LMFDB - Embedded newform 930.2.n.d.721.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.2
Root			$-0.479361 - 0.348276i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.d.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.775623 + 0.563523i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.775623 + 0.563523i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-2.21249 - 1.60747i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-1.28425 - 3.95250i) q^{13} +(0.775623 - 0.563523i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.90079 + 1.38100i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-0.657125 + 2.02242i) q^{19} +(0.809017 + 0.587785i) q^{20} +(0.296261 - 0.911799i) q^{21} +(-2.21249 + 1.60747i) q^{22} +(-5.05256 + 3.67090i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -4.15591 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.296261 - 0.911799i) q^{28} +(-1.74635 + 5.37471i) q^{29} +1.00000 q^{30} +(-0.480387 - 5.54700i) q^{31} +1.00000 q^{32} +(-0.845097 + 2.60094i) q^{33} +(0.726037 + 2.23451i) q^{34} +(-0.775623 - 0.563523i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(1.72038 + 1.24993i) q^{38} +(-3.36220 + 2.44278i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.07885 + 3.32035i) q^{41} +(-0.775623 - 0.563523i) q^{42} +(-2.42808 + 7.47285i) q^{43} +(0.845097 + 2.60094i) q^{44} +(0.809017 - 0.587785i) q^{45} +(1.92991 + 5.93964i) q^{46} +(-2.41182 - 7.42283i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.87909 - 5.78323i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.90079 + 1.38100i) q^{51} +(-1.28425 + 3.95250i) q^{52} +(-1.50532 + 1.09368i) q^{53} +(0.809017 - 0.587785i) q^{54} +(2.21249 + 1.60747i) q^{55} -0.958722 q^{56} +2.12650 q^{57} +(4.57201 + 3.32176i) q^{58} +(2.11135 + 6.49806i) q^{59} +(0.309017 - 0.951057i) q^{60} +8.57645 q^{61} +(-5.42396 - 1.25724i) q^{62} -0.958722 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.28425 + 3.95250i) q^{65} +(2.21249 + 1.60747i) q^{66} +8.28809 q^{67} +2.34951 q^{68} +(5.05256 + 3.67090i) q^{69} +(-0.775623 + 0.563523i) q^{70} +(2.58230 - 1.87615i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-1.40520 - 1.02094i) q^{73} +(-2.11803 + 6.51864i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(1.72038 - 1.24993i) q^{76} +(-0.810213 - 2.49358i) q^{77} +(1.28425 + 3.95250i) q^{78} +(-4.56982 + 3.32017i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.82446 + 2.05209i) q^{82} +(-2.73614 + 8.42098i) q^{83} +(-0.775623 + 0.563523i) q^{84} +(1.90079 - 1.38100i) q^{85} +(6.35679 + 4.61848i) q^{86} +5.65131 q^{87} +2.73479 q^{88} +(-7.57763 - 5.50547i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(1.23123 - 3.78935i) q^{91} +6.24531 q^{92} +(-5.12706 + 2.17099i) q^{93} -7.80482 q^{94} +(0.657125 - 2.02242i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-12.9129 - 9.38180i) q^{97} -6.08085 q^{98} +2.73479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	0.775623	+	0.563523i	0.293158	+	0.212992i	0.724636	−	0.689132i	$-0.242008\pi$
$7$	0.775623	+	0.563523i	0.293158	+	0.212992i	−0.431478	+	0.902123i	$0.642008\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.309017	+	0.951057i	−0.0977198	+	0.300750i
$11$	−2.21249	−	1.60747i	−0.667092	−	0.484670i	0.201959	−	0.979394i	$-0.435269\pi$
$11$	−2.21249	−	1.60747i	−0.667092	−	0.484670i	−0.869050	+	0.494724i	$0.835269\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	−1.28425	−	3.95250i	−0.356186	−	1.09623i	−0.955319	−	0.295577i	$-0.904488\pi$
$13$	−1.28425	−	3.95250i	−0.356186	−	1.09623i	0.599133	−	0.800649i	$-0.295512\pi$
$14$	0.775623	−	0.563523i	0.207294	−	0.150608i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.90079	+	1.38100i	−0.461009	+	0.334943i	−0.793927	−	0.608013i	$-0.791967\pi$
$17$	−1.90079	+	1.38100i	−0.461009	+	0.334943i	0.332918	+	0.942956i	$0.391967\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	−0.657125	+	2.02242i	−0.150755	+	0.463976i	−0.997706	−	0.0676949i	$-0.978436\pi$
$19$	−0.657125	+	2.02242i	−0.150755	+	0.463976i	0.846951	+	0.531671i	$0.178436\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	0.296261	−	0.911799i	0.0646496	−	0.198971i
$22$	−2.21249	+	1.60747i	−0.471705	+	0.342714i
$23$	−5.05256	+	3.67090i	−1.05353	+	0.765436i	−0.972881	−	0.231306i	$-0.925700\pi$
$23$	−5.05256	+	3.67090i	−1.05353	+	0.765436i	−0.0806513	+	0.996742i	$0.525700\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	−4.15591			−0.815040
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.296261	−	0.911799i	−0.0559882	−	0.172314i
$29$	−1.74635	+	5.37471i	−0.324289	+	0.998059i	0.647471	+	0.762090i	$0.275827\pi$
$29$	−1.74635	+	5.37471i	−0.324289	+	0.998059i	−0.971760	+	0.235970i	$0.924173\pi$
$30$	1.00000			0.182574
$31$	−0.480387	−	5.54700i	−0.0862801	−	0.996271i
$31$	−0.480387	−	5.54700i	−0.0862801	−	0.996271i
$32$	1.00000			0.176777
$33$	−0.845097	+	2.60094i	−0.147113	+	0.452766i
$34$	0.726037	+	2.23451i	0.124514	+	0.383216i
$35$	−0.775623	−	0.563523i	−0.131104	−	0.0952527i
$36$	1.00000			0.166667
$37$	−6.85410			−1.12681			−0.563404	−	0.826182i	$-0.690508\pi$
$37$	−6.85410			−1.12681			−0.563404	+	0.826182i	$0.690508\pi$
$38$	1.72038	+	1.24993i	0.279082	+	0.202765i
$39$	−3.36220	+	2.44278i	−0.538383	+	0.391158i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−1.07885	+	3.32035i	−0.168488	+	0.518552i	−0.999276	−	0.0380363i	$-0.987890\pi$
$41$	−1.07885	+	3.32035i	−0.168488	+	0.518552i	0.830789	+	0.556588i	$0.187890\pi$
$42$	−0.775623	−	0.563523i	−0.119681	−	0.0869535i
$43$	−2.42808	+	7.47285i	−0.370278	+	1.13960i	0.576331	+	0.817216i	$0.304484\pi$
$43$	−2.42808	+	7.47285i	−0.370278	+	1.13960i	−0.946609	+	0.322383i	$0.895516\pi$
$44$	0.845097	+	2.60094i	0.127403	+	0.392107i
