LMFDB - Embedded newform 930.2.j.f.497.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.3
Root			$-3.16053i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.f.683.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 - 1.33991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 - 1.33991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-2.23483 - 0.0743018i) q^{10} +1.30913i q^{11} +(1.70711 - 0.292893i) q^{12} +(-1.74632 + 1.74632i) q^{13} -1.89492 q^{14} +(2.33991 - 3.08623i) q^{15} -1.00000 q^{16} +(-5.36459 + 5.36459i) q^{17} +(-1.29289 + 2.70711i) q^{18} +4.34772i q^{19} +(-1.63280 + 1.52773i) q^{20} +(1.89492 - 2.67982i) q^{21} +(0.925698 + 0.925698i) q^{22} +(4.75413 + 4.75413i) q^{23} +(1.00000 - 1.41421i) q^{24} +(-0.332104 + 4.98896i) q^{25} +2.46967i q^{26} +(-2.53553 - 4.53553i) q^{27} +(-1.33991 + 1.33991i) q^{28} -5.50825 q^{29} +(-0.527726 - 3.83686i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.23483 + 0.383437i) q^{33} +7.58667i q^{34} +(-0.140796 + 4.23483i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(3.07430 + 3.07430i) q^{38} +(-3.49264 - 2.46967i) q^{39} +(-0.0743018 + 2.23483i) q^{40} -2.81281i q^{41} +(-0.555010 - 3.23483i) q^{42} +(3.50044 - 3.50044i) q^{43} +1.30913 q^{44} +(5.95387 + 3.09054i) q^{45} +6.72335 q^{46} +(-3.66790 + 3.66790i) q^{47} +(-0.292893 - 1.70711i) q^{48} -3.40927i q^{49} +(3.29289 + 3.76256i) q^{50} +(-10.7292 - 7.58667i) q^{51} +(1.74632 + 1.74632i) q^{52} +(-6.45082 - 6.45082i) q^{53} +(-5.00000 - 1.41421i) q^{54} +(2.13756 - 2.00000i) q^{55} +1.89492i q^{56} +(-7.42202 + 1.27342i) q^{57} +(-3.89492 + 3.89492i) q^{58} -11.3765 q^{59} +(-3.08623 - 2.33991i) q^{60} +12.5481 q^{61} +(0.707107 - 0.707107i) q^{62} +(5.12975 + 2.44993i) q^{63} +1.00000i q^{64} +(5.51929 + 0.183501i) q^{65} +(-1.30913 + 1.85140i) q^{66} +(5.52512 + 5.52512i) q^{67} +(5.36459 + 5.36459i) q^{68} +(-6.72335 + 9.50825i) q^{69} +(2.89492 + 3.09404i) q^{70} -10.3477i q^{71} +(2.70711 + 1.29289i) q^{72} +(-1.87025 + 1.87025i) q^{73} -2.82843 q^{74} +(-8.61396 + 0.894295i) q^{75} +4.34772 q^{76} +(1.75413 - 1.75413i) q^{77} +(-4.21598 + 0.723349i) q^{78} -4.64493i q^{79} +(1.52773 + 1.63280i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-1.98896 - 1.98896i) q^{82} +(-11.2871 - 11.2871i) q^{83} +(-2.67982 - 1.89492i) q^{84} +(16.9549 + 0.563703i) q^{85} -4.95037i q^{86} +(-1.61333 - 9.40317i) q^{87} +(0.925698 - 0.925698i) q^{88} -7.16053 q^{89} +(6.39536 - 2.02468i) q^{90} +4.67982 q^{91} +(4.75413 - 4.75413i) q^{92} +(0.292893 + 1.70711i) q^{93} +5.18719i q^{94} +(7.09898 - 6.64213i) q^{95} +(-1.41421 - 1.00000i) q^{96} +(-1.49632 - 1.49632i) q^{97} +(-2.41072 - 2.41072i) q^{98} +(-1.30913 - 3.70279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q + 8 * q^3 + 4 * q^7	$ 8 q + 8 q^{3} + 4 q^{7} + 8 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} - 16 q^{18} - 4 q^{20} + 12 q^{21} + 4 q^{22} + 12 q^{23} + 8 q^{24} - 4 q^{25} + 8 q^{27} + 4 q^{28} + 8 q^{29} + 8 q^{30} + 8 q^{31} - 24 q^{35} + 8 q^{36} - 16 q^{37} + 28 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{42} - 8 q^{43} - 4 q^{44} - 4 q^{45} + 28 q^{46} - 28 q^{47} - 8 q^{48} + 32 q^{50} - 8 q^{51} + 4 q^{52} + 12 q^{53} - 40 q^{54} - 20 q^{55} - 32 q^{57} - 28 q^{58} - 24 q^{59} + 56 q^{61} + 20 q^{63} + 36 q^{65} + 4 q^{66} - 16 q^{67} + 4 q^{68} - 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} - 12 q^{77} + 12 q^{78} + 56 q^{81} + 28 q^{82} + 12 q^{83} + 8 q^{84} + 32 q^{85} + 36 q^{87} + 4 q^{88} - 36 q^{89} + 12 q^{90} + 8 q^{91} + 12 q^{92} + 8 q^{93} + 36 q^{95} + 12 q^{97} - 32 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 4 * q^7 + 8 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 - 4 * q^17 - 16 * q^18 - 4 * q^20 + 12 * q^21 + 4 * q^22 + 12 * q^23 + 8 * q^24 - 4 * q^25 + 8 * q^27 + 4 * q^28 + 8 * q^29 + 8 * q^30 + 8 * q^31 - 24 * q^35 + 8 * q^36 - 16 * q^37 + 28 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^42 - 8 * q^43 - 4 * q^44 - 4 * q^45 + 28 * q^46 - 28 * q^47 - 8 * q^48 + 32 * q^50 - 8 * q^51 + 4 * q^52 + 12 * q^53 - 40 * q^54 - 20 * q^55 - 32 * q^57 - 28 * q^58 - 24 * q^59 + 56 * q^61 + 20 * q^63 + 36 * q^65 + 4 * q^66 - 16 * q^67 + 4 * q^68 - 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 56 * q^81 + 28 * q^82 + 12 * q^83 + 8 * q^84 + 32 * q^85 + 36 * q^87 + 4 * q^88 - 36 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 + 8 * q^93 + 36 * q^95 + 12 * q^97 - 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	−1.52773	−	1.63280i	−0.683220	−	0.730213i
$5$	−1.52773	−	1.63280i	−0.683220	−	0.730213i
$6$	1.41421	+	1.00000i	0.577350	+	0.408248i
$7$	−1.33991	−	1.33991i	−0.506439	−	0.506439i	0.406992	−	0.913432i	$-0.366578\pi$
$7$	−1.33991	−	1.33991i	−0.506439	−	0.506439i	−0.913432	+	0.406992i	$0.866578\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$	−2.23483	−	0.0743018i	−0.706716	−	0.0234963i
$11$			1.30913i			0.394719i	0.980331	+	0.197360i	$0.0632366\pi$
$11$			1.30913i			0.394719i	−0.980331	+	0.197360i	$0.936763\pi$
$12$	1.70711	−	0.292893i	0.492799	−	0.0845510i
$13$	−1.74632	+	1.74632i	−0.484341	+	0.484341i	−0.906515	−	0.422174i	$-0.861267\pi$
$13$	−1.74632	+	1.74632i	−0.484341	+	0.484341i	0.422174	+	0.906515i	$0.361267\pi$
$14$	−1.89492			−0.506439
$15$	2.33991	−	3.08623i	0.604163	−	0.796861i
$16$	−1.00000			−0.250000
$17$	−5.36459	+	5.36459i	−1.30110	+	1.30110i	−0.373456	+	0.927648i	$0.621827\pi$
$17$	−5.36459	+	5.36459i	−1.30110	+	1.30110i	−0.927648	+	0.373456i	$0.878173\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$			4.34772i			0.997435i	0.866765	+	0.498718i	$0.166196\pi$
$19$			4.34772i			0.997435i	−0.866765	+	0.498718i	$0.833804\pi$
$20$	−1.63280	+	1.52773i	−0.365106	+	0.341610i
$21$	1.89492	−	2.67982i	0.413506	−	0.584785i
$22$	0.925698	+	0.925698i	0.197360	+	0.197360i
$23$	4.75413	+	4.75413i	0.991304	+	0.991304i	0.999963	−	0.00865885i	$-0.00275623\pi$
$23$	4.75413	+	4.75413i	0.991304	+	0.991304i	−0.00865885	+	0.999963i	$0.502756\pi$
$24$	1.00000	−	1.41421i	0.204124	−	0.288675i
$25$	−0.332104	+	4.98896i	−0.0664208	+	0.997792i
$26$			2.46967i			0.484341i
$27$	−2.53553	−	4.53553i	−0.487964	−	0.872864i
$28$	−1.33991	+	1.33991i	−0.253220	+	0.253220i
$29$	−5.50825			−1.02286			−0.511428	−	0.859326i	$-0.670883\pi$
$29$	−5.50825			−1.02286			−0.511428	+	0.859326i	$0.670883\pi$
$30$	−0.527726	−	3.83686i	−0.0963492	−	0.700512i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.23483	+	0.383437i	−0.389035	+	0.0667478i
$34$			7.58667i			1.30110i
$35$	−0.140796	+	4.23483i	−0.0237989	+	0.715817i
$36$	1.00000	+	2.82843i	0.166667	+	0.471405i
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	3.07430	+	3.07430i	0.498718	+	0.498718i
$39$	−3.49264	−	2.46967i	−0.559269	−	0.395463i
$40$	−0.0743018	+	2.23483i	−0.0117481	+	0.353358i
$41$		−	2.81281i		−	0.439287i	−0.975580	−	0.219644i	$-0.929511\pi$
$41$		−	2.81281i		−	0.439287i	0.975580	−	0.219644i	$-0.0704895\pi$
$42$	−0.555010	−	3.23483i	−0.0856398	−	0.499146i
$43$	3.50044	−	3.50044i	0.533813	−	0.533813i	−0.387892	−	0.921705i	$-0.626797\pi$
$43$	3.50044	−	3.50044i	0.533813	−	0.533813i	0.921705	+	0.387892i	$0.126797\pi$
$44$	1.30913			0.197360
$45$	5.95387	+	3.09054i	0.887550	+	0.460711i
$46$	6.72335			0.991304
$47$	−3.66790	+	3.66790i	−0.535018	+	0.535018i	−0.922061	−	0.387044i	$-0.873496\pi$
$47$	−3.66790	+	3.66790i	−0.535018	+	0.535018i	0.387044	+	0.922061i	$0.373496\pi$
$48$	−0.292893	−	1.70711i	−0.0422755	−	0.246400i
$49$		−	3.40927i		−	0.487039i
$50$	3.29289	+	3.76256i	0.465685	+	0.532106i
$51$	−10.7292	−	7.58667i	−1.50239	−	1.06235i
$52$	1.74632	+	1.74632i	0.242171	+	0.242171i
$53$	−6.45082	−	6.45082i	−0.886088	−	0.886088i	0.108057	−	0.994145i	$-0.465537\pi$
$53$	−6.45082	−	6.45082i	−0.886088	−	0.886088i	−0.994145	+	0.108057i	$0.965537\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$	2.13756	−	2.00000i	0.288229	−	0.269680i
$56$			1.89492i			0.253220i
$57$	−7.42202	+	1.27342i	−0.983071	+	0.168668i
$58$	−3.89492	+	3.89492i	−0.511428	+	0.511428i
$59$	−11.3765			−1.48110			−0.740548	−	0.672003i	$-0.765434\pi$
$59$	−11.3765			−1.48110			−0.740548	+	0.672003i	$0.765434\pi$
$60$	−3.08623	−	2.33991i	−0.398431	−	0.302081i
$61$	12.5481			1.60662			0.803309	−	0.595562i	$-0.203071\pi$
$61$	12.5481			1.60662			0.803309	+	0.595562i	$0.203071\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	5.12975	+	2.44993i	0.646288	+	0.308662i
$64$			1.00000i			0.125000i
$65$	5.51929	+	0.183501i	0.684584	+	0.0227605i
$66$	−1.30913	+	1.85140i	−0.161143	+	0.227891i
$67$	5.52512	+	5.52512i	0.675001	+	0.675001i	0.958865	−	0.283864i	$-0.0916164\pi$
$67$	5.52512	+	5.52512i	0.675001	+	0.675001i	−0.283864	+	0.958865i	$0.591616\pi$
$68$	5.36459	+	5.36459i	0.650552	+	0.650552i
