LMFDB - Embedded newform 930.2.j.c.683.2

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			683.2
Root			$3.16053i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.c.497.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 + 1.33991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) 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} +(-0.292893 - 1.70711i) q^{12} +(-1.74632 - 1.74632i) q^{13} +1.89492 q^{14} +(-2.12975 + 3.23483i) q^{15} -1.00000 q^{16} +(5.36459 + 5.36459i) q^{17} +(-2.70711 - 1.29289i) 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} +(-4.53553 + 2.53553i) q^{27} +(-1.33991 - 1.33991i) q^{28} +5.50825 q^{29} +(3.79334 - 0.781409i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.383437 - 2.23483i) 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} +(-3.23483 + 0.555010i) q^{42} +(3.50044 + 3.50044i) q^{43} -1.30913 q^{44} +(2.68826 - 6.14600i) q^{45} +6.72335 q^{46} +(3.66790 + 3.66790i) q^{47} +(1.70711 - 0.292893i) 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} +(1.27342 + 7.42202i) q^{57} +(-3.89492 - 3.89492i) q^{58} +11.3765 q^{59} +(-3.23483 - 2.12975i) q^{60} +12.5481 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-2.44993 + 5.12975i) 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} +(1.29289 - 2.70711i) q^{72} +(-1.87025 - 1.87025i) q^{73} +2.82843 q^{74} +(2.02817 + 8.41941i) q^{75} +4.34772 q^{76} +(-1.75413 - 1.75413i) q^{77} +(-0.723349 - 4.21598i) 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} +(-9.40317 + 1.61333i) q^{87} +(0.925698 + 0.925698i) q^{88} +7.16053 q^{89} +(-6.24676 + 2.44499i) q^{90} +4.67982 q^{91} +(-4.75413 - 4.75413i) q^{92} +(-1.70711 + 0.292893i) 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^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 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} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 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} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 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^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * 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 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * 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 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$			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	−0.913432	−	0.406992i	$-0.866578\pi$
$7$	−1.33991	+	1.33991i	−0.506439	+	0.506439i	0.406992	+	0.913432i	$0.366578\pi$
$8$	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	$0.936763\pi$
$12$	−0.292893	−	1.70711i	−0.0845510	−	0.492799i
$13$	−1.74632	−	1.74632i	−0.484341	−	0.484341i	0.422174	−	0.906515i	$-0.361267\pi$
$13$	−1.74632	−	1.74632i	−0.484341	−	0.484341i	−0.906515	+	0.422174i	$0.861267\pi$
$14$	1.89492			0.506439
$15$	−2.12975	+	3.23483i	−0.549900	+	0.835230i
$16$	−1.00000			−0.250000
$17$	5.36459	+	5.36459i	1.30110	+	1.30110i	0.927648	+	0.373456i	$0.121827\pi$
$17$	5.36459	+	5.36459i	1.30110	+	1.30110i	0.373456	+	0.927648i	$0.378173\pi$
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$		−	4.34772i		−	0.997435i	−0.866765	−	0.498718i	$-0.833804\pi$
$19$		−	4.34772i		−	0.997435i	0.866765	−	0.498718i	$-0.166196\pi$
$20$	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	$-0.997244\pi$
$23$	−4.75413	+	4.75413i	−0.991304	+	0.991304i	0.00865885	+	0.999963i	$0.497244\pi$
$24$	−1.00000	+	1.41421i	−0.204124	+	0.288675i
$25$	−0.332104	−	4.98896i	−0.0664208	−	0.997792i
$26$			2.46967i			0.484341i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	−1.33991	−	1.33991i	−0.253220	−	0.253220i
$29$	5.50825			1.02286			0.511428	−	0.859326i	$-0.329117\pi$
$29$	5.50825			1.02286			0.511428	+	0.859326i	$0.329117\pi$
$30$	3.79334	−	0.781409i	0.692565	−	0.142665i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.383437	−	2.23483i	−0.0667478	−	0.389035i
$34$		−	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	−0.852129	−	0.523331i	$-0.824689\pi$
$37$	−2.00000	+	2.00000i	−0.328798	+	0.328798i	0.523331	+	0.852129i	$0.324689\pi$
$38$	−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	$-0.0704895\pi$
$42$	−3.23483	+	0.555010i	−0.499146	+	0.0856398i
$43$	3.50044	+	3.50044i	0.533813	+	0.533813i	0.921705	−	0.387892i	$-0.126797\pi$
$43$	3.50044	+	3.50044i	0.533813	+	0.533813i	−0.387892	+	0.921705i	$0.626797\pi$
$44$	−1.30913			−0.197360
$45$	2.68826	−	6.14600i	0.400742	−	0.916191i
$46$	6.72335			0.991304
$47$	3.66790	+	3.66790i	0.535018	+	0.535018i	0.922061	−	0.387044i	$-0.126504\pi$
$47$	3.66790	+	3.66790i	0.535018	+	0.535018i	−0.387044	+	0.922061i	$0.626504\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$			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	$-0.534463\pi$
$53$	6.45082	−	6.45082i	0.886088	−	0.886088i	0.994145	+	0.108057i	$0.0344628\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$	2.13756	+	2.00000i	0.288229	+	0.269680i
$56$			1.89492i			0.253220i
$57$	1.27342	+	7.42202i	0.168668	+	0.983071i
$58$	−3.89492	−	3.89492i	−0.511428	−	0.511428i
$59$	11.3765			1.48110			0.740548	−	0.672003i	$-0.234566\pi$
$59$	11.3765			1.48110			0.740548	+	0.672003i	$0.234566\pi$
$60$	−3.23483	−	2.12975i	−0.417615	−	0.274950i
$61$	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
$63$	−2.44993	+	5.12975i	−0.308662	+	0.646288i
$64$		−	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	−0.283864	−	0.958865i	$-0.591616\pi$
$67$	5.52512	−	5.52512i	0.675001	−	0.675001i	0.958865	+	0.283864i	$0.0916164\pi$
$68$	−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	$-0.210450\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	−1.87025	−	1.87025i	−0.218896	−	0.218896i	0.589137	−	0.808033i	$-0.299468\pi$
$73$	−1.87025	−	1.87025i	−0.218896	−	0.218896i	−0.808033	+	0.589137i	$0.799468\pi$
$74$	2.82843			0.328798
$75$	2.02817	+	8.41941i	0.234193	+	0.972190i