$45$	0.809017	−	0.587785i	0.120601	−	0.0876219i
$46$	1.92991	+	5.93964i	0.284549	+	0.875753i
$47$	−2.41182	−	7.42283i	−0.351800	−	1.08273i	−0.957841	−	0.287297i	$-0.907243\pi$
$47$	−2.41182	−	7.42283i	−0.351800	−	1.08273i	0.606041	−	0.795433i	$-0.292757\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−1.87909	−	5.78323i	−0.268441	−	0.826176i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	1.90079	+	1.38100i	0.266164	+	0.193379i
$52$	−1.28425	+	3.95250i	−0.178093	+	0.548113i
$53$	−1.50532	+	1.09368i	−0.206771	+	0.150228i	−0.686352	−	0.727270i	$-0.740789\pi$
$53$	−1.50532	+	1.09368i	−0.206771	+	0.150228i	0.479580	+	0.877498i	$0.340789\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	2.21249	+	1.60747i	0.298332	+	0.216751i
$56$	−0.958722			−0.128115
$57$	2.12650			0.281662
$58$	4.57201	+	3.32176i	0.600334	+	0.436168i
$59$	2.11135	+	6.49806i	0.274874	+	0.845975i	0.989253	+	0.146216i	$0.0467094\pi$
$59$	2.11135	+	6.49806i	0.274874	+	0.845975i	−0.714379	+	0.699759i	$0.753291\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	8.57645			1.09810			0.549051	−	0.835789i	$-0.314989\pi$
$61$	8.57645			1.09810			0.549051	+	0.835789i	$0.314989\pi$
$62$	−5.42396	−	1.25724i	−0.688844	−	0.159670i
$63$	−0.958722			−0.120788
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.28425	+	3.95250i	0.159291	+	0.490247i
$66$	2.21249	+	1.60747i	0.272339	+	0.197866i
$67$	8.28809			1.01255			0.506276	−	0.862372i	$-0.331022\pi$
$67$	8.28809			1.01255			0.506276	+	0.862372i	$0.331022\pi$
$68$	2.34951			0.284919
$69$	5.05256	+	3.67090i	0.608257	+	0.441925i
$70$	−0.775623	+	0.563523i	−0.0927046	+	0.0673539i
$71$	2.58230	−	1.87615i	0.306462	−	0.222658i	−0.423915	−	0.905702i	$-0.639344\pi$
$71$	2.58230	−	1.87615i	0.306462	−	0.222658i	0.730377	+	0.683044i	$0.239344\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	−1.40520	−	1.02094i	−0.164466	−	0.119492i	0.502508	−	0.864573i	$-0.332411\pi$
$73$	−1.40520	−	1.02094i	−0.164466	−	0.119492i	−0.666974	+	0.745081i	$0.732411\pi$
$74$	−2.11803	+	6.51864i	−0.246216	+	0.757776i
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	1.72038	−	1.24993i	0.197341	−	0.143376i
$77$	−0.810213	−	2.49358i	−0.0923324	−	0.284170i
$78$	1.28425	+	3.95250i	0.145412	+	0.447533i
$79$	−4.56982	+	3.32017i	−0.514145	+	0.373548i	−0.814394	−	0.580313i	$-0.802930\pi$
$79$	−4.56982	+	3.32017i	−0.514145	+	0.373548i	0.300249	+	0.953861i	$0.402930\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.82446	+	2.05209i	0.311909	+	0.226615i
$83$	−2.73614	+	8.42098i	−0.300331	+	0.924323i	0.681048	+	0.732239i	$0.261525\pi$
$83$	−2.73614	+	8.42098i	−0.300331	+	0.924323i	−0.981379	+	0.192084i	$0.938475\pi$
$84$	−0.775623	+	0.563523i	−0.0846274	+	0.0614854i
$85$	1.90079	−	1.38100i	0.206170	−	0.149791i
$86$	6.35679	+	4.61848i	0.685470	+	0.498023i
$87$	5.65131			0.605884
$88$	2.73479			0.291530
$89$	−7.57763	−	5.50547i	−0.803227	−	0.583578i	0.108632	−	0.994082i	$-0.465353\pi$
$89$	−7.57763	−	5.50547i	−0.803227	−	0.583578i	−0.911859	+	0.410504i	$0.865353\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	1.23123	−	3.78935i	0.129068	−	0.397232i
$92$	6.24531			0.651119
$93$	−5.12706	+	2.17099i	−0.531652	+	0.225121i
$94$	−7.80482			−0.805006
$95$	0.657125	−	2.02242i	0.0674196	−	0.207496i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−12.9129	−	9.38180i	−1.31111	−	0.952578i	−0.999998	−	0.00220519i	$-0.999298\pi$
$97$	−12.9129	−	9.38180i	−1.31111	−	0.952578i	−0.311114	−	0.950373i	$-0.600702\pi$
$98$	−6.08085			−0.614259
$99$	2.73479			0.274857
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−2.77615	+	2.01699i	−0.276237	+	0.200698i	−0.717275	−	0.696791i	$-0.754611\pi$
$101$	−2.77615	+	2.01699i	−0.276237	+	0.200698i	0.441037	+	0.897489i	$0.354611\pi$
$102$	1.90079	−	1.38100i	0.188206	−	0.136740i
$103$	5.06570	−	15.5906i	0.499138	−	1.53619i	−0.311268	−	0.950322i	$-0.600754\pi$
$103$	5.06570	−	15.5906i	0.499138	−	1.53619i	0.810407	−	0.585868i	$-0.199246\pi$
$104$	3.36220	+	2.44278i	0.329691	+	0.239534i
$105$	−0.296261	+	0.911799i	−0.0289122	+	0.0889825i
$106$	0.574981	+	1.76961i	0.0558471	+	0.171880i
$107$	3.81292	−	2.77025i	0.368609	−	0.267810i	−0.388025	−	0.921649i	$-0.626843\pi$
$107$	3.81292	−	2.77025i	0.368609	−	0.267810i	0.756634	+	0.653839i	$0.226843\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	1.52978	+	4.70816i	0.146526	+	0.450960i	0.997204	−	0.0747265i	$-0.0238084\pi$
$109$	1.52978	+	4.70816i	0.146526	+	0.450960i	−0.850678	+	0.525687i	$0.823808\pi$
$110$	2.21249	−	1.60747i	0.210953	−	0.153266i
$111$	2.11803	+	6.51864i	0.201035	+	0.618722i
$112$	−0.296261	+	0.911799i	−0.0279941	+	0.0861569i
$113$	−7.77068	−	5.64573i	−0.731004	−	0.531105i	0.158877	−	0.987298i	$-0.449213\pi$
$113$	−7.77068	−	5.64573i	−0.731004	−	0.531105i	−0.889881	+	0.456193i	$0.849213\pi$
$114$	0.657125	−	2.02242i	0.0615454	−	0.189417i
$115$	5.05256	−	3.67090i	0.471154	−	0.342313i
$116$	4.57201	−	3.32176i	0.424500	−	0.308417i
$117$	3.36220	+	2.44278i	0.310835	+	0.225835i
$118$	6.83246			0.628979
$119$	−2.25252			−0.206489
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−1.08802	−	3.34859i	−0.0989111	−	0.304417i
$122$	2.65027	−	8.15669i	0.239944	−	0.738472i
$123$	3.49122			0.314793
$124$	−2.87180	+	4.76998i	−0.257896	+	0.428357i
$125$	−1.00000			−0.0894427
$126$	−0.296261	+	0.911799i	−0.0263931	+	0.0812295i
$127$	−5.50749	−	16.9503i	−0.488711	−	1.50410i	−0.826533	−	0.562888i	$-0.809690\pi$
$127$	−5.50749	−	16.9503i	−0.488711	−	1.50410i	0.337822	−	0.941210i	$-0.390310\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	7.85742			0.691807
$130$	4.15591			0.364497
$131$	−13.2592	−	9.63337i	−1.15846	−	0.841672i	−0.168879	−	0.985637i	$-0.554015\pi$