$69$	−6.72335	+	9.50825i	−0.809396	+	1.14466i
$70$	2.89492	+	3.09404i	0.346009	+	0.369808i
$71$		−	10.3477i		−	1.22805i	−0.789287	−	0.614024i	$-0.789550\pi$
$71$		−	10.3477i		−	1.22805i	0.789287	−	0.614024i	$-0.210450\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−1.87025	+	1.87025i	−0.218896	+	0.218896i	−0.808033	−	0.589137i	$-0.799468\pi$
$73$	−1.87025	+	1.87025i	−0.218896	+	0.218896i	0.589137	+	0.808033i	$0.299468\pi$
$74$	−2.82843			−0.328798
$75$	−8.61396	+	0.894295i	−0.994654	+	0.103264i
$76$	4.34772			0.498718
$77$	1.75413	−	1.75413i	0.199901	−	0.199901i
$78$	−4.21598	+	0.723349i	−0.477366	+	0.0819031i
$79$		−	4.64493i		−	0.522595i	−0.965258	−	0.261298i	$-0.915850\pi$
$79$		−	4.64493i		−	0.522595i	0.965258	−	0.261298i	$-0.0841504\pi$
$80$	1.52773	+	1.63280i	0.170805	+	0.182553i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	−1.98896	−	1.98896i	−0.219644	−	0.219644i
$83$	−11.2871	−	11.2871i	−1.23891	−	1.23891i	−0.960445	−	0.278470i	$-0.910173\pi$
$83$	−11.2871	−	11.2871i	−1.23891	−	1.23891i	−0.278470	−	0.960445i	$-0.589827\pi$
$84$	−2.67982	−	1.89492i	−0.292393	−	0.206753i
$85$	16.9549	+	0.563703i	1.83902	+	0.0611422i
$86$		−	4.95037i		−	0.533813i
$87$	−1.61333	−	9.40317i	−0.172967	−	1.00813i
$88$	0.925698	−	0.925698i	0.0986798	−	0.0986798i
$89$	−7.16053			−0.759015			−0.379507	−	0.925189i	$-0.623907\pi$
$89$	−7.16053			−0.759015			−0.379507	+	0.925189i	$0.623907\pi$
$90$	6.39536	−	2.02468i	0.674131	−	0.213420i
$91$	4.67982			0.490579
$92$	4.75413	−	4.75413i	0.495652	−	0.495652i
$93$	0.292893	+	1.70711i	0.0303716	+	0.177019i
$94$			5.18719i			0.535018i
$95$	7.09898	−	6.64213i	0.728340	−	0.681468i
$96$	−1.41421	−	1.00000i	−0.144338	−	0.102062i
$97$	−1.49632	−	1.49632i	−0.151929	−	0.151929i	0.627050	−	0.778979i	$-0.284262\pi$
$97$	−1.49632	−	1.49632i	−0.151929	−	0.151929i	−0.778979	+	0.627050i	$0.784262\pi$
$98$	−2.41072	−	2.41072i	−0.243519	−	0.243519i
$99$	−1.30913	−	3.70279i	−0.131573	−	0.372145i
$100$	4.98896	+	0.332104i	0.498896	+	0.0332104i
$101$			13.4647i			1.33979i	0.742456	+	0.669895i	$0.233661\pi$
$101$			13.4647i			1.33979i	−0.742456	+	0.669895i	$0.766339\pi$
$102$	−12.9513	+	2.22208i	−1.28237	+	0.220019i
$103$	−10.4032	+	10.4032i	−1.02506	+	1.02506i	−0.0253770	+	0.999678i	$0.508079\pi$
$103$	−10.4032	+	10.4032i	−1.02506	+	1.02506i	−0.999678	+	0.0253770i	$0.991921\pi$
$104$	2.46967			0.242171
$105$	−7.27055	+	1.00000i	−0.709533	+	0.0975900i
$106$	−9.12283			−0.886088
$107$	−8.11871	+	8.11871i	−0.784866	+	0.784866i	−0.980647	−	0.195782i	$-0.937276\pi$
$107$	−8.11871	+	8.11871i	−0.784866	+	0.784866i	0.195782	+	0.980647i	$0.437276\pi$
$108$	−4.53553	+	2.53553i	−0.436432	+	0.243982i
$109$			0.305448i			0.0292566i	0.999893	+	0.0146283i	$0.00465650\pi$
$109$			0.305448i			0.0292566i	−0.999893	+	0.0146283i	$0.995344\pi$
$110$	0.0972711	−	2.92570i	0.00927443	−	0.278954i
$111$	2.82843	−	4.00000i	0.268462	−	0.379663i
$112$	1.33991	+	1.33991i	0.126610	+	0.126610i
$113$	1.51148	+	1.51148i	0.142189	+	0.142189i	0.774618	−	0.632429i	$-0.217942\pi$
$113$	1.51148	+	1.51148i	0.142189	+	0.142189i	−0.632429	+	0.774618i	$0.717942\pi$
$114$	−4.34772	+	6.14860i	−0.407201	+	0.575869i
$115$	0.499557	−	15.0256i	0.0465839	−	1.40114i
$116$			5.50825i			0.511428i
$117$	3.19301	−	6.68565i	0.295194	−	0.618089i
$118$	−8.04441	+	8.04441i	−0.740548	+	0.740548i
$119$	14.3761			1.31786
$120$	−3.83686	+	0.527726i	−0.350256	+	0.0481746i
$121$	9.28617			0.844197
$122$	8.87284	−	8.87284i	0.803309	−	0.803309i
$123$	4.80177	−	0.823854i	0.432961	−	0.0742844i
$124$		−	1.00000i		−	0.0898027i
$125$	8.65336	−	7.07950i	0.773980	−	0.633210i
$126$	5.35965	−	1.89492i	0.477475	−	0.168813i
$127$	−2.40811	−	2.40811i	−0.213685	−	0.213685i	0.592146	−	0.805831i	$-0.298281\pi$
$127$	−2.40811	−	2.40811i	−0.213685	−	0.213685i	−0.805831	+	0.592146i	$0.798281\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	7.00089	+	4.95037i	0.616394	+	0.435856i
$130$	4.03248	−	3.77297i	0.353672	−	0.330912i
$131$			8.82321i			0.770888i	0.922731	+	0.385444i	$0.125952\pi$
$131$			8.82321i			0.770888i	−0.922731	+	0.385444i	$0.874048\pi$
$132$	0.383437	+	2.23483i	0.0333739	+	0.194517i
$133$	5.82556	−	5.82556i	0.505140	−	0.505140i
$134$	7.81370			0.675001
$135$	−3.53204	+	11.0691i	−0.303990	+	0.952675i
$136$	7.58667			0.650552
$137$	−12.2546	+	12.2546i	−1.04698	+	1.04698i	−0.0481377	+	0.998841i	$0.515329\pi$
$137$	−12.2546	+	12.2546i	−1.04698	+	1.04698i	−0.998841	+	0.0481377i	$0.984671\pi$
$138$	1.96922	+	11.4775i	0.167631	+	0.977027i
$139$		−	10.0563i		−	0.852968i	−0.904495	−	0.426484i	$-0.859752\pi$
$139$		−	10.0563i		−	0.852968i	0.904495	−	0.426484i	$-0.140248\pi$
$140$	4.23483	+	0.140796i	0.357909	+	0.0118994i
$141$	−7.33579	−	5.18719i	−0.617785	−	0.436840i
$142$	−7.31694	−	7.31694i	−0.614024	−	0.614024i
$143$	−2.28617	−	2.28617i	−0.191179	−	0.191179i
$144$	2.82843	−	1.00000i	0.235702	−	0.0833333i
$145$	8.41510	+	8.99390i	0.698836	+	0.746903i
$146$			2.64493i			0.218896i
$147$	5.81999	−	0.998553i	0.480025	−	0.0823593i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	18.7711			1.53779			0.768893	−	0.639378i	$-0.220808\pi$
$149$	18.7711			1.53779			0.768893	+	0.639378i	$0.220808\pi$
$150$	−5.45862	+	6.72335i	−0.445695	+	0.548959i
$151$	4.51902			0.367752			0.183876	−	0.982949i	$-0.441135\pi$
$151$	4.51902			0.367752			0.183876	+	0.982949i	$0.441135\pi$
$152$	3.07430	−	3.07430i	0.249359	−	0.249359i
$153$	9.80876	−	20.5379i	0.792991	−	1.66039i
$154$		−	2.48071i		−	0.199901i
$155$	−1.52773	−	1.63280i	−0.122710	−	0.131150i
$156$	−2.46967	+	3.49264i	−0.197732	+	0.279635i
$157$	11.5063	+	11.5063i	0.918300	+	0.918300i	0.996906	−	0.0786055i	$-0.0250467\pi$
$157$	11.5063	+	11.5063i	0.918300	+	0.918300i	−0.0786055	+	0.996906i	$0.525047\pi$
$158$	−3.28446	−	3.28446i	−0.261298	−	0.261298i
$159$	9.12283	−	12.9016i	0.723488	−	1.02317i
$160$	2.23483	+	0.0743018i	0.176679	+	0.00587407i
$161$		−	12.7402i		−	1.00407i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−0.105079	+	0.105079i	−0.00823039	+	0.00823039i	−0.711210	−	0.702980i	$-0.751852\pi$
$163$	−0.105079	+	0.105079i	−0.00823039	+	0.00823039i	0.702980	+	0.711210i	$0.251852\pi$
$164$	−2.81281			−0.219644
$165$	4.04029	+	3.06326i	0.314536	+	0.238474i
$166$	−15.9623			−1.23891
$167$	0.887114	−	0.887114i	0.0686469	−	0.0686469i	−0.671950	−	0.740597i	$-0.734543\pi$
$167$	0.887114	−	0.887114i	0.0686469	−	0.0686469i	0.740597	+	0.671950i	$0.234543\pi$
$168$	−3.23483	+	0.555010i	−0.249573	+	0.0428199i
$169$			6.90075i			0.530827i
$170$	12.3876	−	11.5904i	0.950082	−	0.888940i
$171$	−4.34772	−	12.2972i	−0.332478	−	0.940391i
$172$	−3.50044	−	3.50044i	−0.266906	−	0.266906i
$173$	16.8692	+	16.8692i	1.28254	+	1.28254i	0.939219	+	0.343319i	$0.111551\pi$
$173$	16.8692	+	16.8692i	1.28254	+	1.28254i	0.343319	+	0.939219i	$0.388449\pi$
$174$	−7.78984	−	5.50825i	−0.590546	−	0.417579i
$175$	7.12975	−	6.23977i	0.538959	−	0.471683i
$176$		−	1.30913i		−	0.0986798i
$177$	−3.33210	−	19.4209i	−0.250456	−	1.45977i
$178$	−5.06326	+	5.06326i	−0.379507	+	0.379507i
$179$	12.3622			0.923992			0.461996	−	0.886882i	$-0.347133\pi$
$179$	12.3622			0.923992			0.461996	+	0.886882i	$0.347133\pi$
$180$	3.09054	−	5.95387i	0.230356	−	0.443775i
$181$	0.00582690			0.000433110			0.000216555	−	1.00000i	$-0.499931\pi$
$181$	0.00582690			0.000433110			0.000216555		1.00000i	$0.499931\pi$
$182$	3.30913	−	3.30913i	0.245289	−	0.245289i
$183$	3.67525	+	21.4209i	0.271682	+	1.58348i
$184$		−	6.72335i		−	0.495652i
$185$	−0.210157	+	6.32106i	−0.0154511	+	0.464734i
$186$	1.41421	+	1.00000i	0.103695	+	0.0733236i
$187$	−7.02297	−	7.02297i	−0.513570	−	0.513570i
$188$	3.66790	+	3.66790i	0.267509	+	0.267509i
$189$	−2.67982	+	9.47461i	−0.194928	+	0.689176i
$190$	0.323043	−	9.71643i	0.0234360	−	0.704904i
$191$			4.58453i			0.331725i	0.986149	+	0.165863i	$0.0530408\pi$
$191$			4.58453i			0.331725i	−0.986149	+	0.165863i	$0.946959\pi$
$192$	−1.70711	+	0.292893i	−0.123200	+	0.0211377i
$193$	−16.9513	+	16.9513i	−1.22018	+	1.22018i	−0.252610	+	0.967568i	$0.581289\pi$
$193$	−16.9513	+	16.9513i	−1.22018	+	1.22018i	−0.967568	+	0.252610i	$0.918711\pi$
$194$	−2.11612			−0.151929
$195$	1.30331	+	9.47577i	0.0933318	+	0.678574i
$196$	−3.40927			−0.243519
$197$	10.6096	−	10.6096i	0.755906	−	0.755906i	−0.219669	−	0.975575i	$-0.570498\pi$
$197$	10.6096	−	10.6096i	0.755906	−	0.755906i	0.975575	+	0.219669i	$0.0704977\pi$
$198$	−3.54397	−	1.69257i	−0.251859	−	0.120286i
$199$		−	4.67866i		−	0.331662i	−0.986154	−	0.165831i	$-0.946969\pi$
$199$		−	4.67866i		−	0.331662i	0.986154	−	0.165831i	$-0.0530306\pi$
$200$	3.76256	−	3.29289i	0.266053	−	0.232843i
$201$	−7.81370	+	11.0502i	−0.551136	+	0.779424i
$202$	9.52100	+	9.52100i	0.669895	+	0.669895i
$203$	7.38057	+	7.38057i	0.518014	+	0.518014i
