LMFDB - Embedded newform 731.2.m.b.87.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.10
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00313 - 1.00313i) q^{2} +(-1.37786 + 0.570727i) q^{3} +0.0125460i q^{4} +(-0.979244 - 2.36410i) q^{5} +(1.95469 + 0.809657i) q^{6} +(1.38293 - 3.33870i) q^{7} +(-1.99368 + 1.99368i) q^{8} +(-0.548561 + 0.548561i) q^{9} +O(q^{10})$	\(q+(-1.00313 - 1.00313i) q^{2} +(-1.37786 + 0.570727i) q^{3} +0.0125460i q^{4} +(-0.979244 - 2.36410i) q^{5} +(1.95469 + 0.809657i) q^{6} +(1.38293 - 3.33870i) q^{7} +(-1.99368 + 1.99368i) q^{8} +(-0.548561 + 0.548561i) q^{9} +(-1.38920 + 3.35382i) q^{10} +(-4.88656 - 2.02408i) q^{11} +(-0.00716031 - 0.0172865i) q^{12} -2.49841i q^{13} +(-4.73642 + 1.96189i) q^{14} +(2.69851 + 2.69851i) q^{15} +4.02493 q^{16} +(-0.269071 - 4.11432i) q^{17} +1.10056 q^{18} +(3.95069 + 3.95069i) q^{19} +(0.0296599 - 0.0122855i) q^{20} +5.38952i q^{21} +(2.87144 + 6.93228i) q^{22} +(-2.73286 - 1.13199i) q^{23} +(1.60916 - 3.88485i) q^{24} +(-1.09453 + 1.09453i) q^{25} +(-2.50624 + 2.50624i) q^{26} +(2.15494 - 5.20249i) q^{27} +(0.0418871 + 0.0173502i) q^{28} +(-0.915903 - 2.21119i) q^{29} -5.41393i q^{30} +(-4.16970 + 1.72715i) q^{31} +(-0.0501831 - 0.0501831i) q^{32} +7.88817 q^{33} +(-3.85729 + 4.39711i) q^{34} -9.24725 q^{35} +(-0.00688222 - 0.00688222i) q^{36} +(1.24147 - 0.514233i) q^{37} -7.92612i q^{38} +(1.42591 + 3.44245i) q^{39} +(6.66556 + 2.76096i) q^{40} +(0.0108141 - 0.0261075i) q^{41} +(5.40640 - 5.40640i) q^{42} +(0.707107 - 0.707107i) q^{43} +(0.0253940 - 0.0613066i) q^{44} +(1.83403 + 0.759680i) q^{45} +(1.60589 + 3.87695i) q^{46} +10.3190i q^{47} +(-5.54578 + 2.29714i) q^{48} +(-4.28464 - 4.28464i) q^{49} +2.19592 q^{50} +(2.71889 + 5.51537i) q^{51} +0.0313450 q^{52} +(7.37211 + 7.37211i) q^{53} +(-7.38047 + 3.05709i) q^{54} +13.5344i q^{55} +(3.89916 + 9.41341i) q^{56} +(-7.69824 - 3.18872i) q^{57} +(-1.29934 + 3.13688i) q^{58} +(5.84239 - 5.84239i) q^{59} +(-0.0338554 + 0.0338554i) q^{60} +(-5.81324 + 14.0344i) q^{61} +(5.91531 + 2.45020i) q^{62} +(1.07286 + 2.59010i) q^{63} -7.94919i q^{64} +(-5.90651 + 2.44656i) q^{65} +(-7.91288 - 7.91288i) q^{66} +3.51876 q^{67} +(0.0516180 - 0.00337576i) q^{68} +4.41155 q^{69} +(9.27621 + 9.27621i) q^{70} +(-6.96833 + 2.88638i) q^{71} -2.18731i q^{72} +(0.633365 + 1.52908i) q^{73} +(-1.76120 - 0.729512i) q^{74} +(0.883430 - 2.13279i) q^{75} +(-0.0495651 + 0.0495651i) q^{76} +(-13.5156 + 13.5156i) q^{77} +(2.02286 - 4.88361i) q^{78} +(-11.8762 - 4.91929i) q^{79} +(-3.94139 - 9.51536i) q^{80} +6.07081i q^{81} +(-0.0370372 + 0.0153413i) q^{82} +(3.16512 + 3.16512i) q^{83} -0.0676167 q^{84} +(-9.46318 + 4.66503i) q^{85} -1.41864 q^{86} +(2.52397 + 2.52397i) q^{87} +(13.7776 - 5.70686i) q^{88} -10.6684i q^{89} +(-1.07771 - 2.60183i) q^{90} +(-8.34144 - 3.45514i) q^{91} +(0.0142019 - 0.0342864i) q^{92} +(4.75952 - 4.75952i) q^{93} +(10.3513 - 10.3513i) q^{94} +(5.47115 - 13.2085i) q^{95} +(0.0977859 + 0.0405042i) q^{96} +(2.43532 + 5.87939i) q^{97} +8.59612i q^{98} +(3.79091 - 1.57025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00313	−	1.00313i	−0.709321	−	0.709321i	0.257071	−	0.966392i	$-0.417242\pi$
$2$	−1.00313	−	1.00313i	−0.709321	−	0.709321i	−0.966392	+	0.257071i	$0.917242\pi$
$3$	−1.37786	+	0.570727i	−0.795506	+	0.329509i	−0.743155	−	0.669119i	$-0.766671\pi$
$3$	−1.37786	+	0.570727i	−0.795506	+	0.329509i	−0.0523509	+	0.998629i	$0.516671\pi$
$4$			0.0125460i			0.00627298i
$5$	−0.979244	−	2.36410i	−0.437931	−	1.05726i	−0.976662	−	0.214781i	$-0.931096\pi$
$5$	−0.979244	−	2.36410i	−0.437931	−	1.05726i	0.538731	−	0.842478i	$-0.318904\pi$
$6$	1.95469	+	0.809657i	0.797997	+	0.330541i
$7$	1.38293	−	3.33870i	0.522700	−	1.26191i	−0.413520	−	0.910495i	$-0.635701\pi$
$7$	1.38293	−	3.33870i	0.522700	−	1.26191i	0.936220	−	0.351414i	$-0.114299\pi$
$8$	−1.99368	+	1.99368i	−0.704872	+	0.704872i
$9$	−0.548561	+	0.548561i	−0.182854	+	0.182854i
$10$	−1.38920	+	3.35382i	−0.439303	+	1.06057i
$11$	−4.88656	−	2.02408i	−1.47335	−	0.610283i	−0.505732	−	0.862691i	$-0.668778\pi$
$11$	−4.88656	−	2.02408i	−1.47335	−	0.610283i	−0.967621	+	0.252408i	$0.918778\pi$
$12$	−0.00716031	−	0.0172865i	−0.00206700	−	0.00499019i
$13$		−	2.49841i		−	0.692935i	−0.938062	−	0.346468i	$-0.887381\pi$
$13$		−	2.49841i		−	0.692935i	0.938062	−	0.346468i	$-0.112619\pi$
$14$	−4.73642	+	1.96189i	−1.26586	+	0.524337i
$15$	2.69851	+	2.69851i	0.696753	+	0.696753i
$16$	4.02493			1.00623
$17$	−0.269071	−	4.11432i	−0.0652594	−	0.997868i
$17$	−0.269071	−	4.11432i	−0.0652594	−	0.997868i
$18$	1.10056			0.259404
$19$	3.95069	+	3.95069i	0.906350	+	0.906350i	0.995976	−	0.0896259i	$-0.0285671\pi$
$19$	3.95069	+	3.95069i	0.906350	+	0.906350i	−0.0896259	+	0.995976i	$0.528567\pi$
$20$	0.0296599	−	0.0122855i	0.00663216	−	0.00274713i
$21$			5.38952i			1.17609i
$22$	2.87144	+	6.93228i	0.612194	+	1.47797i
$23$	−2.73286	−	1.13199i	−0.569841	−	0.236036i	0.0791102	−	0.996866i	$-0.474792\pi$
$23$	−2.73286	−	1.13199i	−0.569841	−	0.236036i	−0.648951	+	0.760830i	$0.724792\pi$
$24$	1.60916	−	3.88485i	0.328468	−	0.792991i
$25$	−1.09453	+	1.09453i	−0.218907	+	0.218907i
$26$	−2.50624	+	2.50624i	−0.491514	+	0.491514i
$27$	2.15494	−	5.20249i	0.414718	−	1.00122i
$28$	0.0418871	+	0.0173502i	0.00791592	+	0.00327888i
$29$	−0.915903	−	2.21119i	−0.170079	−	0.410607i	0.815740	−	0.578419i	$-0.196330\pi$
$29$	−0.915903	−	2.21119i	−0.170079	−	0.410607i	−0.985819	+	0.167812i	$0.946330\pi$
$30$		−	5.41393i		−	0.988444i
$31$	−4.16970	+	1.72715i	−0.748900	+	0.310204i	−0.724293	−	0.689493i	$-0.757833\pi$
$31$	−4.16970	+	1.72715i	−0.748900	+	0.310204i	−0.0246071	+	0.999697i	$0.507833\pi$
$32$	−0.0501831	−	0.0501831i	−0.00887120	−	0.00887120i
$33$	7.88817			1.37315
$34$	−3.85729	+	4.39711i	−0.661519	+	0.754099i
$35$	−9.24725			−1.56307
$36$	−0.00688222	−	0.00688222i	−0.00114704	−	0.00114704i
$37$	1.24147	−	0.514233i	0.204096	−	0.0845394i	−0.278294	−	0.960496i	$-0.589769\pi$
$37$	1.24147	−	0.514233i	0.204096	−	0.0845394i	0.482390	+	0.875957i	$0.339769\pi$
$38$		−	7.92612i		−	1.28579i
$39$	1.42591	+	3.44245i	0.228329	+	0.551234i
$40$	6.66556	+	2.76096i	1.05392	+	0.436547i
$41$	0.0108141	−	0.0261075i	0.00168888	−	0.00407731i	−0.923033	−	0.384721i	$-0.874298\pi$
$41$	0.0108141	−	0.0261075i	0.00168888	−	0.00407731i	0.924722	+	0.380644i	$0.124298\pi$
$42$	5.40640	−	5.40640i	0.834226	−	0.834226i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	0.0253940	−	0.0613066i	0.00382829	−	0.00924231i
$45$	1.83403	+	0.759680i	0.273401	+	0.113246i
$46$	1.60589	+	3.87695i	0.236775	+	0.571626i
$47$			10.3190i			1.50518i	0.658487	+	0.752592i	$0.271197\pi$
$47$			10.3190i			1.50518i	−0.658487	+	0.752592i	$0.728803\pi$
$48$	−5.54578	+	2.29714i	−0.800465	+	0.331563i
$49$	−4.28464	−	4.28464i	−0.612092	−	0.612092i
$50$	2.19592			0.310550
$51$	2.71889	+	5.51537i	0.380721	+	0.772306i
$52$	0.0313450			0.00434677
$53$	7.37211	+	7.37211i	1.01264	+	1.01264i	0.999919	+	0.0127178i	$0.00404831\pi$
$53$	7.37211	+	7.37211i	1.01264	+	1.01264i	0.0127178	+	0.999919i	$0.495952\pi$
$54$	−7.38047	+	3.05709i	−1.00435	+	0.416017i
$55$			13.5344i			1.82498i
$56$	3.89916	+	9.41341i	0.521047	+	1.25792i
$57$	−7.69824	−	3.18872i	−1.01966	−	0.422356i
$58$	−1.29934	+	3.13688i	−0.170612	+	0.411893i
$59$	5.84239	−	5.84239i	0.760614	−	0.760614i	−0.215819	−	0.976433i	$-0.569242\pi$
$59$	5.84239	−	5.84239i	0.760614	−	0.760614i	0.976433	+	0.215819i	$0.0692422\pi$
$60$	−0.0338554	+	0.0338554i	−0.00437072	+	0.00437072i
$61$	−5.81324	+	14.0344i	−0.744309	+	1.79692i	−0.156929	+	0.987610i	$0.550159\pi$
$61$	−5.81324	+	14.0344i	−0.744309	+	1.79692i	−0.587380	+	0.809311i	$0.699841\pi$
$62$	5.91531	+	2.45020i	0.751245	+	0.311176i
$63$	1.07286	+	2.59010i	0.135167	+	0.326322i
$64$		−	7.94919i		−	0.993649i
$65$	−5.90651	+	2.44656i	−0.732612	+	0.303458i
$66$	−7.91288	−	7.91288i	−0.974008	−	0.974008i
$67$	3.51876			0.429885			0.214943	−	0.976627i	$-0.431044\pi$
$67$	3.51876			0.429885			0.214943	+	0.976627i	$0.431044\pi$
$68$	0.0516180	−	0.00337576i	0.00625960	−	0.000409371i
$69$	4.41155			0.531088
$70$	9.27621	+	9.27621i	1.10872	+	1.10872i
$71$	−6.96833	+	2.88638i	−0.826989	+	0.342550i	−0.755710	−	0.654906i	$-0.772708\pi$
$71$	−6.96833	+	2.88638i	−0.826989	+	0.342550i	−0.0712789	+	0.997456i	$0.522708\pi$
$72$		−	2.18731i		−	0.257777i
$73$	0.633365	+	1.52908i	0.0741298	+	0.178965i	0.956601	−	0.291402i	$-0.0941216\pi$
$73$	0.633365	+	1.52908i	0.0741298	+	0.178965i	−0.882471	+	0.470367i	$0.844122\pi$
$74$	−1.76120	−	0.729512i	−0.204735	−	0.0848041i
$75$	0.883430	−	2.13279i	0.102010	−	0.246273i
$76$	−0.0495651	+	0.0495651i	−0.00568551	+	0.00568551i
$77$	−13.5156	+	13.5156i	−1.54024	+	1.54024i