$131$	−13.2592	−	9.63337i	−1.15846	−	0.841672i	−0.989583	+	0.143965i	$0.954015\pi$
$132$	2.21249	−	1.60747i	0.192573	−	0.139912i
$133$	−1.64936	+	1.19833i	−0.143018	+	0.103909i
$134$	2.56116	−	7.88244i	0.221251	−	0.680939i
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$	0.726037	−	2.23451i	0.0622572	−	0.191608i
$137$	−5.62385	−	17.3084i	−0.480478	−	1.47876i	−0.838425	−	0.545018i	$-0.816523\pi$
$137$	−5.62385	−	17.3084i	−0.480478	−	1.47876i	0.357947	−	0.933742i	$-0.383477\pi$
$138$	5.05256	−	3.67090i	0.430103	−	0.312488i
$139$	6.11561	+	18.8219i	0.518719	+	1.59645i	0.776411	+	0.630227i	$0.217038\pi$
$139$	6.11561	+	18.8219i	0.518719	+	1.59645i	−0.257692	+	0.966227i	$0.582962\pi$
$140$	0.296261	+	0.911799i	0.0250387	+	0.0770611i
$141$	−6.31423	+	4.58756i	−0.531754	+	0.386342i
$142$	−0.986350	−	3.03567i	−0.0827727	−	0.254748i
$143$	−3.51214	+	10.8093i	−0.293700	+	0.903916i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	1.74635	−	5.37471i	0.145027	−	0.446346i
$146$	−1.40520	+	1.02094i	−0.116295	+	0.0844933i
$147$	−4.91951	+	3.57423i	−0.405755	+	0.294798i
$148$	5.54508	+	4.02874i	0.455803	+	0.331160i
$149$	−5.72968			−0.469394			−0.234697	−	0.972069i	$-0.575410\pi$
$149$	−5.72968			−0.469394			−0.234697	+	0.972069i	$0.575410\pi$
$150$	−1.00000			−0.0816497
$151$	12.6414	+	9.18453i	1.02874	+	0.747426i	0.968057	−	0.250731i	$-0.0806708\pi$
$151$	12.6414	+	9.18453i	1.02874	+	0.747426i	0.0606872	+	0.998157i	$0.480671\pi$
$152$	−0.657125	−	2.02242i	−0.0532999	−	0.164040i
$153$	0.726037	−	2.23451i	0.0586966	−	0.180650i
$154$	−2.62191			−0.211279
$155$	0.480387	+	5.54700i	0.0385856	+	0.445546i
$156$	4.15591			0.332739
$157$	5.64572	−	17.3757i	0.450577	−	1.38673i	−0.425672	−	0.904877i	$-0.639962\pi$
$157$	5.64572	−	17.3757i	0.450577	−	1.38673i	0.876250	−	0.481857i	$-0.160038\pi$
$158$	1.74552	+	5.37214i	0.138866	+	0.427385i
$159$	1.50532	+	1.09368i	0.119380	+	0.0867343i
$160$	−1.00000			−0.0790569
$161$	−5.98752			−0.471883
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	5.31217	−	3.85952i	0.416081	−	0.302301i	−0.359978	−	0.932961i	$-0.617216\pi$
$163$	5.31217	−	3.85952i	0.416081	−	0.302301i	0.776059	+	0.630660i	$0.217216\pi$
$164$	2.82446	−	2.05209i	0.220553	−	0.160241i
$165$	0.845097	−	2.60094i	0.0657907	−	0.202483i
$166$	7.16332	+	5.20445i	0.555981	+	0.403944i
$167$	−2.83336	+	8.72018i	−0.219252	+	0.674788i	0.779573	+	0.626312i	$0.215436\pi$
$167$	−2.83336	+	8.72018i	−0.219252	+	0.674788i	−0.998824	+	0.0484757i	$0.984564\pi$
$168$	0.296261	+	0.911799i	0.0228571	+	0.0703468i
$169$	−3.45576	+	2.51075i	−0.265827	+	0.193135i
$170$	−0.726037	−	2.23451i	−0.0556845	−	0.171379i
$171$	−0.657125	−	2.02242i	−0.0502516	−	0.154659i
$172$	6.35679	−	4.61848i	0.484701	−	0.352156i
$173$	−0.367551	−	1.13120i	−0.0279444	−	0.0860039i	0.936112	−	0.351703i	$-0.114397\pi$
$173$	−0.367551	−	1.13120i	−0.0279444	−	0.0860039i	−0.964056	+	0.265699i	$0.914397\pi$
$174$	1.74635	−	5.37471i	0.132391	−	0.407456i
$175$	0.775623	+	0.563523i	0.0586316	+	0.0425983i
$176$	0.845097	−	2.60094i	0.0637016	−	0.196053i
$177$	5.52758	−	4.01602i	0.415478	−	0.301863i
$178$	−7.57763	+	5.50547i	−0.567967	+	0.412652i
$179$	−2.93035	−	2.12903i	−0.219025	−	0.159131i	0.472863	−	0.881136i	$-0.343221\pi$
$179$	−2.93035	−	2.12903i	−0.219025	−	0.159131i	−0.691888	+	0.722005i	$0.743221\pi$
$180$	−1.00000			−0.0745356
$181$	9.88614			0.734831			0.367416	−	0.930057i	$-0.380243\pi$
$181$	9.88614			0.734831			0.367416	+	0.930057i	$0.380243\pi$
$182$	−3.22341	−	2.34195i	−0.238935	−	0.173597i
$183$	−2.65027	−	8.15669i	−0.195913	−	0.602960i
$184$	1.92991	−	5.93964i	0.142275	−	0.437876i
$185$	6.85410			0.503924
$186$	0.480387	+	5.54700i	0.0352237	+	0.406726i
$187$	6.42541			0.469872
$188$	−2.41182	+	7.42283i	−0.175900	+	0.541365i
$189$	0.296261	+	0.911799i	0.0215499	+	0.0663236i
$190$	−1.72038	−	1.24993i	−0.124809	−	0.0906792i
$191$	−7.36976			−0.533257			−0.266629	−	0.963799i	$-0.585910\pi$
$191$	−7.36976			−0.533257			−0.266629	+	0.963799i	$0.585910\pi$
$192$	−1.00000			−0.0721688
$193$	−21.6670	−	15.7420i	−1.55962	−	1.13313i	−0.936317	−	0.351156i	$-0.885789\pi$
$193$	−21.6670	−	15.7420i	−1.55962	−	1.13313i	−0.623307	−	0.781977i	$-0.714211\pi$
$194$	−12.9129	+	9.38180i	−0.927096	+	0.673574i
$195$	3.36220	−	2.44278i	0.240772	−	0.174931i
$196$	−1.87909	+	5.78323i	−0.134220	+	0.413088i
$197$	−2.32609	−	1.69000i	−0.165727	−	0.120408i	0.501830	−	0.864966i	$-0.332660\pi$
$197$	−2.32609	−	1.69000i	−0.165727	−	0.120408i	−0.667557	+	0.744558i	$0.732660\pi$
$198$	0.845097	−	2.60094i	0.0600584	−	0.184841i
$199$	4.28910	+	13.2005i	0.304047	+	0.935759i	0.980031	+	0.198843i	$0.0637185\pi$
$199$	4.28910	+	13.2005i	0.304047	+	0.935759i	−0.675985	+	0.736916i	$0.736281\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−2.56116	−	7.88244i	−0.180650	−	0.555985i
$202$	1.06039	+	3.26356i	0.0746091	+	0.229623i
$203$	−4.38328	+	3.18464i	−0.307646	+	0.223518i
$204$	−0.726037	−	2.23451i	−0.0508328	−	0.156447i
$205$	1.07885	−	3.32035i	0.0753499	−	0.231903i
$206$	−13.2622	−	9.63554i	−0.924020	−	0.671340i
$207$	1.92991	−	5.93964i	0.134138	−	0.412834i
$208$	3.36220	−	2.44278i	0.233127	−	0.169376i
$209$	4.70487	−	3.41829i	0.325443	−	0.236448i
$210$	0.775623	+	0.563523i	0.0535230	+	0.0388868i
$211$	3.51431			0.241935			0.120967	−	0.992656i	$-0.461400\pi$
$211$	3.51431			0.241935			0.120967	+	0.992656i	$0.461400\pi$
$212$	1.86068			0.127792
$213$	−2.58230	−	1.87615i	−0.176936	−	0.128552i
$214$	−1.45640	−	4.48235i	−0.0995578	−	0.306407i
$215$	2.42808	−	7.47285i	0.165593	−	0.509644i
$216$	−1.00000			−0.0680414
$217$	2.75326	−	4.57309i	0.186904	−	0.310442i
$218$	4.95046			0.335287
$219$	−0.536738	+	1.65191i	−0.0362694	+	0.111626i
$220$	−0.845097	−	2.60094i	−0.0569764	−	0.175355i