$204$	−7.58667	+	10.7292i	−0.531173	+	0.751193i
$205$	−4.59277	+	4.29721i	−0.320773	+	0.300130i
$206$			14.7123i			1.02506i
$207$	−18.2008	−	8.69257i	−1.26504	−	0.604175i
$208$	1.74632	−	1.74632i	0.121085	−	0.121085i
$209$	−5.69175			−0.393707
$210$	−4.43395	+	5.84816i	−0.305972	+	0.403562i
$211$	−11.3551			−0.781715			−0.390858	−	0.920451i	$-0.627822\pi$
$211$	−11.3551			−0.781715			−0.390858	+	0.920451i	$0.627822\pi$
$212$	−6.45082	+	6.45082i	−0.443044	+	0.443044i
$213$	17.6647	−	3.03078i	1.21036	−	0.207665i
$214$			11.4816i			0.784866i
$215$	−11.0633	−	0.367822i	−0.754508	−	0.0250852i
$216$	−1.41421	+	5.00000i	−0.0962250	+	0.340207i
$217$	−1.33991	−	1.33991i	−0.0909591	−	0.0909591i
$218$	0.215984	+	0.215984i	0.0146283	+	0.0146283i
$219$	−3.74049	−	2.64493i	−0.252759	−	0.178728i
$220$	−2.00000	−	2.13756i	−0.134840	−	0.144114i
$221$		−	18.7365i		−	1.26036i
$222$	−0.828427	−	4.82843i	−0.0556004	−	0.324063i
$223$	11.0613	−	11.0613i	0.740718	−	0.740718i	−0.231998	−	0.972716i	$-0.574526\pi$
$223$	11.0613	−	11.0613i	0.740718	−	0.740718i	0.972716	+	0.231998i	$0.0745263\pi$
$224$	1.89492			0.126610
$225$	−4.04963	−	14.4430i	−0.269975	−	0.962867i
$226$	2.13756			0.142189
$227$	−10.1647	+	10.1647i	−0.674652	+	0.674652i	−0.958785	−	0.284133i	$-0.908294\pi$
$227$	−10.1647	+	10.1647i	−0.674652	+	0.674652i	0.284133	+	0.958785i	$0.408294\pi$
$228$	1.27342	+	7.42202i	0.0843341	+	0.491535i
$229$		−	13.4188i		−	0.886738i	−0.896339	−	0.443369i	$-0.853783\pi$
$229$		−	13.4188i		−	0.886738i	0.896339	−	0.443369i	$-0.146217\pi$
$230$	−10.2714	−	10.9779i	−0.677278	−	0.723862i
$231$	3.50825	+	2.48071i	0.230826	+	0.163219i
$232$	3.89492	+	3.89492i	0.255714	+	0.255714i
$233$	9.55096	+	9.55096i	0.625704	+	0.625704i	0.946984	−	0.321280i	$-0.104113\pi$
$233$	9.55096	+	9.55096i	0.625704	+	0.625704i	−0.321280	+	0.946984i	$0.604113\pi$
$234$	−2.46967	−	6.98527i	−0.161447	−	0.456641i
$235$	11.5925	+	0.385417i	0.756211	+	0.0251419i
$236$			11.3765i			0.740548i
$237$	7.92939	−	1.36047i	0.515069	−	0.0883719i
$238$	10.1655	−	10.1655i	0.658930	−	0.658930i
$239$	−28.4935			−1.84309			−0.921546	−	0.388268i	$-0.873073\pi$
$239$	−28.4935			−1.84309			−0.921546	+	0.388268i	$0.873073\pi$
$240$	−2.33991	+	3.08623i	−0.151041	+	0.199215i
$241$	−10.4697			−0.674410			−0.337205	−	0.941431i	$-0.609482\pi$
$241$	−10.4697			−0.674410			−0.337205	+	0.941431i	$0.609482\pi$
$242$	6.56631	−	6.56631i	0.422098	−	0.422098i
$243$	11.7071	+	10.2929i	0.751011	+	0.660289i
$244$		−	12.5481i		−	0.803309i
$245$	−5.56668	+	5.20844i	−0.355642	+	0.332755i
$246$	2.81281	−	3.97792i	0.179338	−	0.253623i
$247$	−7.59250	−	7.59250i	−0.483099	−	0.483099i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	15.9623	−	22.5741i	1.01157	−	1.43058i
$250$	1.11289	−	11.1248i	0.0703851	−	0.703595i
$251$		−	27.8155i		−	1.75570i	−0.478938	−	0.877848i	$-0.658978\pi$
$251$		−	27.8155i		−	1.75570i	0.478938	−	0.877848i	$-0.341022\pi$
$252$	2.44993	−	5.12975i	0.154331	−	0.323144i
$253$	−6.22379	+	6.22379i	−0.391286	+	0.391286i
$254$	−3.40559			−0.213685
$255$	4.00369	+	29.1090i	0.250721	+	1.82288i
$256$	1.00000			0.0625000
$257$	−4.61162	+	4.61162i	−0.287665	+	0.287665i	−0.836156	−	0.548491i	$-0.815202\pi$
$257$	−4.61162	+	4.61162i	−0.287665	+	0.287665i	0.548491	+	0.836156i	$0.315202\pi$
$258$	8.45082	−	1.44993i	0.526125	−	0.0902688i
$259$			5.35965i			0.333032i
$260$	0.183501	−	5.51929i	0.0113802	−	0.342292i
$261$	15.5797	−	5.50825i	0.964358	−	0.340952i
$262$	6.23895	+	6.23895i	0.385444	+	0.385444i
$263$	1.18350	+	1.18350i	0.0729778	+	0.0729778i	0.742654	−	0.669676i	$-0.233567\pi$
$263$	1.18350	+	1.18350i	0.0729778	+	0.0729778i	−0.669676	+	0.742654i	$0.733567\pi$
$264$	1.85140	+	1.30913i	0.113946	+	0.0805717i
$265$	−0.677843	+	20.3880i	−0.0416396	+	1.25243i
$266$		−	8.23859i		−	0.505140i
$267$	−2.09727	−	12.2238i	−0.128351	−	0.748084i
$268$	5.52512	−	5.52512i	0.337500	−	0.337500i
$269$	1.84316			0.112379			0.0561896	−	0.998420i	$-0.482105\pi$
$269$	1.84316			0.112379			0.0561896	+	0.998420i	$0.482105\pi$
$270$	5.32950	+	10.3246i	0.324343	+	0.628332i
$271$	−15.8832			−0.964838			−0.482419	−	0.875941i	$-0.660242\pi$
$271$	−15.8832			−0.964838			−0.482419	+	0.875941i	$0.660242\pi$
$272$	5.36459	−	5.36459i	0.325276	−	0.325276i
$273$	1.37069	+	7.98896i	0.0829578	+	0.483514i
$274$			17.3306i			1.04698i
$275$	−6.53122	−	0.434769i	−0.393847	−	0.0262176i
$276$	9.50825	+	6.72335i	0.572329	+	0.404698i
$277$	−1.16916	−	1.16916i	−0.0702480	−	0.0702480i	0.671110	−	0.741358i	$-0.265818\pi$
$277$	−1.16916	−	1.16916i	−0.0702480	−	0.0702480i	−0.741358	+	0.671110i	$0.765818\pi$
$278$	−7.11091	−	7.11091i	−0.426484	−	0.426484i
$279$	−2.82843	+	1.00000i	−0.169334	+	0.0598684i
$280$	3.09404	−	2.89492i	0.184904	−	0.173005i
$281$		−	5.69059i		−	0.339472i	−0.985490	−	0.169736i	$-0.945708\pi$
$281$		−	5.69059i		−	0.339472i	0.985490	−	0.169736i	$-0.0542915\pi$
$282$	−8.85508	+	1.51929i	−0.527313	+	0.0904725i
$283$	−0.590360	+	0.590360i	−0.0350933	+	0.0350933i	−0.724436	−	0.689342i	$-0.757900\pi$
$283$	−0.590360	+	0.590360i	−0.0350933	+	0.0350933i	0.689342	+	0.724436i	$0.257900\pi$
$284$	−10.3477			−0.614024
$285$	13.4181	+	10.1733i	0.794817	+	0.602613i
$286$	−3.23313			−0.191179
$287$	−3.76892	+	3.76892i	−0.222472	+	0.222472i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$		−	40.5576i		−	2.38574i
$290$	12.3100	+	0.409273i	0.722869	+	0.0240333i
$291$	2.11612	−	2.99265i	0.124049	−	0.175432i
$292$	1.87025	+	1.87025i	0.109448	+	0.109448i
$293$	−5.10139	−	5.10139i	−0.298026	−	0.298026i	0.542214	−	0.840240i	$-0.317586\pi$
$293$	−5.10139	−	5.10139i	−0.298026	−	0.298026i	−0.840240	+	0.542214i	$0.817586\pi$
$294$	3.40927	−	4.82144i	0.198833	−	0.281192i
$295$	17.3802	+	18.5756i	1.01191	+	1.08152i
$296$			2.82843i			0.164399i
$297$	5.93763	−	3.31936i	0.344536	−	0.192609i
$298$	13.2731	−	13.2731i	0.768893	−	0.768893i
$299$	−16.6044			−0.960259
$300$	0.894295	+	8.61396i	0.0516321	+	0.497327i
$301$	−9.38057			−0.540687
$302$	3.19543	−	3.19543i	0.183876	−	0.183876i
$303$	−22.9857	+	3.94373i	−1.32050	+	0.226561i
$304$		−	4.34772i		−	0.249359i
$305$	−19.1700	−	20.4886i	−1.09767	−	1.17317i
$306$	−7.58667	−	21.4584i	−0.433701	−	1.22669i
$307$	6.63514	+	6.63514i	0.378687	+	0.378687i	0.870628	−	0.491941i	$-0.163712\pi$
$307$	6.63514	+	6.63514i	0.378687	+	0.378687i	−0.491941	+	0.870628i	$0.663712\pi$
$308$	−1.75413	−	1.75413i	−0.0999506	−	0.0999506i
$309$	−20.8063	−	14.7123i	−1.18363	−	0.836954i
$310$	−2.23483	−	0.0743018i	−0.126930	−	0.00422006i
$311$			23.4363i			1.32895i	0.747311	+	0.664474i	$0.231345\pi$
$311$			23.4363i			1.32895i	−0.747311	+	0.664474i	$0.768655\pi$
$312$	0.723349	+	4.21598i	0.0409515	+	0.238683i
$313$	−6.44060	+	6.44060i	−0.364044	+	0.364044i	−0.865299	−	0.501255i	$-0.832872\pi$
$313$	−6.44060	+	6.44060i	−0.364044	+	0.364044i	0.501255	+	0.865299i	$0.332872\pi$
$314$	16.2723			0.918300
$315$	−3.83660	−	12.1187i	−0.216168	−	0.682812i
$316$	−4.64493			−0.261298
$317$	−18.9985	+	18.9985i	−1.06706	+	1.06706i	−0.0694770	+	0.997584i	$0.522133\pi$
$317$	−18.9985	+	18.9985i	−1.06706	+	1.06706i	−0.997584	+	0.0694770i	$0.977867\pi$
$318$	−2.67202	−	15.5737i	−0.149839	−	0.873327i
$319$		−	7.21104i		−	0.403741i
$320$	1.63280	−	1.52773i	0.0912766	−	0.0854025i
$321$	−16.2374	−	11.4816i	−0.906285	−	0.640840i
$322$	−9.00869	−	9.00869i	−0.502035	−	0.502035i
$323$	−23.3237	−	23.3237i	−1.29777	−	1.29777i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−8.13235	−	9.29227i	−0.451101	−	0.515442i
$326$			0.148604i			0.00823039i
$327$	−0.521432	+	0.0894635i	−0.0288352	+	0.00494735i
$328$	−1.98896	+	1.98896i	−0.109822	+	0.109822i
$329$	9.82931			0.541908
$330$	5.02297	−	0.690865i	0.276505	−	0.0380309i
$331$	4.04810			0.222504			0.111252	−	0.993792i	$-0.464514\pi$
$331$	4.04810			0.222504			0.111252	+	0.993792i	$0.464514\pi$
$332$	−11.2871	+	11.2871i	−0.619457	+	0.619457i
$333$	7.65685	+	3.65685i	0.419593	+	0.200394i
$334$		−	1.25457i		−	0.0686469i
$335$	0.580572	−	17.4623i	0.0317200	−	0.954068i
$336$	−1.89492	+	2.67982i	−0.103376	+	0.146196i
$337$	6.07018	+	6.07018i	0.330664	+	0.330664i	0.852839	−	0.522175i	$-0.174879\pi$
$337$	6.07018	+	6.07018i	0.330664	+	0.330664i	−0.522175	+	0.852839i	$0.674879\pi$
$338$	4.87957	+	4.87957i	0.265413	+	0.265413i
$339$	−2.13756	+	3.02297i	−0.116096	+	0.164185i
$340$	0.563703	−	16.9549i	0.0305711	−	0.919511i
$341$			1.30913i			0.0708936i
$342$	−11.7697	−	5.62114i	−0.636435	−	0.303956i
$343$	−13.9475	+	13.9475i	−0.753095	+	0.753095i
$344$	−4.95037			−0.266906
$345$	25.7966	−	3.54809i	1.38884	−	0.191023i
$346$	23.8566			1.28254
$347$	17.7567	−	17.7567i	0.953231	−	0.953231i	−0.0457236	−	0.998954i	$-0.514559\pi$
$347$	17.7567	−	17.7567i	0.953231	−	0.953231i	0.998954	+	0.0457236i	$0.0145593\pi$