$78$	2.02286	−	4.88361i	0.229044	−	0.552960i
$79$	−11.8762	−	4.91929i	−1.33618	−	0.553463i	−0.403767	−	0.914862i	$-0.632299\pi$
$79$	−11.8762	−	4.91929i	−1.33618	−	0.553463i	−0.932411	+	0.361399i	$0.882299\pi$
$80$	−3.94139	−	9.51536i	−0.440661	−	1.06385i
$81$			6.07081i			0.674535i
$82$	−0.0370372	+	0.0153413i	−0.00409007	+	0.00169416i
$83$	3.16512	+	3.16512i	0.347417	+	0.347417i	0.859147	−	0.511730i	$-0.170995\pi$
$83$	3.16512	+	3.16512i	0.347417	+	0.347417i	−0.511730	+	0.859147i	$0.670995\pi$
$84$	−0.0676167			−0.00737759
$85$	−9.46318	+	4.66503i	−1.02643	+	0.505994i
$86$	−1.41864			−0.152976
$87$	2.52397	+	2.52397i	0.270598	+	0.270598i
$88$	13.7776	−	5.70686i	1.46870	−	0.608354i
$89$		−	10.6684i		−	1.13085i	−0.824800	−	0.565424i	$-0.808713\pi$
$89$		−	10.6684i		−	1.13085i	0.824800	−	0.565424i	$-0.191287\pi$
$90$	−1.07771	−	2.60183i	−0.113601	−	0.274257i
$91$	−8.34144	−	3.45514i	−0.874421	−	0.362197i
$92$	0.0142019	−	0.0342864i	0.00148065	−	0.00357460i
$93$	4.75952	−	4.75952i	0.493539	−	0.493539i
$94$	10.3513	−	10.3513i	1.06766	−	1.06766i
$95$	5.47115	−	13.2085i	0.561328	−	1.35517i
$96$	0.0977859	+	0.0405042i	0.00998023	+	0.00413395i
$97$	2.43532	+	5.87939i	0.247270	+	0.596962i	0.997970	−	0.0636809i	$-0.0202840\pi$
$97$	2.43532	+	5.87939i	0.247270	+	0.596962i	−0.750701	+	0.660642i	$0.770284\pi$
$98$			8.59612i			0.868340i
$99$	3.79091	−	1.57025i	0.381001	−	0.157816i
$100$	−0.0137320	−	0.0137320i	−0.00137320	−	0.00137320i
$101$	6.54297			0.651050			0.325525	−	0.945533i	$-0.394459\pi$
$101$	6.54297			0.651050			0.325525	+	0.945533i	$0.394459\pi$
$102$	2.80524	−	8.26005i	0.277760	−	0.817867i
$103$	−2.36708			−0.233235			−0.116618	−	0.993177i	$-0.537205\pi$
$103$	−2.36708			−0.233235			−0.116618	+	0.993177i	$0.537205\pi$
$104$	4.98103	+	4.98103i	0.488430	+	0.488430i
$105$	12.7414	−	5.27766i	1.24343	−	0.515046i
$106$		−	14.7904i		−	1.43657i
$107$	5.78746	+	13.9722i	0.559495	+	1.35074i	0.910167	+	0.414242i	$0.135953\pi$
$107$	5.78746	+	13.9722i	0.559495	+	1.35074i	−0.350672	+	0.936498i	$0.614047\pi$
$108$	0.0652702	+	0.0270358i	0.00628062	+	0.00260152i
$109$	5.39621	−	13.0276i	0.516863	−	1.24782i	−0.422958	−	0.906149i	$-0.639008\pi$
$109$	5.39621	−	13.0276i	0.516863	−	1.24782i	0.939821	−	0.341668i	$-0.110992\pi$
$110$	13.5768	−	13.5768i	1.29450	−	1.29450i
$111$	−1.41708	+	1.41708i	−0.134503	+	0.134503i
$112$	5.56622	−	13.4380i	0.525958	−	1.26978i
$113$	−17.6715	−	7.31976i	−1.66239	−	0.688585i	−0.664136	−	0.747612i	$-0.731200\pi$
$113$	−17.6715	−	7.31976i	−1.66239	−	0.688585i	−0.998256	+	0.0590266i	$0.981200\pi$
$114$	4.52365	+	10.9211i	0.423678	+	1.02285i
$115$			7.56926i			0.705837i
$116$	0.0277414	−	0.0114909i	0.00257573	−	0.00106690i
$117$	1.37053	+	1.37053i	0.126706	+	0.126706i
$118$	−11.7214			−1.07904
$119$	−14.1086	−	4.79148i	−1.29333	−	0.439234i
$120$	−10.7599			−0.982243
$121$	12.0034	+	12.0034i	1.09122	+	1.09122i
$122$	19.9098	−	8.24691i	1.80255	−	0.746640i
$123$			0.0421443i			0.00380002i
$124$	−0.0216687	−	0.0523128i	−0.00194591	−	0.00469783i
$125$	−8.16111	−	3.38044i	−0.729952	−	0.302356i
$126$	1.52200	−	3.67443i	0.135590	−	0.327344i
$127$	1.88479	−	1.88479i	0.167248	−	0.167248i	−0.618520	−	0.785769i	$-0.712268\pi$
$127$	1.88479	−	1.88479i	0.167248	−	0.167248i	0.785769	+	0.618520i	$0.212268\pi$
$128$	−8.07445	+	8.07445i	−0.713687	+	0.713687i
$129$	−0.570727	+	1.37786i	−0.0502497	+	0.121313i
$130$	8.37922	+	3.47079i	0.734906	+	0.304408i
$131$	−2.57626	−	6.21963i	−0.225089	−	0.543412i	0.770478	−	0.637466i	$-0.220017\pi$
$131$	−2.57626	−	6.21963i	−0.225089	−	0.543412i	−0.995567	+	0.0940540i	$0.970017\pi$
$132$			0.0989647i			0.00861377i
$133$	18.6537	−	7.72661i	1.61748	−	0.669982i
$134$	−3.52978	−	3.52978i	−0.304927	−	0.304927i
$135$	−14.4094			−1.24017
$136$	8.73906	+	7.66618i	0.749369	+	0.657370i
$137$	−9.47931			−0.809872			−0.404936	−	0.914345i	$-0.632706\pi$
$137$	−9.47931			−0.809872			−0.404936	+	0.914345i	$0.632706\pi$
$138$	−4.42536	−	4.42536i	−0.376712	−	0.376712i
$139$	−1.07951	+	0.447149i	−0.0915632	+	0.0379267i	−0.427995	−	0.903781i	$-0.640780\pi$
$139$	−1.07951	+	0.447149i	−0.0915632	+	0.0379267i	0.336432	+	0.941708i	$0.390780\pi$
$140$		−	0.116016i		−	0.00980511i
$141$	−5.88934	−	14.2181i	−0.495972	−	1.19738i
$142$	9.88557	+	4.09474i	0.829579	+	0.343623i
$143$	−5.05699	+	12.2086i	−0.422886	+	1.02094i
$144$	−2.20792	+	2.20792i	−0.183994	+	0.183994i
$145$	−4.33058	+	4.33058i	−0.359635	+	0.359635i
$146$	0.898519	−	2.16922i	0.0743619	−	0.179526i
$147$	8.34899	+	3.45826i	0.688613	+	0.285233i
$148$	0.00645154	+	0.0155754i	0.000530313	+	0.00128029i
$149$		−	20.8446i		−	1.70766i	−0.520552	−	0.853830i	$-0.674274\pi$
$149$		−	20.8446i		−	1.70766i	0.520552	−	0.853830i	$-0.325726\pi$
$150$	−3.02567	+	1.25327i	−0.247045	+	0.102329i
$151$	−12.1417	−	12.1417i	−0.988074	−	0.988074i	0.0118560	−	0.999930i	$-0.496226\pi$
$151$	−12.1417	−	12.1417i	−0.988074	−	0.988074i	−0.999930	+	0.0118560i	$0.996226\pi$
$152$	−15.7528			−1.27772
$153$	2.40456	+	2.10935i	0.194397	+	0.170531i
$154$	27.1158			2.18505
$155$	8.16630	+	8.16630i	0.655933	+	0.655933i
$156$	−0.0431889	+	0.0178894i	−0.00345788	+	0.00143230i
$157$		−	24.7152i		−	1.97249i	−0.165304	−	0.986243i	$-0.552861\pi$
$157$		−	24.7152i		−	1.97249i	0.165304	−	0.986243i	$-0.447139\pi$
$158$	6.97871	+	16.8481i	0.555196	+	1.34036i
$159$	−14.3652	−	5.95025i	−1.13923	−	0.471885i
$160$	−0.0694965	+	0.167779i	−0.00549418	+	0.0132641i
$161$	−7.55873	+	7.55873i	−0.595712	+	0.595712i
$162$	6.08983	−	6.08983i	0.478462	−	0.478462i
$163$	−1.15946	+	2.79917i	−0.0908156	+	0.219248i	−0.962760	−	0.270356i	$-0.912859\pi$
$163$	−1.15946	+	2.79917i	−0.0908156	+	0.219248i	0.871945	+	0.489604i	$0.162859\pi$
$164$	0.000327543	0	0.000135673i	2.55768e−5	0	1.05943e-5i
$165$	−7.72445	−	18.6485i	−0.601347	−	1.45178i
$166$		−	6.35006i		−	0.492861i
$167$	12.3431	−	5.11268i	0.955138	−	0.395631i	0.149978	−	0.988689i	$-0.452080\pi$
$167$	12.3431	−	5.11268i	0.955138	−	0.395631i	0.805160	+	0.593058i	$0.202080\pi$
$168$	−10.7450	−	10.7450i	−0.828993	−	0.828993i
$169$	6.75793			0.519841
$170$	14.1725	+	4.81318i	1.08698	+	0.369154i
$171$	−4.33439			−0.331459
$172$	0.00887133	+	0.00887133i	0.000676432	+	0.000676432i
$173$	8.48165	−	3.51321i	0.644848	−	0.267105i	−0.0361990	−	0.999345i	$-0.511525\pi$
$173$	8.48165	−	3.51321i	0.644848	−	0.267105i	0.681047	+	0.732240i	$0.261525\pi$
$174$		−	5.06374i		−	0.383881i
$175$	2.14065	+	5.16798i	0.161818	+	0.390663i
$176$	−19.6681	−	8.14679i	−1.48254	−	0.614087i
$177$	−4.71556	+	11.3844i	−0.354444	+	0.855702i
$178$	−10.7018	+	10.7018i	−0.802135	+	0.802135i
$179$	−9.67478	+	9.67478i	−0.723127	+	0.723127i	−0.969241	−	0.246114i	$-0.920846\pi$
$179$	−9.67478	+	9.67478i	−0.723127	+	0.723127i	0.246114	+	0.969241i	$0.420846\pi$
$180$	−0.00953091	+	0.0230097i	−0.000710392	+	0.00171504i
$181$	0.357522	+	0.148090i	0.0265744	+	0.0110075i	0.395931	−	0.918280i	$-0.370422\pi$
$181$	0.357522	+	0.148090i	0.0265744	+	0.0110075i	−0.369357	+	0.929288i	$0.620422\pi$
$182$	4.90161	+	11.8335i	0.363331	+	0.877159i
$183$		−	22.6552i		−	1.67472i
$184$	7.70527	−	3.19163i	0.568040	−	0.235290i
$185$	−2.43140	−	2.43140i	−0.178760	−	0.178760i
$186$	−9.54884			−0.700155
$187$	−7.01287	+	20.6495i	−0.512832	+	1.51004i
$188$	−0.129462			−0.00944198
$189$	−14.3894	−	14.3894i	−1.04667	−	1.04667i
$190$	−18.7382	+	7.76160i	−1.35941	+	0.563086i
$191$			23.9759i			1.73483i	0.497582	+	0.867417i	$0.334221\pi$
$191$			23.9759i			1.73483i	−0.497582	+	0.867417i	$0.665779\pi$
$192$	4.53682	+	10.9528i	0.327416	+	0.790453i
$193$	−2.62960	−	1.08922i	−0.189283	−	0.0784035i	0.286029	−	0.958221i	$-0.407665\pi$
$193$	−2.62960	−	1.08922i	−0.189283	−	0.0784035i	−0.475312	+	0.879818i	$0.657665\pi$
$194$	3.45485	−	8.34075i	0.248044	−	0.598831i
$195$	6.74200	−	6.74200i	0.482805	−	0.482805i
$196$	0.0537549	−	0.0537549i	0.00383964	−	0.00383964i
$197$	5.71069	−	13.7868i	0.406870	−	0.982271i	−0.579086	−	0.815267i	$-0.696590\pi$
$197$	5.71069	−	13.7868i	0.406870	−	0.982271i	0.985956	−	0.167005i	$-0.0534096\pi$
$198$	−5.37794	−	2.22762i	−0.382194	−	0.158310i
$199$	−0.924329	−	2.23153i	−0.0655240	−	0.158189i	0.887726	−	0.460373i	$-0.152284\pi$
$199$	−0.924329	−	2.23153i	−0.0655240	−	0.158189i	−0.953250	+	0.302184i	$0.902284\pi$
$200$		−	4.36429i		−	0.308602i
$201$	−4.84835	+	2.00825i	−0.341976	+	0.141651i
$202$	−6.56346	−	6.56346i	−0.461804	−	0.461804i
$203$	−8.64911			−0.607049
$204$	−0.0691956	+	0.0341111i	−0.00484466	+	0.00238825i
$205$	−0.0723104			−0.00505038
$206$	2.37449	+	2.37449i	0.165439	+	0.165439i
$207$	2.12011	−	0.878177i	0.147358	−	0.0610375i
$208$		−	10.0559i		−	0.697255i
$209$	−11.3088	−	27.3018i	−0.782243	−	1.88850i
$210$	−18.0755	−	7.48711i	−1.24733	−	0.516659i