$221$	7.89950	+	5.73933i	0.531378	+	0.386069i
$222$	6.85410			0.460017
$223$	−17.2311			−1.15388			−0.576939	−	0.816787i	$-0.695753\pi$
$223$	−17.2311			−1.15388			−0.576939	+	0.816787i	$0.695753\pi$
$224$	0.775623	+	0.563523i	0.0518235	+	0.0376520i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−7.77068	+	5.64573i	−0.516898	+	0.375548i
$227$	−3.48150	+	10.7150i	−0.231075	+	0.711177i	0.766543	+	0.642194i	$0.221975\pi$
$227$	−3.48150	+	10.7150i	−0.231075	+	0.711177i	−0.997618	+	0.0689831i	$0.978025\pi$
$228$	−1.72038	−	1.24993i	−0.113935	−	0.0827784i
$229$	−0.940847	+	2.89563i	−0.0621729	+	0.191349i	−0.977318	−	0.211775i	$-0.932076\pi$
$229$	−0.940847	+	2.89563i	−0.0621729	+	0.191349i	0.915146	+	0.403124i	$0.132076\pi$
$230$	−1.92991	−	5.93964i	−0.127254	−	0.391649i
$231$	−2.12117	+	1.54112i	−0.139562	+	0.101398i
$232$	−1.74635	−	5.37471i	−0.114654	−	0.352867i
$233$	−4.56991	−	14.0648i	−0.299385	−	0.921412i	−0.981713	−	0.190366i	$-0.939032\pi$
$233$	−4.56991	−	14.0648i	−0.299385	−	0.921412i	0.682328	−	0.731046i	$-0.260968\pi$
$234$	3.36220	−	2.44278i	0.219794	−	0.159690i
$235$	2.41182	+	7.42283i	0.157330	+	0.484212i
$236$	2.11135	−	6.49806i	0.137437	−	0.422988i
$237$	4.56982	+	3.32017i	0.296842	+	0.215668i
$238$	−0.696068	+	2.14228i	−0.0451194	+	0.138863i
$239$	−5.02138	+	3.64824i	−0.324806	+	0.235985i	−0.738223	−	0.674556i	$-0.764335\pi$
$239$	−5.02138	+	3.64824i	−0.324806	+	0.235985i	0.413418	+	0.910542i	$0.364335\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	12.4276	+	9.02920i	0.800534	+	0.581622i	0.911071	−	0.412250i	$-0.135257\pi$
$241$	12.4276	+	9.02920i	0.800534	+	0.581622i	−0.110537	+	0.993872i	$0.535257\pi$
$242$	−3.52091			−0.226333
$243$	−1.00000			−0.0641500
$244$	−6.93849	−	5.04111i	−0.444191	−	0.322724i
$245$	1.87909	+	5.78323i	0.120050	+	0.369477i
$246$	1.07885	−	3.32035i	0.0687848	−	0.211698i
$247$	8.83754			0.562319
$248$	3.64909	+	4.20525i	0.231717	+	0.267034i
$249$	8.85434			0.561121
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−5.95736	−	18.3349i	−0.376026	−	1.15729i	−0.942784	−	0.333404i	$-0.891803\pi$
$251$	−5.95736	−	18.3349i	−0.376026	−	1.15729i	0.566759	−	0.823884i	$-0.308197\pi$
$252$	0.775623	+	0.563523i	0.0488596	+	0.0354986i
$253$	17.0796			1.07379
$254$	−17.8226			−1.11829
$255$	−1.90079	−	1.38100i	−0.119032	−	0.0864819i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	18.6851	−	13.5755i	1.16554	−	0.846817i	0.175075	−	0.984555i	$-0.443983\pi$
$257$	18.6851	−	13.5755i	1.16554	−	0.846817i	0.990469	+	0.137739i	$0.0439834\pi$
$258$	2.42808	−	7.47285i	0.151165	−	0.465239i
$259$	−5.31620	−	3.86244i	−0.330332	−	0.240001i
$260$	1.28425	−	3.95250i	0.0796455	−	0.245124i
$261$	−1.74635	−	5.37471i	−0.108096	−	0.332686i
$262$	−13.2592	+	9.63337i	−0.819156	+	0.595152i
$263$	1.77697	+	5.46895i	0.109573	+	0.337230i	0.990776	−	0.135507i	$-0.0432662\pi$
$263$	1.77697	+	5.46895i	0.109573	+	0.337230i	−0.881204	+	0.472737i	$0.843266\pi$
$264$	−0.845097	−	2.60094i	−0.0520121	−	0.160077i
$265$	1.50532	−	1.09368i	0.0924710	−	0.0671841i
$266$	0.630001	+	1.93894i	0.0386278	+	0.118884i
$267$	−2.89440	+	8.90804i	−0.177134	+	0.545163i
$268$	−6.70520	−	4.87162i	−0.409586	−	0.297581i
$269$	3.88325	−	11.9514i	0.236766	−	0.728691i	−0.760116	−	0.649787i	$-0.774858\pi$
$269$	3.88325	−	11.9514i	0.236766	−	0.728691i	0.996882	−	0.0789037i	$-0.0251420\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	14.1964	−	10.3143i	0.862368	−	0.626547i	−0.0661602	−	0.997809i	$-0.521075\pi$
$271$	14.1964	−	10.3143i	0.862368	−	0.626547i	0.928528	+	0.371262i	$0.121075\pi$
$272$	−1.90079	−	1.38100i	−0.115252	−	0.0837357i
$273$	−3.98436			−0.241144
$274$	−18.1992			−1.09945
$275$	−2.21249	−	1.60747i	−0.133418	−	0.0969341i
$276$	−1.92991	−	5.93964i	−0.116167	−	0.357525i
$277$	4.25934	−	13.1089i	0.255919	−	0.787638i	−0.737728	−	0.675098i	$-0.764101\pi$
$277$	4.25934	−	13.1089i	0.255919	−	0.787638i	0.993647	−	0.112540i	$-0.0358986\pi$
$278$	19.7905			1.18696
$279$	3.64909	+	4.20525i	0.218465	+	0.251762i
$280$	0.958722			0.0572946
$281$	1.92991	−	5.93966i	0.115129	−	0.354331i	−0.876845	−	0.480773i	$-0.840356\pi$
$281$	1.92991	−	5.93966i	0.115129	−	0.354331i	0.991974	+	0.126443i	$0.0403560\pi$
$282$	2.41182	+	7.42283i	0.143622	+	0.442023i
$283$	17.2411	+	12.5264i	1.02488	+	0.744619i	0.967278	−	0.253721i	$-0.0816544\pi$
$283$	17.2411	+	12.5264i	1.02488	+	0.744619i	0.0576024	+	0.998340i	$0.481654\pi$
$284$	−3.19190			−0.189404
$285$	−2.12650			−0.125963
$286$	9.19491	+	6.68049i	0.543707	+	0.395026i
$287$	−2.70787	+	1.96738i	−0.159841	+	0.116131i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−3.54746	+	10.9180i	−0.208674	+	0.642233i
$290$	−4.57201	−	3.32176i	−0.268477	−	0.195060i
$291$	−4.93231	+	15.1801i	−0.289137	+	0.889872i
$292$	0.536738	+	1.65191i	0.0314102	+	0.0966707i
$293$	1.17626	−	0.854606i	0.0687181	−	0.0499266i	−0.552896	−	0.833250i	$-0.686477\pi$
$293$	1.17626	−	0.854606i	0.0687181	−	0.0499266i	0.621614	+	0.783324i	$0.286477\pi$
$294$	1.87909	+	5.78323i	0.109591	+	0.337285i
$295$	−2.11135	−	6.49806i	−0.122927	−	0.378332i
$296$	5.54508	−	4.02874i	0.322302	−	0.234166i
$297$	−0.845097	−	2.60094i	−0.0490375	−	0.150922i
$298$	−1.77057	+	5.44925i	−0.102566	+	0.315667i
$299$	20.9980	+	15.2559i	1.21434	+	0.882273i
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$	−6.09439	+	4.42784i	−0.351275	+	0.255216i
$302$	12.6414	−	9.18453i	0.727432	−	0.528510i
$303$	2.77615	+	2.01699i	0.159486	+	0.115873i
$304$	−2.12650			−0.121963
$305$	−8.57645			−0.491086
$306$	−1.90079	−	1.38100i	−0.108661	−	0.0789468i
$307$	1.85086	+	5.69635i	0.105634	+	0.325108i	0.989879	−	0.141916i	$-0.0453262\pi$
$307$	1.85086	+	5.69635i	0.105634	+	0.325108i	−0.884245	+	0.467024i	$0.845326\pi$