$348$	−9.40317	+	1.61333i	−0.504063	+	0.0864835i
$349$		−	12.4731i		−	0.667669i	−0.942632	−	0.333834i	$-0.891657\pi$
$349$		−	12.4731i		−	0.667669i	0.942632	−	0.333834i	$-0.108343\pi$
$350$	0.629311	−	9.45368i	0.0336381	−	0.505321i
$351$	12.3483	+	3.49264i	0.659105	+	0.186423i
$352$	−0.925698	−	0.925698i	−0.0493399	−	0.0493399i
$353$	2.56282	+	2.56282i	0.136405	+	0.136405i	0.772012	−	0.635607i	$-0.219250\pi$
$353$	2.56282	+	2.56282i	0.136405	+	0.136405i	−0.635607	+	0.772012i	$0.719250\pi$
$354$	−16.0888	−	11.3765i	−0.855111	−	0.604655i
$355$	−16.8958	+	15.8085i	−0.896736	+	0.839027i
$356$			7.16053i			0.379507i
$357$	4.21068	+	24.5416i	0.222853	+	1.29888i
$358$	8.74138	−	8.74138i	0.461996	−	0.461996i
$359$	−3.97334			−0.209705			−0.104853	−	0.994488i	$-0.533437\pi$
$359$	−3.97334			−0.209705			−0.104853	+	0.994488i	$0.533437\pi$
$360$	−2.02468	−	6.39536i	−0.106710	−	0.337065i
$361$	0.0973369			0.00512300
$362$	0.00412024	−	0.00412024i	0.000216555	−	0.000216555i
$363$	2.71985	+	15.8525i	0.142755	+	0.832039i
$364$		−	4.67982i		−	0.245289i
$365$	5.91097	+	0.196523i	0.309394	+	0.0102865i
$366$	17.7457	+	12.5481i	0.927581	+	0.655899i
$367$	17.9779	+	17.9779i	0.938440	+	0.938440i	0.998212	−	0.0597724i	$-0.0190375\pi$
$367$	17.9779	+	17.9779i	0.938440	+	0.938440i	−0.0597724	+	0.998212i	$0.519037\pi$
$368$	−4.75413	−	4.75413i	−0.247826	−	0.247826i
$369$	2.81281	+	7.95583i	0.146429	+	0.414164i
$370$	4.32106	+	4.61827i	0.224641	+	0.240092i
$371$			17.2871i			0.897499i
$372$	1.70711	−	0.292893i	0.0885094	−	0.0151858i
$373$	−17.2008	+	17.2008i	−0.890625	+	0.890625i	−0.994582	−	0.103957i	$-0.966850\pi$
$373$	−17.2008	+	17.2008i	−0.890625	+	0.890625i	0.103957	+	0.994582i	$0.466850\pi$
$374$	−9.93198			−0.513570
$375$	14.6200	+	12.6987i	0.754972	+	0.655757i
$376$	5.18719			0.267509
$377$	9.61916	−	9.61916i	0.495412	−	0.495412i
$378$	4.80464	+	8.59448i	0.247124	+	0.442052i
$379$		−	14.4899i		−	0.744294i	−0.928174	−	0.372147i	$-0.878622\pi$
$379$		−	14.4899i		−	0.744294i	0.928174	−	0.372147i	$-0.121378\pi$
$380$	−6.64213	−	7.09898i	−0.340734	−	0.364170i
$381$	3.40559	−	4.81623i	0.174473	−	0.246743i
$382$	3.24175	+	3.24175i	0.165863	+	0.165863i
$383$	24.7567	+	24.7567i	1.26501	+	1.26501i	0.948634	+	0.316375i	$0.102466\pi$
$383$	24.7567	+	24.7567i	1.26501	+	1.26501i	0.316375	+	0.948634i	$0.397534\pi$
$384$	−1.00000	+	1.41421i	−0.0510310	+	0.0721688i
$385$	−5.54397	−	0.184321i	−0.282547	−	0.00939387i
$386$			23.9727i			1.22018i
$387$	−6.40031	+	13.4012i	−0.325346	+	0.681221i
$388$	−1.49632	+	1.49632i	−0.0759643	+	0.0759643i
$389$	33.0438			1.67539			0.837693	−	0.546142i	$-0.183904\pi$
$389$	33.0438			1.67539			0.837693	+	0.546142i	$0.183904\pi$
$390$	7.62196	+	5.77880i	0.385953	+	0.292621i
$391$	−51.0078			−2.57958
$392$	−2.41072	+	2.41072i	−0.121760	+	0.121760i
$393$	−15.0622	+	2.58426i	−0.759786	+	0.130359i
$394$		−	15.0043i		−	0.755906i
$395$	−7.58426	+	7.09618i	−0.381605	+	0.357047i
$396$	−3.70279	+	1.30913i	−0.186072	+	0.0657865i
$397$	6.05133	+	6.05133i	0.303708	+	0.303708i	0.842463	−	0.538755i	$-0.181105\pi$
$397$	6.05133	+	6.05133i	0.303708	+	0.303708i	−0.538755	+	0.842463i	$0.681105\pi$
$398$	−3.30831	−	3.30831i	−0.165831	−	0.165831i
$399$	11.6511	+	8.23859i	0.583286	+	0.412445i
$400$	0.332104	−	4.98896i	0.0166052	−	0.249448i
$401$		−	25.3585i		−	1.26634i	−0.774012	−	0.633171i	$-0.781753\pi$
$401$		−	25.3585i		−	1.26634i	0.774012	−	0.633171i	$-0.218247\pi$
$402$	2.28858	+	13.3388i	0.114144	+	0.665280i
$403$	−1.74632	+	1.74632i	−0.0869903	+	0.0869903i
$404$	13.4647			0.669895
$405$	−19.9306	−	2.78751i	−0.990361	−	0.138512i
$406$	10.4377			0.518014
$407$	2.61827	−	2.61827i	0.129783	−	0.129783i
$408$	2.22208	+	12.9513i	0.110010	+	0.641183i
$409$			10.0337i			0.496136i	0.968743	+	0.248068i	$0.0797957\pi$
$409$			10.0337i			0.496136i	−0.968743	+	0.248068i	$0.920204\pi$
$410$	−0.208997	+	6.28617i	−0.0103216	+	0.310452i
$411$	−24.5091	−	17.3306i	−1.20895	−	0.854854i
$412$	10.4032	+	10.4032i	0.512528	+	0.512528i
$413$	15.2435	+	15.2435i	0.750085	+	0.750085i
$414$	−19.0165	+	6.72335i	−0.934610	+	0.330435i
$415$	−1.18603	+	35.6731i	−0.0582198	+	1.75112i
$416$		−	2.46967i		−	0.121085i
$417$	17.1672	−	2.94543i	0.840684	−	0.144238i
$418$	−4.02468	+	4.02468i	−0.196853	+	0.196853i
$419$	26.8198			1.31023			0.655116	−	0.755528i	$-0.272620\pi$
$419$	26.8198			1.31023			0.655116	+	0.755528i	$0.272620\pi$
$420$	1.00000	+	7.27055i	0.0487950	+	0.354767i
$421$	18.6954			0.911160			0.455580	−	0.890195i	$-0.349432\pi$
$421$	18.6954			0.911160			0.455580	+	0.890195i	$0.349432\pi$
$422$	−8.02925	+	8.02925i	−0.390858	+	0.390858i
$423$	6.70648	−	14.0423i	0.326080	−	0.682759i
$424$			9.12283i			0.443044i
$425$	−24.9821	−	28.5453i	−1.21181	−	1.38465i
$426$	10.3477	−	14.6339i	0.501349	−	0.709014i
$427$	−16.8133	−	16.8133i	−0.813654	−	0.813654i
$428$	8.11871	+	8.11871i	0.392433	+	0.392433i
$429$	3.23313	−	4.57233i	0.156097	−	0.220754i
$430$	−8.08300	+	7.56282i	−0.389797	+	0.364711i
$431$		−	17.2267i		−	0.829779i	−0.909872	−	0.414889i	$-0.863820\pi$
$431$		−	17.2267i		−	0.829779i	0.909872	−	0.414889i	$-0.136180\pi$
$432$	2.53553	+	4.53553i	0.121991	+	0.218216i
$433$	−9.70944	+	9.70944i	−0.466606	+	0.466606i	−0.900813	−	0.434207i	$-0.857029\pi$
$433$	−9.70944	+	9.70944i	−0.466606	+	0.466606i	0.434207	+	0.900813i	$0.357029\pi$
$434$	−1.89492			−0.0909591
$435$	−12.8888	+	16.9997i	−0.617972	+	0.815074i
$436$	0.305448			0.0146283
$437$	−20.6696	+	20.6696i	−0.988761	+	0.988761i
$438$	−4.51517	+	0.774681i	−0.215743	+	0.0370157i
$439$			26.9329i			1.28544i	0.766103	+	0.642718i	$0.222193\pi$
$439$			26.9329i			1.28544i	−0.766103	+	0.642718i	$0.777807\pi$
$440$	−2.92570	−	0.0972711i	−0.139477	−	0.00463722i
$441$	3.40927	+	9.64288i	0.162346	+	0.459185i
$442$	−13.2487	−	13.2487i	−0.630178	−	0.630178i
$443$	−23.3635	−	23.3635i	−1.11003	−	1.11003i	−0.993145	−	0.116888i	$-0.962708\pi$
$443$	−23.3635	−	23.3635i	−1.11003	−	1.11003i	−0.116888	−	0.993145i	$-0.537292\pi$
$444$	−4.00000	−	2.82843i	−0.189832	−	0.134231i
$445$	10.9393	+	11.6918i	0.518574	+	0.554242i
$446$		−	15.6430i		−	0.740718i
$447$	5.49792	+	32.0442i	0.260043	+	1.51564i
$448$	1.33991	−	1.33991i	0.0633049	−	0.0633049i
$449$	26.7530			1.26255			0.631277	−	0.775558i	$-0.282531\pi$
$449$	26.7530			1.26255			0.631277	+	0.775558i	$0.282531\pi$
$450$	−13.0763	−	7.34923i	−0.616421	−	0.346446i
$451$	3.68235			0.173395
$452$	1.51148	−	1.51148i	0.0710943	−	0.0710943i
$453$	1.32359	+	7.71445i	0.0621877	+	0.362456i
$454$			14.3750i			0.674652i
$455$	−7.14949	−	7.64124i	−0.335173	−	0.358227i
$456$	6.14860	+	4.34772i	0.287935	+	0.203601i
$457$	25.1188	+	25.1188i	1.17501	+	1.17501i	0.981000	+	0.194007i	$0.0621484\pi$
$457$	25.1188	+	25.1188i	1.17501	+	1.17501i	0.194007	+	0.981000i	$0.437852\pi$
$458$	−9.48852	−	9.48852i	−0.443369	−	0.443369i
$459$	37.9334	+	10.7292i	1.77058	+	0.500795i
$460$	−15.0256	−	0.499557i	−0.700570	−	0.0232920i
$461$			5.36953i			0.250084i	0.992151	+	0.125042i	$0.0399065\pi$
$461$			5.36953i			0.250084i	−0.992151	+	0.125042i	$0.960093\pi$
$462$	4.23483	−	0.726583i	0.197022	−	0.0338037i
$463$	−4.97423	+	4.97423i	−0.231172	+	0.231172i	−0.813182	−	0.582010i	$-0.802267\pi$
$463$	−4.97423	+	4.97423i	−0.231172	+	0.231172i	0.582010	+	0.813182i	$0.302267\pi$
$464$	5.50825			0.255714
$465$	2.33991	−	3.08623i	0.108511	−	0.143120i
$466$	13.5071			0.625704
$467$	−15.3051	+	15.3051i	−0.708235	+	0.708235i	−0.966164	−	0.257929i	$-0.916960\pi$
$467$	−15.3051	+	15.3051i	−0.708235	+	0.708235i	0.257929	+	0.966164i	$0.416960\pi$
$468$	−6.68565	−	3.19301i	−0.309044	−	0.147597i
$469$		−	14.8063i		−	0.683693i
$470$	8.46967	−	7.92460i	0.390677	−	0.365535i
$471$	−16.2723	+	23.0125i	−0.749789	+	1.06036i
$472$	8.04441	+	8.04441i	0.370274	+	0.370274i
$473$	4.58255	+	4.58255i	0.210706	+	0.210706i
$474$	4.64493	−	6.56892i	0.213349	−	0.301720i
$475$	−21.6906	−	1.44390i	−0.995233	−	0.0662505i
$476$		−	14.3761i		−	0.658930i
$477$	24.6965	+	11.7948i	1.13077	+	0.540049i
$478$	−20.1480	+	20.1480i	−0.921546	+	0.921546i
$479$	−16.3832			−0.748569			−0.374284	−	0.927314i	$-0.622112\pi$
$479$	−16.3832			−0.748569			−0.374284	+	0.927314i	$0.622112\pi$
$480$	0.527726	+	3.83686i	0.0240873	+	0.175128i
$481$	6.98527			0.318501
$482$	−7.40317	+	7.40317i	−0.337205	+	0.337205i
$483$	21.7489	−	3.73152i	0.989610	−	0.169790i
$484$		−	9.28617i		−	0.422098i
$485$	−0.157232	+	4.72918i	−0.00713952	+	0.214741i
$486$	15.5563	−	1.00000i	0.705650	−	0.0453609i
$487$	−7.85481	−	7.85481i	−0.355935	−	0.355935i	0.506377	−	0.862312i	$-0.330984\pi$
$487$	−7.85481	−	7.85481i	−0.355935	−	0.355935i	−0.862312	+	0.506377i	$0.830984\pi$
$488$	−8.87284	−	8.87284i	−0.401655	−	0.401655i
$489$	−0.210157	−	0.148604i	−0.00950364	−	0.00672009i