$211$	−2.10093	+	5.07209i	−0.144634	+	0.349177i	−0.979550	−	0.201200i	$-0.935516\pi$
$211$	−2.10093	+	5.07209i	−0.144634	+	0.349177i	0.834916	+	0.550377i	$0.185516\pi$
$212$	−0.0924901	+	0.0924901i	−0.00635225	+	0.00635225i
$213$	7.95403	−	7.95403i	0.545001	−	0.545001i
$214$	8.21033	−	19.8215i	0.561247	−	1.35497i
$215$	−2.36410	−	0.979244i	−0.161231	−	0.0667839i
$216$	6.07582	+	14.6683i	0.413408	+	0.998054i
$217$			16.3099i			1.10719i
$218$	−18.4815	+	7.65529i	−1.25173	+	0.518482i
$219$	−1.74537	−	1.74537i	−0.117941	−	0.117941i
$220$	−0.169802			−0.0114480
$221$	−10.2793	+	0.672252i	−0.691458	+	0.0452205i
$222$	2.84303			0.190812
$223$	−1.87600	−	1.87600i	−0.125626	−	0.125626i	0.641498	−	0.767125i	$-0.278313\pi$
$223$	−1.87600	−	1.87600i	−0.125626	−	0.125626i	−0.767125	+	0.641498i	$0.778313\pi$
$224$	−0.236946	+	0.0981462i	−0.0158316	+	0.00655767i
$225$		−	1.20084i		−	0.0800558i
$226$	10.3841	+	25.0695i	0.690742	+	1.66760i
$227$	17.0134	+	7.04716i	1.12922	+	0.467737i	0.867514	−	0.497412i	$-0.165716\pi$
$227$	17.0134	+	7.04716i	1.12922	+	0.467737i	0.261702	+	0.965149i	$0.415716\pi$
$228$	0.0400055	−	0.0965818i	0.00264943	−	0.00639628i
$229$	−5.20699	+	5.20699i	−0.344088	+	0.344088i	−0.857902	−	0.513814i	$-0.828232\pi$
$229$	−5.20699	+	5.20699i	−0.344088	+	0.344088i	0.513814	+	0.857902i	$0.328232\pi$
$230$	7.59296	−	7.59296i	0.500665	−	0.500665i
$231$	10.9088	−	26.3362i	0.717748	−	1.73280i
$232$	6.23441	+	2.58238i	0.409309	+	0.169541i
$233$	−1.97802	−	4.77535i	−0.129584	−	0.312844i	0.845749	−	0.533580i	$-0.179154\pi$
$233$	−1.97802	−	4.77535i	−0.129584	−	0.312844i	−0.975333	+	0.220737i	$0.929154\pi$
$234$		−	2.74965i		−	0.179750i
$235$	24.3952	−	10.1048i	1.59137	−	0.659167i
$236$	0.0732983	+	0.0732983i	0.00477132	+	0.00477132i
$237$	19.1713			1.24531
$238$	9.34626	+	18.9592i	0.605828	+	1.22894i
$239$	−21.9217			−1.41799			−0.708997	−	0.705211i	$-0.750852\pi$
$239$	−21.9217			−1.41799			−0.708997	+	0.705211i	$0.750852\pi$
$240$	10.8613	+	10.8613i	0.701097	+	0.701097i
$241$	−19.5438	+	8.09532i	−1.25893	+	0.521465i	−0.909581	−	0.415527i	$-0.863597\pi$
$241$	−19.5438	+	8.09532i	−1.25893	+	0.521465i	−0.349348	+	0.936993i	$0.613597\pi$
$242$		−	24.0820i		−	1.54805i
$243$	3.00004	+	7.24275i	0.192453	+	0.464623i
$244$	−0.176075	−	0.0729326i	−0.0112720	−	0.00466903i
$245$	−5.93363	+	14.3251i	−0.379086	+	0.915194i
$246$	0.0422762	−	0.0422762i	0.00269543	−	0.00269543i
$247$	9.87045	−	9.87045i	0.628042	−	0.628042i
$248$	4.86966	−	11.7564i	0.309224	−	0.746532i
$249$	−6.16750	−	2.55466i	−0.390849	−	0.161895i
$250$	4.79564	+	11.5777i	0.303303	+	0.732238i
$251$			19.4382i			1.22693i	0.789722	+	0.613464i	$0.210225\pi$
$251$			19.4382i			1.22693i	−0.789722	+	0.613464i	$0.789775\pi$
$252$	−0.0324953	+	0.0134600i	−0.00204701	+	0.000847900i
$253$	11.0631	+	11.0631i	0.695528	+	0.695528i
$254$	−3.78139			−0.237266
$255$	10.3765	−	11.8286i	0.649799	−	0.740738i
$256$	0.301091			0.0188182
$257$	−16.6936	−	16.6936i	−1.04132	−	1.04132i	−0.999109	−	0.0422090i	$-0.986560\pi$
$257$	−16.6936	−	16.6936i	−1.04132	−	1.04132i	−0.0422090	−	0.999109i	$-0.513440\pi$
$258$	1.95469	−	0.809657i	0.121693	−	0.0504071i
$259$		−	4.85603i		−	0.301739i
$260$	−0.0306944	−	0.0741028i	−0.00190358	−	0.00459566i
$261$	1.71540	+	0.710542i	0.106181	+	0.0439814i
$262$	−3.65479	+	8.82344i	−0.225794	+	0.545114i
$263$	−10.9806	+	10.9806i	−0.677093	+	0.677093i	−0.959341	−	0.282248i	$-0.908920\pi$
$263$	−10.9806	+	10.9806i	−0.677093	+	0.677093i	0.282248	+	0.959341i	$0.408920\pi$
$264$	−15.7265	+	15.7265i	−0.967898	+	0.967898i
$265$	10.2093	−	24.6475i	0.627155	−	1.51408i
$266$	−26.4629	−	10.9613i	−1.62254	−	0.672080i
$267$	6.08874	+	14.6995i	0.372625	+	0.899596i
$268$			0.0441462i			0.00269666i
$269$	−9.69199	+	4.01455i	−0.590931	+	0.244772i	−0.658051	−	0.752973i	$-0.728619\pi$
$269$	−9.69199	+	4.01455i	−0.590931	+	0.244772i	0.0671202	+	0.997745i	$0.478619\pi$
$270$	14.4546	+	14.4546i	0.879676	+	0.879676i
$271$	−6.18248			−0.375559			−0.187779	−	0.982211i	$-0.560129\pi$
$271$	−6.18248			−0.375559			−0.187779	+	0.982211i	$0.560129\pi$
$272$	−1.08300	−	16.5599i	−0.0656662	−	1.00409i
$273$	13.4653			0.814954
$274$	9.50899	+	9.50899i	0.574459	+	0.574459i
$275$	7.56392	−	3.13308i	0.456122	−	0.188932i
$276$			0.0553471i			0.00333150i
$277$	6.07098	+	14.6566i	0.364770	+	0.880632i	0.994589	+	0.103890i	$0.0331291\pi$
$277$	6.07098	+	14.6566i	0.364770	+	0.880632i	−0.629819	+	0.776742i	$0.716871\pi$
$278$	1.53144	+	0.634345i	0.0918499	+	0.0380455i
$279$	1.33989	−	3.23478i	0.0802170	−	0.193661i
$280$	18.4360	−	18.4360i	1.10176	−	1.10176i
$281$	21.3571	−	21.3571i	1.27406	−	1.27406i	0.330119	−	0.943939i	$-0.392911\pi$
$281$	21.3571	−	21.3571i	1.27406	−	1.27406i	0.943939	−	0.330119i	$-0.107089\pi$
$282$	−8.35487	+	20.1704i	−0.497525	+	1.20113i
$283$	−3.71783	−	1.53998i	−0.221002	−	0.0915421i	0.269435	−	0.963019i	$-0.413163\pi$
$283$	−3.71783	−	1.53998i	−0.221002	−	0.0915421i	−0.490437	+	0.871476i	$0.663163\pi$
$284$	−0.0362124	−	0.0874244i	−0.00214881	−	0.00518768i
$285$			21.3220i			1.26300i
$286$	17.3197	−	7.17406i	1.02414	−	0.424211i
$287$	−0.0722099	−	0.0722099i	−0.00426241	−	0.00426241i
$288$	0.0550570			0.00324426
$289$	−16.8552	+	2.21409i	−0.991482	+	0.130241i
$290$	8.68828			0.510194
$291$	−6.71105	−	6.71105i	−0.393409	−	0.393409i
$292$	−0.0191838	+	0.00794617i	−0.00112264	+	0.000465014i
$293$		−	13.7171i		−	0.801363i	−0.916217	−	0.400681i	$-0.868773\pi$
$293$		−	13.7171i		−	0.801363i	0.916217	−	0.400681i	$-0.131227\pi$
$294$	−4.90604	−	11.8442i	−0.286126	−	0.690769i
$295$	−19.5331	−	8.09089i	−1.13726	−	0.471070i
$296$	−1.44987	+	3.50030i	−0.0842721	+	0.203451i
$297$	−21.0605	+	21.0605i	−1.22205	+	1.22205i
$298$	−20.9099	+	20.9099i	−1.21128	+	1.21128i
$299$	−2.82817	+	6.82782i	−0.163558	+	0.394863i
$300$	0.0267579	+	0.0110835i	0.00154487	+	0.000639905i
$301$	−1.38293	−	3.33870i	−0.0797110	−	0.192439i
$302$			24.3594i			1.40172i
$303$	−9.01528	+	3.73425i	−0.517914	+	0.214527i
$304$	15.9013	+	15.9013i	0.911999	+	0.911999i
$305$	38.8714			2.22577
$306$	−0.296129	−	4.52804i	−0.0169286	−	0.258851i
$307$	−21.5146			−1.22790			−0.613952	−	0.789343i	$-0.710421\pi$
$307$	−21.5146			−1.22790			−0.613952	+	0.789343i	$0.710421\pi$
$308$	−0.169566	−	0.169566i	−0.00966191	−	0.00966191i
$309$	3.26149	−	1.35096i	0.185540	−	0.0768532i
$310$		−	16.3837i		−	0.930534i
$311$	−5.40312	−	13.0443i	−0.306383	−	0.739674i	−0.999817	−	0.0191535i	$-0.993903\pi$
$311$	−5.40312	−	13.0443i	−0.306383	−	0.739674i	0.693433	−	0.720521i	$-0.256097\pi$
$312$	−9.70595	−	4.02034i	−0.549491	−	0.227607i
$313$	−4.65531	+	11.2389i	−0.263134	+	0.635261i	−0.999129	−	0.0417255i	$-0.986715\pi$
$313$	−4.65531	+	11.2389i	−0.263134	+	0.635261i	0.735995	+	0.676987i	$0.236715\pi$
$314$	−24.7926	+	24.7926i	−1.39913	+	1.39913i
$315$	5.07268	−	5.07268i	0.285813	−	0.285813i
$316$	0.0617172	−	0.148998i	0.00347186	−	0.00838182i
$317$	4.95006	+	2.05038i	0.278023	+	0.115161i	0.517338	−	0.855781i	$-0.326923\pi$
$317$	4.95006	+	2.05038i	0.278023	+	0.115161i	−0.239315	+	0.970942i	$0.576923\pi$
$318$	8.44127	+	20.3790i	0.473363	+	1.14280i
$319$			12.6590i			0.708765i
$320$	−18.7927	+	7.78419i	−1.05054	+	0.435150i
$321$	−15.9486	−	15.9486i	−0.890163	−	0.890163i
$322$	15.1648			0.845102
$323$	15.1914	−	17.3174i	0.845270	−	0.963565i
$324$	−0.0761642			−0.00423134
$325$	2.73460	+	2.73460i	0.151688	+	0.151688i
$326$	3.97103	−	1.64485i	0.219935	−	0.0911000i
$327$			21.0299i			1.16296i
$328$	0.0304901	+	0.0736097i	0.00168354	+	0.00406442i
$329$	34.4521	+	14.2705i	1.89940	+	0.786759i
$330$	−10.9582	+	26.4555i	−0.603230	+	1.45633i
$331$	−22.0217	+	22.0217i	−1.21042	+	1.21042i	−0.239534	+	0.970888i	$0.576995\pi$
$331$	−22.0217	+	22.0217i	−1.21042	+	1.21042i	−0.970888	+	0.239534i	$0.923005\pi$
$332$	−0.0397095	+	0.0397095i	−0.00217934	+	0.00217934i
$333$	−0.398933	+	0.963109i	−0.0218614	+	0.0527780i
$334$	−17.5104	−	7.25306i	−0.958129	−	0.396870i
$335$	−3.44572	−	8.31872i	−0.188260	−	0.454500i
$336$			21.6925i			1.18342i
$337$	20.1357	−	8.34046i	1.09686	−	0.454334i	0.240466	−	0.970658i	$-0.422700\pi$
$337$	20.1357	−	8.34046i	1.09686	−	0.454334i	0.856393	+	0.516324i	$0.172700\pi$
$338$	−6.77909	−	6.77909i	−0.368734	−	0.368734i
$339$	28.5263			1.54934
$340$	−0.0585273	−	0.118725i	−0.00317409	−	0.00643875i
$341$	23.8714			1.29271
$342$	4.34796	+	4.34796i	0.235111	+	0.235111i
$343$	3.14037	−	1.30079i	0.169564	−	0.0702358i
$344$			2.81949i			0.152017i
$345$	−4.31998	−	10.4294i	−0.232580	−	0.561498i
$346$	−12.0324	−	4.98399i	−0.646867	−	0.267941i
$347$	−2.33085	+	5.62718i	−0.125127	+	0.302083i	−0.974013	−	0.226493i	$-0.927274\pi$
$347$	−2.33085	+	5.62718i	−0.125127	+	0.302083i	0.848886	+	0.528576i	$0.177274\pi$
