0.0658040	+	0.0952451i
$793$	11.6107	+	48.8951i	0.412307	+	1.73631i
$794$	−6.98728	+	12.1023i	−0.247969	+	0.429496i
$795$	20.4374	+	12.9300i	0.724841	+	0.458582i
$796$			0.745911i			0.0264381i
$797$	20.9559	+	36.2967i	0.742297	+	1.28570i	0.951447	+	0.307812i	$0.0995969\pi$
$797$	20.9559	+	36.2967i	0.742297	+	1.28570i	−0.209150	+	0.977884i	$0.567070\pi$
$798$	−18.2878	+	3.35098i	−0.647381	+	0.118623i
$799$	19.5023	+	33.7790i	0.689943	+	1.19502i
$800$	11.6414	+	6.72118i	0.411587	+	0.237630i
$801$	21.8168	+	46.0295i	0.770860	+	1.62637i
$802$	−37.3418			−1.31859
$803$	−4.84700			−0.171047
$804$	−13.9103	−	0.563586i	−0.490577	−	0.0198761i
$805$	19.0879	+	84.6751i	0.672759	+	2.98441i
$806$	−4.25194	+	1.00967i	−0.149768	+	0.0355641i
$807$	−8.43991	+	13.3402i	−0.297099	+	0.469599i
$808$	−4.51075	+	2.60428i	−0.158688	+	0.0916184i
$809$	−3.07875	+	1.77752i	−0.108243	+	0.0624942i	−0.553144	−	0.833086i	$-0.686572\pi$
$809$	−3.07875	+	1.77752i	−0.108243	+	0.0624942i	0.444901	+	0.895580i	$0.353239\pi$
$810$	6.23300	−	38.1442i	0.219005	−	1.34025i
$811$			12.7250i			0.446836i	0.974723	+	0.223418i	$0.0717215\pi$
$811$			12.7250i			0.446836i	−0.974723	+	0.223418i	$0.928279\pi$
$812$	−4.15032	+	3.83028i	−0.145648	+	0.134417i
$813$	−34.8245	−	22.0322i	−1.22135	−	0.772704i
$814$	−3.30060	−	5.71681i	−0.115686	−	0.200374i
$815$	−11.4003			−0.399336
$816$	−3.62652	+	5.73213i	−0.126953	+	0.200665i
$817$			13.7634i			0.481521i
$818$	−8.10672			−0.283445
$819$	22.3724	+	17.8459i	0.781754	+	0.623587i
$820$	8.66235			0.302502
$821$			29.3856i			1.02556i	0.858519	+	0.512782i	$0.171385\pi$
$821$			29.3856i			1.02556i	−0.858519	+	0.512782i	$0.828615\pi$
$822$	−0.904121	+	1.42907i	−0.0315348	+	0.0498444i
$823$	1.70192			0.0593253			0.0296627	−	0.999560i	$-0.490557\pi$
$823$	1.70192			0.0593253			0.0296627	+	0.999560i	$0.490557\pi$
$824$	−3.31605	−	5.74356i	−0.115520	−	0.200087i
$825$	21.3675	+	13.5185i	0.743921	+	0.470653i
$826$	−4.15480	−	1.29379i	−0.144564	−	0.0450168i
$827$			11.9648i			0.416057i	0.978123	+	0.208029i	$0.0667047\pi$
$827$			11.9648i			0.416057i	−0.978123	+	0.208029i	$0.933295\pi$
$828$	−20.7098	+	9.81594i	−0.719717	+	0.341128i
$829$	10.0985	−	5.83037i	0.350735	−	0.202497i	−0.314274	−	0.949332i	$-0.601761\pi$
$829$	10.0985	−	5.83037i	0.350735	−	0.202497i	0.665009	+	0.746835i	$0.268428\pi$
$830$	16.8339	−	9.71904i	0.584312	−	0.337353i
$831$	−14.8956	+	23.5441i	−0.516721	+	0.816737i
$832$	−2.47541	−	2.62151i	−0.0858195	−	0.0908846i
$833$	−22.5667	−	15.5636i	−0.781888	−	0.539245i
$834$	−8.31952	−	0.337072i	−0.288081	−	0.0116718i
$835$	−105.709			−3.65822
$836$	4.40601			0.152385
$837$	−5.03250	−	3.78680i	−0.173949	−	0.130891i
$838$	11.7663	+	6.79325i	0.406459	+	0.234669i