$76$	4.34772			0.498718
$77$	−1.75413	−	1.75413i	−0.199901	−	0.199901i
$78$	−0.723349	−	4.21598i	−0.0819031	−	0.477366i
$79$			4.64493i			0.522595i	0.965258	+	0.261298i	$0.0841504\pi$
$79$			4.64493i			0.522595i	−0.965258	+	0.261298i	$0.915850\pi$
$80$	−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	0.278470	−	0.960445i	$-0.410173\pi$
$83$	11.2871	−	11.2871i	1.23891	−	1.23891i	0.960445	−	0.278470i	$-0.0898273\pi$
$84$	2.67982	+	1.89492i	0.292393	+	0.206753i
$85$	16.9549	−	0.563703i	1.83902	−	0.0611422i
$86$		−	4.95037i		−	0.533813i
$87$	−9.40317	+	1.61333i	−1.00813	+	0.172967i
$88$	0.925698	+	0.925698i	0.0986798	+	0.0986798i
$89$	7.16053			0.759015			0.379507	−	0.925189i	$-0.376093\pi$
$89$	7.16053			0.759015			0.379507	+	0.925189i	$0.376093\pi$
$90$	−6.24676	+	2.44499i	−0.658466	+	0.257725i
$91$	4.67982			0.490579
$92$	−4.75413	−	4.75413i	−0.495652	−	0.495652i
$93$	−1.70711	+	0.292893i	−0.177019	+	0.0303716i
$94$		−	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	−0.778979	−	0.627050i	$-0.784262\pi$
$97$	−1.49632	+	1.49632i	−0.151929	+	0.151929i	0.627050	+	0.778979i	$0.284262\pi$
$98$	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	$0.766339\pi$
$102$	2.22208	+	12.9513i	0.220019	+	1.28237i
$103$	−10.4032	−	10.4032i	−1.02506	−	1.02506i	−0.999678	−	0.0253770i	$-0.991921\pi$
$103$	−10.4032	−	10.4032i	−1.02506	−	1.02506i	−0.0253770	−	0.999678i	$-0.508079\pi$
$104$	−2.46967			−0.242171
$105$	−1.48071	−	7.18807i	−0.144502	−	0.701484i
$106$	−9.12283			−0.886088
$107$	8.11871	+	8.11871i	0.784866	+	0.784866i	0.980647	−	0.195782i	$-0.0627245\pi$
$107$	8.11871	+	8.11871i	0.784866	+	0.784866i	−0.195782	+	0.980647i	$0.562724\pi$
$108$	−2.53553	−	4.53553i	−0.243982	−	0.436432i
$109$		−	0.305448i		−	0.0292566i	−0.999893	−	0.0146283i	$-0.995344\pi$
$109$		−	0.305448i		−	0.0292566i	0.999893	−	0.0146283i	$-0.00465650\pi$
$110$	−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	$-0.782058\pi$
$113$	−1.51148	+	1.51148i	−0.142189	+	0.142189i	0.632429	+	0.774618i	$0.282058\pi$
$114$	4.34772	−	6.14860i	0.407201	−	0.575869i
$115$	0.499557	+	15.0256i	0.0465839	+	1.40114i
$116$			5.50825i			0.511428i
$117$	−6.68565	−	3.19301i	−0.618089	−	0.295194i
$118$	−8.04441	−	8.04441i	−0.740548	−	0.740548i
$119$	−14.3761			−1.31786
$120$	0.781409	+	3.79334i	0.0713325	+	0.346283i
$121$	9.28617			0.844197
$122$	−8.87284	−	8.87284i	−0.803309	−	0.803309i
$123$	0.823854	+	4.80177i	0.0742844	+	0.432961i
$124$			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	−0.805831	−	0.592146i	$-0.798281\pi$
$127$	−2.40811	+	2.40811i	−0.213685	+	0.213685i	0.592146	+	0.805831i	$0.298281\pi$
$128$	−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	$0.874048\pi$
$132$	2.23483	−	0.383437i	0.194517	−	0.0333739i
$133$	5.82556	+	5.82556i	0.505140	+	0.505140i
$134$	−7.81370			−0.675001
$135$	−2.78902	+	11.2792i	−0.240041	+	0.970763i
$136$	7.58667			0.650552
$137$	12.2546	+	12.2546i	1.04698	+	1.04698i	0.998841	+	0.0481377i	$0.0153286\pi$
$137$	12.2546	+	12.2546i	1.04698	+	1.04698i	0.0481377	+	0.998841i	$0.484671\pi$
$138$	−11.4775	+	1.96922i	−0.977027	+	0.167631i
$139$			10.0563i			0.852968i	0.904495	+	0.426484i	$0.140248\pi$
$139$			10.0563i			0.852968i	−0.904495	+	0.426484i	$0.859752\pi$
$140$	−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
$147$	−0.998553	−	5.81999i	−0.0823593	−	0.480025i
$148$	−2.00000	−	2.00000i	−0.164399	−	0.164399i
$149$	−18.7711			−1.53779			−0.768893	−	0.639378i	$-0.779192\pi$
$149$	−18.7711			−1.53779			−0.768893	+	0.639378i	$0.779192\pi$
$150$	4.51929	−	7.38756i	0.368999	−	0.603192i
$151$	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
$153$	20.5379	+	9.80876i	1.66039	+	0.792991i
$154$			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	−0.0786055	−	0.996906i	$-0.525047\pi$
$157$	11.5063	−	11.5063i	0.918300	−	0.918300i	0.996906	+	0.0786055i	$0.0250467\pi$
$158$	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
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	−0.105079	−	0.105079i	−0.00823039	−	0.00823039i	0.702980	−	0.711210i	$-0.251852\pi$
$163$	−0.105079	−	0.105079i	−0.00823039	−	0.00823039i	−0.711210	+	0.702980i	$0.751852\pi$
$164$	2.81281			0.219644
$165$	−4.23483	−	2.78814i	−0.329681	−	0.217056i
$166$	−15.9623			−1.23891
$167$	−0.887114	−	0.887114i	−0.0686469	−	0.0686469i	0.671950	−	0.740597i	$-0.265457\pi$
$167$	−0.887114	−	0.887114i	−0.0686469	−	0.0686469i	−0.740597	+	0.671950i	$0.765457\pi$
$168$	−0.555010	−	3.23483i	−0.0428199	−	0.249573i
$169$		−	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	−0.343319	+	0.939219i	$0.611551\pi$
$173$	−16.8692	+	16.8692i	−1.28254	+	1.28254i	−0.939219	+	0.343319i	$0.888449\pi$
$174$	7.78984	+	5.50825i	0.590546	+	0.417579i
$175$	7.12975	+	6.23977i	0.538959	+	0.471683i
$176$		−	1.30913i		−	0.0986798i
$177$	−19.4209	+	3.33210i	−1.45977	+	0.250456i
$178$	−5.06326	−	5.06326i	−0.379507	−	0.379507i
$179$	−12.3622			−0.923992			−0.461996	−	0.886882i	$-0.652867\pi$
$179$	−12.3622			−0.923992			−0.461996	+	0.886882i	$0.652867\pi$
$180$	6.14600	+	2.68826i	0.458096	+	0.200371i
$181$	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
$183$	−21.4209	+	3.67525i	−1.58348	+	0.271682i
$184$			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	$0.946959\pi$
$192$	0.292893	+	1.70711i	0.0211377	+	0.123200i
$193$	−16.9513	−	16.9513i	−1.22018	−	1.22018i	−0.967568	−	0.252610i	$-0.918711\pi$
$193$	−16.9513	−	16.9513i	−1.22018	−	1.22018i	−0.252610	−	0.967568i	$-0.581289\pi$
$194$	2.11612			0.151929
$195$	9.36827	−	1.92982i	0.670876	−	0.138197i
$196$	−3.40927			−0.243519
$197$	−10.6096	−	10.6096i	−0.755906	−	0.755906i	0.219669	−	0.975575i	$-0.429502\pi$
$197$	−10.6096	−	10.6096i	−0.755906	−	0.755906i	−0.975575	+	0.219669i	$0.929502\pi$
$198$	1.69257	−	3.54397i	0.120286	−	0.251859i
$199$			4.67866i			0.331662i	0.986154	+	0.165831i	$0.0530306\pi$