$490$	−0.253315	+	7.61916i	−0.0114436	+	0.344198i
$491$			34.0475i			1.53654i	0.640126	+	0.768270i	$0.278882\pi$
$491$			34.0475i			1.53654i	−0.640126	+	0.768270i	$0.721118\pi$
$492$	−0.823854	−	4.80177i	−0.0371422	−	0.216481i
$493$	29.5495	−	29.5495i	1.33084	−	1.33084i
$494$	−10.7374			−0.483099
$495$	−4.04594	+	7.79442i	−0.181851	+	0.350333i
$496$	−1.00000			−0.0449013
$497$	−13.8650	+	13.8650i	−0.621932	+	0.621932i
$498$	−4.67525	−	27.2494i	−0.209503	−	1.22107i
$499$			0.442369i			0.0198031i	0.999951	+	0.00990157i	$0.00315182\pi$
$499$			0.442369i			0.0198031i	−0.999951	+	0.00990157i	$0.996848\pi$
$500$	−7.07950	−	8.65336i	−0.316605	−	0.386990i
$501$	1.77423	+	1.25457i	0.0792666	+	0.0560500i
$502$	−19.6685	−	19.6685i	−0.877848	−	0.877848i
$503$	−0.431356	−	0.431356i	−0.0192332	−	0.0192332i	0.697425	−	0.716658i	$-0.254329\pi$
$503$	−0.431356	−	0.431356i	−0.0192332	−	0.0192332i	−0.716658	+	0.697425i	$0.754329\pi$
$504$	−1.89492	−	5.35965i	−0.0844065	−	0.238738i
$505$	21.9853	−	20.5704i	0.978332	−	0.915372i
$506$			8.80177i			0.391286i
$507$	−11.7803	+	2.02118i	−0.523182	+	0.0897639i
$508$	−2.40811	+	2.40811i	−0.106843	+	0.106843i
$509$	−11.4584			−0.507882			−0.253941	−	0.967220i	$-0.581727\pi$
$509$	−11.4584			−0.507882			−0.253941	+	0.967220i	$0.581727\pi$
$510$	23.4142	+	17.7521i	1.03680	+	0.786078i
$511$	5.01193			0.221715
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	19.7192	−	11.0238i	0.870625	−	0.486712i
$514$			6.52182i			0.287665i
$515$	32.8796	+	1.09315i	1.44885	+	0.0481700i
$516$	4.95037	−	7.00089i	0.217928	−	0.308197i
$517$	−4.80177	−	4.80177i	−0.211182	−	0.211182i
$518$	3.78984	+	3.78984i	0.166516	+	0.166516i
$519$	−23.8566	+	33.7383i	−1.04719	+	1.48095i
$520$	−3.77297	−	4.03248i	−0.165456	−	0.176836i
$521$			28.0633i			1.22948i	0.788731	+	0.614738i	$0.210738\pi$
$521$			28.0633i			1.22948i	−0.788731	+	0.614738i	$0.789262\pi$
$522$	7.12158	−	14.9114i	0.311703	−	0.652655i
$523$	17.9033	−	17.9033i	0.782858	−	0.782858i	−0.197454	−	0.980312i	$-0.563267\pi$
$523$	17.9033	−	17.9033i	0.782858	−	0.782858i	0.980312	+	0.197454i	$0.0632672\pi$
$524$	8.82321			0.385444
$525$	12.7402	+	10.3437i	0.556029	+	0.451435i
$526$	1.67372			0.0729778
$527$	−5.36459	+	5.36459i	−0.233685	+	0.233685i
$528$	2.23483	−	0.383437i	0.0972586	−	0.0166869i
$529$			22.2034i			0.965366i
$530$	13.9372	+	14.8958i	0.605393	+	0.647033i
$531$	32.1776	−	11.3765i	1.39639	−	0.493699i
$532$	−5.82556	−	5.82556i	−0.252570	−	0.252570i
$533$	4.91206	+	4.91206i	0.212765	+	0.212765i
$534$	−10.1265	−	7.16053i	−0.438217	−	0.309866i
$535$	25.6594	+	0.853103i	1.10935	+	0.0368829i
$536$		−	7.81370i		−	0.337500i
$537$	3.62080	+	21.1036i	0.156249	+	0.910685i
$538$	1.30331	−	1.30331i	0.0561896	−	0.0561896i
$539$	4.46320			0.192244
$540$	11.0691	+	3.53204i	0.476338	+	0.151995i
$541$	−15.0757			−0.648156			−0.324078	−	0.946030i	$-0.605054\pi$
$541$	−15.0757			−0.648156			−0.324078	+	0.946030i	$0.605054\pi$
$542$	−11.2311	+	11.2311i	−0.482419	+	0.482419i
$543$	0.00170666	+	0.00994714i	7.32397e−5	+	0.000426873i
$544$		−	7.58667i		−	0.325276i
$545$	0.498736	−	0.466640i	0.0213635	−	0.0199887i
$546$	6.61827	+	4.67982i	0.283236	+	0.200278i
$547$	11.0600	+	11.0600i	0.472893	+	0.472893i	0.902849	−	0.429957i	$-0.141471\pi$
$547$	11.0600	+	11.0600i	0.472893	+	0.472893i	−0.429957	+	0.902849i	$0.641471\pi$
$548$	12.2546	+	12.2546i	0.523489	+	0.523489i
$549$	−35.4914	+	12.5481i	−1.51473	+	0.535539i
$550$	−4.92570	+	4.31084i	−0.210032	+	0.183815i
$551$		−	23.9483i		−	1.02023i
$552$	11.4775	−	1.96922i	0.488514	−	0.0838157i
$553$	−6.22379	+	6.22379i	−0.264663	+	0.264663i
$554$	−1.65344			−0.0702480
$555$	−10.8523	+	1.49264i	−0.460654	+	0.0633589i
$556$	−10.0563			−0.426484
$557$	9.15272	−	9.15272i	0.387813	−	0.387813i	−0.486093	−	0.873907i	$-0.661579\pi$
$557$	9.15272	−	9.15272i	0.387813	−	0.387813i	0.873907	+	0.486093i	$0.161579\pi$
$558$	−1.29289	+	2.70711i	−0.0547325	+	0.114601i
$559$			12.2258i			0.517095i
$560$	0.140796	−	4.23483i	0.00594972	−	0.178954i
$561$	9.93198	−	14.0459i	0.419328	−	0.593020i
$562$	−4.02386	−	4.02386i	−0.169736	−	0.169736i
$563$	−23.0321	−	23.0321i	−0.970688	−	0.970688i	0.0288945	−	0.999582i	$-0.490801\pi$
$563$	−23.0321	−	23.0321i	−0.970688	−	0.970688i	−0.999582	+	0.0288945i	$0.990801\pi$
$564$	−5.18719	+	7.33579i	−0.218420	+	0.308893i
$565$	0.158825	−	4.77709i	0.00668181	−	0.200974i
$566$			0.834895i			0.0350933i
$567$	−16.9591	−	1.79970i	−0.712214	−	0.0755802i
$568$	−7.31694	+	7.31694i	−0.307012	+	0.307012i
$569$	−19.7684			−0.828733			−0.414367	−	0.910110i	$-0.635997\pi$
$569$	−19.7684			−0.828733			−0.414367	+	0.910110i	$0.635997\pi$
$570$	16.6816	−	2.29441i	0.698715	−	0.0961021i
$571$	28.0308			1.17305			0.586527	−	0.809930i	$-0.300495\pi$
$571$	28.0308			1.17305			0.586527	+	0.809930i	$0.300495\pi$
$572$	−2.28617	+	2.28617i	−0.0955894	+	0.0955894i
$573$	−7.82629	+	1.34278i	−0.326948	+	0.0560954i
$574$			5.33006i			0.222472i
$575$	−25.2970	+	22.1393i	−1.05496	+	0.923271i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−28.9740	−	28.9740i	−1.20620	−	1.20620i	−0.972248	−	0.233954i	$-0.924834\pi$
$577$	−28.9740	−	28.9740i	−1.20620	−	1.20620i	−0.233954	−	0.972248i	$-0.575166\pi$
$578$	−28.6786	−	28.6786i	−1.19287	−	1.19287i
$579$	−33.9025	−	23.9727i	−1.40894	−	0.996272i
$580$	8.99390	−	8.41510i	0.373451	−	0.349418i
$581$			30.2473i			1.25487i
$582$	−0.619797	−	3.61244i	−0.0256914	−	0.149741i
$583$	8.44499	−	8.44499i	0.349756	−	0.349756i
$584$	2.64493			0.109448
$585$	−15.7944	+	5.00027i	−0.653019	+	0.206736i
$586$	−7.21446			−0.298026
$587$	−15.8009	+	15.8009i	−0.652172	+	0.652172i	−0.953516	−	0.301343i	$-0.902565\pi$
$587$	−15.8009	+	15.8009i	−0.652172	+	0.652172i	0.301343	+	0.953516i	$0.402565\pi$
$588$	−0.998553	−	5.81999i	−0.0411796	−	0.240012i
$589$			4.34772i			0.179145i
$590$	25.4246	+	0.845296i	1.04671	+	0.0348003i
$591$	21.2193	+	15.0043i	0.872845	+	0.617194i
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$	14.7665	+	14.7665i	0.606387	+	0.606387i	0.942000	−	0.335613i	$-0.108943\pi$
$593$	14.7665	+	14.7665i	0.606387	+	0.606387i	−0.335613	+	0.942000i	$0.608943\pi$
$594$	1.85140	−	6.54567i	0.0759637	−	0.268572i
$595$	−21.9628	−	23.4734i	−0.900388	−	0.962317i
$596$		−	18.7711i		−	0.768893i
$597$	7.98698	−	1.37035i	0.326885	−	0.0560846i
$598$	−11.7411	+	11.7411i	−0.480129	+	0.480129i
$599$	41.7822			1.70718			0.853588	−	0.520949i	$-0.174422\pi$
$599$	41.7822			1.70718			0.853588	+	0.520949i	$0.174422\pi$
$600$	6.72335	+	5.45862i	0.274480	+	0.222847i
$601$	−6.41153			−0.261532			−0.130766	−	0.991413i	$-0.541744\pi$
$601$	−6.41153			−0.261532			−0.130766	+	0.991413i	$0.541744\pi$
$602$	−6.63306	+	6.63306i	−0.270344	+	0.270344i
$603$	−21.1525	−	10.1023i	−0.861397	−	0.411397i
$604$		−	4.51902i		−	0.183876i
$605$	−14.1867	−	15.1625i	−0.576772	−	0.616443i
$606$	−13.4647	+	19.0420i	−0.546967	+	0.773528i
$607$	−22.7744	−	22.7744i	−0.924385	−	0.924385i	0.0729509	−	0.997336i	$-0.476758\pi$
$607$	−22.7744	−	22.7744i	−0.924385	−	0.924385i	−0.997336	+	0.0729509i	$0.976758\pi$
$608$	−3.07430	−	3.07430i	−0.124679	−	0.124679i
$609$	−10.4377	+	14.7611i	−0.422957	+	0.598152i
$610$	−28.0429	−	0.932346i	−1.13542	−	0.0377496i
$611$		−	12.8106i		−	0.518262i
$612$	−20.5379	−	9.80876i	−0.830197	−	0.396496i
$613$	31.6523	−	31.6523i	1.27842	−	1.27842i	0.336872	−	0.941550i	$-0.390631\pi$
$613$	31.6523	−	31.6523i	1.27842	−	1.27842i	0.941550	−	0.336872i	$-0.109369\pi$
$614$	9.38350			0.378687
$615$	−8.68098	−	6.58173i	−0.350051	−	0.265401i
$616$	−2.48071			−0.0999506
$617$	25.0215	−	25.0215i	1.00733	−	1.00733i	0.00735502	−	0.999973i	$-0.497659\pi$
$617$	25.0215	−	25.0215i	1.00733	−	1.00733i	0.999973	−	0.00735502i	$-0.00234120\pi$
$618$	−25.1155	+	4.30913i	−1.01029	+	0.173339i
$619$		−	13.5269i		−	0.543692i	−0.962341	−	0.271846i	$-0.912366\pi$
$619$		−	13.5269i		−	0.543692i	0.962341	−	0.271846i	$-0.0876341\pi$
$620$	−1.63280	+	1.52773i	−0.0655750	+	0.0613550i
$621$	9.50825	−	33.6167i	0.381553	−	1.34899i
$622$	16.5719	+	16.5719i	0.664474	+	0.664474i
$623$	9.59448	+	9.59448i	0.384395	+	0.384395i
$624$	3.49264	+	2.46967i	0.139817	+	0.0988658i
$625$	−24.7794	−	3.31371i	−0.991177	−	0.132548i
$626$			9.10838i			0.364044i
$627$	−1.66708	−	9.71643i	−0.0665766	−	0.388037i
$628$	11.5063	−	11.5063i	0.459150	−	0.459150i
$629$	21.4584			0.855600
$630$	−11.2821	−	5.85634i	−0.449490	−	0.233322i
$631$	−7.61854			−0.303289			−0.151645	−	0.988435i	$-0.548457\pi$
$631$	−7.61854			−0.303289			−0.151645	+	0.988435i	$0.548457\pi$
$632$	−3.28446	+	3.28446i	−0.130649	+	0.130649i
$633$	−3.32582	−	19.3843i	−0.132190	−	0.770458i
$634$			26.8679i			1.06706i
$635$	−0.253041	+	7.61092i	−0.0100416	+	0.302030i
$636$	−12.9016	−	9.12283i	−0.511583	−	0.361744i