$839$	−15.1044	−	26.1616i	−0.521461	−	0.903197i	−0.999688	−	0.0249613i	$-0.992054\pi$
$839$	−15.1044	−	26.1616i	−0.521461	−	0.903197i	0.478227	−	0.878236i	$-0.341280\pi$
$840$	−18.5375	−	6.60694i	−0.639604	−	0.227961i
$841$	−12.2217	−	21.1686i	−0.421438	−	0.729952i
$842$		−	28.4439i		−	0.980242i
$843$	−5.96767	−	3.77554i	−0.205538	−	0.130036i
$844$	−8.40841	+	14.5638i	−0.289430	+	0.501307i
$845$	49.8680	−	25.0986i	1.71551	−	0.863420i
$846$	−24.5832	−	16.9843i	−0.845188	−	0.583933i
$847$	−17.6218	−	19.0942i	−0.605492	−	0.656084i
$848$	2.81574	+	1.62567i	0.0966930	+	0.0558257i
$849$	−0.652607	+	16.1075i	−0.0223974	+	0.552807i
$850$	45.5897	+	26.3212i	1.56371	+	0.902810i
$851$		−	46.4368i		−	1.59183i
$852$	−0.217794	+	5.37553i	−0.00746150	+	0.184163i
$853$		−	24.1160i		−	0.825715i	−0.910796	−	0.412858i	$-0.864531\pi$
$853$		−	24.1160i		−	0.825715i	0.910796	−	0.412858i	$-0.135469\pi$
$854$	25.0101	+	27.0998i	0.855827	+	0.927336i
$855$	−47.2331	+	22.3873i	−1.61534	+	0.765629i
$856$	5.60143			0.191453
$857$	10.2452	−	17.7452i	0.349970	−	0.606166i	−0.636274	−	0.771463i	$-0.719525\pi$
$857$	10.2452	−	17.7452i	0.349970	−	0.606166i	0.986244	+	0.165297i	$0.0528584\pi$
$858$	−4.45276	−	5.11546i	−0.152015	−	0.174639i
$859$	−48.7579	+	28.1504i	−1.66360	+	0.960479i	−0.692623	+	0.721300i	$0.743545\pi$
$859$	−48.7579	+	28.1504i	−1.66360	+	0.960479i	−0.970975	+	0.239179i	$0.923122\pi$
$860$	−7.28419	+	12.6166i	−0.248389	+	0.430222i
$861$	−9.09214	+	1.66600i	−0.309859	+	0.0567773i
$862$	6.05914	+	10.4947i	0.206375	+	0.357452i
$863$	3.63343	−	2.09776i	0.123683	−	0.0714087i	−0.436882	−	0.899519i	$-0.643917\pi$
$863$	3.63343	−	2.09776i	0.123683	−	0.0714087i	0.560565	+	0.828110i	$0.310584\pi$
$864$	0.629682	−	5.15786i	0.0214222	−	0.175474i
$865$	48.6433			1.65392
$866$	3.13154	+	5.42399i	0.106414	+	0.184315i
$867$	1.54065	−	2.43518i	0.0523233	−	0.0827029i
$868$	−2.35661	+	2.17489i	−0.0799886	+	0.0738205i
$869$	−4.39445	−	2.53714i	−0.149071	−	0.0860665i
$870$	−8.48904	+	13.4179i	−0.287805	+	0.454909i
$871$	8.29964	−	27.7664i	0.281223	−	0.940829i
$872$	10.4622	+	6.04035i	0.354295	+	0.204552i
$873$	−30.7274	−	21.2293i	−1.03997	−	0.718502i
$874$	26.8420	+	15.4973i	0.907945	+	0.524203i
$875$	−28.5193	+	91.5850i	−0.964129	+	3.09614i
$876$	6.84585	−	3.59109i	0.231300	−	0.121332i
$877$	−1.98631	+	3.44039i	−0.0670730	+	0.116174i	−0.897612	−	0.440787i	$-0.854699\pi$
$877$	−1.98631	+	3.44039i	−0.0670730	+	0.116174i	0.830539	+	0.556961i	$0.188033\pi$
$878$	−32.8000			−1.10695
$879$	17.9195	+	0.726021i	0.604408	+	0.0244881i
$880$	4.03889	+	2.33185i	0.136151	+	0.0786067i
$881$	−6.30198	+	10.9153i	−0.212319	+	0.367747i	−0.952440	−	0.304727i	$-0.901435\pi$