$348$	−0.0316656	+	0.0316656i	−0.00169745	+	0.00169745i
$349$	6.45598	−	6.45598i	0.345581	−	0.345581i	−0.512880	−	0.858461i	$-0.671421\pi$
$349$	6.45598	−	6.45598i	0.345581	−	0.345581i	0.858461	+	0.512880i	$0.171421\pi$
$350$	3.03681	−	7.33152i	0.162325	−	0.391886i
$351$	−12.9980	−	5.38393i	−0.693780	−	0.287373i
$352$	0.143648	+	0.346797i	0.00765647	+	0.0184843i
$353$			24.7803i			1.31892i	0.751738	+	0.659462i	$0.229216\pi$
$353$			24.7803i			1.31892i	−0.751738	+	0.659462i	$0.770784\pi$
$354$	16.1504	−	6.68970i	0.858382	−	0.355554i
$355$	13.6474	+	13.6474i	0.724328	+	0.724328i
$356$	0.133845			0.00709378
$357$	22.1742	−	1.45017i	1.17358	−	0.0767510i
$358$	19.4102			1.02586
$359$	12.5022	+	12.5022i	0.659843	+	0.659843i	0.955343	−	0.295500i	$-0.0954862\pi$
$359$	12.5022	+	12.5022i	0.659843	+	0.659843i	−0.295500	+	0.955343i	$0.595486\pi$
$360$	−5.17102	+	2.14191i	−0.272537	+	0.112888i
$361$			12.2158i			0.642939i
$362$	−0.210087	−	0.507196i	−0.0110419	−	0.0266576i
$363$	−23.3896	−	9.68830i	−1.22764	−	0.508504i
$364$	0.0433480	−	0.104651i	0.00227205	−	0.00548522i
$365$	2.99468	−	2.99468i	0.156749	−	0.156749i
$366$	−22.7261	+	22.7261i	−1.18791	+	1.18791i
$367$	6.02909	−	14.5555i	0.314716	−	0.759791i	−0.684802	−	0.728730i	$-0.740111\pi$
$367$	6.02909	−	14.5555i	0.314716	−	0.759791i	0.999517	−	0.0310617i	$-0.00988883\pi$
$368$	−10.9996	−	4.55618i	−0.573393	−	0.237507i
$369$	0.00838937	+	0.0202537i	0.000436733	+	0.00105437i
$370$			4.87803i			0.253597i
$371$	34.8084	−	14.4181i	1.80716	−	0.748550i
$372$	0.0597127	+	0.0597127i	0.00309596	+	0.00309596i
$373$	26.2514			1.35925			0.679624	−	0.733561i	$-0.262143\pi$
$373$	26.2514			1.35925			0.679624	+	0.733561i	$0.262143\pi$
$374$	27.7490	−	13.6793i	1.43487	−	0.707340i
$375$	13.1742			0.680310
$376$	−20.5728	−	20.5728i	−1.06096	−	1.06096i
$377$	−5.52446	+	2.28831i	−0.284524	+	0.117854i
$378$			28.8689i			1.48486i
$379$	−0.377647	−	0.911721i	−0.0193984	−	0.0468320i	0.913884	−	0.405976i	$-0.133069\pi$
$379$	−0.377647	−	0.911721i	−0.0193984	−	0.0468320i	−0.933282	+	0.359145i	$0.883069\pi$
$380$	0.165713	+	0.0686408i	0.00850092	+	0.00352120i
$381$	−1.52127	+	3.67268i	−0.0779372	+	0.188157i
$382$	24.0510	−	24.0510i	1.23055	−	1.23055i
$383$	−6.15224	+	6.15224i	−0.314365	+	0.314365i	−0.846598	−	0.532233i	$-0.821353\pi$
$383$	−6.15224	+	6.15224i	−0.314365	+	0.314365i	0.532233	+	0.846598i	$0.321353\pi$
$384$	6.51713	−	15.7337i	0.332576	−	0.802909i
$385$	45.1873	+	18.7172i	2.30296	+	0.953916i
$386$	1.54521	+	3.73046i	0.0786490	+	0.189875i
$387$			0.775782i			0.0394352i
$388$	−0.0737625	+	0.0305534i	−0.00374473	+	0.00155112i
$389$	18.3657	+	18.3657i	0.931179	+	0.931179i	0.997780	−	0.0666003i	$-0.0212152\pi$
$389$	18.3657	+	18.3657i	0.931179	+	0.931179i	−0.0666003	+	0.997780i	$0.521215\pi$
$390$	−13.5262			−0.684928
$391$	−3.92202	+	11.5484i	−0.198345	+	0.584030i
$392$	17.0844			0.862892
$393$	7.09942	+	7.09942i	0.358119	+	0.358119i
$394$	−19.5586	+	8.10143i	−0.985347	+	0.408144i
$395$			32.8938i			1.65507i
$396$	0.0197002	+	0.0475605i	0.000989973	+	0.00239001i
$397$	−16.8834	−	6.99332i	−0.847352	−	0.350985i	−0.0836041	−	0.996499i	$-0.526643\pi$
$397$	−16.8834	−	6.99332i	−0.847352	−	0.350985i	−0.763748	+	0.645514i	$0.776643\pi$
$398$	−1.31129	+	3.16574i	−0.0657292	+	0.158684i
$399$	−21.2923	+	21.2923i	−1.06595	+	1.06595i
$400$	−4.40542	+	4.40542i	−0.220271	+	0.220271i
$401$	11.8227	−	28.5425i	0.590397	−	1.42534i	−0.292723	−	0.956197i	$-0.594561\pi$
$401$	11.8227	−	28.5425i	0.590397	−	1.42534i	0.883120	−	0.469147i	$-0.155439\pi$
$402$	6.87807	+	2.84899i	0.343047	+	0.142095i
$403$	4.31512	+	10.4176i	0.214952	+	0.518939i
$404$			0.0820878i			0.00408402i
$405$	14.3520	−	5.94481i	0.713158	−	0.295400i
$406$	8.67620	+	8.67620i	0.430593	+	0.430593i
$407$	−7.10736			−0.352299
$408$	−16.4165	−	5.57528i	−0.812736	−	0.276017i
$409$	−35.4687			−1.75382			−0.876908	−	0.480659i	$-0.840397\pi$
$409$	−35.4687			−1.75382			−0.876908	+	0.480659i	$0.840397\pi$
$410$	0.0725369	+	0.0725369i	0.00358234	+	0.00358234i
$411$	13.0611	−	5.41009i	0.644258	−	0.266860i
$412$		−	0.0296973i		−	0.00146308i
$413$	−11.4263	−	27.5856i	−0.562253	−	1.35740i
$414$	−3.00767	−	1.24582i	−0.147819	−	0.0612286i
$415$	4.38325	−	10.5821i	0.215165	−	0.519455i
$416$	−0.125378	+	0.125378i	−0.00614717	+	0.00614717i
$417$	1.23222	−	1.23222i	0.0603418	−	0.0603418i
$418$	−16.0431	+	38.7314i	−0.784693	+	1.89442i
$419$	−28.2420	−	11.6982i	−1.37971	−	0.571495i	−0.435307	−	0.900282i	$-0.643360\pi$
$419$	−28.2420	−	11.6982i	−1.37971	−	0.571495i	−0.944404	+	0.328787i	$0.893360\pi$
$420$	0.0662132	+	0.159853i	0.00323087	+	0.00780002i
$421$		−	28.3261i		−	1.38053i	−0.723557	−	0.690264i	$-0.757494\pi$
$421$		−	28.3261i		−	1.38053i	0.723557	−	0.690264i	$-0.242506\pi$
$422$	7.19548	−	2.98046i	0.350270	−	0.145087i
$423$	−5.66061	−	5.66061i	−0.275228	−	0.275228i
$424$	−29.3952			−1.42756
$425$	4.79776	+	4.20875i	0.232726	+	0.204154i
$426$	−15.9579			−0.773161
$427$	38.8173	+	38.8173i	1.87850	+	1.87850i
$428$	−0.175294	+	0.0726092i	−0.00847316	+	0.00350970i
$429$		−	19.7079i		−	0.951507i
$430$	1.38920	+	3.35382i	0.0669930	+	0.161735i
$431$	−21.2628	−	8.80734i	−1.02419	−	0.424235i	−0.193580	−	0.981084i	$-0.562010\pi$
$431$	−21.2628	−	8.80734i	−1.02419	−	0.424235i	−0.830613	+	0.556850i	$0.812010\pi$
$432$	8.67349	−	20.9397i	0.417304	−	1.00746i
$433$	5.92072	−	5.92072i	0.284532	−	0.284532i	−0.550382	−	0.834913i	$-0.685518\pi$
$433$	5.92072	−	5.92072i	0.284532	−	0.284532i	0.834913	+	0.550382i	$0.185518\pi$
$434$	16.3610	−	16.3610i	0.785351	−	0.785351i
$435$	3.49534	−	8.43850i	0.167589	−	0.404595i
$436$	0.163444	+	0.0677006i	0.00782753	+	0.00324227i
$437$	−6.32455	−	15.2688i	−0.302544	−	0.730406i
$438$			3.50168i			0.167317i
$439$	−17.4499	+	7.22799i	−0.832839	+	0.344973i	−0.758026	−	0.652224i	$-0.773836\pi$
$439$	−17.4499	+	7.22799i	−0.832839	+	0.344973i	−0.0748129	+	0.997198i	$0.523836\pi$
$440$	−26.9832	−	26.9832i	−1.28638	−	1.28638i
$441$	4.70078			0.223847
$442$	10.9858	+	9.63710i	0.522542	+	0.458390i
$443$	0.721630			0.0342857			0.0171428	−	0.999853i	$-0.494543\pi$
$443$	0.721630			0.0342857			0.0171428	+	0.999853i	$0.494543\pi$
$444$	−0.0177786	−	0.0177786i	−0.000843735	−	0.000843735i
$445$	−25.2212	+	10.4470i	−1.19560	+	0.495234i
$446$			3.76375i			0.178219i
$447$	11.8966	+	28.7209i	0.562690	+	1.35845i
$448$	−26.5399	−	10.9932i	−1.25389	−	0.519380i
$449$	−8.25385	+	19.9265i	−0.389523	+	0.940392i	0.600518	+	0.799611i	$0.294961\pi$
$449$	−8.25385	+	19.9265i	−0.389523	+	0.940392i	−0.990041	+	0.140780i	$0.955039\pi$
$450$	−1.20460	+	1.20460i	−0.0567853	+	0.0567853i
$451$	−0.105687	+	0.105687i	−0.00497662	+	0.00497662i
$452$	0.0918334	−	0.221705i	0.00431948	−	0.0104281i
$453$	23.6590	+	9.79989i	1.11160	+	0.460439i
$454$	−9.99741	−	24.1359i	−0.469202	−	1.13275i
$455$			23.1035i			1.08311i
$456$	21.7051	−	8.99054i	1.01643	−	0.421021i
$457$	−1.64978	−	1.64978i	−0.0771735	−	0.0771735i	0.667466	−	0.744640i	$-0.267379\pi$
$457$	−1.64978	−	1.64978i	−0.0771735	−	0.0771735i	−0.744640	+	0.667466i	$0.767379\pi$
$458$	10.4466			0.488137
$459$	−21.9845	−	7.46627i	−1.02615	−	0.348495i
$460$	−0.0949636			−0.00442770
$461$	−6.73038	−	6.73038i	−0.313465	−	0.313465i	0.532785	−	0.846250i	$-0.321145\pi$
$461$	−6.73038	−	6.73038i	−0.313465	−	0.313465i	−0.846250	+	0.532785i	$0.821145\pi$
$462$	−37.3617	+	15.4757i	−1.73822	+	0.719995i
$463$			10.8382i			0.503695i	0.967767	+	0.251847i	$0.0810381\pi$
$463$			10.8382i			0.503695i	−0.967767	+	0.251847i	$0.918962\pi$
$464$	−3.68645	−	8.89988i	−0.171139	−	0.413167i
$465$	−15.9127	−	6.59126i	−0.737934	−	0.305662i
$466$	−2.80610	+	6.77452i	−0.129990	+	0.313823i
$467$	3.61955	−	3.61955i	0.167493	−	0.167493i	−0.618384	−	0.785876i	$-0.712212\pi$
$467$	3.61955	−	3.61955i	0.167493	−	0.167493i	0.785876	+	0.618384i	$0.212212\pi$
$468$	−0.0171946	+	0.0171946i	−0.000794822	+	0.000794822i
$469$	4.86621	−	11.7481i	0.224701	−	0.542476i
$470$	−34.6081	−	14.3351i	−1.59635	−	0.661231i
$471$	14.1056	+	34.0540i	0.649952	+	1.56912i
$472$			23.2957i			1.07227i
$473$	−4.88656	+	2.02408i	−0.224684	+	0.0930673i
$474$	−19.2313	−	19.2313i	−0.883324	−	0.883324i
$475$	−8.64832			−0.396812
$476$	0.0601137	−	0.177005i	0.00275531	−	0.00811303i
$477$	−8.08810			−0.370329
$478$	21.9903	+	21.9903i	1.00581	+	1.00581i
$479$	12.6436	−	5.23716i	0.577701	−	0.239292i	−0.0746482	−	0.997210i	$-0.523783\pi$
$479$	12.6436	−	5.23716i	0.577701	−	0.239292i	0.652350	+	0.757918i	$0.273783\pi$
$480$		−	0.270840i		−	0.0123621i
$481$	−1.28477	−	3.10170i	−0.0585803	−	0.141425i
$482$	27.7257	+	11.4844i	1.26287	+	0.523098i
$483$	6.10088	−	14.7288i	0.277599	−	0.670184i
$484$	−0.150594	+	0.150594i	−0.00684518	+	0.00684518i