$199$			4.67866i			0.331662i	−0.986154	+	0.165831i	$0.946969\pi$
$200$	−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
$207$	−8.69257	+	18.2008i	−0.604175	+	1.26504i
$208$	1.74632	+	1.74632i	0.121085	+	0.121085i
$209$	5.69175			0.393707
$210$	−4.03572	+	6.12975i	−0.278491	+	0.422993i
$211$	−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
$213$	3.03078	+	17.6647i	0.207665	+	1.21036i
$214$		−	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
$222$	−4.82843	+	0.828427i	−0.324063	+	0.0556004i
$223$	11.0613	+	11.0613i	0.740718	+	0.740718i	0.972716	−	0.231998i	$-0.0745263\pi$
$223$	11.0613	+	11.0613i	0.740718	+	0.740718i	−0.231998	+	0.972716i	$0.574526\pi$
$224$	−1.89492			−0.126610
$225$	−5.92829	−	13.7788i	−0.395219	−	0.918587i
$226$	2.13756			0.142189
$227$	10.1647	+	10.1647i	0.674652	+	0.674652i	0.958785	−	0.284133i	$-0.0917058\pi$
$227$	10.1647	+	10.1647i	0.674652	+	0.674652i	−0.284133	+	0.958785i	$0.591706\pi$
$228$	−7.42202	+	1.27342i	−0.491535	+	0.0843341i
$229$			13.4188i			0.886738i	0.896339	+	0.443369i	$0.146217\pi$
$229$			13.4188i			0.886738i	−0.896339	+	0.443369i	$0.853783\pi$
$230$	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	$-0.895887\pi$
$233$	−9.55096	+	9.55096i	−0.625704	+	0.625704i	0.321280	+	0.946984i	$0.395887\pi$
$234$	2.46967	+	6.98527i	0.161447	+	0.456641i
$235$	11.5925	−	0.385417i	0.756211	−	0.0251419i
$236$			11.3765i			0.740548i
$237$	−1.36047	−	7.92939i	−0.0883719	−	0.515069i
$238$	10.1655	+	10.1655i	0.658930	+	0.658930i
$239$	28.4935			1.84309			0.921546	−	0.388268i	$-0.126927\pi$
$239$	28.4935			1.84309			0.921546	+	0.388268i	$0.126927\pi$
$240$	2.12975	−	3.23483i	0.137475	−	0.208808i
$241$	−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
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$			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	$-0.341022\pi$
$252$	−5.12975	−	2.44993i	−0.323144	−	0.154331i
$253$	−6.22379	−	6.22379i	−0.391286	−	0.391286i
$254$	3.40559			0.213685
$255$	−28.7788	+	5.92829i	−1.80220	+	0.371244i
$256$	1.00000			0.0625000
$257$	4.61162	+	4.61162i	0.287665	+	0.287665i	0.836156	−	0.548491i	$-0.184798\pi$
$257$	4.61162	+	4.61162i	0.287665	+	0.287665i	−0.548491	+	0.836156i	$0.684798\pi$
$258$	1.44993	+	8.45082i	0.0902688	+	0.526125i
$259$		−	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	$-0.766433\pi$
$263$	−1.18350	+	1.18350i	−0.0729778	+	0.0729778i	0.669676	+	0.742654i	$0.266433\pi$
$264$	−1.85140	−	1.30913i	−0.113946	−	0.0805717i
$265$	−0.677843	−	20.3880i	−0.0416396	−	1.25243i
$266$		−	8.23859i		−	0.505140i
$267$	−12.2238	+	2.09727i	−0.748084	+	0.128351i
$268$	5.52512	+	5.52512i	0.337500	+	0.337500i
$269$	−1.84316			−0.112379			−0.0561896	−	0.998420i	$-0.517895\pi$
$269$	−1.84316			−0.112379			−0.0561896	+	0.998420i	$0.517895\pi$
$270$	9.94777	−	6.00349i	0.605402	−	0.365361i
$271$	−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
$273$	−7.98896	+	1.37069i	−0.483514	+	0.0829578i
$274$		−	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	−0.741358	−	0.671110i	$-0.765818\pi$
$277$	−1.16916	+	1.16916i	−0.0702480	+	0.0702480i	0.671110	+	0.741358i	$0.265818\pi$
$278$	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	$-0.0542915\pi$
$282$	1.51929	+	8.85508i	0.0904725	+	0.527313i
$283$	−0.590360	−	0.590360i	−0.0350933	−	0.0350933i	0.689342	−	0.724436i	$-0.257900\pi$
$283$	−0.590360	−	0.590360i	−0.0350933	−	0.0350933i	−0.724436	+	0.689342i	$0.757900\pi$
$284$	10.3477			0.614024
$285$	14.0641	+	9.25957i	0.833088	+	0.548490i
$286$	−3.23313			−0.191179
$287$	3.76892	+	3.76892i	0.222472	+	0.222472i
$288$	2.70711	+	1.29289i	0.159518	+	0.0761845i
$289$			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	$-0.682414\pi$
$293$	5.10139	−	5.10139i	0.298026	−	0.298026i	0.840240	+	0.542214i	$0.182414\pi$
$294$	−3.40927	+	4.82144i	−0.198833	+	0.281192i
$295$	17.3802	−	18.5756i	1.01191	−	1.08152i
$296$			2.82843i			0.164399i
$297$	−3.31936	−	5.93763i	−0.192609	−	0.344536i
$298$	13.2731	+	13.2731i	0.768893	+	0.768893i
$299$	16.6044			0.960259
$300$	−8.41941	+	2.02817i	−0.486095	+	0.117096i
$301$	−9.38057			−0.540687
$302$	−3.19543	−	3.19543i	−0.183876	−	0.183876i
$303$	−3.94373	−	22.9857i	−0.226561	−	1.32050i
$304$			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	−0.491941	−	0.870628i	$-0.663712\pi$
$307$	6.63514	−	6.63514i	0.378687	−	0.378687i	0.870628	+	0.491941i	$0.163712\pi$
$308$	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	$0.768655\pi$
$312$	4.21598	−	0.723349i	0.238683	−	0.0409515i
$313$	−6.44060	−	6.44060i	−0.364044	−	0.364044i	0.501255	−	0.865299i	$-0.332872\pi$
$313$	−6.44060	−	6.44060i	−0.364044	−	0.364044i	−0.865299	+	0.501255i	$0.832872\pi$
$314$	−16.2723			−0.918300
$315$	4.63306	+	11.8371i	0.261044	+	0.666946i
$316$	−4.64493			−0.261298
$317$	18.9985	+	18.9985i	1.06706	+	1.06706i	0.997584	+	0.0694770i	$0.0221330\pi$
$317$	18.9985	+	18.9985i	1.06706	+	1.06706i	0.0694770	+	0.997584i	$0.477867\pi$
$318$	15.5737	−	2.67202i	0.873327	−	0.149839i
$319$			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
$327$	0.0894635	+	0.521432i	0.00494735	+	0.0288352i
$328$	−1.98896	−	1.98896i	−0.109822	−	0.109822i
$329$	−9.82931			−0.541908
$330$	1.02297	+	4.96599i	0.0563126	+	0.273369i
$331$	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
$333$	−3.65685	+	7.65685i	−0.200394	+	0.419593i
$334$			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	−0.522175	−	0.852839i	$-0.674879\pi$
$337$	6.07018	−	6.07018i	0.330664	−	0.330664i	0.852839	+	0.522175i	$0.174879\pi$
$338$	−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
$342$	−5.62114	+	11.7697i	−0.303956	+	0.636435i
$343$	−13.9475	−	13.9475i	−0.753095	−	0.753095i
$344$	4.95037			0.266906
$345$	−5.25368	−	25.5039i	−0.282849	−	1.37309i
$346$	23.8566			1.28254
$347$	−17.7567	−	17.7567i	−0.953231	−	0.953231i	0.0457236	−	0.998954i	$-0.485441\pi$