$881$	−6.30198	+	10.9153i	−0.212319	+	0.367747i	0.740121	+	0.672474i	$0.234768\pi$
$882$	20.7279	+	3.36949i	0.697945	+	0.113457i
$883$	25.7438			0.866349			0.433175	−	0.901310i	$-0.357393\pi$
$883$	25.7438			0.866349			0.433175	+	0.901310i	$0.357393\pi$
$884$	−9.69411	−	10.2663i	−0.326048	−	0.345292i
$885$	−12.2239	−	0.495262i	−0.410903	−	0.0166481i
$886$	9.17053	+	15.8838i	0.308090	+	0.533627i
$887$	30.9903			1.04055			0.520277	−	0.853998i	$-0.325829\pi$
$887$	30.9903			1.04055			0.520277	+	0.853998i	$0.325829\pi$
$888$	8.89726	+	5.62898i	0.298572	+	0.188896i
$889$	−31.3274	−	33.9450i	−1.05069	−	1.13848i
$890$	63.1481	−	36.4586i	2.11673	−	1.22209i
$891$	1.57620	−	9.64591i	0.0528047	−	0.323150i
$892$	−19.8957	−	11.4868i	−0.666158	−	0.384606i
$893$			40.4091i			1.35224i
$894$	3.37469	+	6.43332i	0.112866	+	0.215162i
$895$	15.4816	+	8.93833i	0.517494	+	0.298775i
$896$	−2.52611	−	0.786623i	−0.0843914	−	0.0262792i
$897$	−9.13422	−	46.8257i	−0.304983	−	1.56347i
$898$	8.41050	+	14.5674i	0.280662	+	0.486121i
$899$	1.29365	+	2.24067i	0.0431457	+	0.0747306i
$900$	−40.1949	−	3.26241i	−1.33983	−	0.108747i
$901$	11.0269	+	6.36638i	0.367359	+	0.212095i
$902$	2.19054			0.0729368
$903$	5.21909	−	14.6435i	0.173681	−	0.487306i
$904$	−6.82976	−	11.8295i	−0.227154	−	0.393443i
$905$	56.5950	−	32.6751i	1.88128	−	1.08616i
$906$	−13.8875	+	7.28486i	−0.461380	+	0.242023i
$907$	11.3846	+	19.7187i	0.378020	+	0.654749i	0.990774	−	0.135524i	$-0.0432718\pi$
$907$	11.3846	+	19.7187i	0.378020	+	0.654749i	−0.612754	+	0.790273i	$0.709938\pi$
$908$	9.58859			0.318208
$909$	8.88199	−	12.8558i	0.294597	−	0.426402i
$910$	22.8716	−	33.9874i	0.758187	−	1.12667i
$911$		−	30.1970i		−	1.00047i	−0.865889	−	0.500236i	$-0.833247\pi$
$911$		−	30.1970i		−	1.00047i	0.865889	−	0.500236i	$-0.166753\pi$
$912$	−6.22300	+	3.26436i	−0.206064	+	0.108094i
$913$	4.25695	−	2.45775i	0.140884	−	0.0813397i
$914$		−	36.7626i		−	1.21600i
$915$	87.6130	+	55.4297i	2.89640	+	1.83245i
$916$	−5.98689	+	3.45653i	−0.197812	+	0.114207i
$917$	24.7781	−	5.58561i	0.818246	−	0.184453i
$918$	2.46594	−	20.1990i	0.0813880	−	0.666666i
$919$	−4.24405	+	7.35091i	−0.139998	+	0.242484i	−0.927496	−	0.373834i	$-0.878043\pi$
$919$	−4.24405	+	7.35091i	−0.139998	+	0.242484i	0.787497	+	0.616318i	$0.211376\pi$
$920$	16.4036	+	28.4119i	0.540812	+	0.936714i
$921$	5.31595	+	3.36322i	0.175167	+	0.110822i
$922$	12.2793	−	7.08949i	0.404399	−	0.233480i
$923$	−10.7301	−	3.20734i	−0.353187	−	0.105571i
$924$	−4.68776	−	1.67076i	−0.154216	−	0.0549640i
$925$	40.8551	−	70.7631i	1.34331	−	2.32668i
$926$			23.7992i			0.782091i
$927$	16.3694	+	11.3095i	0.537642	+	0.371452i
$928$	−1.06731	+	1.84864i	−0.0350362	+	0.0606845i
$929$	−11.8231	+	20.4782i	−0.387903	+	0.671868i	−0.992167	−	0.124916i	$-0.960134\pi$