$485$	11.5147	−	11.5147i	0.522856	−	0.522856i
$486$	4.25599	−	10.2749i	0.193056	−	0.466078i
$487$	4.32296	+	1.79063i	0.195892	+	0.0811411i	0.478473	−	0.878102i	$-0.341191\pi$
$487$	4.32296	+	1.79063i	0.195892	+	0.0811411i	−0.282581	+	0.959243i	$0.591191\pi$
$488$	−16.3904	−	39.5698i	−0.741956	−	1.79124i
$489$		−	4.51859i		−	0.204338i
$490$	20.3221	−	8.41770i	0.918060	−	0.380273i
$491$	−8.95836	−	8.95836i	−0.404285	−	0.404285i	0.475455	−	0.879740i	$-0.342283\pi$
$491$	−8.95836	−	8.95836i	−0.404285	−	0.404285i	−0.879740	+	0.475455i	$0.842283\pi$
$492$	−0.000528740	0		−2.38374e−5	0
$493$	−8.85108	+	4.36328i	−0.398632	+	0.196512i
$494$	−19.8027			−0.890966
$495$	−7.42444	−	7.42444i	−0.333704	−	0.333704i
$496$	−16.7828	+	6.95165i	−0.753568	+	0.312138i
$497$			27.2568i			1.22264i
$498$	3.62415	+	8.74948i	0.162402	+	0.392073i
$499$	30.6017	+	12.6757i	1.36992	+	0.567440i	0.941767	−	0.336265i	$-0.109164\pi$
$499$	30.6017	+	12.6757i	1.36992	+	0.567440i	0.428155	+	0.903706i	$0.359164\pi$
$500$	0.0424109	−	0.102389i	0.00189667	−	0.00457897i
$501$	−14.0891	+	14.0891i	−0.629453	+	0.629453i
$502$	19.4991	−	19.4991i	0.870286	−	0.870286i
$503$	−11.8376	+	28.5784i	−0.527811	+	1.27425i	0.405143	+	0.914254i	$0.367222\pi$
$503$	−11.8376	+	28.5784i	−0.527811	+	1.27425i	−0.932954	+	0.359996i	$0.882778\pi$
$504$	−7.30276	−	3.02490i	−0.325291	−	0.134740i
$505$	−6.40716	−	15.4683i	−0.285115	−	0.688329i
$506$		−	22.1954i		−	0.986706i
$507$	−9.31146	+	3.85693i	−0.413536	+	0.171292i
$508$	0.0236465	+	0.0236465i	0.00104915	+	0.00104915i
$509$	−4.72584			−0.209469			−0.104735	−	0.994500i	$-0.533399\pi$
$509$	−4.72584			−0.209469			−0.104735	+	0.994500i	$0.533399\pi$
$510$	−22.2746	+	1.45673i	−0.986337	+	0.0645053i
$511$	5.98103			0.264585
$512$	15.8469	+	15.8469i	0.700339	+	0.700339i
$513$	29.0669	−	12.0399i	1.28333	−	0.531574i
$514$			33.4917i			1.47726i
$515$	2.31795	+	5.59602i	0.102141	+	0.246590i
$516$	−0.0172865	−	0.00716031i	−0.000760997	−	0.000315215i
$517$	20.8865	−	50.4245i	0.918588	−	2.21767i
$518$	−4.87124	+	4.87124i	−0.214030	+	0.214030i
$519$	−9.68141	+	9.68141i	−0.424967	+	0.424967i
$520$	6.89803	−	16.6533i	0.302499	−	0.730296i
$521$	−5.08626	−	2.10680i	−0.222833	−	0.0923006i	0.268474	−	0.963287i	$-0.413481\pi$
$521$	−5.08626	−	2.10680i	−0.222833	−	0.0923006i	−0.491307	+	0.870986i	$0.663481\pi$
$522$	−1.00800	−	2.43354i	−0.0441192	−	0.106513i
$523$			9.75640i			0.426617i	0.976985	+	0.213309i	$0.0684240\pi$
$523$			9.75640i			0.426617i	−0.976985	+	0.213309i	$0.931576\pi$
$524$	0.0780312	−	0.0323216i	0.00340881	−	0.00141198i
$525$	−5.89901	−	5.89901i	−0.257454	−	0.257454i
$526$	22.0300			0.960553
$527$	8.22797	+	16.6907i	0.358416	+	0.727060i
$528$	31.7494			1.38171
$529$	−10.0763	−	10.0763i	−0.438101	−	0.438101i
$530$	−34.9660	+	14.4834i	−1.51883	+	0.629119i
$531$			6.40981i			0.278162i
$532$	0.0969377	+	0.234028i	0.00420278	+	0.0101464i
$533$	−0.0652273	−	0.0270180i	−0.00282531	−	0.00117028i
$534$	8.63775	−	20.8534i	0.373792	−	0.902413i
$535$	27.3643	−	27.3643i	1.18306	−	1.18306i
$536$	−7.01528	+	7.01528i	−0.303014	+	0.303014i
$537$	7.80880	−	18.8521i	0.336975	−	0.813529i
$538$	13.7495	+	5.69521i	0.592781	+	0.245538i
$539$	12.2647	+	29.6096i	0.528278	+	1.27538i
$540$		−	0.180780i		−	0.00777953i
$541$	−29.9927	+	12.4234i	−1.28949	+	0.534124i	−0.918833	−	0.394647i	$-0.870867\pi$
$541$	−29.9927	+	12.4234i	−1.28949	+	0.534124i	−0.370656	+	0.928770i	$0.620867\pi$
$542$	6.20184	+	6.20184i	0.266392	+	0.266392i
$543$	−0.577133			−0.0247671
$544$	−0.192966	+	0.219972i	−0.00827336	+	0.00943122i
$545$	−36.0828			−1.54562
$546$	−13.5074	−	13.5074i	−0.578064	−	0.578064i
$547$	−11.4266	+	4.73307i	−0.488568	+	0.202372i	−0.613348	−	0.789813i	$-0.710178\pi$
$547$	−11.4266	+	4.73307i	−0.488568	+	0.202372i	0.124780	+	0.992184i	$0.460178\pi$
$548$		−	0.118927i		−	0.00508031i
$549$	−4.50981	−	10.8876i	−0.192474	−	0.464673i
$550$	−10.7305	−	4.44472i	−0.457550	−	0.189523i
$551$	5.11726	−	12.3542i	0.218002	−	0.526305i
$552$	−8.79520	+	8.79520i	−0.374349	+	0.374349i
$553$	−32.8480	+	32.8480i	−1.39684	+	1.39684i
$554$	8.61255	−	20.7925i	0.365912	−	0.883390i
$555$	4.73778	+	1.96245i	0.201108	+	0.0833016i
$556$	−0.00560991	−	0.0135435i	−0.000237913	−	0.000574374i
$557$			5.58103i			0.236476i	0.992985	+	0.118238i	$0.0377245\pi$
$557$			5.58103i			0.236476i	−0.992985	+	0.118238i	$0.962275\pi$
$558$	−4.58899	+	1.90082i	−0.194268	+	0.0804683i
$559$	−1.76664	−	1.76664i	−0.0747211	−	0.0747211i
$560$	−37.2196			−1.57281
$561$	−2.12248	−	32.4544i	−0.0896113	−	1.37023i
$562$	−42.8480			−1.80743
$563$	−16.9050	−	16.9050i	−0.712462	−	0.712462i	0.254588	−	0.967050i	$-0.418060\pi$
$563$	−16.9050	−	16.9050i	−0.712462	−	0.712462i	−0.967050	+	0.254588i	$0.918060\pi$
$564$	0.178380	−	0.0738874i	0.00751115	−	0.00311122i
$565$			48.9450i			2.05913i
$566$	2.18468	+	5.27428i	0.0918288	+	0.221694i
$567$	20.2686	+	8.39553i	0.851202	+	0.352579i
$568$	8.13810	−	19.6471i	0.341467	−	0.824375i
$569$	4.96305	−	4.96305i	0.208062	−	0.208062i	−0.595381	−	0.803443i	$-0.702999\pi$
$569$	4.96305	−	4.96305i	0.208062	−	0.208062i	0.803443	+	0.595381i	$0.202999\pi$
$570$	21.3887	−	21.3887i	0.895876	−	0.895876i
$571$	0.879148	−	2.12245i	0.0367912	−	0.0888219i	−0.904416	−	0.426652i	$-0.859693\pi$
$571$	0.879148	−	2.12245i	0.0367912	−	0.0888219i	0.941207	+	0.337830i	$0.109693\pi$
$572$	−0.153169	−	0.0634447i	−0.00640432	−	0.00265276i
$573$	−13.6837	−	33.0353i	−0.571644	−	1.38007i
$574$			0.144872i			0.00604684i
$575$	4.23021	−	1.75221i	0.176412	−	0.0730722i
$576$	4.36062	+	4.36062i	0.181692	+	0.181692i
$577$	18.9938			0.790721			0.395360	−	0.918526i	$-0.370620\pi$
$577$	18.9938			0.790721			0.395360	+	0.918526i	$0.370620\pi$
$578$	19.1290	+	14.6870i	0.795662	+	0.610897i
$579$	4.24485			0.176410
$580$	−0.0543313	−	0.0543313i	−0.00225598	−	0.00225598i
$581$	14.9445	−	6.19023i	0.620004	−	0.256814i
$582$			13.4641i			0.558106i
$583$	−21.1025	−	50.9460i	−0.873977	−	2.10997i
$584$	−4.31122	−	1.78576i	−0.178399	−	0.0738955i
$585$	1.89799	−	4.58216i	0.0784724	−	0.189449i
$586$	−13.7601	+	13.7601i	−0.568424	+	0.568424i
$587$	−2.92899	+	2.92899i	−0.120892	+	0.120892i	−0.764965	−	0.644072i	$-0.777244\pi$
$587$	−2.92899	+	2.92899i	−0.120892	+	0.120892i	0.644072	+	0.764965i	$0.277244\pi$
$588$	−0.0433872	+	0.104746i	−0.00178926	+	0.00431965i
$589$	−23.2966	−	9.64976i	−0.959919	−	0.397611i
$590$	11.4781	+	27.7105i	0.472545	+	1.14082i
$591$			22.2555i			0.915470i
$592$	4.99683	−	2.06975i	0.205368	−	0.0850663i
$593$	13.1437	+	13.1437i	0.539747	+	0.539747i	0.923455	−	0.383707i	$-0.125353\pi$
$593$	13.1437	+	13.1437i	0.539747	+	0.539747i	−0.383707	+	0.923455i	$0.625353\pi$
$594$	42.2529			1.73366
$595$	2.48817	+	38.0461i	0.102005	+	1.55974i
$596$	0.261516			0.0107121
$597$	2.54719	+	2.54719i	0.104249	+	0.104249i
$598$	9.68623	−	4.01217i	0.396099	−	0.164070i
$599$			14.1209i			0.576963i	0.957486	+	0.288481i	$0.0931503\pi$
$599$			14.1209i			0.576963i	−0.957486	+	0.288481i	$0.906850\pi$
$600$	2.49082	+	6.01337i	0.101687	+	0.245495i
$601$	−22.0000	−	9.11269i	−0.897398	−	0.371714i	−0.114179	−	0.993460i	$-0.536424\pi$
$601$	−22.0000	−	9.11269i	−0.897398	−	0.371714i	−0.783219	+	0.621746i	$0.786424\pi$
$602$	−1.96189	+	4.73642i	−0.0799606	+	0.193042i
$603$	−1.93026	+	1.93026i	−0.0786061	+	0.0786061i
$604$	0.152329	−	0.152329i	0.00619816	−	0.00619816i
$605$	16.6230	−	40.1315i	0.675822	−	1.63158i
$606$	12.7895	+	5.29756i	0.519536	+	0.215199i
$607$	4.78765	+	11.5584i	0.194325	+	0.469141i	0.990767	−	0.135573i	$-0.0432874\pi$
$607$	4.78765	+	11.5584i	0.194325	+	0.469141i	−0.796443	+	0.604714i	$0.793287\pi$
$608$		−	0.396515i		−	0.0160808i
$609$	11.9172	−	4.93628i	0.482911	−	0.200028i
$610$	−38.9931	−	38.9931i	−1.57878	−	1.57878i
$611$	25.7812			1.04299
$612$	−0.0264638	+	0.0301674i	−0.00106974	+	0.00121945i
$613$	33.9768			1.37231			0.686156	−	0.727455i	$-0.259297\pi$
$613$	33.9768			1.37231			0.686156	+	0.727455i	$0.259297\pi$
$614$	21.5820	+	21.5820i	0.870979	+	0.870979i
$615$	0.0996334	−	0.0412695i	0.00401761	−	0.00166415i
$616$		−	53.8914i		−	2.17135i
$617$	7.75710	+	18.7273i	0.312289	+	0.753932i	0.999619	+	0.0275875i	$0.00878248\pi$
$617$	7.75710	+	18.7273i	0.312289	+	0.753932i	−0.687330	+	0.726345i	$0.741218\pi$
$618$	−4.62689	−	1.91652i	−0.186121	−	0.0770938i
$619$	2.44777	−	5.90944i	0.0983842	−	0.237520i	−0.867023	−	0.498269i	$-0.833969\pi$
$619$	2.44777	−	5.90944i	0.0983842	−	0.237520i	0.965407	+	0.260748i	$0.0839693\pi$
$620$	−0.102454	+	0.102454i	−0.00411465	+	0.00411465i
$621$	−11.7783	+	11.7783i	−0.472647	+	0.472647i
$622$	−7.66510	+	18.5052i	−0.307343	+	0.741991i
$623$	−35.6186	−	14.7537i	−1.42703	−	0.591094i
$624$	5.73920	+	13.8557i	0.229752	+	0.554670i