$347$	−17.7567	−	17.7567i	−0.953231	−	0.953231i	−0.998954	+	0.0457236i	$0.985441\pi$
$348$	−1.61333	−	9.40317i	−0.0864835	−	0.504063i
$349$			12.4731i			0.667669i	0.942632	+	0.333834i	$0.108343\pi$
$349$			12.4731i			0.667669i	−0.942632	+	0.333834i	$0.891657\pi$
$350$	−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	$-0.780750\pi$
$353$	−2.56282	+	2.56282i	−0.136405	+	0.136405i	0.635607	+	0.772012i	$0.280750\pi$
$354$	16.0888	+	11.3765i	0.855111	+	0.604655i
$355$	−16.8958	−	15.8085i	−0.896736	−	0.839027i
$356$			7.16053i			0.379507i
$357$	24.5416	−	4.21068i	1.29888	−	0.222853i
$358$	8.74138	+	8.74138i	0.461996	+	0.461996i
$359$	3.97334			0.209705			0.104853	−	0.994488i	$-0.466563\pi$
$359$	3.97334			0.209705			0.104853	+	0.994488i	$0.466563\pi$
$360$	−2.44499	−	6.24676i	−0.128862	−	0.329233i
$361$	0.0973369			0.00512300
$362$	−0.00412024	−	0.00412024i	−0.000216555	−	0.000216555i
$363$	−15.8525	+	2.71985i	−0.832039	+	0.142755i
$364$			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	−0.0597724	−	0.998212i	$-0.519037\pi$
$367$	17.9779	−	17.9779i	0.938440	−	0.938440i	0.998212	+	0.0597724i	$0.0190375\pi$
$368$	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
$372$	−0.292893	−	1.70711i	−0.0151858	−	0.0885094i
$373$	−17.2008	−	17.2008i	−0.890625	−	0.890625i	0.103957	−	0.994582i	$-0.466850\pi$
$373$	−17.2008	−	17.2008i	−0.890625	−	0.890625i	−0.994582	+	0.103957i	$0.966850\pi$
$374$	9.93198			0.513570
$375$	16.8457	+	9.55096i	0.869911	+	0.493209i
$376$	5.18719			0.267509
$377$	−9.61916	−	9.61916i	−0.495412	−	0.495412i
$378$	−8.59448	+	4.80464i	−0.442052	+	0.247124i
$379$			14.4899i			0.744294i	0.928174	+	0.372147i	$0.121378\pi$
$379$			14.4899i			0.744294i	−0.928174	+	0.372147i	$0.878622\pi$
$380$	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	−0.316375	+	0.948634i	$0.602466\pi$
$383$	−24.7567	+	24.7567i	−1.26501	+	1.26501i	−0.948634	+	0.316375i	$0.897534\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$	−5.54397	+	0.184321i	−0.282547	+	0.00939387i
$386$			23.9727i			1.22018i
$387$	13.4012	+	6.40031i	0.681221	+	0.325346i
$388$	−1.49632	−	1.49632i	−0.0759643	−	0.0759643i
$389$	−33.0438			−1.67539			−0.837693	−	0.546142i	$-0.816096\pi$
$389$	−33.0438			−1.67539			−0.837693	+	0.546142i	$0.816096\pi$
$390$	−7.98896	−	5.25978i	−0.404537	−	0.266339i
$391$	−51.0078			−2.57958
$392$	2.41072	+	2.41072i	0.121760	+	0.121760i
$393$	−2.58426	−	15.0622i	−0.130359	−	0.759786i
$394$			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	−0.538755	−	0.842463i	$-0.681105\pi$
$397$	6.05133	−	6.05133i	0.303708	−	0.303708i	0.842463	+	0.538755i	$0.181105\pi$
$398$	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	$-0.218247\pi$
$402$	13.3388	−	2.28858i	0.665280	−	0.114144i
$403$	−1.74632	−	1.74632i	−0.0869903	−	0.0869903i
$404$	−13.4647			−0.669895
$405$	1.45754	−	20.0718i	0.0724260	−	0.997374i
$406$	10.4377			0.518014
$407$	−2.61827	−	2.61827i	−0.129783	−	0.129783i
$408$	−12.9513	+	2.22208i	−0.641183	+	0.110010i
$409$		−	10.0337i		−	0.496136i	−0.968743	−	0.248068i	$-0.920204\pi$
$409$		−	10.0337i		−	0.496136i	0.968743	−	0.248068i	$-0.0797957\pi$
$410$	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
$417$	−2.94543	−	17.1672i	−0.144238	−	0.840684i
$418$	−4.02468	−	4.02468i	−0.196853	−	0.196853i
$419$	−26.8198			−1.31023			−0.655116	−	0.755528i	$-0.727380\pi$
$419$	−26.8198			−1.31023			−0.655116	+	0.755528i	$0.727380\pi$
$420$	7.18807	−	1.48071i	0.350742	−	0.0722511i
$421$	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
$423$	14.0423	+	6.70648i	0.682759	+	0.326080i
$424$		−	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	$-0.136180\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	−9.70944	−	9.70944i	−0.466606	−	0.466606i	0.434207	−	0.900813i	$-0.357029\pi$
$433$	−9.70944	−	9.70944i	−0.466606	−	0.466606i	−0.900813	+	0.434207i	$0.857029\pi$
$434$	1.89492			0.0909591
$435$	−11.7312	+	17.8183i	−0.562469	+	0.854321i
$436$	0.305448			0.0146283
$437$	20.6696	+	20.6696i	0.988761	+	0.988761i
$438$	−0.774681	−	4.51517i	−0.0370157	−	0.215743i
$439$		−	26.9329i		−	1.28544i	−0.766103	−	0.642718i	$-0.777807\pi$
$439$		−	26.9329i		−	1.28544i	0.766103	−	0.642718i	$-0.222193\pi$
$440$	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	0.116888	−	0.993145i	$-0.462708\pi$
$443$	23.3635	−	23.3635i	1.11003	−	1.11003i	0.993145	−	0.116888i	$-0.0372918\pi$
$444$	4.00000	+	2.82843i	0.189832	+	0.134231i
$445$	10.9393	−	11.6918i	0.518574	−	0.554242i
$446$		−	15.6430i		−	0.740718i
$447$	32.0442	−	5.49792i	1.51564	−	0.260043i
$448$	1.33991	+	1.33991i	0.0633049	+	0.0633049i
$449$	−26.7530			−1.26255			−0.631277	−	0.775558i	$-0.717469\pi$
$449$	−26.7530			−1.26255			−0.631277	+	0.775558i	$0.717469\pi$
$450$	−5.55115	+	13.9350i	−0.261684	+	0.656903i
$451$	3.68235			0.173395
$452$	−1.51148	−	1.51148i	−0.0710943	−	0.0710943i
$453$	−7.71445	+	1.32359i	−0.362456	+	0.0621877i
$454$		−	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	0.194007	−	0.981000i	$-0.437852\pi$
$457$	25.1188	−	25.1188i	1.17501	−	1.17501i	0.981000	−	0.194007i	$-0.0621484\pi$
$458$	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	$0.960093\pi$
$462$	−0.726583	−	4.23483i	−0.0338037	−	0.197022i
$463$	−4.97423	−	4.97423i	−0.231172	−	0.231172i	0.582010	−	0.813182i	$-0.302267\pi$
$463$	−4.97423	−	4.97423i	−0.231172	−	0.231172i	−0.813182	+	0.582010i	$0.802267\pi$
$464$	−5.50825			−0.255714
$465$	−2.12975	+	3.23483i	−0.0987650	+	0.150012i
$466$	13.5071			0.625704
$467$	15.3051	+	15.3051i	0.708235	+	0.708235i	0.966164	−	0.257929i	$-0.0830401\pi$
$467$	15.3051	+	15.3051i	0.708235	+	0.708235i	−0.257929	+	0.966164i	$0.583040\pi$
$468$	3.19301	−	6.68565i	0.147597	−	0.309044i
$469$			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
$477$	11.7948	−	24.6965i	0.540049	−	1.13077i
$478$	−20.1480	−	20.1480i	−0.921546	−	0.921546i