$929$	−11.8231	+	20.4782i	−0.387903	+	0.671868i	0.604264	+	0.796784i	$0.293467\pi$
$930$	−4.82019	+	7.61887i	−0.158060	+	0.249833i
$931$	−12.1850	−	25.6534i	−0.399348	−	0.840755i
$932$	−13.8432	+	7.99238i	−0.453450	+	0.261799i
$933$	12.1551	+	23.1718i	0.397941	+	0.758612i
$934$	4.74288	−	2.73830i	0.155192	−	0.0895999i
$935$	15.8169	+	9.13190i	0.517269	+	0.298645i
$936$	10.0790	+	3.92602i	0.329443	+	0.128326i
$937$			40.7293i			1.33057i	0.746591	+	0.665284i	$0.231689\pi$
$937$			40.7293i			1.33057i	−0.746591	+	0.665284i	$0.768311\pi$
$938$	−4.67648	−	20.7452i	−0.152692	−	0.677353i
$939$	1.76115	−	43.4682i	0.0574729	−	1.41853i
$940$	−21.3862	+	37.0421i	−0.697542	+	1.20818i
$941$	18.6395	−	32.2845i	0.607629	−	1.05244i	−0.384001	−	0.923333i	$-0.625454\pi$
$941$	18.6395	−	32.2845i	0.607629	−	1.05244i	0.991630	−	0.129111i	$-0.0412125\pi$
$942$	5.12477	+	9.76959i	0.166974	+	0.318310i
$943$	13.3450	+	7.70476i	0.434574	+	0.250902i
$944$	−1.64474			−0.0535318
$945$	58.7427	−	5.90804i	1.91090	−	0.192189i
$946$	−1.84203	+	3.19048i	−0.0598895	+	0.103732i
$947$			37.7597i			1.22703i	0.789684	+	0.613513i	$0.210244\pi$
$947$			37.7597i			1.22703i	−0.789684	+	0.613513i	$0.789756\pi$
$948$	8.08641	+	0.327627i	0.262634	+	0.0106408i
$949$	3.71794	+	15.6571i	0.120689	+	0.508250i
$950$	27.2690	+	47.2312i	0.884722	+	1.53238i
$951$	0.768288	−	18.9627i	0.0249134	−	0.614907i
$952$	−9.89264	−	3.08054i	−0.320622	−	0.0998409i
$953$	30.1541	−	17.4095i	0.976786	−	0.563948i	0.0754876	−	0.997147i	$-0.475949\pi$
$953$	30.1541	−	17.4095i	0.976786	−	0.563948i	0.901298	+	0.433199i	$0.142615\pi$
$954$	−9.72205	−	0.789089i	−0.314763	−	0.0255477i
$955$		−	12.6249i		−	0.408531i
$956$		−	15.7358i		−	0.508931i
$957$	−2.14671	+	3.39312i	−0.0693932	+	0.109684i
$958$	11.2010	−	6.46693i	0.361889	−	0.208937i
$959$	−2.46632	−	0.768005i	−0.0796416	−	0.0248002i
$960$	−7.43212	−	0.301118i	−0.239871	−	0.00971855i
$961$	−14.7654	−	25.5745i	−0.476305	−	0.824984i
$962$	−15.9350	+	15.0469i	−0.513766	+	0.485133i
$963$	−15.1850	+	7.19729i	−0.489329	+	0.231929i
$964$			18.3268i			0.590268i
$965$	1.02040	−	1.76738i	0.0328478	−	0.0568940i
$966$	−22.6819	−	26.6667i	−0.729778	−	0.857989i
$967$	20.8316			0.669898			0.334949	−	0.942236i	$-0.391281\pi$
$967$	20.8316			0.669898			0.334949	+	0.942236i	$0.391281\pi$
$968$	−8.50493	−	4.91032i	−0.273359	−	0.157824i
$969$	−24.3703	+	12.7838i	−0.782886	+	0.410674i
$970$	−26.7314	+	46.3001i	−0.858294	+	1.48661i
$971$	25.7278	−	44.5619i	0.825645	−	1.43006i	−0.0757798	−	0.997125i	$-0.524145\pi$
$971$	25.7278	−	44.5619i	0.825645	−	1.43006i	0.901425	−	0.432935i	$-0.142522\pi$
$972$	4.92033	+	14.7916i	0.157820	+	0.474440i