$637$	5.95367	+	5.95367i	0.235893	+	0.235893i
$638$	−5.09898	−	5.09898i	−0.201870	−	0.201870i
$639$	10.3477	+	29.2678i	0.409349	+	1.15782i
$640$	0.0743018	−	2.23483i	0.00293704	−	0.0883395i
$641$			27.0147i			1.06702i	0.845795	+	0.533509i	$0.179127\pi$
$641$			27.0147i			1.06702i	−0.845795	+	0.533509i	$0.820873\pi$
$642$	−19.6003	+	3.36288i	−0.773562	+	0.132722i
$643$	−22.7661	+	22.7661i	−0.897805	+	0.897805i	−0.995242	−	0.0974363i	$-0.968936\pi$
$643$	−22.7661	+	22.7661i	−0.897805	+	0.897805i	0.0974363	+	0.995242i	$0.468936\pi$
$644$	−12.7402			−0.502035
$645$	−2.61244	−	18.9939i	−0.102865	−	0.747884i
$646$	−32.9847			−1.29777
$647$	1.65399	−	1.65399i	0.0650250	−	0.0650250i	−0.673846	−	0.738871i	$-0.735359\pi$
$647$	1.65399	−	1.65399i	0.0650250	−	0.0650250i	0.738871	+	0.673846i	$0.235359\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$		−	14.8934i		−	0.584617i
$650$	−12.3211	−	0.820187i	−0.483272	−	0.0321704i
$651$	1.89492	−	2.67982i	0.0742678	−	0.105031i
$652$	0.105079	+	0.105079i	0.00411520	+	0.00411520i
$653$	−21.6841	−	21.6841i	−0.848565	−	0.848565i	0.141389	−	0.989954i	$-0.454843\pi$
$653$	−21.6841	−	21.6841i	−0.848565	−	0.848565i	−0.989954	+	0.141389i	$0.954843\pi$
$654$	−0.305448	+	0.431968i	−0.0119439	+	0.0168913i
$655$	14.4066	−	13.4795i	0.562912	−	0.526686i
$656$			2.81281i			0.109822i
$657$	3.41961	−	7.16010i	0.133412	−	0.279342i
$658$	6.95037	−	6.95037i	0.270954	−	0.270954i
$659$	−16.5520			−0.644776			−0.322388	−	0.946608i	$-0.604486\pi$
$659$	−16.5520			−0.644776			−0.322388	+	0.946608i	$0.604486\pi$
$660$	3.06326	−	4.04029i	0.119237	−	0.157268i
$661$	−37.1356			−1.44441			−0.722205	−	0.691679i	$-0.756871\pi$
$661$	−37.1356			−1.44441			−0.722205	+	0.691679i	$0.756871\pi$
$662$	2.86244	−	2.86244i	0.111252	−	0.111252i
$663$	31.9853	−	5.48781i	1.24221	−	0.213129i
$664$			15.9623i			0.619457i
$665$	−18.4119	−	0.612142i	−0.713982	−	0.0237378i
$666$	8.00000	−	2.82843i	0.309994	−	0.109599i
$667$	−26.1869	−	26.1869i	−1.01396	−	1.01396i
$668$	−0.887114	−	0.887114i	−0.0343235	−	0.0343235i
$669$	22.1226	+	15.6430i	0.855308	+	0.604794i
$670$	−11.9372	−	12.7582i	−0.461174	−	0.492894i
$671$			16.4271i			0.634163i
$672$	0.555010	+	3.23483i	0.0214100	+	0.124786i
$673$	−18.2328	+	18.2328i	−0.702821	+	0.702821i	−0.965015	−	0.262194i	$-0.915554\pi$
$673$	−18.2328	+	18.2328i	−0.702821	+	0.702821i	0.262194	+	0.965015i	$0.415554\pi$
$674$	8.58453			0.330664
$675$	23.4697	−	11.1434i	0.903347	−	0.428910i
$676$	6.90075			0.265413
$677$	−25.1358	+	25.1358i	−0.966048	+	0.966048i	−0.999442	−	0.0333940i	$-0.989368\pi$
$677$	−25.1358	+	25.1358i	−0.966048	+	0.966048i	0.0333940	+	0.999442i	$0.489368\pi$
$678$	0.626077	+	3.64905i	0.0240444	+	0.140141i
$679$			4.00988i			0.153885i
$680$	−11.5904	−	12.3876i	−0.444470	−	0.475041i
$681$	−20.3293	−	14.3750i	−0.779021	−	0.550851i
$682$	0.925698	+	0.925698i	0.0354468	+	0.0354468i
$683$	−13.0152	−	13.0152i	−0.498011	−	0.498011i	0.412807	−	0.910818i	$-0.364548\pi$
$683$	−13.0152	−	13.0152i	−0.498011	−	0.498011i	−0.910818	+	0.412807i	$0.864548\pi$
$684$	−12.2972	+	4.34772i	−0.470195	+	0.166239i
$685$	38.7309	+	1.28769i	1.47983	+	0.0492002i
$686$			19.7248i			0.753095i
$687$	22.9073	−	3.93027i	0.873968	−	0.149949i
$688$	−3.50044	+	3.50044i	−0.133453	+	0.133453i
$689$	22.5304			0.858338
$690$	15.7320	−	20.7498i	0.598909	−	0.789931i
$691$	−43.9053			−1.67024			−0.835119	−	0.550070i	$-0.814601\pi$
$691$	−43.9053			−1.67024			−0.835119	+	0.550070i	$0.814601\pi$
$692$	16.8692	−	16.8692i	0.641269	−	0.641269i
$693$	−3.20729	+	6.71554i	−0.121835	+	0.255102i
$694$		−	25.1118i		−	0.953231i
$695$	−16.4200	+	15.3633i	−0.622848	+	0.582764i
$696$	−5.50825	+	7.78984i	−0.208790	+	0.295273i
$697$	15.0896	+	15.0896i	0.571558	+	0.571558i
$698$	−8.81980	−	8.81980i	−0.333834	−	0.333834i
$699$	−13.5071	+	19.1019i	−0.510885	+	0.722501i
$700$	−6.23977	−	7.12975i	−0.235841	−	0.269479i
$701$			4.67181i			0.176452i	0.996100	+	0.0882259i	$0.0281197\pi$
$701$			4.67181i			0.176452i	−0.996100	+	0.0882259i	$0.971880\pi$
$702$	11.2013	−	6.26192i	0.422764	−	0.236341i
$703$	8.69544	−	8.69544i	0.327955	−	0.327955i
$704$	−1.30913			−0.0493399
$705$	2.73742	+	19.9025i	0.103097	+	0.749572i
$706$	3.62437			0.136405
$707$	18.0415	−	18.0415i	0.678522	−	0.678522i
$708$	−19.4209	+	3.33210i	−0.729883	+	0.125228i
$709$		−	34.5708i		−	1.29833i	−0.760646	−	0.649167i	$-0.775118\pi$
$709$		−	34.5708i		−	1.29833i	0.760646	−	0.649167i	$-0.224882\pi$
$710$	−0.768854	+	23.1254i	−0.0288546	+	0.867882i
$711$	4.64493	+	13.1378i	0.174198	+	0.492707i
$712$	5.06326	+	5.06326i	0.189754	+	0.189754i
$713$	4.75413	+	4.75413i	0.178043	+	0.178043i
$714$	20.3309	+	14.3761i	0.760866	+	0.538014i
$715$	−0.240227	+	7.22550i	−0.00898398	+	0.270218i
$716$		−	12.3622i		−	0.461996i
$717$	−8.34556	−	48.6415i	−0.311671	−	1.81655i
$718$	−2.80958	+	2.80958i	−0.104853	+	0.104853i
$719$	35.9553			1.34091			0.670453	−	0.741952i	$-0.266100\pi$
$719$	35.9553			1.34091			0.670453	+	0.741952i	$0.266100\pi$
$720$	−5.95387	−	3.09054i	−0.221888	−	0.115178i
$721$	27.8787			1.03826
$722$	0.0688276	−	0.0688276i	0.00256150	−	0.00256150i
$723$	−3.06649	−	17.8728i	−0.114044	−	0.664698i
$724$		−	0.00582690i		−	0.000216555i
$725$	1.82931	−	27.4804i	0.0679390	−	1.02060i
$726$	13.1326	+	9.28617i	0.487397	+	0.344642i
$727$	9.01238	+	9.01238i	0.334251	+	0.334251i	0.854198	−	0.519948i	$-0.174049\pi$
$727$	9.01238	+	9.01238i	0.334251	+	0.334251i	−0.519948	+	0.854198i	$0.674049\pi$
$728$	−3.30913	−	3.30913i	−0.122645	−	0.122645i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	4.31865	−	4.04072i	0.159840	−	0.149554i
$731$			37.5569i			1.38909i
$732$	21.4209	−	3.67525i	0.791740	−	0.135841i
$733$	−13.6035	+	13.6035i	−0.502458	+	0.502458i	−0.912201	−	0.409743i	$-0.865618\pi$
$733$	−13.6035	+	13.6035i	−0.502458	+	0.502458i	0.409743	+	0.912201i	$0.365618\pi$
$734$	25.4246			0.938440
$735$	−10.5218	−	7.97740i	−0.388102	−	0.294251i
$736$	−6.72335			−0.247826
$737$	−7.23313	+	7.23313i	−0.266436	+	0.266436i
$738$	7.61458	+	3.63667i	0.280297	+	0.133868i
$739$		−	7.56118i		−	0.278142i	−0.990282	−	0.139071i	$-0.955588\pi$
$739$		−	7.56118i		−	0.278142i	0.990282	−	0.139071i	$-0.0444117\pi$
$740$	6.32106	+	0.210157i	0.232367	+	0.00772553i
$741$	10.7374	−	15.1850i	0.394449	−	0.557835i
$742$	12.2238	+	12.2238i	0.448750	+	0.448750i
$743$	5.94778	+	5.94778i	0.218203	+	0.218203i	0.807741	−	0.589538i	$-0.200690\pi$
$743$	5.94778	+	5.94778i	0.218203	+	0.218203i	−0.589538	+	0.807741i	$0.700690\pi$
$744$	1.00000	−	1.41421i	0.0366618	−	0.0518476i
$745$	−28.6770	−	30.6495i	−1.05065	−	1.12291i
$746$			24.3256i			0.890625i
$747$	43.2117	+	20.6376i	1.58103	+	0.755089i
$748$	−7.02297	+	7.02297i	−0.256785	+	0.256785i
$749$	21.7567			0.794973
$750$	19.3172	−	1.35857i	0.705364	−	0.0496079i
$751$	−16.5568			−0.604168			−0.302084	−	0.953281i	$-0.597682\pi$
$751$	−16.5568			−0.604168			−0.302084	+	0.953281i	$0.597682\pi$
$752$	3.66790	−	3.66790i	0.133754	−	0.133754i
$753$	47.4840	−	8.14696i	1.73041	−	0.296892i
$754$		−	13.6035i		−	0.495412i
$755$	−6.90382	−	7.37868i	−0.251256	−	0.268537i
$756$	9.47461	+	2.67982i	0.344588	+	0.0974642i
$757$	−34.3170	−	34.3170i	−1.24727	−	1.24727i	−0.956919	−	0.290353i	$-0.906227\pi$
$757$	−34.3170	−	34.3170i	−1.24727	−	1.24727i	−0.290353	−	0.956919i	$-0.593773\pi$
$758$	−10.2459	−	10.2459i	−0.372147	−	0.372147i
$759$	−12.4476	−	8.80177i	−0.451819	−	0.319484i
$760$	−9.71643	−	0.323043i	−0.352452	−	0.0117180i
$761$			3.62624i			0.131451i	0.997838	+	0.0657255i	$0.0209362\pi$
$761$			3.62624i			0.131451i	−0.997838	+	0.0657255i	$0.979064\pi$
$762$	−0.997473	−	5.81370i	−0.0361346	−	0.210608i
$763$	0.409273	−	0.409273i	0.0148167	−	0.0148167i
$764$	4.58453			0.165863
$765$	−48.5195	+	15.3606i	−1.75423	+	0.555362i
$766$	35.0113			1.26501
$767$	19.8670	−	19.8670i	0.717356	−	0.717356i
$768$	0.292893	+	1.70711i	0.0105689	+	0.0615999i
$769$			1.52093i			0.0548462i	0.999624	+	0.0274231i	$0.00873015\pi$
$769$			1.52093i			0.0548462i	−0.999624	+	0.0274231i	$0.991270\pi$
$770$	−4.05051	+	3.78984i	−0.145970	+	0.136576i
$771$	−9.22325	−	6.52182i	−0.332167	−	0.234878i
$772$	16.9513	+	16.9513i	0.610089	+	0.610089i
$773$	−8.91707	−	8.91707i	−0.320725	−	0.320725i	0.528320	−	0.849045i	$-0.322822\pi$
$773$	−8.91707	−	8.91707i	−0.320725	−	0.320725i	−0.849045	+	0.528320i	$0.822822\pi$
$774$	4.95037	+	14.0018i	0.177938	+	0.503283i
$775$	−0.332104	+	4.98896i	−0.0119295	+	0.179209i
$776$			2.11612i			0.0759643i
$777$	−9.14949	+	1.56980i	−0.328236	+	0.0563164i
$778$	23.3655	−	23.3655i	0.837693	−	0.837693i
$779$	12.2293			0.438161
$780$	9.47577	−	1.30331i	0.339287	−	0.0466659i
$781$	13.5466			0.484734
$782$	−36.0680	+	36.0680i	−1.28979	+	1.28979i
$783$	13.9664	+	24.9829i	0.499117	+	0.892814i