$479$	16.3832			0.748569			0.374284	−	0.927314i	$-0.377888\pi$
$479$	16.3832			0.748569			0.374284	+	0.927314i	$0.377888\pi$
$480$	−3.79334	+	0.781409i	−0.173141	+	0.0356663i
$481$	6.98527			0.318501
$482$	7.40317	+	7.40317i	0.337205	+	0.337205i
$483$	3.73152	+	21.7489i	0.169790	+	0.989610i
$484$			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	−0.862312	−	0.506377i	$-0.830984\pi$
$487$	−7.85481	+	7.85481i	−0.355935	+	0.355935i	0.506377	+	0.862312i	$0.330984\pi$
$488$	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	$0.721118\pi$
$492$	−4.80177	+	0.823854i	−0.216481	+	0.0371422i
$493$	29.5495	+	29.5495i	1.33084	+	1.33084i
$494$	10.7374			0.483099
$495$	8.04594	+	3.51929i	0.361638	+	0.158180i
$496$	−1.00000			−0.0449013
$497$	13.8650	+	13.8650i	0.621932	+	0.621932i
$498$	27.2494	−	4.67525i	1.22107	−	0.209503i
$499$		−	0.442369i		−	0.0198031i	−0.999951	−	0.00990157i	$-0.996848\pi$
$499$		−	0.442369i		−	0.0198031i	0.999951	−	0.00990157i	$-0.00315182\pi$
$500$	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	$-0.745671\pi$
$503$	0.431356	−	0.431356i	0.0192332	−	0.0192332i	0.716658	+	0.697425i	$0.245671\pi$
$504$	1.89492	+	5.35965i	0.0844065	+	0.238738i
$505$	21.9853	+	20.5704i	0.978332	+	0.915372i
$506$			8.80177i			0.391286i
$507$	2.02118	+	11.7803i	0.0897639	+	0.523182i
$508$	−2.40811	−	2.40811i	−0.106843	−	0.106843i
$509$	11.4584			0.507882			0.253941	−	0.967220i	$-0.418273\pi$
$509$	11.4584			0.507882			0.253941	+	0.967220i	$0.418273\pi$
$510$	24.5416	+	16.1578i	1.08672	+	0.715477i
$511$	5.01193			0.221715
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.0238	+	19.7192i	0.486712	+	0.870625i
$514$		−	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	$0.789262\pi$
$522$	−14.9114	−	7.12158i	−0.652655	−	0.311703i
$523$	17.9033	+	17.9033i	0.782858	+	0.782858i	0.980312	−	0.197454i	$-0.0632672\pi$
$523$	17.9033	+	17.9033i	0.782858	+	0.782858i	−0.197454	+	0.980312i	$0.563267\pi$
$524$	−8.82321			−0.385444
$525$	−13.9988	−	8.56370i	−0.610959	−	0.373751i
$526$	1.67372			0.0729778
$527$	5.36459	+	5.36459i	0.233685	+	0.233685i
$528$	0.383437	+	2.23483i	0.0166869	+	0.0972586i
$529$		−	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
$537$	21.1036	−	3.62080i	0.910685	−	0.156249i
$538$	1.30331	+	1.30331i	0.0561896	+	0.0561896i
$539$	−4.46320			−0.192244
$540$	−11.2792	−	2.78902i	−0.485381	−	0.120020i
$541$	−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
$543$	−0.00994714	+	0.00170666i	−0.000426873	+	7.32397e-5i
$544$			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	−0.429957	−	0.902849i	$-0.641471\pi$
$547$	11.0600	−	11.0600i	0.472893	−	0.472893i	0.902849	+	0.429957i	$0.141471\pi$
$548$	−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
$552$	−1.96922	−	11.4775i	−0.0838157	−	0.488514i
$553$	−6.22379	−	6.22379i	−0.264663	−	0.264663i
$554$	1.65344			0.0702480
$555$	−2.21016	−	10.7292i	−0.0938159	−	0.455428i
$556$	−10.0563			−0.426484
$557$	−9.15272	−	9.15272i	−0.387813	−	0.387813i	0.486093	−	0.873907i	$-0.338421\pi$
$557$	−9.15272	−	9.15272i	−0.387813	−	0.387813i	−0.873907	+	0.486093i	$0.838421\pi$
$558$	−2.70711	−	1.29289i	−0.114601	−	0.0547325i
$559$		−	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	$-0.509199\pi$
$563$	23.0321	−	23.0321i	0.970688	−	0.970688i	0.999582	+	0.0288945i	$0.00919868\pi$
$564$	5.18719	−	7.33579i	0.218420	−	0.308893i
$565$	0.158825	+	4.77709i	0.00668181	+	0.200974i
$566$			0.834895i			0.0350933i
$567$	−1.79970	+	16.9591i	−0.0755802	+	0.712214i
$568$	−7.31694	−	7.31694i	−0.307012	−	0.307012i
$569$	19.7684			0.828733			0.414367	−	0.910110i	$-0.364003\pi$
$569$	19.7684			0.828733			0.414367	+	0.910110i	$0.364003\pi$
$570$	−3.39735	−	16.4924i	−0.142299	−	0.690789i
$571$	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
$573$	−1.34278	−	7.82629i	−0.0560954	−	0.326948i
$574$		−	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	−0.233954	+	0.972248i	$0.575166\pi$
$577$	−28.9740	+	28.9740i	−1.20620	+	1.20620i	−0.972248	+	0.233954i	$0.924834\pi$
$578$	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
$582$	−3.61244	+	0.619797i	−0.149741	+	0.0256914i
$583$	8.44499	+	8.44499i	0.349756	+	0.349756i
$584$	−2.64493			−0.109448
$585$	−15.4274	+	6.03831i	−0.637845	+	0.249653i
$586$	−7.21446			−0.298026
$587$	15.8009	+	15.8009i	0.652172	+	0.652172i	0.953516	−	0.301343i	$-0.0974350\pi$
$587$	15.8009	+	15.8009i	0.652172	+	0.652172i	−0.301343	+	0.953516i	$0.597435\pi$
$588$	5.81999	−	0.998553i	0.240012	−	0.0411796i
$589$		−	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	$-0.891057\pi$
$593$	−14.7665	+	14.7665i	−0.606387	+	0.606387i	0.335613	+	0.942000i	$0.391057\pi$
$594$	−1.85140	+	6.54567i	−0.0759637	+	0.268572i
$595$	−21.9628	+	23.4734i	−0.900388	+	0.962317i
$596$		−	18.7711i		−	0.768893i
$597$	−1.37035	−	7.98698i	−0.0560846	−	0.326885i
$598$	−11.7411	−	11.7411i	−0.480129	−	0.480129i
$599$	−41.7822			−1.70718			−0.853588	−	0.520949i	$-0.825578\pi$
$599$	−41.7822			−1.70718			−0.853588	+	0.520949i	$0.825578\pi$
$600$	7.38756	+	4.51929i	0.301596	+	0.184499i
$601$	−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
$603$	10.1023	−	21.1525i	0.411397	−	0.861397i
$604$			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	−0.997336	−	0.0729509i	$-0.976758\pi$
$607$	−22.7744	+	22.7744i	−0.924385	+	0.924385i	0.0729509	+	0.997336i	$0.476758\pi$
$608$	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
$612$	−9.80876	+	20.5379i	−0.396496	+	0.830197i
$613$	31.6523	+	31.6523i	1.27842	+	1.27842i	0.941550	+	0.336872i	$0.109369\pi$
$613$	31.6523	+	31.6523i	1.27842	+	1.27842i	0.336872	+	0.941550i	$0.390631\pi$
$614$	−9.38350			−0.378687
$615$	9.09898	+	5.99060i	0.366906	+	0.241564i
$616$	−2.48071			−0.0999506
$617$	−25.0215	−	25.0215i	−1.00733	−	1.00733i	−0.999973	−	0.00735502i	$-0.997659\pi$
$617$	−25.0215	−	25.0215i	−1.00733	−	1.00733i	−0.00735502	−	0.999973i	$-0.502341\pi$