$625$			30.3435i			1.21374i
$626$	15.9440	−	6.60422i	0.637251	−	0.263958i
$627$	31.1637	+	31.1637i	1.24456	+	1.24456i
$628$	0.310075			0.0123734
$629$	−2.44976	−	4.96943i	−0.0976783	−	0.198144i
$630$	−10.1771			−0.405467
$631$	13.0309	+	13.0309i	0.518754	+	0.518754i	0.917194	−	0.398441i	$-0.130448\pi$
$631$	13.0309	+	13.0309i	0.518754	+	0.518754i	−0.398441	+	0.917194i	$0.630448\pi$
$632$	33.4848	−	13.8699i	1.33195	−	0.551714i
$633$		−	8.18766i		−	0.325430i
$634$	−2.90876	−	7.02236i	−0.115522	−	0.278894i
$635$	−6.30152	−	2.61017i	−0.250068	−	0.103582i
$636$	0.0746515	−	0.180225i	0.00296013	−	0.00714637i
$637$	−10.7048	+	10.7048i	−0.424140	+	0.424140i
$638$	12.6986	−	12.6986i	0.502742	−	0.502742i
$639$	2.23920	−	5.40591i	0.0885814	−	0.213854i
$640$	26.9957	+	11.1820i	1.06710	+	0.442007i
$641$	3.18385	+	7.68649i	0.125754	+	0.303598i	0.974201	−	0.225683i	$-0.0724615\pi$
$641$	3.18385	+	7.68649i	0.125754	+	0.303598i	−0.848446	+	0.529282i	$0.822462\pi$
$642$			31.9970i			1.26282i
$643$	7.68550	−	3.18344i	0.303087	−	0.125543i	−0.225957	−	0.974137i	$-0.572551\pi$
$643$	7.68550	−	3.18344i	0.303087	−	0.125543i	0.529043	+	0.848595i	$0.322551\pi$
$644$	−0.0948315	−	0.0948315i	−0.00373688	−	0.00373688i
$645$	3.81628			0.150266
$646$	−32.6106	+	2.13269i	−1.28305	+	0.0839096i
$647$	−36.5927			−1.43861			−0.719304	−	0.694695i	$-0.755539\pi$
$647$	−36.5927			−1.43861			−0.719304	+	0.694695i	$0.755539\pi$
$648$	−12.1032	−	12.1032i	−0.475461	−	0.475461i
$649$	−40.3746	+	16.7237i	−1.58484	+	0.656464i
$650$		−	5.48632i		−	0.215191i
$651$	−9.30849	−	22.4727i	−0.364828	−	0.880774i
$652$	−0.0351183	−	0.0145465i	−0.00137534	−	0.000569684i
$653$	6.17743	−	14.9136i	0.241741	−	0.583615i	−0.755714	−	0.654901i	$-0.772710\pi$
$653$	6.17743	−	14.9136i	0.241741	−	0.583615i	0.997456	+	0.0712857i	$0.0227102\pi$
$654$	21.0958	−	21.0958i	0.824910	−	0.824910i
$655$	−12.1811	+	12.1811i	−0.475954	+	0.475954i
$656$	0.0435260	−	0.105081i	0.00169940	−	0.00410272i
$657$	−1.18623	−	0.491354i	−0.0462793	−	0.0191695i
$658$	−20.2448	−	48.8752i	−0.789223	−	1.90535i
$659$		−	11.6390i		−	0.453393i	−0.973966	−	0.226696i	$-0.927208\pi$
$659$		−	11.6390i		−	0.453393i	0.973966	−	0.226696i	$-0.0727925\pi$
$660$	0.233963	−	0.0969105i	0.00910699	−	0.00377224i
$661$	−21.8626	−	21.8626i	−0.850357	−	0.850357i	0.139820	−	0.990177i	$-0.455348\pi$
$661$	−21.8626	−	21.8626i	−0.850357	−	0.850357i	−0.990177	+	0.139820i	$0.955348\pi$
$662$	44.1813			1.71716
$663$	13.7797	−	6.79292i	0.535158	−	0.263815i
$664$	−12.6205			−0.489769
$665$	−36.5330	−	36.5330i	−1.41669	−	1.41669i
$666$	1.36631	−	0.565943i	0.0529433	−	0.0219298i
$667$			7.07966i			0.274125i
$668$	0.0641434	+	0.154856i	0.00248178	+	0.00599156i
$669$	3.65554	+	1.51418i	0.141332	+	0.0585414i
$670$	−4.88825	+	11.8013i	−0.188850	+	0.455923i
$671$	56.8135	−	56.8135i	2.19326	−	2.19326i
$672$	0.270463	−	0.270463i	0.0104333	−	0.0104333i
$673$	7.07091	−	17.0707i	0.272564	−	0.658027i	−0.727028	−	0.686608i	$-0.759099\pi$
$673$	7.07091	−	17.0707i	0.272564	−	0.658027i	0.999591	+	0.0285811i	$0.00909887\pi$
$674$	−28.5653	−	11.8321i	−1.10029	−	0.455757i
$675$	3.33564	+	8.05295i	0.128389	+	0.309958i
$676$			0.0847847i			0.00326095i
$677$	−32.6558	+	13.5265i	−1.25507	+	0.519865i	−0.908391	−	0.418121i	$-0.862689\pi$
$677$	−32.6558	+	13.5265i	−1.25507	+	0.519865i	−0.346674	+	0.937986i	$0.612689\pi$
$678$	−28.6157	−	28.6157i	−1.09898	−	1.09898i
$679$	22.9974			0.882559
$680$	9.56597	−	28.1671i	0.366838	−	1.08016i
$681$	−27.4640			−1.05242
$682$	−23.9461	−	23.9461i	−0.916944	−	0.916944i
$683$	40.8783	−	16.9324i	1.56417	−	0.647899i	0.578359	−	0.815782i	$-0.303693\pi$
$683$	40.8783	−	16.9324i	1.56417	−	0.647899i	0.985807	+	0.167883i	$0.0536932\pi$
$684$		−	0.0543790i		−	0.00207923i
$685$	9.28255	+	22.4101i	0.354668	+	0.856244i
$686$	−4.45507	−	1.84535i	−0.170095	−	0.0704558i
$687$	4.20272	−	10.1463i	0.160344	−	0.387104i
$688$	2.84606	−	2.84606i	0.108505	−	0.108505i
$689$	18.4186	−	18.4186i	0.701692	−	0.701692i
$690$	−6.12851	+	14.7955i	−0.233308	+	0.563256i
$691$	35.5331	+	14.7183i	1.35174	+	0.559910i	0.936777	−	0.349927i	$-0.113794\pi$
$691$	35.5331	+	14.7183i	1.35174	+	0.559910i	0.414966	+	0.909837i	$0.363794\pi$
$692$	0.0440766	+	0.106410i	0.00167554	+	0.00404512i
$693$		−	14.8282i		−	0.563278i
$694$	7.98295	−	3.30665i	0.303029	−	0.125519i
$695$	2.11421	+	2.11421i	0.0801967	+	0.0801967i
$696$	−10.0640			−0.381473
$697$	−0.110324	−	0.0374678i	−0.00417883	−	0.00141919i
$698$	−12.9524			−0.490256
$699$	5.45084	+	5.45084i	0.206170	+	0.206170i
$700$	−0.0648373	+	0.0268565i	−0.00245062	+	0.00101508i
$701$		−	40.3312i		−	1.52329i	−0.647996	−	0.761644i	$-0.724393\pi$
$701$		−	40.3312i		−	1.52329i	0.647996	−	0.761644i	$-0.275607\pi$
$702$	7.63787	+	18.4395i	0.288273	+	0.695952i
$703$	6.93622	+	2.87308i	0.261605	+	0.108360i
$704$	−16.0898	+	38.8442i	−0.606407	+	1.46400i
$705$	−27.8460	+	27.8460i	−1.04874	+	1.04874i
$706$	24.8579	−	24.8579i	0.935541	−	0.935541i
$707$	9.04849	−	21.8450i	0.340304	−	0.821566i
$708$	−0.142828	−	0.0591613i	−0.00536780	−	0.00222342i
$709$	7.15756	+	17.2799i	0.268808	+	0.648960i	0.999428	−	0.0338247i	$-0.0107688\pi$
$709$	7.15756	+	17.2799i	0.268808	+	0.648960i	−0.730620	+	0.682784i	$0.760769\pi$
$710$		−	27.3803i		−	1.02756i
$711$	9.21336	−	3.81630i	0.345528	−	0.143122i
$712$	21.2694	+	21.2694i	0.797103	+	0.797103i
$713$	13.3503			0.499973
$714$	−23.6983	−	20.7889i	−0.886888	−	0.778006i
$715$	33.8145			1.26459
$716$	−0.121379	−	0.121379i	−0.00453616	−	0.00453616i
$717$	30.2049	−	12.5113i	1.12802	−	0.467242i
$718$		−	25.0828i		−	0.936081i
$719$	12.7850	+	30.8658i	0.476802	+	1.15110i	0.961101	+	0.276199i	$0.0890748\pi$
$719$	12.7850	+	30.8658i	0.476802	+	1.15110i	−0.484299	+	0.874903i	$0.660925\pi$
$720$	7.38185	+	3.05766i	0.275105	+	0.113952i
$721$	−3.27351	+	7.90296i	−0.121912	+	0.294322i
$722$	12.2541	−	12.2541i	0.456050	−	0.456050i
$723$	22.3084	−	22.3084i	0.829658	−	0.829658i
$724$	−0.00185793	+	0.00448545i	−6.90496e−5	+	0.000166700i
$725$	3.42270	+	1.41773i	0.127116	+	0.0526532i
$726$	13.7442	+	33.1815i	0.510096	+	1.23148i
$727$		−	42.3788i		−	1.57174i	−0.618389	−	0.785872i	$-0.712215\pi$
$727$		−	42.3788i		−	1.57174i	0.618389	−	0.785872i	$-0.287785\pi$
$728$	23.5186	−	9.74172i	0.871657	−	0.361052i
$729$	−21.1454	−	21.1454i	−0.783163	−	0.783163i
$730$	−6.00812			−0.222371
$731$	−3.09952	−	2.71900i	−0.114640	−	0.100566i
$732$	0.284231			0.0105055
$733$	−11.6728	−	11.6728i	−0.431143	−	0.431143i	0.457874	−	0.889017i	$-0.348611\pi$
$733$	−11.6728	−	11.6728i	−0.431143	−	0.431143i	−0.889017	+	0.457874i	$0.848611\pi$
$734$	−20.6491	+	8.55312i	−0.762171	+	0.315701i
$735$		−	23.1243i		−	0.852954i
$736$	0.0803367	+	0.193950i	0.00296125	+	0.00714909i
$737$	−17.1946	−	7.12225i	−0.633373	−	0.262352i
$738$	0.0119015	−	0.0287328i	0.000438101	−	0.00105767i
$739$	14.6461	−	14.6461i	0.538765	−	0.538765i	−0.384401	−	0.923166i	$-0.625592\pi$
$739$	14.6461	−	14.6461i	0.538765	−	0.538765i	0.923166	+	0.384401i	$0.125592\pi$
$740$	0.0305042	−	0.0305042i	0.00112136	−	0.00112136i
$741$	−7.96673	+	19.2334i	−0.292665	+	0.706556i
$742$	−49.3806	−	20.4541i	−1.81282	−	0.750895i
$743$	3.56806	+	8.61406i	0.130899	+	0.316019i	0.975717	−	0.219035i	$-0.0702910\pi$
$743$	3.56806	+	8.61406i	0.130899	+	0.316019i	−0.844817	+	0.535055i	$0.820291\pi$
$744$			18.9779i			0.695763i
$745$	−49.2789	+	20.4120i	−1.80544	+	0.747837i
$746$	−26.3336	−	26.3336i	−0.964143	−	0.964143i
$747$	−3.47252			−0.127053
$748$	−0.259067	−	0.0879831i	−0.00947244	−	0.00321698i
$749$	54.6525			1.99696
$750$	−13.2154	−	13.2154i	−0.482558	−	0.482558i
$751$	−39.7802	+	16.4775i	−1.45160	+	0.601273i	−0.962580	−	0.270998i	$-0.912646\pi$
$751$	−39.7802	+	16.4775i	−1.45160	+	0.601273i	−0.489022	+	0.872272i	$0.662646\pi$
$752$			41.5334i			1.51457i
$753$	−11.0939	−	26.7831i	−0.404284	−	0.976029i
$754$	7.83723	+	3.24629i	0.285415	+	0.118223i
$755$	−16.8145	+	40.5938i	−0.611942	+	1.47736i
$756$	0.180529	−	0.180529i	0.00656576	−	0.00656576i
$757$	−13.1138	+	13.1138i	−0.476630	+	0.476630i	−0.904052	−	0.427422i	$-0.859422\pi$
$757$	−13.1138	+	13.1138i	−0.476630	+	0.476630i	0.427422	+	0.904052i	$0.359422\pi$
$758$	−0.535747	+	1.29341i	−0.0194592	+	0.0469786i
$759$	−21.5573	−	8.92932i	−0.782480	−	0.324114i
$760$	15.4258	+	37.2412i	0.559553	+	1.35088i
$761$			45.9325i			1.66505i	0.553987	+	0.832526i	$0.313106\pi$
$761$			45.9325i			1.66505i	−0.553987	+	0.832526i	$0.686894\pi$
$762$	5.21021	−	2.15814i	0.188746	−	0.0781812i
$763$	−36.0326	−	36.0326i	−1.30447	−	1.30447i
$764$	−0.300800			−0.0108826
$765$	2.63208	−	7.75019i	0.0951630	−	0.280209i
$766$	12.3430			0.445971
$767$	−14.5967	−	14.5967i	−0.527056	−	0.527056i