$784$			3.40927i			0.121760i
$785$	1.20906	−	36.3659i	0.0431533	−	1.29796i
$786$	−8.82321	+	12.4779i	−0.314714	+	0.445072i
$787$	27.2682	+	27.2682i	0.972006	+	0.972006i	0.999619	−	0.0276123i	$-0.00879037\pi$
$787$	27.2682	+	27.2682i	0.972006	+	0.972006i	−0.0276123	+	0.999619i	$0.508790\pi$
$788$	−10.6096	−	10.6096i	−0.377953	−	0.377953i
$789$	−1.67372	+	2.36700i	−0.0595861	+	0.0842675i
$790$	−0.345126	+	10.3806i	−0.0122790	+	0.369326i
$791$		−	4.05051i		−	0.144020i
$792$	−1.69257	+	3.54397i	−0.0601429	+	0.125929i
$793$	−21.9130	+	21.9130i	−0.778152	+	0.778152i
$794$	8.55788			0.303708
$795$	−35.0030	+	4.81436i	−1.24143	+	0.170748i
$796$	−4.67866			−0.165831
$797$	−23.5030	+	23.5030i	−0.832520	+	0.832520i	−0.987861	−	0.155341i	$-0.950352\pi$
$797$	−23.5030	+	23.5030i	−0.832520	+	0.832520i	0.155341	+	0.987861i	$0.450352\pi$
$798$	14.0641	−	2.41303i	0.497865	−	0.0854202i
$799$		−	39.3535i		−	1.39223i
$800$	−3.29289	−	3.76256i	−0.116421	−	0.133027i
$801$	20.2530	−	7.16053i	0.715606	−	0.253005i
$802$	−17.9312	−	17.9312i	−0.633171	−	0.633171i
$803$	−2.44840	−	2.44840i	−0.0864023	−	0.0864023i
$804$	11.0502	+	7.81370i	0.389712	+	0.275568i
$805$	−20.8023	+	19.4636i	−0.733184	+	0.686001i
$806$			2.46967i			0.0869903i
$807$	0.539848	+	3.14646i	0.0190035	+	0.110761i
$808$	9.52100	−	9.52100i	0.334948	−	0.334948i
$809$	−29.9087			−1.05154			−0.525768	−	0.850628i	$-0.676222\pi$
$809$	−29.9087			−1.05154			−0.525768	+	0.850628i	$0.676222\pi$
$810$	−16.0641	+	12.1220i	−0.564437	+	0.425924i
$811$	−1.40533			−0.0493479			−0.0246739	−	0.999696i	$-0.507855\pi$
$811$	−1.40533			−0.0493479			−0.0246739	+	0.999696i	$0.507855\pi$
$812$	7.38057	−	7.38057i	0.259007	−	0.259007i
$813$	−4.65209	−	27.1144i	−0.163156	−	0.950943i
$814$		−	3.70279i		−	0.129783i
$815$	0.332104	+	0.0110415i	0.0116331	+	0.000386767i
$816$	10.7292	+	7.58667i	0.375596	+	0.265587i
$817$	15.2189	+	15.2189i	0.532443	+	0.532443i
$818$	7.09492	+	7.09492i	0.248068	+	0.248068i
$819$	−13.2365	+	4.67982i	−0.462522	+	0.163526i
$820$	4.29721	+	4.59277i	0.150065	+	0.160387i
$821$		−	16.9090i		−	0.590128i	−0.955477	−	0.295064i	$-0.904659\pi$
$821$		−	16.9090i		−	0.590128i	0.955477	−	0.295064i	$-0.0953411\pi$
$822$	−29.5851	+	5.07601i	−1.03190	+	0.177046i
$823$	−19.2227	+	19.2227i	−0.670061	+	0.670061i	−0.957730	−	0.287669i	$-0.907120\pi$
$823$	−19.2227	+	19.2227i	−0.670061	+	0.670061i	0.287669	+	0.957730i	$0.407120\pi$
$824$	14.7123			0.512528
$825$	−1.17075	−	11.2768i	−0.0407604	−	0.392609i
$826$	21.5576			0.750085
$827$	22.7919	−	22.7919i	0.792552	−	0.792552i	−0.189357	−	0.981908i	$-0.560640\pi$
$827$	22.7919	−	22.7919i	0.792552	−	0.792552i	0.981908	+	0.189357i	$0.0606403\pi$
$828$	−8.69257	+	18.2008i	−0.302088	+	0.632522i
$829$		−	35.3312i		−	1.22710i	−0.789655	−	0.613551i	$-0.789740\pi$
$829$		−	35.3312i		−	1.22710i	0.789655	−	0.613551i	$-0.210260\pi$
$830$	24.3860	+	26.0633i	0.846451	+	0.904671i
$831$	1.65344	−	2.33832i	0.0573572	−	0.0811154i
$832$	−1.74632	−	1.74632i	−0.0605427	−	0.0605427i
$833$	18.2893	+	18.2893i	0.633688	+	0.633688i
$834$	10.0563	−	14.2218i	0.348223	−	0.492461i
$835$	−2.80375	−	0.0932167i	−0.0970278	−	0.00322590i
$836$			5.69175i			0.196853i
$837$	−2.53553	−	4.53553i	−0.0876409	−	0.156771i
$838$	18.9645	−	18.9645i	0.655116	−	0.655116i
$839$	9.14241			0.315631			0.157816	−	0.987469i	$-0.449555\pi$
$839$	9.14241			0.315631			0.157816	+	0.987469i	$0.449555\pi$
$840$	5.84816	+	4.43395i	0.201781	+	0.152986i
$841$	1.34083			0.0462354
$842$	13.2197	−	13.2197i	0.455580	−	0.455580i
$843$	9.71445	−	1.66674i	0.334583	−	0.0574054i
$844$			11.3551i			0.390858i
$845$	11.2676	−	10.5425i	0.387616	−	0.362671i
$846$	−5.18719	−	14.6716i	−0.178339	−	0.504419i
$847$	−12.4426	−	12.4426i	−0.427534	−	0.427534i
$848$	6.45082	+	6.45082i	0.221522	+	0.221522i
$849$	−1.18072	−	0.834895i	−0.0405222	−	0.0286535i
$850$	−37.8496	−	2.51957i	−1.29823	−	0.0864204i
$851$		−	19.0165i		−	0.651877i
$852$	−3.03078	−	17.6647i	−0.103833	−	0.605181i
$853$	0.613783	−	0.613783i	0.0210155	−	0.0210155i	−0.696521	−	0.717536i	$-0.745270\pi$
$853$	0.613783	−	0.613783i	0.0210155	−	0.0210155i	0.717536	+	0.696521i	$0.245270\pi$
$854$	−23.7776			−0.813654
$855$	−13.4368	+	25.8857i	−0.459529	+	0.885274i
$856$	11.4816			0.392433
$857$	−12.3462	+	12.3462i	−0.421737	+	0.421737i	−0.885802	−	0.464064i	$-0.846391\pi$
$857$	−12.3462	+	12.3462i	−0.421737	+	0.421737i	0.464064	+	0.885802i	$0.346391\pi$
$858$	−0.946961	−	5.51929i	−0.0323287	−	0.188426i
$859$			31.5163i			1.07532i	0.843161	+	0.537662i	$0.180692\pi$
$859$			31.5163i			1.07532i	−0.843161	+	0.537662i	$0.819308\pi$
$860$	−0.367822	+	11.0633i	−0.0125426	+	0.377254i
$861$	−7.53784	−	5.33006i	−0.256889	−	0.181648i
$862$	−12.1811	−	12.1811i	−0.414889	−	0.414889i
$863$	−8.10553	−	8.10553i	−0.275916	−	0.275916i	0.555561	−	0.831476i	$-0.312504\pi$
$863$	−8.10553	−	8.10553i	−0.275916	−	0.275916i	−0.831476	+	0.555561i	$0.812504\pi$
$864$	5.00000	+	1.41421i	0.170103	+	0.0481125i
$865$	1.77259	−	53.3155i	0.0602698	−	1.81278i
$866$			13.7312i			0.466606i
$867$	69.2362	−	11.8790i	2.35138	−	0.403434i
$868$	−1.33991	+	1.33991i	−0.0454796	+	0.0454796i
$869$	6.08084			0.206278
$870$	2.90685	+	21.1344i	0.0985514	+	0.716523i
$871$	−19.2972			−0.653862
$872$	0.215984	−	0.215984i	0.00731415	−	0.00731415i
$873$	5.72856	+	2.73592i	0.193882	+	0.0925968i
$874$			29.2312i			0.988761i
$875$	−21.0806	−	2.10883i	−0.712656	−	0.0712915i
$876$	−2.64493	+	3.74049i	−0.0893638	+	0.126379i
$877$	32.5143	+	32.5143i	1.09793	+	1.09793i	0.994653	+	0.103278i	$0.0329332\pi$
$877$	32.5143	+	32.5143i	1.09793	+	1.09793i	0.103278	+	0.994653i	$0.467067\pi$
$878$	19.0444	+	19.0444i	0.642718	+	0.642718i
$879$	7.21446	−	10.2028i	0.243338	−	0.344131i
$880$	−2.13756	+	2.00000i	−0.0720572	+	0.0674200i
$881$			45.3738i			1.52868i	0.644811	+	0.764342i	$0.276936\pi$
$881$			45.3738i			1.52868i	−0.644811	+	0.764342i	$0.723064\pi$
$882$	9.22927	+	4.40783i	0.310766	+	0.148419i
$883$	12.5798	−	12.5798i	0.423342	−	0.423342i	−0.463010	−	0.886353i	$-0.653231\pi$
$883$	12.5798	−	12.5798i	0.423342	−	0.423342i	0.886353	+	0.463010i	$0.153231\pi$
$884$	−18.7365			−0.630178
$885$	−26.6200	+	35.1105i	−0.894823	+	1.18023i
$886$	−33.0410			−1.11003
$887$	17.1081	−	17.1081i	0.574435	−	0.574435i	−0.358930	−	0.933365i	$-0.616858\pi$
$887$	17.1081	−	17.1081i	0.574435	−	0.574435i	0.933365	+	0.358930i	$0.116858\pi$
$888$	−4.82843	+	0.828427i	−0.162031	+	0.0278002i
$889$			6.45332i			0.216437i
$890$	16.0026	+	0.532040i	0.536408	+	0.0178340i
$891$	7.40559	+	9.16394i	0.248096	+	0.307004i
$892$	−11.0613	−	11.0613i	−0.370359	−	0.370359i
$893$	−15.9470	−	15.9470i	−0.533645	−	0.533645i
$894$	26.5463	+	18.7711i	0.887841	+	0.627798i
$895$	−18.8860	−	20.1850i	−0.631290	−	0.674711i
$896$		−	1.89492i		−	0.0633049i
$897$	−4.86332	−	28.3455i	−0.162382	−	0.946430i
$898$	18.9172	−	18.9172i	0.631277	−	0.631277i
$899$	−5.50825			−0.183710
$900$	−14.4430	+	4.04963i	−0.481434	+	0.134988i
$901$	69.2120			2.30578
$902$	2.60382	−	2.60382i	0.0866976	−	0.0866976i
$903$	−2.74751	−	16.0136i	−0.0914313	−	0.532900i
$904$		−	2.13756i		−	0.0710943i
$905$	−0.00890191	−	0.00951419i	−0.000295909	−	0.000316262i
$906$	6.39086	+	4.51902i	0.212322	+	0.150134i
$907$	−24.5342	−	24.5342i	−0.814646	−	0.814646i	0.170680	−	0.985326i	$-0.445403\pi$
$907$	−24.5342	−	24.5342i	−0.814646	−	0.814646i	−0.985326	+	0.170680i	$0.945403\pi$
$908$	10.1647	+	10.1647i	0.337326	+	0.337326i
$909$	−13.4647	−	38.0840i	−0.446597	−	1.26317i
$910$	−10.4586	−	0.347719i	−0.346700	−	0.0115268i
$911$		−	17.4844i		−	0.579284i	−0.957135	−	0.289642i	$-0.906464\pi$
$911$		−	17.4844i		−	0.579284i	0.957135	−	0.289642i	$-0.0935362\pi$
$912$	7.42202	−	1.27342i	0.245768	−	0.0421671i
$913$	14.7763	−	14.7763i	0.489023	−	0.489023i
$914$	35.5233			1.17501
$915$	29.3614	−	38.7263i	0.970659	−	1.28025i
$916$	−13.4188			−0.443369
$917$	11.8223	−	11.8223i	0.390408	−	0.390408i
$918$	34.4096	−	19.2363i	1.13569	−	0.634891i
$919$			50.1999i			1.65594i	0.560772	+	0.827970i	$0.310504\pi$
$919$			50.1999i			1.65594i	−0.560772	+	0.827970i	$0.689496\pi$
$920$	−10.9779	+	10.2714i	−0.361931	+	0.338639i
$921$	−9.38350	+	13.2703i	−0.309197	+	0.437270i
$922$	3.79683	+	3.79683i	0.125042	+	0.125042i
$923$	18.0704	+	18.0704i	0.594795	+	0.594795i
$924$	2.48071	−	3.50825i	0.0816093	−	0.115413i
$925$	10.6421	−	9.31371i	0.349911	−	0.306233i
$926$			7.03462i			0.231172i
$927$	19.0214	−	39.8278i	0.624746	−	1.30812i
$928$	3.89492	−	3.89492i	0.127857	−	0.127857i
$929$	39.4235			1.29344			0.646721	−	0.762727i	$-0.276140\pi$
$929$	39.4235			1.29344			0.646721	+	0.762727i	$0.276140\pi$
$930$	−0.527726	−	3.83686i	−0.0173048	−	0.125816i
$931$	14.8226			0.485790
$932$	9.55096	−	9.55096i	0.312852	−	0.312852i