$618$	−4.30913	−	25.1155i	−0.173339	−	1.01029i
$619$			13.5269i			0.543692i	0.962341	+	0.271846i	$0.0876341\pi$
$619$			13.5269i			0.543692i	−0.962341	+	0.271846i	$0.912366\pi$
$620$	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
$627$	−9.71643	+	1.66708i	−0.388037	+	0.0665766i
$628$	11.5063	+	11.5063i	0.459150	+	0.459150i
$629$	−21.4584			−0.855600
$630$	5.09404	−	11.6462i	0.202951	−	0.463995i
$631$	−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
$633$	19.3843	−	3.32582i	0.770458	−	0.132190i
$634$		−	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	$0.820873\pi$
$642$	3.36288	+	19.6003i	0.132722	+	0.773562i
$643$	−22.7661	−	22.7661i	−0.897805	−	0.897805i	0.0974363	−	0.995242i	$-0.468936\pi$
$643$	−22.7661	−	22.7661i	−0.897805	−	0.897805i	−0.995242	+	0.0974363i	$0.968936\pi$
$644$	12.7402			0.502035
$645$	−18.7784	+	3.86826i	−0.739400	+	0.152313i
$646$	−32.9847			−1.29777
$647$	−1.65399	−	1.65399i	−0.0650250	−	0.0650250i	0.673846	−	0.738871i	$-0.264641\pi$
$647$	−1.65399	−	1.65399i	−0.0650250	−	0.0650250i	−0.738871	+	0.673846i	$0.764641\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$			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	$-0.545157\pi$
$653$	21.6841	−	21.6841i	0.848565	−	0.848565i	0.989954	+	0.141389i	$0.0451568\pi$
$654$	0.305448	−	0.431968i	0.0119439	−	0.0168913i
$655$	14.4066	+	13.4795i	0.562912	+	0.526686i
$656$			2.81281i			0.109822i
$657$	−7.16010	−	3.41961i	−0.279342	−	0.133412i
$658$	6.95037	+	6.95037i	0.270954	+	0.270954i
$659$	16.5520			0.644776			0.322388	−	0.946608i	$-0.395514\pi$
$659$	16.5520			0.644776			0.322388	+	0.946608i	$0.395514\pi$
$660$	2.78814	−	4.23483i	0.108528	−	0.164841i
$661$	−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
$663$	5.48781	+	31.9853i	0.213129	+	1.24221i
$664$		−	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
$672$	3.23483	−	0.555010i	0.124786	−	0.0214100i
$673$	−18.2328	−	18.2328i	−0.702821	−	0.702821i	0.262194	−	0.965015i	$-0.415554\pi$
$673$	−18.2328	−	18.2328i	−0.702821	−	0.702821i	−0.965015	+	0.262194i	$0.915554\pi$
$674$	−8.58453			−0.330664
$675$	14.1559	+	21.7855i	0.544863	+	0.838525i
$676$	6.90075			0.265413
$677$	25.1358	+	25.1358i	0.966048	+	0.966048i	0.999442	−	0.0333940i	$-0.0106316\pi$
$677$	25.1358	+	25.1358i	0.966048	+	0.966048i	−0.0333940	+	0.999442i	$0.510632\pi$
$678$	−3.64905	+	0.626077i	−0.140141	+	0.0240444i
$679$		−	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	$-0.635452\pi$
$683$	13.0152	−	13.0152i	0.498011	−	0.498011i	0.910818	+	0.412807i	$0.135452\pi$
$684$	12.2972	−	4.34772i	0.470195	−	0.166239i
$685$	38.7309	−	1.28769i	1.47983	−	0.0492002i
$686$			19.7248i			0.753095i
$687$	−3.93027	−	22.9073i	−0.149949	−	0.873968i
$688$	−3.50044	−	3.50044i	−0.133453	−	0.133453i
$689$	−22.5304			−0.858338
$690$	−14.3191	+	21.7489i	−0.545118	+	0.827967i
$691$	−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
$693$	−6.71554	−	3.20729i	−0.255102	−	0.121835i
$694$			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	$0.971880\pi$
$702$	−6.26192	−	11.2013i	−0.236341	−	0.422764i
$703$	8.69544	+	8.69544i	0.327955	+	0.327955i
$704$	1.30913			0.0493399
$705$	−19.6767	+	4.05331i	−0.741069	+	0.152657i
$706$	3.62437			0.136405
$707$	−18.0415	−	18.0415i	−0.678522	−	0.678522i
$708$	−3.33210	−	19.4209i	−0.125228	−	0.729883i
$709$			34.5708i			1.29833i	0.760646	+	0.649167i	$0.224882\pi$
$709$			34.5708i			1.29833i	−0.760646	+	0.649167i	$0.775118\pi$
$710$	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
$717$	−48.6415	+	8.34556i	−1.81655	+	0.311671i
$718$	−2.80958	−	2.80958i	−0.104853	−	0.104853i
$719$	−35.9553			−1.34091			−0.670453	−	0.741952i	$-0.733900\pi$
$719$	−35.9553			−1.34091			−0.670453	+	0.741952i	$0.733900\pi$
$720$	−2.68826	+	6.14600i	−0.100185	+	0.229048i
$721$	27.8787			1.03826
$722$	−0.0688276	−	0.0688276i	−0.00256150	−	0.00256150i
$723$	17.8728	−	3.06649i	0.664698	−	0.114044i
$724$			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	−0.519948	−	0.854198i	$-0.674049\pi$
$727$	9.01238	−	9.01238i	0.334251	−	0.334251i	0.854198	+	0.519948i	$0.174049\pi$
$728$	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
$732$	−3.67525	−	21.4209i	−0.135841	−	0.791740i
$733$	−13.6035	−	13.6035i	−0.502458	−	0.502458i	0.409743	−	0.912201i	$-0.365618\pi$
$733$	−13.6035	−	13.6035i	−0.502458	−	0.502458i	−0.912201	+	0.409743i	$0.865618\pi$
$734$	−25.4246			−0.938440
$735$	−11.0284	−	7.26091i	−0.406790	−	0.267823i
$736$	−6.72335			−0.247826
$737$	7.23313	+	7.23313i	0.266436	+	0.266436i
$738$	−3.63667	+	7.61458i	−0.133868	+	0.280297i
$739$			7.56118i			0.278142i	0.990282	+	0.139071i	$0.0444117\pi$
$739$			7.56118i			0.278142i	−0.990282	+	0.139071i	$0.955588\pi$
$740$	−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	$-0.799310\pi$
$743$	−5.94778	+	5.94778i	−0.218203	+	0.218203i	0.589538	+	0.807741i	$0.299310\pi$
$744$	−1.00000	+	1.41421i	−0.0366618	+	0.0518476i
$745$	−28.6770	+	30.6495i	−1.05065	+	1.12291i
$746$			24.3256i			0.890625i
$747$	20.6376	−	43.2117i	0.755089	−	1.58103i
$748$	−7.02297	−	7.02297i	−0.256785	−	0.256785i
$749$	−21.7567			−0.794973
$750$	−5.15820	−	18.6653i	−0.188351	−	0.681560i
$751$	−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
$753$	8.14696	+	47.4840i	0.296892	+	1.73041i
$754$			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	−0.290353	+	0.956919i	$0.593773\pi$
$757$	−34.3170	+	34.3170i	−1.24727	+	1.24727i	−0.956919	+	0.290353i	$0.906227\pi$
$758$	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	$0.979064\pi$
$762$	−5.81370	+	0.997473i	−0.210608	+	0.0361346i
$763$	0.409273	+	0.409273i	0.0148167	+	0.0148167i
$764$	−4.58453			−0.165863
$765$	47.3921	−	18.5493i	1.71347	−	0.670653i
$766$	35.0113			1.26501
$767$	−19.8670	−	19.8670i	−0.717356	−	0.717356i
$768$	−1.70711	+	0.292893i	−0.0615999	+	0.0105689i
$769$		−	1.52093i		−	0.0548462i	−0.999624	−	0.0274231i	$-0.991270\pi$