$768$	−0.414860	+	0.171841i	−0.0149700	+	0.00620077i
$769$		−	13.7458i		−	0.495685i	−0.968800	−	0.247842i	$-0.920279\pi$
$769$		−	13.7458i		−	0.495685i	0.968800	−	0.247842i	$-0.0797215\pi$
$770$	−26.5530	−	64.1046i	−0.956903	−	2.31017i
$771$	32.5289	+	13.4739i	1.17150	+	0.485250i
$772$	0.0136652	−	0.0329908i	0.000491823	−	0.00118737i
$773$	27.3406	−	27.3406i	0.983373	−	0.983373i	−0.0164914	−	0.999864i	$-0.505250\pi$
$773$	27.3406	−	27.3406i	0.983373	−	0.983373i	0.999864	+	0.0164914i	$0.00524962\pi$
$774$	0.778212	−	0.778212i	0.0279722	−	0.0279722i
$775$	2.67345	−	6.45429i	0.0960333	−	0.231845i
$776$	−16.5769	−	6.86636i	−0.595075	−	0.246488i
$777$	2.77147	+	6.69092i	0.0994259	+	0.240035i
$778$		−	36.8465i		−	1.32101i
$779$	0.145866	−	0.0604195i	0.00522618	−	0.00216475i
$780$	0.0845849	+	0.0845849i	0.00302862	+	0.00302862i
$781$	39.8934			1.42750
$782$	15.5189	−	7.65030i	0.554955	−	0.273574i
$783$	−13.4774			−0.481642
$784$	−17.2454	−	17.2454i	−0.615908	−	0.615908i
$785$	−58.4292	+	24.2022i	−2.08543	+	0.863813i
$786$		−	14.2433i		−	0.508042i
$787$	−10.2732	−	24.8017i	−0.366200	−	0.884084i	−0.994366	−	0.106005i	$-0.966194\pi$
$787$	−10.2732	−	24.8017i	−0.366200	−	0.884084i	0.628166	−	0.778079i	$-0.283806\pi$
$788$	0.172969	+	0.0716461i	0.00616177	+	0.00255229i
$789$	8.86277	−	21.3966i	0.315523	−	0.761740i
$790$	32.9968	−	32.9968i	1.17397	−	1.17397i
$791$	−48.8769	+	48.8769i	−1.73786	+	1.73786i
$792$	−4.42728	+	10.6884i	−0.157317	+	0.379796i
$793$	35.0637	+	14.5239i	1.24515	+	0.515758i
$794$	9.92102	+	23.9515i	0.352084	+	0.850006i
$795$			39.7875i			1.41112i
$796$	0.0279966	−	0.0115966i	0.000992315	−	0.000411030i
$797$	−7.58480	−	7.58480i	−0.268667	−	0.268667i	0.559896	−	0.828563i	$-0.310841\pi$
$797$	−7.58480	−	7.58480i	−0.268667	−	0.268667i	−0.828563	+	0.559896i	$0.810841\pi$
$798$	42.7180			1.51220
$799$	42.4557	−	2.77655i	1.50197	−	0.0982274i
$800$	0.109854			0.00388393
$801$	5.85227	+	5.85227i	0.206780	+	0.206780i
$802$	−40.4916	+	16.7722i	−1.42981	+	0.592246i
$803$		−	8.75392i		−	0.308919i
$804$	−0.0251954	−	0.0608271i	−0.000888574	−	0.00214521i
$805$	25.2715	+	10.4678i	0.890702	+	0.368941i
$806$	6.12161	−	14.7789i	0.215625	−	0.520564i
$807$	11.0630	−	11.0630i	0.389434	−	0.389434i
$808$	−13.0446	+	13.0446i	−0.458907	+	0.458907i
$809$	−15.8042	+	38.1547i	−0.555646	+	1.34145i	0.357536	+	0.933899i	$0.383617\pi$
$809$	−15.8042	+	38.1547i	−0.555646	+	1.34145i	−0.913183	+	0.407550i	$0.866383\pi$
$810$	−20.3604	−	8.43355i	−0.715392	−	0.296325i
$811$	15.4858	+	37.3860i	0.543779	+	1.31280i	0.922038	+	0.387099i	$0.126523\pi$
$811$	15.4858	+	37.3860i	0.543779	+	1.31280i	−0.378259	+	0.925700i	$0.623477\pi$
$812$		−	0.108511i		−	0.00380800i
$813$	8.51857	−	3.52851i	0.298759	−	0.123750i
$814$	7.12961	+	7.12961i	0.249893	+	0.249893i
$815$	7.75293			0.271573
$816$	10.9434	+	22.1990i	0.383094	+	0.777121i
$817$	5.58711			0.195468
$818$	35.5798	+	35.5798i	1.24402	+	1.24402i
$819$	6.47115	−	2.68044i	0.226120	−	0.0936620i
$820$		0	0.000907203i		0	3.16809e-5i
$821$	14.9810	+	36.1674i	0.522842	+	1.26225i	0.936131	+	0.351651i	$0.114380\pi$
$821$	14.9810	+	36.1674i	0.522842	+	1.26225i	−0.413289	+	0.910600i	$0.635620\pi$
$822$	−18.5291	−	7.67499i	−0.646275	−	0.267696i
$823$	13.9834	−	33.7588i	0.487429	−	1.17676i	−0.468580	−	0.883421i	$-0.655234\pi$
$823$	13.9834	−	33.7588i	0.487429	−	1.17676i	0.956009	−	0.293337i	$-0.0947659\pi$
$824$	4.71919	−	4.71919i	0.164401	−	0.164401i
$825$	−8.63387	+	8.63387i	−0.300593	+	0.300593i
$826$	−16.2099	+	39.1341i	−0.564014	+	1.36165i
$827$	1.98560	+	0.822465i	0.0690463	+	0.0285999i	0.416939	−	0.908934i	$-0.363103\pi$
$827$	1.98560	+	0.822465i	0.0690463	+	0.0285999i	−0.347893	+	0.937534i	$0.613103\pi$
$828$	0.0110176	+	0.0265988i	0.000382887	+	0.000924371i
$829$		−	12.5180i		−	0.434767i	−0.976086	−	0.217383i	$-0.930248\pi$
$829$		−	12.5180i		−	0.434767i	0.976086	−	0.217383i	$-0.0697522\pi$
$830$	−15.0122	+	6.21826i	−0.521081	+	0.215839i
$831$	−16.7299	−	16.7299i	−0.580353	−	0.580353i
$832$	−19.8604			−0.688534
$833$	−16.4755	+	18.7813i	−0.570842	+	0.650732i
$834$	−2.47215			−0.0856035
$835$	−24.1738	−	24.1738i	−0.836569	−	0.836569i
$836$	0.342527	−	0.141879i	0.0118465	−	0.00490700i
$837$			25.4147i			0.878460i
$838$	16.5956	+	40.0653i	0.573285	+	1.38403i
$839$	39.8481	+	16.5056i	1.37571	+	0.569838i	0.943331	−	0.331854i	$-0.107674\pi$
$839$	39.8481	+	16.5056i	1.37571	+	0.569838i	0.432380	+	0.901692i	$0.357674\pi$
$840$	−14.8803	+	35.9242i	−0.513418	+	1.23950i
$841$	16.4556	−	16.4556i	0.567436	−	0.567436i
$842$	−28.4148	+	28.4148i	−0.979238	+	0.979238i
$843$	−17.2380	+	41.6161i	−0.593707	+	1.43333i
$844$	−0.0636342	−	0.0263581i	−0.00219038	−	0.000907284i
$845$	−6.61766	−	15.9764i	−0.227654	−	0.549607i
$846$			11.3567i			0.390451i
$847$	56.6756	−	23.4758i	1.94740	−	0.806638i
$848$	29.6723	+	29.6723i	1.01895	+	1.01895i
$849$	6.00155			0.205973
$850$	−0.590860	−	9.03472i	−0.0202663	−	0.309888i
$851$	−3.97487			−0.136257
$852$	0.0997909	+	0.0997909i	0.00341878	+	0.00341878i
$853$	−26.8448	+	11.1195i	−0.919147	+	0.380723i	−0.791551	−	0.611103i	$-0.790726\pi$
$853$	−26.8448	+	11.1195i	−0.919147	+	0.380723i	−0.127596	+	0.991826i	$0.540726\pi$
$854$		−	77.8777i		−	2.66492i
$855$	4.24442	+	10.2469i	0.145156	+	0.350438i
$856$	−39.3943	−	16.3177i	−1.34647	−	0.557726i
$857$	0.465056	−	1.12274i	0.0158860	−	0.0383522i	−0.915737	−	0.401777i	$-0.868393\pi$
$857$	0.465056	−	1.12274i	0.0158860	−	0.0383522i	0.931624	+	0.363425i	$0.118393\pi$
$858$	−19.7696	+	19.7696i	−0.674924	+	0.674924i
$859$	−10.7098	+	10.7098i	−0.365414	+	0.365414i	−0.865801	−	0.500388i	$-0.833191\pi$
$859$	−10.7098	+	10.7098i	−0.365414	+	0.365414i	0.500388	+	0.865801i	$0.333191\pi$
$860$	0.0122855	−	0.0296599i	0.000418934	−	0.00101140i
$861$	0.140707	+	0.0582827i	0.00479528	+	0.00198627i
$862$	12.4945	+	30.1643i	0.425563	+	1.02740i
$863$		−	26.8121i		−	0.912696i	−0.889801	−	0.456348i	$-0.849157\pi$
$863$		−	26.8121i		−	0.912696i	0.889801	−	0.456348i	$-0.150843\pi$
$864$	−0.369218	+	0.152935i	−0.0125611	+	0.00520296i
$865$	−16.6112	−	16.6112i	−0.564798	−	0.564798i
$866$	−11.8785			−0.403649
$867$	21.9604	−	12.6704i	0.745815	−	0.430310i
$868$	−0.204623			−0.00694536
$869$	48.0768	+	48.0768i	1.63089	+	1.63089i
$870$	−11.9712	+	4.95864i	−0.405862	+	0.168114i
$871$		−	8.79132i		−	0.297883i
$872$	15.2145	+	36.7311i	0.515229	+	1.24387i
$873$	−4.56113	−	1.88928i	−0.154371	−	0.0639425i
$874$	−8.97227	+	21.6610i	−0.303492	+	0.732694i
$875$	−22.5726	+	22.5726i	−0.763092	+	0.763092i
$876$	0.0218974	−	0.0218974i	0.000739843	−	0.000739843i
$877$	5.75143	−	13.8852i	0.194212	−	0.468870i	−0.796535	−	0.604593i	$-0.793336\pi$
$877$	5.75143	−	13.8852i	0.194212	−	0.468870i	0.990747	+	0.135723i	$0.0433358\pi$
$878$	24.7552	+	10.2539i	0.835447	+	0.346053i
$879$	7.82873	+	18.9002i	0.264056	+	0.637489i
$880$			54.4751i			1.83635i
$881$	−22.0038	+	9.11427i	−0.741326	+	0.307067i	−0.721197	−	0.692730i	$-0.756408\pi$
$881$	−22.0038	+	9.11427i	−0.741326	+	0.307067i	−0.0201292	+	0.999797i	$0.506408\pi$
$882$	−4.71550	−	4.71550i	−0.158779	−	0.158779i
$883$	−21.8461			−0.735178			−0.367589	−	0.929988i	$-0.619817\pi$
$883$	−21.8461			−0.735178			−0.367589	+	0.929988i	$0.619817\pi$
$884$	−0.00843404	−	0.128963i	−0.000283667	−	0.00433750i
$885$	31.5315			1.05992
$886$	−0.723889	−	0.723889i	−0.0243195	−	0.0243195i
$887$	20.3867	−	8.44444i	0.684518	−	0.283537i	−0.0131962	−	0.999913i	$-0.504201\pi$
$887$	20.3867	−	8.44444i	0.684518	−	0.283537i	0.697714	+	0.716376i	$0.254201\pi$
$888$		−	5.65039i		−	0.189615i
$889$	−3.68621	−	8.89930i	−0.123632	−	0.298473i
$890$	35.7799	+	14.8205i	1.19934	+	0.496784i
$891$	12.2878	−	29.6654i	0.411657	−	0.993828i
$892$	0.0235362	−	0.0235362i	0.000788051	−	0.000788051i
$893$	−40.7672	+	40.7672i	−1.36422	+	1.36422i
$894$	16.8770	−	40.7447i	0.564452	−	1.36271i
$895$	32.3462	+	13.3982i	1.08121	+	0.447853i
$896$	15.7917	+	38.1246i	0.527564	+	1.27365i
$897$		−	11.0219i		−	0.368009i
$898$	28.2686	−	11.7093i	0.943337	−	0.390743i
$899$	7.63808	+	7.63808i	0.254744	+	0.254744i
$900$	0.0150656			0.000502188
$901$	28.3476	−	32.3148i	0.944394	−	1.07656i
$902$	0.212037			0.00706004
$903$	3.81097	+	3.81097i	0.126821	+	0.126821i
$904$	49.8245	−	20.6380i	1.65714	−	0.686409i
$905$		−	0.990235i		−	0.0329165i
$906$	−13.9025	−	33.5637i	−0.461881	−	1.11508i
$907$	25.7465	+	10.6645i	0.854898	+	0.354110i	0.766710	−	0.641994i	$-0.221892\pi$
$907$	25.7465	+	10.6645i	0.854898	+	0.354110i	0.0881878	+	0.996104i	$0.471892\pi$
$908$	−0.0884134	+	0.213449i	−0.00293410	+	0.00708355i
$909$	−3.58922	+	3.58922i	−0.119047	+	0.119047i
$910$	23.1758	−	23.1758i	0.768271	−	0.768271i
$911$	22.5181	−	54.3635i	0.746057	−	1.80114i	0.166812	−	0.985989i	$-0.446653\pi$