$308$	−0.810213	+	2.49358i	−0.0461662	+	0.142085i
$309$	−16.3930			−0.932562
$310$	5.42396	+	1.25724i	0.308060	+	0.0714066i
$311$	11.0106			0.624353			0.312177	−	0.950024i	$-0.398942\pi$
$311$	11.0106			0.624353			0.312177	+	0.950024i	$0.398942\pi$
$312$	1.28425	−	3.95250i	0.0727061	−	0.223766i
$313$	3.34025	+	10.2802i	0.188802	+	0.581073i	0.999993	−	0.00370805i	$-0.00118031\pi$
$313$	3.34025	+	10.2802i	0.188802	+	0.581073i	−0.811191	+	0.584781i	$0.801180\pi$
$314$	−14.7807	−	10.7388i	−0.834122	−	0.606025i
$315$	0.958722			0.0540179
$316$	5.64861			0.317759
$317$	−5.89819	−	4.28529i	−0.331276	−	0.240686i	0.409696	−	0.912222i	$-0.365635\pi$
$317$	−5.89819	−	4.28529i	−0.331276	−	0.240686i	−0.740972	+	0.671536i	$0.765635\pi$
$318$	1.50532	−	1.09368i	0.0844141	−	0.0613304i
$319$	12.5035	−	9.08431i	0.700061	−	0.508624i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	−3.81292	−	2.77025i	−0.212816	−	0.154620i
$322$	−1.85025	+	5.69447i	−0.103110	+	0.317340i
$323$	−1.54392	−	4.75170i	−0.0859060	−	0.264391i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−1.28425	−	3.95250i	−0.0712371	−	0.219245i
$326$	−2.02907	−	6.24483i	−0.112380	−	0.345869i
$327$	4.00500	−	2.90981i	0.221477	−	0.160913i
$328$	−1.07885	−	3.32035i	−0.0595694	−	0.183336i
$329$	2.31227	−	7.11643i	0.127479	−	0.392341i
$330$	−2.21249	−	1.60747i	−0.121794	−	0.0884883i
$331$	−6.45018	+	19.8516i	−0.354534	+	1.09114i	0.601745	+	0.798688i	$0.294472\pi$
$331$	−6.45018	+	19.8516i	−0.354534	+	1.09114i	−0.956279	+	0.292456i	$0.905528\pi$
$332$	7.16332	−	5.20445i	0.393138	−	0.285631i
$333$	5.54508	−	4.02874i	0.303869	−	0.220774i
$334$	7.41783	+	5.38937i	0.405885	+	0.294893i
$335$	−8.28809			−0.452827
$336$	0.958722			0.0523026
$337$	−11.0712	−	8.04367i	−0.603085	−	0.438167i	0.243888	−	0.969803i	$-0.421577\pi$
$337$	−11.0712	−	8.04367i	−0.603085	−	0.438167i	−0.846972	+	0.531637i	$0.821577\pi$
$338$	1.31998	+	4.06249i	0.0717975	+	0.220970i
$339$	−2.96813	+	9.13498i	−0.161207	+	0.496144i
$340$	−2.34951			−0.127420
$341$	−7.85379	+	13.0449i	−0.425306	+	0.706421i
$342$	−2.12650			−0.114988
$343$	3.87535	−	11.9271i	0.209249	−	0.644003i
$344$	−2.42808	−	7.47285i	−0.130913	−	0.402909i
$345$	−5.05256	−	3.67090i	−0.272021	−	0.197635i
$346$	−1.18942			−0.0639436
$347$	−5.13758			−0.275799			−0.137900	−	0.990446i	$-0.544035\pi$
$347$	−5.13758			−0.275799			−0.137900	+	0.990446i	$0.544035\pi$
$348$	−4.57201	−	3.32176i	−0.245085	−	0.178065i
$349$	−24.2676	+	17.6314i	−1.29901	+	0.943788i	−0.999945	−	0.0104446i	$-0.996675\pi$
$349$	−24.2676	+	17.6314i	−1.29901	+	0.943788i	−0.299067	+	0.954232i	$0.596675\pi$
$350$	0.775623	−	0.563523i	0.0414588	−	0.0301216i
$351$	1.28425	−	3.95250i	0.0685480	−	0.210969i
$352$	−2.21249	−	1.60747i	−0.117926	−	0.0856784i
$353$	−6.26800	+	19.2909i	−0.333612	+	1.02675i	0.633790	+	0.773505i	$0.281498\pi$
$353$	−6.26800	+	19.2909i	−0.333612	+	1.02675i	−0.967402	+	0.253247i	$0.918502\pi$
$354$	−2.11135	−	6.49806i	−0.112217	−	0.345368i
$355$	−2.58230	+	1.87615i	−0.137054	+	0.0995757i
$356$	2.89440	+	8.90804i	0.153403	+	0.472125i
$357$	0.696068	+	2.14228i	0.0368398	+	0.113381i
$358$	−2.93035	+	2.12903i	−0.154874	+	0.112523i
$359$	5.90820	+	18.1836i	0.311823	+	0.959693i	0.977042	+	0.213045i	$0.0683380\pi$
$359$	5.90820	+	18.1836i	0.311823	+	0.959693i	−0.665219	+	0.746648i	$0.731662\pi$
$360$	−0.309017	+	0.951057i	−0.0162866	+	0.0501251i
$361$	11.7129	+	8.50995i	0.616470	+	0.447892i
$362$	3.05499	−	9.40228i	0.160566	−	0.494173i
$363$	−2.84848	+	2.06954i	−0.149506	+	0.108623i
$364$	−3.22341	+	2.34195i	−0.168953	+	0.122751i
$365$	1.40520	+	1.02094i	0.0735515	+	0.0534383i
$366$	−8.57645			−0.448298
$367$	3.20735			0.167422			0.0837112	−	0.996490i	$-0.473323\pi$
$367$	3.20735			0.167422			0.0837112	+	0.996490i	$0.473323\pi$
$368$	−5.05256	−	3.67090i	−0.263383	−	0.191359i
$369$	−1.07885	−	3.32035i	−0.0561625	−	0.172851i
$370$	2.11803	−	6.51864i	0.110111	−	0.338888i
$371$	−1.78387			−0.0926140
$372$	5.42396	+	1.25724i	0.281219	+	0.0651850i
$373$	9.29215			0.481129			0.240565	−	0.970633i	$-0.422667\pi$
$373$	9.29215			0.481129			0.240565	+	0.970633i	$0.422667\pi$
$374$	1.98556	−	6.11093i	0.102671	−	0.315989i
$375$	0.309017	+	0.951057i	0.0159576	+	0.0491123i
$376$	6.31423	+	4.58756i	0.325632	+	0.236585i
$377$	23.4863			1.20961
$378$	0.958722			0.0493114
$379$	−16.4899	−	11.9806i	−0.847028	−	0.615402i	0.0772966	−	0.997008i	$-0.475371\pi$
$379$	−16.4899	−	11.9806i	−0.847028	−	0.615402i	−0.924325	+	0.381606i	$0.875371\pi$
$380$	−1.72038	+	1.24993i	−0.0882534	+	0.0641199i
$381$	−14.4188	+	10.4759i	−0.738698	+	0.536695i
$382$	−2.27738	+	7.00906i	−0.116521	+	0.358615i
$383$	21.7816	+	15.8253i	1.11299	+	0.808634i	0.983132	−	0.182898i	$-0.0585479\pi$
$383$	21.7816	+	15.8253i	1.11299	+	0.808634i	0.129858	+	0.991533i	$0.458548\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	0.810213	+	2.49358i	0.0412923	+	0.127085i
$386$	−21.6670	+	15.7420i	−1.10282	+	0.801246i
$387$	−2.42808	−	7.47285i	−0.123426	−	0.379866i
$388$	4.93231	+	15.1801i	0.250400	+	0.770652i
$389$	19.9485	−	14.4934i	1.01143	−	0.734846i	0.0469208	−	0.998899i	$-0.485059\pi$
$389$	19.9485	−	14.4934i	1.01143	−	0.734846i	0.964508	+	0.264052i	$0.0850591\pi$
$390$	−1.28425	−	3.95250i	−0.0650303	−	0.200143i
$391$	4.53433	−	13.9552i	0.229311	−	0.705746i
$392$	4.91951	+	3.57423i	0.248473	+	0.180526i
$393$	−5.06456	+	15.5871i	−0.255473	+	0.786266i
$394$	−2.32609	+	1.69000i	−0.117187	+	0.0851412i
$395$	4.56982	−	3.32017i	0.229933	−	0.167056i
$396$	−2.21249	−	1.60747i	−0.111182	−	0.0807784i
$397$	9.61566			0.482596			0.241298	−	0.970451i	$-0.422427\pi$
$397$	9.61566			0.482596			0.241298	+	0.970451i	$0.422427\pi$
$398$	13.8798			0.695733