$933$	−40.0082	+	6.86432i	−1.30981	+	0.224728i
$934$			21.6447i			0.708235i
$935$	−0.737964	+	22.1963i	−0.0241340	+	0.725897i
$936$	−6.98527	+	2.46967i	−0.228321	+	0.0807236i
$937$	12.3259	+	12.3259i	0.402670	+	0.402670i	0.879173	−	0.476503i	$-0.158096\pi$
$937$	12.3259	+	12.3259i	0.402670	+	0.402670i	−0.476503	+	0.879173i	$0.658096\pi$
$938$	−10.4697	−	10.4697i	−0.341847	−	0.341847i
$939$	−12.8812	−	9.10838i	−0.420362	−	0.297241i
$940$	0.385417	−	11.5925i	0.0125709	−	0.378106i
$941$			27.9228i			0.910258i	0.890425	+	0.455129i	$0.150407\pi$
$941$			27.9228i			0.910258i	−0.890425	+	0.455129i	$0.849593\pi$
$942$	4.76605	+	27.7786i	0.155286	+	0.905075i
$943$	13.3725	−	13.3725i	0.435467	−	0.435467i
$944$	11.3765			0.370274
$945$	19.5642	−	10.0990i	0.636424	−	0.328520i
$946$	6.48071			0.210706
$947$	25.8753	−	25.8753i	0.840833	−	0.840833i	−0.148135	−	0.988967i	$-0.547327\pi$
$947$	25.8753	−	25.8753i	0.840833	−	0.840833i	0.988967	+	0.148135i	$0.0473269\pi$
$948$	−1.36047	−	7.92939i	−0.0441859	−	0.257534i
$949$		−	6.53209i		−	0.212040i
$950$	−16.3586	+	14.3166i	−0.530742	+	0.464491i
$951$	−37.9969	−	26.8679i	−1.23214	−	0.871251i
$952$	−10.1655	−	10.1655i	−0.329465	−	0.329465i
$953$	−3.42614	−	3.42614i	−0.110984	−	0.110984i	0.649434	−	0.760418i	$-0.275006\pi$
$953$	−3.42614	−	3.42614i	−0.110984	−	0.110984i	−0.760418	+	0.649434i	$0.775006\pi$
$954$	25.8033	−	9.12283i	0.835412	−	0.295363i
$955$	7.48565	−	7.00391i	0.242230	−	0.226641i
$956$			28.4935i			0.921546i
$957$	12.3100	−	2.11207i	0.397926	−	0.0682734i
$958$	−11.5847	+	11.5847i	−0.374284	+	0.374284i
$959$	32.8401			1.06046
$960$	3.08623	+	2.33991i	0.0996076	+	0.0755203i
$961$	1.00000			0.0322581
$962$	4.93933	−	4.93933i	0.159250	−	0.159250i
$963$	14.8445	−	31.0819i	0.478357	−	1.00160i
$964$			10.4697i			0.337205i
$965$	53.5750	+	1.78121i	1.72464	+	0.0573393i
$966$	12.7402	−	18.0174i	0.409910	−	0.579700i
$967$	−22.5928	−	22.5928i	−0.726535	−	0.726535i	0.243393	−	0.969928i	$-0.421739\pi$
$967$	−22.5928	−	22.5928i	−0.726535	−	0.726535i	−0.969928	+	0.243393i	$0.921739\pi$
$968$	−6.56631	−	6.56631i	−0.211049	−	0.211049i
$969$	32.9847	−	46.6474i	1.05962	−	1.49853i
$970$	3.23285	+	3.45521i	0.103801	+	0.110940i
$971$		−	34.1559i		−	1.09612i	−0.836440	−	0.548058i	$-0.815367\pi$
$971$		−	34.1559i		−	1.09612i	0.836440	−	0.548058i	$-0.184633\pi$
$972$	10.2929	−	11.7071i	0.330145	−	0.375506i
$973$	−13.4746	+	13.4746i	−0.431976	+	0.431976i
$974$	−11.1084			−0.355935
$975$	13.4810	−	16.6044i	0.431737	−	0.531767i
$976$	−12.5481			−0.401655
$977$	−15.3207	+	15.3207i	−0.490152	+	0.490152i	−0.908354	−	0.418202i	$-0.862661\pi$
$977$	−15.3207	+	15.3207i	−0.490152	+	0.490152i	0.418202	+	0.908354i	$0.362661\pi$
$978$	−0.253682	+	0.0435250i	−0.00811186	+	0.00139178i
$979$		−	9.37410i		−	0.299598i
$980$	5.20844	+	5.56668i	0.166377	+	0.177821i
$981$	−0.305448	−	0.863936i	−0.00975219	−	0.0275834i
$982$	24.0752	+	24.0752i	0.768270	+	0.768270i
$983$	−18.1926	−	18.1926i	−0.580255	−	0.580255i	0.354718	−	0.934973i	$-0.384577\pi$
$983$	−18.1926	−	18.1926i	−0.580255	−	0.580255i	−0.934973	+	0.354718i	$0.884577\pi$
$984$	−3.97792	−	2.81281i	−0.126811	−	0.0896692i
$985$	−33.5321	−	1.11485i	−1.06842	−	0.0355220i
$986$		−	41.7893i		−	1.33084i
$987$	2.87894	+	16.7797i	0.0916376	+	0.534103i
$988$	−7.59250	+	7.59250i	−0.241550	+	0.241550i
$989$	33.2831			1.05834
$990$	2.65057	+	8.37240i	0.0842408	+	0.266092i
$991$	−35.8784			−1.13972			−0.569858	−	0.821743i	$-0.693002\pi$
$991$	−35.8784			−1.13972			−0.569858	+	0.821743i	$0.693002\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	1.18566	+	6.91054i	0.0376258	+	0.219299i
$994$			19.6081i			0.621932i
$995$	−7.63934	+	7.14772i	−0.242184	+	0.226598i
$996$	−22.5741	−	15.9623i	−0.715288	−	0.505785i
$997$	−0.00824048	−	0.00824048i	−0.000260979	−	0.000260979i	0.706976	−	0.707237i	$-0.250059\pi$
$997$	−0.00824048	−	0.00824048i	−0.000260979	−	0.000260979i	−0.707237	+	0.706976i	$0.750059\pi$
$998$	0.312802	+	0.312802i	0.00990157	+	0.00990157i
$999$	−4.00000	+	14.1421i	−0.126554	+	0.447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.f.497.3	yes	8
3.2	odd	2		930.2.j.c.497.2	✓	8
5.3	odd	4		930.2.j.c.683.2	yes	8
15.8	even	4	inner	930.2.j.f.683.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.2	✓	8	3.2	odd	2
930.2.j.c.683.2	yes	8	5.3	odd	4
930.2.j.f.497.3	yes	8	1.1	even	1	trivial
930.2.j.f.683.3	yes	8	15.8	even	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 - 1.33991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 - 1.33991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-2.23483 - 0.0743018i) q^{10} +1.30913i q^{11} +(1.70711 - 0.292893i) q^{12} +(-1.74632 + 1.74632i) q^{13} -1.89492 q^{14} +(2.33991 - 3.08623i) q^{15} -1.00000 q^{16} +(-5.36459 + 5.36459i) q^{17} +(-1.29289 + 2.70711i) q^{18} +4.34772i q^{19} +(-1.63280 + 1.52773i) q^{20} +(1.89492 - 2.67982i) q^{21} +(0.925698 + 0.925698i) q^{22} +(4.75413 + 4.75413i) q^{23} +(1.00000 - 1.41421i) q^{24} +(-0.332104 + 4.98896i) q^{25} +2.46967i q^{26} +(-2.53553 - 4.53553i) q^{27} +(-1.33991 + 1.33991i) q^{28} -5.50825 q^{29} +(-0.527726 - 3.83686i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.23483 + 0.383437i) q^{33} +7.58667i q^{34} +(-0.140796 + 4.23483i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(3.07430 + 3.07430i) q^{38} +(-3.49264 - 2.46967i) q^{39} +(-0.0743018 + 2.23483i) q^{40} -2.81281i q^{41} +(-0.555010 - 3.23483i) q^{42} +(3.50044 - 3.50044i) q^{43} +1.30913 q^{44} +(5.95387 + 3.09054i) q^{45} +6.72335 q^{46} +(-3.66790 + 3.66790i) q^{47} +(-0.292893 - 1.70711i) q^{48} -3.40927i q^{49} +(3.29289 + 3.76256i) q^{50} +(-10.7292 - 7.58667i) q^{51} +(1.74632 + 1.74632i) q^{52} +(-6.45082 - 6.45082i) q^{53} +(-5.00000 - 1.41421i) q^{54} +(2.13756 - 2.00000i) q^{55} +1.89492i q^{56} +(-7.42202 + 1.27342i) q^{57} +(-3.89492 + 3.89492i) q^{58} -11.3765 q^{59} +(-3.08623 - 2.33991i) q^{60} +12.5481 q^{61} +(0.707107 - 0.707107i) q^{62} +(5.12975 + 2.44993i) q^{63} +1.00000i q^{64} +(5.51929 + 0.183501i) q^{65} +(-1.30913 + 1.85140i) q^{66} +(5.52512 + 5.52512i) q^{67} +(5.36459 + 5.36459i) q^{68} +(-6.72335 + 9.50825i) q^{69} +(2.89492 + 3.09404i) q^{70} -10.3477i q^{71} +(2.70711 + 1.29289i) q^{72} +(-1.87025 + 1.87025i) q^{73} -2.82843 q^{74} +(-8.61396 + 0.894295i) q^{75} +4.34772 q^{76} +(1.75413 - 1.75413i) q^{77} +(-4.21598 + 0.723349i) q^{78} -4.64493i q^{79} +(1.52773 + 1.63280i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-1.98896 - 1.98896i) q^{82} +(-11.2871 - 11.2871i) q^{83} +(-2.67982 - 1.89492i) q^{84} +(16.9549 + 0.563703i) q^{85} -4.95037i q^{86} +(-1.61333 - 9.40317i) q^{87} +(0.925698 - 0.925698i) q^{88} -7.16053 q^{89} +(6.39536 - 2.02468i) q^{90} +4.67982 q^{91} +(4.75413 - 4.75413i) q^{92} +(0.292893 + 1.70711i) q^{93} +5.18719i q^{94} +(7.09898 - 6.64213i) q^{95} +(-1.41421 - 1.00000i) q^{96} +(-1.49632 - 1.49632i) q^{97} +(-2.41072 - 2.41072i) q^{98} +(-1.30913 - 3.70279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q + 8 * q^3 + 4 * q^7	\( 8 q + 8 q^{3} + 4 q^{7} + 8 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} - 16 q^{18} - 4 q^{20} + 12 q^{21} + 4 q^{22} + 12 q^{23} + 8 q^{24} - 4 q^{25} + 8 q^{27} + 4 q^{28} + 8 q^{29} + 8 q^{30} + 8 q^{31} - 24 q^{35} + 8 q^{36} - 16 q^{37} + 28 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{42} - 8 q^{43} - 4 q^{44} - 4 q^{45} + 28 q^{46} - 28 q^{47} - 8 q^{48} + 32 q^{50} - 8 q^{51} + 4 q^{52} + 12 q^{53} - 40 q^{54} - 20 q^{55} - 32 q^{57} - 28 q^{58} - 24 q^{59} + 56 q^{61} + 20 q^{63} + 36 q^{65} + 4 q^{66} - 16 q^{67} + 4 q^{68} - 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} - 12 q^{77} + 12 q^{78} + 56 q^{81} + 28 q^{82} + 12 q^{83} + 8 q^{84} + 32 q^{85} + 36 q^{87} + 4 q^{88} - 36 q^{89} + 12 q^{90} + 8 q^{91} + 12 q^{92} + 8 q^{93} + 36 q^{95} + 12 q^{97} - 32 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 4 * q^7 + 8 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 - 4 * q^17 - 16 * q^18 - 4 * q^20 + 12 * q^21 + 4 * q^22 + 12 * q^23 + 8 * q^24 - 4 * q^25 + 8 * q^27 + 4 * q^28 + 8 * q^29 + 8 * q^30 + 8 * q^31 - 24 * q^35 + 8 * q^36 - 16 * q^37 + 28 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^42 - 8 * q^43 - 4 * q^44 - 4 * q^45 + 28 * q^46 - 28 * q^47 - 8 * q^48 + 32 * q^50 - 8 * q^51 + 4 * q^52 + 12 * q^53 - 40 * q^54 - 20 * q^55 - 32 * q^57 - 28 * q^58 - 24 * q^59 + 56 * q^61 + 20 * q^63 + 36 * q^65 + 4 * q^66 - 16 * q^67 + 4 * q^68 - 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 56 * q^81 + 28 * q^82 + 12 * q^83 + 8 * q^84 + 32 * q^85 + 36 * q^87 + 4 * q^88 - 36 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 + 8 * q^93 + 36 * q^95 + 12 * q^97 - 32 * q^98 + 4 * q^99

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