$973$	−2.79693	−	12.4074i	−0.0896654	−	0.397762i
$974$			11.5525i			0.370166i
$975$	27.2780	−	79.3921i	0.873596	−	2.54258i
$976$	12.0708	+	6.96907i	0.386376	+	0.223075i
$977$	−27.4873	+	15.8698i	−0.879397	+	0.507720i	−0.870460	−	0.492240i	$-0.836178\pi$
$977$	−27.4873	+	15.8698i	−0.879397	+	0.507720i	−0.00893756	+	0.999960i	$0.502845\pi$
$978$	4.07179	−	2.13592i	0.130202	−	0.0682991i
$979$	15.9689	−	9.21965i	0.510368	−	0.294661i
$980$	2.40716	−	29.9647i	0.0768938	−	0.957186i
$981$	−36.1233	−	2.93195i	−1.15333	−	0.0936098i
$982$	10.5186	−	18.2188i	0.335663	−	0.581385i
$983$	−5.74547	+	9.95145i	−0.183252	+	0.317402i	−0.942986	−	0.332832i	$-0.891996\pi$
$983$	−5.74547	+	9.95145i	−0.183252	+	0.317402i	0.759734	+	0.650234i	$0.225329\pi$
$984$	−3.09389	+	1.62294i	−0.0986295	+	0.0517375i
$985$		−	75.3184i		−	2.39985i
$986$	−4.17976	+	7.23955i	−0.133111	+	0.230554i
$987$	15.3231	−	42.9931i	0.487741	−	1.36848i
$988$	−3.37968	−	14.2326i	−0.107522	−	0.452798i
$989$	−22.4438	+	12.9579i	−0.713670	+	0.412038i
$990$	−13.9453	−	1.13186i	−0.443209	−	0.0359730i
$991$	−10.9442	−	18.9559i	−0.347654	−	0.602155i	0.638178	−	0.769889i	$-0.279688\pi$
$991$	−10.9442	−	18.9559i	−0.347654	−	0.602155i	−0.985832	+	0.167734i	$0.946355\pi$
$992$	−0.606034	+	1.04968i	−0.0192416	+	0.0333274i
$993$	−4.03403	−	7.69025i	−0.128016	−	0.244043i
$994$	−8.01682	+	1.80719i	−0.254278	+	0.0573207i
$995$	−2.77412	+	1.60164i	−0.0879457	+	0.0507754i
$996$	−4.19155	+	6.62522i	−0.132814	+	0.209928i
$997$		−	12.2249i		−	0.387166i	−0.981084	−	0.193583i	$-0.937989\pi$
$997$		−	12.2249i		−	0.387166i	0.981084	−	0.193583i	$-0.0620109\pi$
$998$	21.5453	−	12.4392i	0.682006	−	0.393756i
$999$	−31.3523	−	3.82756i	−0.991944	−	0.121099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.6	yes	76
3.2	odd	2	inner	546.2.bb.a.269.21	yes	76
7.5	odd	6		546.2.u.a.425.13	yes	76
13.3	even	3		546.2.u.a.185.26	yes	76
21.5	even	6		546.2.u.a.425.26	yes	76
39.29	odd	6		546.2.u.a.185.13	✓	76
91.68	odd	6	inner	546.2.bb.a.341.2	yes	76
273.68	even	6	inner	546.2.bb.a.341.25	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.13	✓	76	39.29	odd	6
546.2.u.a.185.26	yes	76	13.3	even	3
546.2.u.a.425.13	yes	76	7.5	odd	6
546.2.u.a.425.26	yes	76	21.5	even	6
546.2.bb.a.269.6	yes	76	1.1	even	1	trivial
546.2.bb.a.269.21	yes	76	3.2	odd	2	inner
546.2.bb.a.341.2	yes	76	91.68	odd	6	inner