$399$	1.64936	+	1.19833i	0.0825714	+	0.0599917i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	9.68447	−	29.8057i	0.483619	−	1.48843i	−0.350351	−	0.936618i	$-0.613938\pi$
$401$	9.68447	−	29.8057i	0.483619	−	1.48843i	0.833971	−	0.551809i	$-0.186062\pi$
$402$	−8.28809			−0.413372
$403$	−21.3076	+	9.02244i	−1.06141	+	0.449440i
$404$	3.43151			0.170724
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	1.67427	+	5.15286i	0.0830924	+	0.255732i
$407$	15.1647	+	11.0178i	0.751684	+	0.546130i
$408$	−2.34951			−0.116318
$409$	−23.7997			−1.17682			−0.588409	−	0.808564i	$-0.700245\pi$
$409$	−23.7997			−1.17682			−0.588409	+	0.808564i	$0.700245\pi$
$410$	−2.82446	−	2.05209i	−0.139490	−	0.101345i
$411$	−14.7234	+	10.6972i	−0.726254	+	0.527654i
$412$	−13.2622	+	9.63554i	−0.653381	+	0.474709i
$413$	−2.02420	+	6.22983i	−0.0996042	+	0.306550i
$414$	−5.05256	−	3.67090i	−0.248320	−	0.180415i
$415$	2.73614	−	8.42098i	0.134312	−	0.413370i
$416$	−1.28425	−	3.95250i	−0.0629653	−	0.193787i
$417$	16.0109	−	11.6326i	0.784056	−	0.569650i
$418$	−1.79710	−	5.53091i	−0.0878991	−	0.270526i
$419$	8.93842	+	27.5096i	0.436670	+	1.34393i	0.891365	+	0.453285i	$0.149748\pi$
$419$	8.93842	+	27.5096i	0.436670	+	1.34393i	−0.454695	+	0.890647i	$0.650252\pi$
$420$	0.775623	−	0.563523i	0.0378465	−	0.0274971i
$421$	−5.32402	−	16.3857i	−0.259477	−	0.798588i	−0.992914	−	0.118831i	$-0.962085\pi$
$421$	−5.32402	−	16.3857i	−0.259477	−	0.798588i	0.733438	−	0.679757i	$-0.237915\pi$
$422$	1.08598	−	3.34230i	0.0528647	−	0.162701i
$423$	6.31423	+	4.58756i	0.307009	+	0.223055i
$424$	0.574981	−	1.76961i	0.0279235	−	0.0859398i
$425$	−1.90079	+	1.38100i	−0.0922019	+	0.0669886i
$426$	−2.58230	+	1.87615i	−0.125113	+	0.0908997i
$427$	6.65209	+	4.83302i	0.321917	+	0.233886i
$428$	−4.71302			−0.227813
$429$	11.3655			0.548733
$430$	−6.35679	−	4.61848i	−0.306552	−	0.222723i
$431$	5.13116	+	15.7921i	0.247159	+	0.760678i	0.995274	+	0.0971083i	$0.0309593\pi$
$431$	5.13116	+	15.7921i	0.247159	+	0.760678i	−0.748115	+	0.663570i	$0.769041\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−13.3975			−0.643842			−0.321921	−	0.946767i	$-0.604328\pi$
$433$	−13.3975			−0.643842			−0.321921	+	0.946767i	$0.604328\pi$
$434$	−3.49846	−	4.03167i	−0.167932	−	0.193526i
$435$	−5.65131			−0.270960
$436$	1.52978	−	4.70816i	0.0732630	−	0.225480i
$437$	−4.10395	−	12.6307i	−0.196319	−	0.604207i
$438$	1.40520	+	1.02094i	0.0671430	+	0.0487822i
$439$	26.7306			1.27578			0.637890	−	0.770127i	$-0.279807\pi$
$439$	26.7306			1.27578			0.637890	+	0.770127i	$0.279807\pi$
$440$	−2.73479			−0.130376
$441$	4.91951	+	3.57423i	0.234262	+	0.170202i
$442$	7.89950	−	5.73933i	0.375741	−	0.272992i
$443$	−8.85551	+	6.43391i	−0.420738	+	0.305684i	−0.777935	−	0.628345i	$-0.783733\pi$
$443$	−8.85551	+	6.43391i	−0.420738	+	0.305684i	0.357197	+	0.934029i	$0.383733\pi$
$444$	2.11803	−	6.51864i	0.100517	−	0.309361i
$445$	7.57763	+	5.50547i	0.359214	+	0.260984i
$446$	−5.32469	+	16.3877i	−0.252132	+	0.775981i
$447$	1.77057	+	5.44925i	0.0837451	+	0.257741i
$448$	0.775623	−	0.563523i	0.0366447	−	0.0266240i
$449$	7.09321	+	21.8307i	0.334749	+	1.03025i	0.966845	+	0.255363i	$0.0821949\pi$
$449$	7.09321	+	21.8307i	0.334749	+	1.03025i	−0.632096	+	0.774890i	$0.717805\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	7.72430	−	5.61204i	0.363723	−	0.264260i
$452$	2.96813	+	9.13498i	0.139609	+	0.429673i
$453$	4.82859	−	14.8609i	0.226867	−	0.698225i
$454$	9.11469	+	6.62221i	0.427773	+	0.310796i
$455$	−1.23123	+	3.78935i	−0.0577212	+	0.177648i
$456$	−1.72038	+	1.24993i	−0.0805640	+	0.0585332i
$457$	−15.3657	+	11.1638i	−0.718776	+	0.522221i	−0.885993	−	0.463699i	$-0.846522\pi$
$457$	−15.3657	+	11.1638i	−0.718776	+	0.522221i	0.167217	+	0.985920i	$0.446522\pi$
$458$	2.46317	+	1.78960i	0.115096	+	0.0836224i
$459$	−2.34951			−0.109666
$460$	−6.24531			−0.291189
$461$	−20.5772	−	14.9502i	−0.958378	−	0.696302i	−0.00560422	−	0.999984i	$-0.501784\pi$
$461$	−20.5772	−	14.9502i	−0.958378	−	0.696302i	−0.952773	+	0.303682i	$0.901784\pi$
$462$	0.810213	+	2.49358i	0.0376945	+	0.116012i
$463$	−2.22699	+	6.85397i	−0.103497	+	0.318531i	−0.989375	−	0.145388i	$-0.953557\pi$
$463$	−2.22699	+	6.85397i	−0.103497	+	0.318531i	0.885878	+	0.463919i	$0.153557\pi$
$464$	−5.65131			−0.262355
$465$	5.12706	−	2.17099i	0.237762	−	0.100677i
$466$	−14.7886			−0.685067
$467$	−9.68654	+	29.8121i	−0.448239	+	1.37954i	0.430652	+	0.902518i	$0.358283\pi$
$467$	−9.68654	+	29.8121i	−0.448239	+	1.37954i	−0.878892	+	0.477021i	$0.841717\pi$
$468$	−1.28425	−	3.95250i	−0.0593643	−	0.182704i
$469$	6.42843	+	4.67053i	0.296837	+	0.215665i
$470$	7.80482			0.360010
$471$	−18.2699			−0.841834
$472$	−5.52758	−	4.01602i	−0.254427	−	0.184852i
$473$	17.3845	−	12.6306i	0.799340	−	0.580754i
$474$	4.56982	−	3.32017i	0.209899	−	0.152500i
$475$	−0.657125	+	2.02242i	−0.0301510	+	0.0927952i
$476$	1.82233	+	1.32400i	0.0835264	+	0.0606855i
$477$	0.574981	−	1.76961i	0.0263266	−	0.0810248i
$478$	1.91800	+	5.90298i	0.0877271	+	0.269996i
$479$	4.44007	−	3.22590i	0.202872	−	0.147395i	−0.481711	−	0.876330i	$-0.659984\pi$
$479$	4.44007	−	3.22590i	0.202872	−	0.147395i	0.684583	+	0.728935i	$0.259984\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	8.80235	+	27.0908i	0.401353	+	1.23524i
$482$	12.4276	−	9.02920i	0.566063	−	0.411269i
$483$	1.85025	+	5.69447i	0.0841891	+	0.259107i
$484$	−1.08802	+	3.34859i	−0.0494556	+	0.152209i
$485$	12.9129	+	9.38180i	0.586347	+	0.426006i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−20.3357	+	14.7747i	−0.921497	+	0.669507i	−0.943896	−	0.330242i	$-0.892870\pi$
$487$	−20.3357	+	14.7747i	−0.921497	+	0.669507i	0.0223990	+	0.999749i	$0.492870\pi$
$488$	−6.93849	+	5.04111i	−0.314091	+	0.228200i
$489$	−5.31217	−	3.85952i	−0.240225	−	0.174533i