$769$		−	1.52093i		−	0.0548462i	0.999624	−	0.0274231i	$-0.00873015\pi$
$770$	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	$-0.677178\pi$
$773$	8.91707	−	8.91707i	0.320725	−	0.320725i	0.849045	+	0.528320i	$0.177178\pi$
$774$	−4.95037	−	14.0018i	−0.177938	−	0.503283i
$775$	−0.332104	−	4.98896i	−0.0119295	−	0.179209i
$776$			2.11612i			0.0759643i
$777$	1.56980	+	9.14949i	0.0563164	+	0.328236i
$778$	23.3655	+	23.3655i	0.837693	+	0.837693i
$779$	−12.2293			−0.438161
$780$	1.92982	+	9.36827i	0.0690986	+	0.335438i
$781$	13.5466			0.484734
$782$	36.0680	+	36.0680i	1.28979	+	1.28979i
$783$	−24.9829	+	13.9664i	−0.892814	+	0.499117i
$784$		−	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	−0.0276123	−	0.999619i	$-0.508790\pi$
$787$	27.2682	−	27.2682i	0.972006	−	0.972006i	0.999619	+	0.0276123i	$0.00879037\pi$
$788$	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
$792$	3.54397	+	1.69257i	0.125929	+	0.0601429i
$793$	−21.9130	−	21.9130i	−0.778152	−	0.778152i
$794$	−8.55788			−0.303708
$795$	7.12866	+	34.6060i	0.252828	+	1.22735i
$796$	−4.67866			−0.165831
$797$	23.5030	+	23.5030i	0.832520	+	0.832520i	0.987861	−	0.155341i	$-0.0496475\pi$
$797$	23.5030	+	23.5030i	0.832520	+	0.832520i	−0.155341	+	0.987861i	$0.549648\pi$
$798$	2.41303	+	14.0641i	0.0854202	+	0.497865i
$799$			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
$807$	3.14646	−	0.539848i	0.110761	−	0.0190035i
$808$	9.52100	+	9.52100i	0.334948	+	0.334948i
$809$	29.9087			1.05154			0.525768	−	0.850628i	$-0.323778\pi$
$809$	29.9087			1.05154			0.525768	+	0.850628i	$0.323778\pi$
$810$	−15.2235	+	13.1622i	−0.534900	+	0.462474i
$811$	−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
$813$	27.1144	−	4.65209i	0.950943	−	0.163156i
$814$			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	$-0.0953411\pi$
$822$	5.07601	+	29.5851i	0.177046	+	1.03190i
$823$	−19.2227	−	19.2227i	−0.670061	−	0.670061i	0.287669	−	0.957730i	$-0.407120\pi$
$823$	−19.2227	−	19.2227i	−0.670061	−	0.670061i	−0.957730	+	0.287669i	$0.907120\pi$
$824$	−14.7123			−0.512528
$825$	−11.0221	+	2.65515i	−0.383742	+	0.0924404i
$826$	21.5576			0.750085
$827$	−22.7919	−	22.7919i	−0.792552	−	0.792552i	0.189357	−	0.981908i	$-0.439360\pi$
$827$	−22.7919	−	22.7919i	−0.792552	−	0.792552i	−0.981908	+	0.189357i	$0.939360\pi$
$828$	−18.2008	−	8.69257i	−0.632522	−	0.302088i
$829$			35.3312i			1.22710i	0.789655	+	0.613551i	$0.210260\pi$
$829$			35.3312i			1.22710i	−0.789655	+	0.613551i	$0.789740\pi$
$830$	−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
$837$	−4.53553	+	2.53553i	−0.156771	+	0.0876409i
$838$	18.9645	+	18.9645i	0.655116	+	0.655116i
$839$	−9.14241			−0.315631			−0.157816	−	0.987469i	$-0.550445\pi$
$839$	−9.14241			−0.315631			−0.157816	+	0.987469i	$0.550445\pi$
$840$	−6.12975	−	4.03572i	−0.211497	−	0.139245i
$841$	1.34083			0.0462354
$842$	−13.2197	−	13.2197i	−0.455580	−	0.455580i
$843$	1.66674	+	9.71445i	0.0574054	+	0.334583i
$844$		−	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
$852$	−17.6647	+	3.03078i	−0.605181	+	0.103833i
$853$	0.613783	+	0.613783i	0.0210155	+	0.0210155i	0.717536	−	0.696521i	$-0.245270\pi$
$853$	0.613783	+	0.613783i	0.0210155	+	0.0210155i	−0.696521	+	0.717536i	$0.745270\pi$
$854$	23.7776			0.813654
$855$	−26.7211	−	11.6878i	−0.913841	−	0.399714i
$856$	11.4816			0.392433
$857$	12.3462	+	12.3462i	0.421737	+	0.421737i	0.885802	−	0.464064i	$-0.153609\pi$
$857$	12.3462	+	12.3462i	0.421737	+	0.421737i	−0.464064	+	0.885802i	$0.653609\pi$
$858$	5.51929	−	0.946961i	0.188426	−	0.0323287i
$859$		−	31.5163i		−	1.07532i	−0.843161	−	0.537662i	$-0.819308\pi$
$859$		−	31.5163i		−	1.07532i	0.843161	−	0.537662i	$-0.180692\pi$
$860$	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	$-0.687496\pi$
$863$	8.10553	−	8.10553i	0.275916	−	0.275916i	0.831476	+	0.555561i	$0.187496\pi$
$864$	−5.00000	−	1.41421i	−0.170103	−	0.0481125i
$865$	1.77259	+	53.3155i	0.0602698	+	1.81278i
$866$			13.7312i			0.466606i
$867$	−11.8790	−	69.2362i	−0.403434	−	2.35138i
$868$	−1.33991	−	1.33991i	−0.0454796	−	0.0454796i
$869$	−6.08084			−0.206278
$870$	20.8946	−	4.30419i	0.708395	−	0.145926i
$871$	−19.2972			−0.653862
$872$	−0.215984	−	0.215984i	−0.00731415	−	0.00731415i
$873$	−2.73592	+	5.72856i	−0.0925968	+	0.193882i
$874$		−	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	0.103278	−	0.994653i	$-0.467067\pi$
$877$	32.5143	−	32.5143i	1.09793	−	1.09793i	0.994653	−	0.103278i	$-0.0329332\pi$
$878$	−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	$0.723064\pi$
$882$	4.40783	−	9.22927i	0.148419	−	0.310766i
$883$	12.5798	+	12.5798i	0.423342	+	0.423342i	0.886353	−	0.463010i	$-0.153231\pi$
$883$	12.5798	+	12.5798i	0.423342	+	0.423342i	−0.463010	+	0.886353i	$0.653231\pi$
$884$	18.7365			0.630178
$885$	−24.2292	+	36.8011i	−0.814455	+	1.23706i
$886$	−33.0410			−1.11003
$887$	−17.1081	−	17.1081i	−0.574435	−	0.574435i	0.358930	−	0.933365i	$-0.383142\pi$
$887$	−17.1081	−	17.1081i	−0.574435	−	0.574435i	−0.933365	+	0.358930i	$0.883142\pi$
$888$	−0.828427	−	4.82843i	−0.0278002	−	0.162031i
$889$		−	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
$897$	−28.3455	+	4.86332i	−0.946430	+	0.162382i
$898$	18.9172	+	18.9172i	0.631277	+	0.631277i
$899$	5.50825			0.183710
$900$	13.7788	−	5.92829i	0.459293	−	0.197610i
$901$	69.2120			2.30578
$902$	−2.60382	−	2.60382i	−0.0866976	−	0.0866976i
$903$	16.0136	−	2.74751i	0.532900	−	0.0914313i
$904$			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	−0.985326	−	0.170680i	$-0.945403\pi$
$907$	−24.5342	+	24.5342i	−0.814646	+	0.814646i	0.170680	+	0.985326i	$0.445403\pi$
$908$	−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	$-0.0935362\pi$
$912$	−1.27342	−	7.42202i	−0.0421671	−	0.245768i
$913$	14.7763	+	14.7763i	0.489023	+	0.489023i
$914$	−35.5233			−1.17501
$915$	−26.7243	+	40.5910i	−0.883480	+	1.34190i