$911$	22.5181	−	54.3635i	0.746057	−	1.80114i	0.579246	−	0.815153i	$-0.303347\pi$
$912$	−30.9849	−	12.8344i	−1.02601	−	0.424989i
$913$	−9.06010	−	21.8730i	−0.299845	−	0.723891i
$914$			3.30990i			0.109482i
$915$	−53.5592	+	22.1849i	−1.77061	+	0.733411i
$916$	−0.0653266	−	0.0653266i	−0.00215845	−	0.00215845i
$917$	−24.3283			−0.803390
$918$	14.5637	+	29.5430i	0.480674	+	0.975064i
$919$	−3.82848			−0.126290			−0.0631450	−	0.998004i	$-0.520113\pi$
$919$	−3.82848			−0.126290			−0.0631450	+	0.998004i	$0.520113\pi$
$920$	−15.0907	−	15.0907i	−0.497525	−	0.497525i
$921$	29.6441	−	12.2790i	0.976805	−	0.404606i
$922$			13.5029i			0.444695i
$923$	7.21136	+	17.4098i	0.237365	+	0.573050i
$924$	0.330413	+	0.136862i	0.0108698	+	0.00450241i
$925$	−0.795983	+	1.92167i	−0.0261718	+	0.0631842i
$926$	10.8722	−	10.8722i	0.357281	−	0.357281i
$927$	1.29849	−	1.29849i	0.0426479	−	0.0426479i
$928$	−0.0650013	+	0.156927i	−0.00213377	+	0.00515138i
$929$	7.48869	+	3.10192i	0.245696	+	0.101771i	0.502133	−	0.864790i	$-0.332549\pi$
$929$	7.48869	+	3.10192i	0.245696	+	0.101771i	−0.256437	+	0.966561i	$0.582549\pi$
$930$	9.35064	+	22.5744i	0.306620	+	0.740245i
$931$		−	33.8546i		−	1.10954i
$932$	0.0599114	−	0.0248161i	0.00196246	−	0.000812878i
$933$	14.8895	+	14.8895i	0.487459	+	0.487459i
$934$	−7.26177			−0.237613
$935$	55.6848	−	3.64172i	1.82109	−	0.119097i
$936$	−5.46480			−0.178623
$937$	−27.6964	−	27.6964i	−0.904801	−	0.904801i	0.0910460	−	0.995847i	$-0.470979\pi$
$937$	−27.6964	−	27.6964i	−0.904801	−	0.904801i	−0.995847	+	0.0910460i	$0.970979\pi$
$938$	−16.6663	+	6.90342i	−0.544175	+	0.225404i
$939$		−	18.1425i		−	0.592059i
$940$	0.126775	+	0.306061i	0.00413494	+	0.00998262i
$941$	5.24932	+	2.17434i	0.171123	+	0.0708814i	0.466600	−	0.884468i	$-0.345479\pi$
$941$	5.24932	+	2.17434i	0.171123	+	0.0708814i	−0.295477	+	0.955350i	$0.595479\pi$
$942$	20.0108	−	48.3104i	0.651988	−	1.57404i
$943$	−0.0591068	+	0.0591068i	−0.00192478	+	0.00192478i
$944$	23.5152	−	23.5152i	0.765356	−	0.765356i
$945$	−19.9273	+	48.1087i	−0.648234	+	1.56498i
$946$	6.93228	+	2.87144i	0.225388	+	0.0933587i
$947$	−8.65670	−	20.8991i	−0.281305	−	0.679131i	0.718562	−	0.695463i	$-0.244801\pi$
$947$	−8.65670	−	20.8991i	−0.281305	−	0.679131i	−0.999867	+	0.0163328i	$0.994801\pi$
$948$			0.240522i			0.00781179i
$949$	3.82027	−	1.58241i	0.124011	−	0.0513671i
$950$	8.67540	+	8.67540i	0.281467	+	0.281467i
$951$	−7.99068			−0.259115
$952$	37.6806	−	18.5753i	1.22124	−	0.602028i
$953$	−27.6677			−0.896244			−0.448122	−	0.893973i	$-0.647907\pi$
$953$	−27.6677			−0.896244			−0.448122	+	0.893973i	$0.647907\pi$
$954$	8.11343	+	8.11343i	0.262682	+	0.262682i
$955$	56.6815	−	23.4782i	1.83417	−	0.759738i
$956$		−	0.275028i		−	0.00889504i
$957$	−7.22481	−	17.4422i	−0.233545	−	0.563827i
$958$	−17.9368	−	7.42965i	−0.579511	−	0.240041i
$959$	−13.1093	+	31.6485i	−0.423320	+	1.02198i
$960$	21.4510	−	21.4510i	0.692328	−	0.692328i
$961$	−7.51697	+	7.51697i	−0.242483	+	0.242483i
$962$	−1.82262	+	4.40020i	−0.0587637	+	0.141868i
$963$	−10.8394	−	4.48981i	−0.349293	−	0.144682i
$964$	−0.101564	−	0.245196i	−0.00327114	−	0.00789723i
$965$			7.28325i			0.234456i
$966$	−20.8949	+	8.65496i	−0.672283	+	0.278469i
$967$	−12.4000	−	12.4000i	−0.398759	−	0.398759i	0.479036	−	0.877795i	$-0.340986\pi$
$967$	−12.4000	−	12.4000i	−0.398759	−	0.398759i	−0.877795	+	0.479036i	$0.840986\pi$
$968$	−47.8618			−1.53834
$969$	−11.0480	+	32.5310i	−0.354913	+	1.04505i
$970$	−23.1015			−0.741746
$971$	−13.8351	−	13.8351i	−0.443989	−	0.443989i	0.449361	−	0.893350i	$-0.351652\pi$
$971$	−13.8351	−	13.8351i	−0.443989	−	0.443989i	−0.893350	+	0.449361i	$0.851652\pi$
$972$	−0.0908672	+	0.0376384i	−0.00291457	+	0.00120725i
$973$			4.22255i			0.135369i
$974$	−2.54026	−	6.13273i	−0.0813952	−	0.196505i
$975$	−5.32859	−	2.20717i	−0.170651	−	0.0706861i
$976$	−23.3979	+	56.4876i	−0.748949	+	1.80812i
$977$	17.1183	−	17.1183i	0.547663	−	0.547663i	−0.378101	−	0.925764i	$-0.623423\pi$
$977$	17.1183	−	17.1183i	0.547663	−	0.547663i	0.925764	+	0.378101i	$0.123423\pi$
$978$	−4.53274	+	4.53274i	−0.144941	+	0.144941i
$979$	−21.5937	+	52.1318i	−0.690137	+	1.66614i
$980$	−0.179721	−	0.0744431i	−0.00574099	−	0.00237800i
$981$	4.18628	+	10.1066i	0.133658	+	0.322678i
$982$			17.9728i			0.573536i
$983$	−30.6354	+	12.6896i	−0.977118	+	0.404736i	−0.813357	−	0.581764i	$-0.802363\pi$
$983$	−30.6354	+	12.6896i	−0.977118	+	0.404736i	−0.163761	+	0.986500i	$0.552363\pi$
$984$	−0.0840221	−	0.0840221i	−0.00267853	−	0.00267853i
$985$	−38.1857			−1.21670
$986$	13.2557	+	4.50185i	0.422149	+	0.143368i
$987$	−55.6146			−1.77023
$988$	0.123834	+	0.123834i	0.00393969	+	0.00393969i
$989$	−2.73286	+	1.13199i	−0.0868999	+	0.0359951i
$990$			14.8954i			0.473407i
$991$	−15.5918	−	37.6420i	−0.495290	−	1.19574i	−0.951994	−	0.306118i	$-0.900970\pi$
$991$	−15.5918	−	37.6420i	−0.495290	−	1.19574i	0.456703	−	0.889619i	$-0.349030\pi$
$992$	0.295922	+	0.122575i	0.00939552	+	0.00389175i
$993$	17.7744	−	42.9111i	0.564052	−	1.36174i
$994$	27.3422	−	27.3422i	0.867241	−	0.867241i
$995$	−4.37042	+	4.37042i	−0.138552	+	0.138552i
$996$	0.0320507	−	0.0773772i	0.00101556	−	0.00245179i
$997$	−10.6589	−	4.41508i	−0.337572	−	0.139827i	0.207457	−	0.978244i	$-0.433481\pi$
$997$	−10.6589	−	4.41508i	−0.337572	−	0.139827i	−0.545029	+	0.838417i	$0.683481\pi$
$998$	−17.9822	−	43.4129i	−0.569217	−	1.37421i
$999$		−	7.56686i		−	0.239405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.10	✓	116
17.9	even	8	inner	731.2.m.b.689.10	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.10	✓	116	1.1	even	1	trivial
731.2.m.b.689.10	yes	116	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00313 - 1.00313i) q^{2} +(-1.37786 + 0.570727i) q^{3} +0.0125460i q^{4} +(-0.979244 - 2.36410i) q^{5} +(1.95469 + 0.809657i) q^{6} +(1.38293 - 3.33870i) q^{7} +(-1.99368 + 1.99368i) q^{8} +(-0.548561 + 0.548561i) q^{9} +O(q^{10})\)	\(q+(-1.00313 - 1.00313i) q^{2} +(-1.37786 + 0.570727i) q^{3} +0.0125460i q^{4} +(-0.979244 - 2.36410i) q^{5} +(1.95469 + 0.809657i) q^{6} +(1.38293 - 3.33870i) q^{7} +(-1.99368 + 1.99368i) q^{8} +(-0.548561 + 0.548561i) q^{9} +(-1.38920 + 3.35382i) q^{10} +(-4.88656 - 2.02408i) q^{11} +(-0.00716031 - 0.0172865i) q^{12} -2.49841i q^{13} +(-4.73642 + 1.96189i) q^{14} +(2.69851 + 2.69851i) q^{15} +4.02493 q^{16} +(-0.269071 - 4.11432i) q^{17} +1.10056 q^{18} +(3.95069 + 3.95069i) q^{19} +(0.0296599 - 0.0122855i) q^{20} +5.38952i q^{21} +(2.87144 + 6.93228i) q^{22} +(-2.73286 - 1.13199i) q^{23} +(1.60916 - 3.88485i) q^{24} +(-1.09453 + 1.09453i) q^{25} +(-2.50624 + 2.50624i) q^{26} +(2.15494 - 5.20249i) q^{27} +(0.0418871 + 0.0173502i) q^{28} +(-0.915903 - 2.21119i) q^{29} -5.41393i q^{30} +(-4.16970 + 1.72715i) q^{31} +(-0.0501831 - 0.0501831i) q^{32} +7.88817 q^{33} +(-3.85729 + 4.39711i) q^{34} -9.24725 q^{35} +(-0.00688222 - 0.00688222i) q^{36} +(1.24147 - 0.514233i) q^{37} -7.92612i q^{38} +(1.42591 + 3.44245i) q^{39} +(6.66556 + 2.76096i) q^{40} +(0.0108141 - 0.0261075i) q^{41} +(5.40640 - 5.40640i) q^{42} +(0.707107 - 0.707107i) q^{43} +(0.0253940 - 0.0613066i) q^{44} +(1.83403 + 0.759680i) q^{45} +(1.60589 + 3.87695i) q^{46} +10.3190i q^{47} +(-5.54578 + 2.29714i) q^{48} +(-4.28464 - 4.28464i) q^{49} +2.19592 q^{50} +(2.71889 + 5.51537i) q^{51} +0.0313450 q^{52} +(7.37211 + 7.37211i) q^{53} +(-7.38047 + 3.05709i) q^{54} +13.5344i q^{55} +(3.89916 + 9.41341i) q^{56} +(-7.69824 - 3.18872i) q^{57} +(-1.29934 + 3.13688i) q^{58} +(5.84239 - 5.84239i) q^{59} +(-0.0338554 + 0.0338554i) q^{60} +(-5.81324 + 14.0344i) q^{61} +(5.91531 + 2.45020i) q^{62} +(1.07286 + 2.59010i) q^{63} -7.94919i q^{64} +(-5.90651 + 2.44656i) q^{65} +(-7.91288 - 7.91288i) q^{66} +3.51876 q^{67} +(0.0516180 - 0.00337576i) q^{68} +4.41155 q^{69} +(9.27621 + 9.27621i) q^{70} +(-6.96833 + 2.88638i) q^{71} -2.18731i q^{72} +(0.633365 + 1.52908i) q^{73} +(-1.76120 - 0.729512i) q^{74} +(0.883430 - 2.13279i) q^{75} +(-0.0495651 + 0.0495651i) q^{76} +(-13.5156 + 13.5156i) q^{77} +(2.02286 - 4.88361i) q^{78} +(-11.8762 - 4.91929i) q^{79} +(-3.94139 - 9.51536i) q^{80} +6.07081i q^{81} +(-0.0370372 + 0.0153413i) q^{82} +(3.16512 + 3.16512i) q^{83} -0.0676167 q^{84} +(-9.46318 + 4.66503i) q^{85} -1.41864 q^{86} +(2.52397 + 2.52397i) q^{87} +(13.7776 - 5.70686i) q^{88} -10.6684i q^{89} +(-1.07771 - 2.60183i) q^{90} +(-8.34144 - 3.45514i) q^{91} +(0.0142019 - 0.0342864i) q^{92} +(4.75952 - 4.75952i) q^{93} +(10.3513 - 10.3513i) q^{94} +(5.47115 - 13.2085i) q^{95} +(0.0977859 + 0.0405042i) q^{96} +(2.43532 + 5.87939i) q^{97} +8.59612i q^{98} +(3.79091 - 1.57025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

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