$490$	6.08085			0.274705
$491$	−3.16350			−0.142767			−0.0713834	−	0.997449i	$-0.522741\pi$
$491$	−3.16350			−0.142767			−0.0713834	+	0.997449i	$0.522741\pi$
$492$	−2.82446	−	2.05209i	−0.127336	−	0.0925153i
$493$	−4.10306	−	12.6279i	−0.184793	−	0.568733i
$494$	2.73095	−	8.40500i	0.122871	−	0.378159i
$495$	−2.73479			−0.122920
$496$	5.12706	−	2.17099i	0.230212	−	0.0974805i
$497$	3.06014			0.137266
$498$	2.73614	−	8.42098i	0.122609	−	0.377353i
$499$	2.76713	+	8.51635i	0.123874	+	0.381244i	0.993694	−	0.112124i	$-0.0357655\pi$
$499$	2.76713	+	8.51635i	0.123874	+	0.381244i	−0.869820	+	0.493368i	$0.835765\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	9.16894			0.409638
$502$	−19.2784			−0.860439
$503$	−17.4141	−	12.6521i	−0.776454	−	0.564127i	0.127458	−	0.991844i	$-0.459318\pi$
$503$	−17.4141	−	12.6521i	−0.776454	−	0.564127i	−0.903913	+	0.427717i	$0.859318\pi$
$504$	0.775623	−	0.563523i	0.0345490	−	0.0251013i
$505$	2.77615	−	2.01699i	0.123537	−	0.0897549i
$506$	5.27789	−	16.2437i	0.234631	−	0.722120i
$507$	3.45576	+	2.51075i	0.153476	+	0.111507i
$508$	−5.50749	+	16.9503i	−0.244355	+	0.752049i
$509$	3.36528	+	10.3573i	0.149163	+	0.459077i	0.997523	−	0.0703430i	$-0.0224094\pi$
$509$	3.36528	+	10.3573i	0.149163	+	0.459077i	−0.848360	+	0.529421i	$0.822409\pi$
$510$	−1.90079	+	1.38100i	−0.0841684	+	0.0611519i
$511$	−0.514583	−	1.58372i	−0.0227638	−	0.0700598i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.72038	+	1.24993i	−0.0759565	+	0.0551856i
$514$	−7.13706	−	21.9656i	−0.314802	−	0.968862i
$515$	−5.06570	+	15.5906i	−0.223221	+	0.687005i
$516$	−6.35679	−	4.61848i	−0.279842	−	0.203317i
$517$	−6.59583	+	20.2999i	−0.290084	+	0.892788i
$518$	−5.31620	+	3.86244i	−0.233580	+	0.169706i
$519$	−0.962260	+	0.699123i	−0.0422385	+	0.0306881i
$520$	−3.36220	−	2.44278i	−0.147442	−	0.107123i
$521$	−12.2082			−0.534851			−0.267426	−	0.963578i	$-0.586173\pi$
$521$	−12.2082			−0.534851			−0.267426	+	0.963578i	$0.586173\pi$
$522$	−5.65131			−0.247351
$523$	9.09971	+	6.61133i	0.397903	+	0.289093i	0.768686	−	0.639626i	$-0.220911\pi$
$523$	9.09971	+	6.61133i	0.397903	+	0.289093i	−0.370783	+	0.928719i	$0.620911\pi$
$524$	5.06456	+	15.5871i	0.221246	+	0.680927i
$525$	0.296261	−	0.911799i	0.0129299	−	0.0397942i
$526$	5.75040			0.250729
$527$	8.57355	+	9.88027i	0.373470	+	0.430391i
$528$	−2.73479			−0.119017
$529$	4.94548	−	15.2206i	0.215021	−	0.661766i
$530$	−0.574981	−	1.76961i	−0.0249756	−	0.0768669i
$531$	−5.52758	−	4.01602i	−0.239876	−	0.174280i
$532$	2.03872			0.0883899
$533$	14.5092			0.628463
$534$	7.57763	+	5.50547i	0.327916	+	0.238245i
$535$	−3.81292	+	2.77025i	−0.164847	+	0.119768i
$536$	−6.70520	+	4.87162i	−0.289621	+	0.210422i
$537$	−1.11930	+	3.44484i	−0.0483012	+	0.148656i
$538$	−10.1665	−	7.38638i	−0.438308	−	0.318450i
$539$	−5.13891	+	15.8159i	−0.221349	+	0.681241i
$540$	0.309017	+	0.951057i	0.0132980	+	0.0409270i
$541$	−18.0326	+	13.1014i	−0.775281	+	0.563275i	−0.903559	−	0.428463i	$-0.859055\pi$
$541$	−18.0326	+	13.1014i	−0.775281	+	0.563275i	0.128278	+	0.991738i	$0.459055\pi$
$542$	−5.42253	−	16.6888i	−0.232918	−	0.716847i
$543$	−3.05499	−	9.40228i	−0.131102	−	0.403490i
$544$	−1.90079	+	1.38100i	−0.0814957	+	0.0592101i
$545$	−1.52978	−	4.70816i	−0.0655284	−	0.201676i
$546$	−1.23123	+	3.78935i	−0.0526920	+	0.162169i
$547$	−30.3168	−	22.0265i	−1.29625	−	0.941783i	−0.296342	−	0.955082i	$-0.595767\pi$
$547$	−30.3168	−	22.0265i	−1.29625	−	0.941783i	−0.999912	+	0.0132987i	$0.995767\pi$
$548$	−5.62385	+	17.3084i	−0.240239	+	0.739380i
$549$	−6.93849	+	5.04111i	−0.296128	+	0.215149i
$550$	−2.21249	+	1.60747i	−0.0943410	+	0.0685428i
$551$	−9.72238	−	7.06372i	−0.414187	−	0.300925i
$552$	−6.24531			−0.265818
$553$	−5.41545			−0.230288
$554$	−11.1511	−	8.10175i	−0.473765	−	0.344210i
$555$	−2.11803	−	6.51864i	−0.0899055	−	0.276701i
$556$	6.11561	−	18.8219i	0.259360	−	0.798227i
$557$	42.3182			1.79308			0.896540	−	0.442963i	$-0.146073\pi$
$557$	42.3182			1.79308			0.896540	+	0.442963i	$0.146073\pi$
$558$	5.12706	−	2.17099i	0.217046	−	0.0919055i
$559$	32.6547			1.38115
$560$	0.296261	−	0.911799i	0.0125193	−	0.0385305i
$561$	−1.98556	−	6.11093i	−0.0838304	−	0.258004i
$562$	−5.05258	−	3.67091i	−0.213130	−	0.154848i
$563$	41.8901			1.76546			0.882729	−	0.469883i	$-0.155704\pi$
$563$	41.8901			1.76546			0.882729	+	0.469883i	$0.155704\pi$
$564$	7.80482			0.328642
$565$	7.77068	+	5.64573i	0.326915	+	0.237518i
$566$	17.2411	−	12.5264i	0.724700	−	0.526525i
$567$	0.775623	−	0.563523i	0.0325731	−	0.0236657i
$568$	−0.986350	+	3.03567i	−0.0413863	+	0.127374i
$569$	−1.58398	−	1.15083i	−0.0664038	−	0.0482452i	0.554088	−	0.832458i	$-0.313067\pi$
$569$	−1.58398	−	1.15083i	−0.0664038	−	0.0482452i	−0.620492	+	0.784213i	$0.713067\pi$
$570$	−0.657125	+	2.02242i	−0.0275239	+	0.0847100i
$571$	−6.32612	−	19.4698i	−0.264740	−	0.814785i	−0.991753	−	0.128162i	$-0.959092\pi$
$571$	−6.32612	−	19.4698i	−0.264740	−	0.814785i	0.727014	−	0.686623i	$-0.240908\pi$
$572$	9.19491	−	6.68049i	0.384459	−	0.279325i
$573$	2.27738	+	7.00906i	0.0951390	+	0.292808i
$574$	1.03431	+	3.18329i	0.0431715	+	0.132868i
$575$	−5.05256	+	3.67090i	−0.210706	+	0.153087i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−0.350440	+	1.07854i	−0.0145890	+	0.0449003i	−0.958086	−	0.286481i	$-0.907515\pi$
$577$	−0.350440	+	1.07854i	−0.0145890	+	0.0449003i	0.943497	+	0.331381i	$0.107515\pi$
$578$	9.28737	+	6.74767i	0.386304	+	0.280666i
$579$	−8.27605	+	25.4711i	−0.343941	+	1.05854i
$580$	−4.57201	+	3.32176i	−0.189842	+	0.137928i
$581$	−6.86763	+	4.98963i	−0.284917	+	0.207005i
$582$	12.9129	+	9.38180i	0.535259	+	0.388888i
$583$	5.08856			0.210747
$584$	1.73692			0.0718743
$585$	−3.36220	−	2.44278i	−0.139010	−	0.100997i