546.2.bb.a.341.25	yes	76	273.68	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.926039 + 1.46371i) q^{3} -1.00000 q^{4} +(-2.14723 - 3.71911i) q^{5} +(1.46371 + 0.926039i) q^{6} +(-0.786623 + 2.52611i) q^{7} +1.00000i q^{8} +(-1.28490 - 2.71091i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.926039 + 1.46371i) q^{3} -1.00000 q^{4} +(-2.14723 - 3.71911i) q^{5} +(1.46371 + 0.926039i) q^{6} +(-0.786623 + 2.52611i) q^{7} +1.00000i q^{8} +(-1.28490 - 2.71091i) q^{9} +(-3.71911 + 2.14723i) q^{10} +(-0.940488 + 0.542991i) q^{11} +(0.926039 - 1.46371i) q^{12} +(2.47541 + 2.62151i) q^{13} +(2.52611 + 0.786623i) q^{14} +(7.43212 + 0.301118i) q^{15} +1.00000 q^{16} +3.91616 q^{17} +(-2.71091 + 1.28490i) q^{18} +(3.51361 + 2.02858i) q^{19} +(2.14723 + 3.71911i) q^{20} +(-2.96905 - 3.49067i) q^{21} +(0.542991 + 0.940488i) q^{22} +7.63945i q^{23} +(-1.46371 - 0.926039i) q^{24} +(-6.72118 + 11.6414i) q^{25} +(2.62151 - 2.47541i) q^{26} +(5.15786 + 0.629682i) q^{27} +(0.786623 - 2.52611i) q^{28} +(-1.84864 - 1.06731i) q^{29} +(0.301118 - 7.43212i) q^{30} +(-1.04968 - 0.606034i) q^{31} -1.00000i q^{32} +(0.0761468 - 1.87943i) q^{33} -3.91616i q^{34} +(11.0839 - 2.49860i) q^{35} +(1.28490 + 2.71091i) q^{36} -6.07856 q^{37} +(2.02858 - 3.51361i) q^{38} +(-6.12947 + 1.19566i) q^{39} +(3.71911 - 2.14723i) q^{40} +(1.00855 - 1.74686i) q^{41} +(-3.49067 + 2.96905i) q^{42} +(1.69618 + 2.93788i) q^{43} +(0.940488 - 0.542991i) q^{44} +(-7.32319 + 10.5996i) q^{45} +7.63945 q^{46} +(4.97996 + 8.62555i) q^{47} +(-0.926039 + 1.46371i) q^{48} +(-5.76245 - 3.97419i) q^{49} +(11.6414 + 6.72118i) q^{50} +(-3.62652 + 5.73213i) q^{51} +(-2.47541 - 2.62151i) q^{52} +(2.81574 + 1.62567i) q^{53} +(0.629682 - 5.15786i) q^{54} +(4.03889 + 2.33185i) q^{55} +(-2.52611 - 0.786623i) q^{56} +(-6.22300 + 3.26436i) q^{57} +(-1.06731 + 1.84864i) q^{58} -1.64474 q^{59} +(-7.43212 - 0.301118i) q^{60} +(12.0708 + 6.96907i) q^{61} +(-0.606034 + 1.04968i) q^{62} +(7.85878 - 1.11334i) q^{63} -1.00000 q^{64} +(4.43442 - 14.8353i) q^{65} +(-1.87943 - 0.0761468i) q^{66} +(-4.01884 - 6.96084i) q^{67} -3.91616 q^{68} +(-11.1819 - 7.07443i) q^{69} +(-2.49860 - 11.0839i) q^{70} +(-2.68997 + 1.55305i) q^{71} +(2.71091 - 1.28490i) q^{72} +(3.86528 + 2.23162i) q^{73} +6.07856i q^{74} +(-10.8156 - 20.6183i) q^{75} +(-3.51361 - 2.02858i) q^{76} +(-0.631845 - 2.80290i) q^{77} +(1.19566 + 6.12947i) q^{78} +(2.33626 + 4.04652i) q^{79} +(-2.14723 - 3.71911i) q^{80} +(-5.69805 + 6.96651i) q^{81} +(-1.74686 - 1.00855i) q^{82} -4.52632 q^{83} +(2.96905 + 3.49067i) q^{84} +(-8.40889 - 14.5646i) q^{85} +(2.93788 - 1.69618i) q^{86} +(3.27414 - 1.71750i) q^{87} +(-0.542991 - 0.940488i) q^{88} -16.9794 q^{89} +(10.5996 + 7.32319i) q^{90} +(-8.56944 + 4.19102i) q^{91} -7.63945i q^{92} +(1.85910 - 0.975219i) q^{93} +(8.62555 - 4.97996i) q^{94} -17.4233i q^{95} +(1.46371 + 0.926039i) q^{96} +(10.7814 - 6.22463i) q^{97} +(-3.97419 + 5.76245i) q^{98} +(2.68043 + 1.85189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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