$916$	−13.4188			−0.443369
$917$	−11.8223	−	11.8223i	−0.390408	−	0.390408i
$918$	19.2363	+	34.4096i	0.634891	+	1.13569i
$919$		−	50.1999i		−	1.65594i	−0.560772	−	0.827970i	$-0.689496\pi$
$919$		−	50.1999i		−	1.65594i	0.560772	−	0.827970i	$-0.310504\pi$
$920$	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
$927$	−39.8278	−	19.0214i	−1.30812	−	0.624746i
$928$	3.89492	+	3.89492i	0.127857	+	0.127857i
$929$	−39.4235			−1.29344			−0.646721	−	0.762727i	$-0.723860\pi$
$929$	−39.4235			−1.29344			−0.646721	+	0.762727i	$0.723860\pi$
$930$	3.79334	−	0.781409i	0.124388	−	0.0256234i
$931$	14.8226			0.485790
$932$	−9.55096	−	9.55096i	−0.312852	−	0.312852i
$933$	−6.86432	−	40.0082i	−0.224728	−	1.30981i
$934$		−	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	−0.476503	−	0.879173i	$-0.658096\pi$
$937$	12.3259	−	12.3259i	0.402670	−	0.402670i	0.879173	+	0.476503i	$0.158096\pi$
$938$	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	$0.849593\pi$
$942$	27.7786	−	4.76605i	0.905075	−	0.155286i
$943$	13.3725	+	13.3725i	0.435467	+	0.435467i
$944$	−11.3765			−0.370274
$945$	−11.3761	−	18.8502i	−0.370066	−	0.613198i
$946$	6.48071			0.210706
$947$	−25.8753	−	25.8753i	−0.840833	−	0.840833i	0.148135	−	0.988967i	$-0.452673\pi$
$947$	−25.8753	−	25.8753i	−0.840833	−	0.840833i	−0.988967	+	0.148135i	$0.952673\pi$
$948$	7.92939	−	1.36047i	0.257534	−	0.0441859i
$949$			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	$-0.724994\pi$
$953$	3.42614	−	3.42614i	0.110984	−	0.110984i	0.760418	+	0.649434i	$0.224994\pi$
$954$	−25.8033	+	9.12283i	−0.835412	+	0.295363i
$955$	7.48565	+	7.00391i	0.242230	+	0.226641i
$956$			28.4935i			0.921546i
$957$	−2.11207	−	12.3100i	−0.0682734	−	0.397926i
$958$	−11.5847	−	11.5847i	−0.374284	−	0.374284i
$959$	−32.8401			−1.06046
$960$	3.23483	+	2.12975i	0.104404	+	0.0687375i
$961$	1.00000			0.0322581
$962$	−4.93933	−	4.93933i	−0.159250	−	0.159250i
$963$	31.0819	+	14.8445i	1.00160	+	0.478357i
$964$		−	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	−0.969928	−	0.243393i	$-0.921739\pi$
$967$	−22.5928	+	22.5928i	−0.726535	+	0.726535i	0.243393	+	0.969928i	$0.421739\pi$
$968$	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	$-0.184633\pi$
$972$	−11.7071	−	10.2929i	−0.375506	−	0.330145i
$973$	−13.4746	−	13.4746i	−0.431976	−	0.431976i
$974$	11.1084			0.355935
$975$	11.1611	−	18.2448i	0.357443	−	0.584301i
$976$	−12.5481			−0.401655
$977$	15.3207	+	15.3207i	0.490152	+	0.490152i	0.908354	−	0.418202i	$-0.137339\pi$
$977$	15.3207	+	15.3207i	0.490152	+	0.490152i	−0.418202	+	0.908354i	$0.637339\pi$
$978$	−0.0435250	−	0.253682i	−0.00139178	−	0.00811186i
$979$			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	$-0.615423\pi$
$983$	18.1926	−	18.1926i	0.580255	−	0.580255i	0.934973	+	0.354718i	$0.115423\pi$
$984$	3.97792	+	2.81281i	0.126811	+	0.0896692i
$985$	−33.5321	+	1.11485i	−1.06842	+	0.0355220i
$986$		−	41.7893i		−	1.33084i
$987$	16.7797	−	2.87894i	0.534103	−	0.0916376i
$988$	−7.59250	−	7.59250i	−0.241550	−	0.241550i
$989$	−33.2831			−1.05834
$990$	−3.20082	−	8.17785i	−0.101729	−	0.259909i
$991$	−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
$993$	−6.91054	+	1.18566i	−0.219299	+	0.0376258i
$994$		−	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	−0.707237	−	0.706976i	$-0.750059\pi$
$997$	−0.00824048	+	0.00824048i	−0.000260979	+	0.000260979i	0.706976	+	0.707237i	$0.250059\pi$
$998$	−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.c.683.2	yes	8
3.2	odd	2		930.2.j.f.683.3	yes	8
5.2	odd	4		930.2.j.f.497.3	yes	8
15.2	even	4	inner	930.2.j.c.497.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.2	✓	8	15.2	even	4	inner
930.2.j.c.683.2	yes	8	1.1	even	1	trivial
930.2.j.f.497.3	yes	8	5.2	odd	4
930.2.j.f.683.3	yes	8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(1.52773 - 1.63280i) q^{5} +(1.41421 + 1.00000i) q^{6} +(-1.33991 + 1.33991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) 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} +(-0.292893 - 1.70711i) q^{12} +(-1.74632 - 1.74632i) q^{13} +1.89492 q^{14} +(-2.12975 + 3.23483i) q^{15} -1.00000 q^{16} +(5.36459 + 5.36459i) q^{17} +(-2.70711 - 1.29289i) 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} +(-4.53553 + 2.53553i) q^{27} +(-1.33991 - 1.33991i) q^{28} +5.50825 q^{29} +(3.79334 - 0.781409i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.383437 - 2.23483i) 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} +(-3.23483 + 0.555010i) q^{42} +(3.50044 + 3.50044i) q^{43} -1.30913 q^{44} +(2.68826 - 6.14600i) q^{45} +6.72335 q^{46} +(3.66790 + 3.66790i) q^{47} +(1.70711 - 0.292893i) 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} +(1.27342 + 7.42202i) q^{57} +(-3.89492 - 3.89492i) q^{58} +11.3765 q^{59} +(-3.23483 - 2.12975i) q^{60} +12.5481 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-2.44993 + 5.12975i) 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} +(1.29289 - 2.70711i) q^{72} +(-1.87025 - 1.87025i) q^{73} +2.82843 q^{74} +(2.02817 + 8.41941i) q^{75} +4.34772 q^{76} +(-1.75413 - 1.75413i) q^{77} +(-0.723349 - 4.21598i) 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} +(-9.40317 + 1.61333i) q^{87} +(0.925698 + 0.925698i) q^{88} +7.16053 q^{89} +(-6.24676 + 2.44499i) q^{90} +4.67982 q^{91} +(-4.75413 - 4.75413i) q^{92} +(-1.70711 + 0.292893i) 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	\( 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) \) 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^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * 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 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * 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 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * 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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