$586$	−0.449293	−	1.38278i	−0.0185601	−	0.0571222i
$587$	−5.75176	+	17.7021i	−0.237401	+	0.730644i	0.759393	+	0.650632i	$0.225496\pi$
$587$	−5.75176	+	17.7021i	−0.237401	+	0.730644i	−0.996794	+	0.0800122i	$0.974504\pi$
$588$	6.08085			0.250770
$589$	11.5341	+	2.67353i	0.475253	+	0.110161i
$590$	−6.83246			−0.281288
$591$	−0.888488	+	2.73448i	−0.0365475	+	0.112482i
$592$	−2.11803	−	6.51864i	−0.0870507	−	0.267914i
$593$	−23.2002	−	16.8559i	−0.952717	−	0.692190i	−0.00126934	−	0.999999i	$-0.500404\pi$
$593$	−23.2002	−	16.8559i	−0.952717	−	0.692190i	−0.951448	+	0.307810i	$0.900404\pi$
$594$	−2.73479			−0.112210
$595$	2.25252			0.0923445
$596$	4.63541	+	3.36782i	0.189874	+	0.137951i
$597$	11.2290	−	8.15836i	0.459573	−	0.333899i
$598$	20.9980	−	15.2559i	0.858671	−	0.623861i
$599$	13.0130	−	40.0498i	0.531695	−	1.63639i	−0.218988	−	0.975728i	$-0.570275\pi$
$599$	13.0130	−	40.0498i	0.531695	−	1.63639i	0.750683	−	0.660662i	$-0.229725\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−7.32123	+	22.5324i	−0.298639	+	0.919117i	0.683336	+	0.730104i	$0.260529\pi$
$601$	−7.32123	+	22.5324i	−0.298639	+	0.919117i	−0.981975	+	0.189012i	$0.939471\pi$
$602$	2.32785	+	7.16439i	0.0948761	+	0.291999i
$603$	−6.70520	+	4.87162i	−0.273057	+	0.198388i
$604$	−4.82859	−	14.8609i	−0.196473	−	0.604681i
$605$	1.08802	+	3.34859i	0.0442344	+	0.136140i
$606$	2.77615	−	2.01699i	0.112773	−	0.0819346i
$607$	8.34791	+	25.6922i	0.338831	+	1.04282i	0.964804	+	0.262971i	$0.0847022\pi$
$607$	8.34791	+	25.6922i	0.338831	+	1.04282i	−0.625972	+	0.779845i	$0.715298\pi$
$608$	−0.657125	+	2.02242i	−0.0266499	+	0.0820201i
$609$	4.38328	+	3.18464i	0.177620	+	0.129048i
$610$	−2.65027	+	8.15669i	−0.107306	+	0.330255i
$611$	−26.2414	+	19.0655i	−1.06161	+	0.771306i
$612$	−1.90079	+	1.38100i	−0.0768349	+	0.0558238i
$613$	−20.5773	−	14.9502i	−0.831107	−	0.603835i	0.0887650	−	0.996053i	$-0.471708\pi$
$613$	−20.5773	−	14.9502i	−0.831107	−	0.603835i	−0.919872	+	0.392218i	$0.871708\pi$
$614$	5.98950			0.241717
$615$	−3.49122			−0.140780
$616$	2.12117	+	1.54112i	0.0854642	+	0.0620934i
$617$	10.0895	+	31.0522i	0.406187	+	1.25012i	0.919900	+	0.392153i	$0.128270\pi$
$617$	10.0895	+	31.0522i	0.406187	+	1.25012i	−0.513713	+	0.857962i	$0.671730\pi$
$618$	−5.06570	+	15.5906i	−0.203772	+	0.627147i
$619$	−25.4102			−1.02132			−0.510661	−	0.859782i	$-0.670599\pi$
$619$	−25.4102			−1.02132			−0.510661	+	0.859782i	$0.670599\pi$
$620$	2.87180	−	4.76998i	0.115334	−	0.191567i
$621$	−6.24531			−0.250616
$622$	3.40246	−	10.4717i	0.136426	−	0.419877i
$623$	−2.77492	−	8.54033i	−0.111175	−	0.342161i
$624$	−3.36220	−	2.44278i	−0.134596	−	0.0977895i
$625$	1.00000			0.0400000
$626$	10.8093			0.432026
$627$	−4.70487	−	3.41829i	−0.187894	−	0.136513i
$628$	−14.7807	+	10.7388i	−0.589813	+	0.428525i
$629$	13.0282	−	9.46555i	0.519469	−	0.377416i
$630$	0.296261	−	0.911799i	0.0118033	−	0.0363269i
$631$	−4.09537	−	2.97546i	−0.163034	−	0.118451i	0.503277	−	0.864125i	$-0.332128\pi$
$631$	−4.09537	−	2.97546i	−0.163034	−	0.118451i	−0.666311	+	0.745674i	$0.732128\pi$
$632$	1.74552	−	5.37214i	0.0694329	−	0.213692i
$633$	−1.08598	−	3.34230i	−0.0431639	−	0.132845i
$634$	−5.89819	+	4.28529i	−0.234247	+	0.170191i
$635$	5.50749	+	16.9503i	0.218558	+	0.672653i
$636$	−0.574981	−	1.76961i	−0.0227995	−	0.0701695i
$637$	−20.4450	+	14.8542i	−0.810062	+	0.588544i
$638$	−4.77591	−	14.6987i	−0.189080	−	0.581928i
$639$	−0.986350	+	3.03567i	−0.0390194	+	0.120089i
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	−12.7747	+	39.3166i	−0.504572	+	1.55291i	0.296917	+	0.954903i	$0.404042\pi$
$641$	−12.7747	+	39.3166i	−0.504572	+	1.55291i	−0.801489	+	0.598010i	$0.795958\pi$
$642$	−3.81292	+	2.77025i	−0.150484	+	0.109333i
$643$	7.58368	−	5.50986i	0.299071	−	0.217288i	−0.428122	−	0.903721i	$-0.640825\pi$
$643$	7.58368	−	5.50986i	0.299071	−	0.217288i	0.727193	+	0.686433i	$0.240825\pi$
$644$	4.84401	+	3.51938i	0.190881	+	0.138683i
$645$	−7.85742			−0.309386
$646$	−4.99623			−0.196574
$647$	−9.79017	−	7.11297i	−0.384891	−	0.279640i	0.378468	−	0.925615i	$-0.376451\pi$
$647$	−9.79017	−	7.11297i	−0.384891	−	0.279640i	−0.763359	+	0.645975i	$0.776451\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	5.77409	−	17.7708i	0.226653	−	0.697566i
$650$	−4.15591			−0.163008
$651$	−5.20007	−	1.20535i	−0.203807	−	0.0472413i
$652$	−6.56620			−0.257152
$653$	0.501277	−	1.54277i	0.0196165	−	0.0603734i	−0.940769	−	0.339048i	$-0.889895\pi$
$653$	0.501277	−	1.54277i	0.0196165	−	0.0603734i	0.960386	+	0.278675i	$0.0898951\pi$
$654$	−1.52978	−	4.70816i	−0.0598189	−	0.184104i
$655$	13.2592	+	9.63337i	0.518080	+	0.376407i
$656$	−3.49122			−0.136309
$657$	1.73692			0.0677638
$658$	−6.05360	−	4.39820i	−0.235994	−	0.171460i
$659$	−2.01918	+	1.46702i	−0.0786559	+	0.0571469i	−0.626418	−	0.779487i	$-0.715480\pi$
$659$	−2.01918	+	1.46702i	−0.0786559	+	0.0571469i	0.547762	+	0.836634i	$0.315480\pi$
$660$	−2.21249	+	1.60747i	−0.0861212	+	0.0625707i
$661$	7.98338	−	24.5703i	0.310518	−	0.955675i	−0.667043	−	0.745020i	$-0.732440\pi$
$661$	7.98338	−	24.5703i	0.310518	−	0.955675i	0.977560	−	0.210656i	$-0.0675599\pi$
$662$	16.8868	+	12.2690i	0.656324	+	0.476847i
$663$	3.01734	−	9.28642i	0.117184	−	0.360655i
$664$	−2.73614	−	8.42098i	−0.106183	−	0.326797i
$665$	1.64936	−	1.19833i	0.0639596	−	0.0464693i
$666$	−2.11803	−	6.51864i	−0.0820721	−	0.252592i
$667$	−10.9065	−	33.5668i	−0.422302	−	1.29971i
$668$	7.41783	−	5.38937i	0.287004	−	0.208521i
$669$	5.32469	+	16.3877i	0.205865	+	0.633586i
$670$	−2.56116	+	7.88244i	−0.0989463	+	0.304525i
$671$	−18.9753	−	13.7864i	−0.732534	−	0.532217i
$672$	0.296261	−	0.911799i	0.0114285	−	0.0351734i
$673$	−31.2479	+	22.7030i	−1.20452	+	0.875135i	−0.994722	−	0.102610i	$-0.967281\pi$
$673$	−31.2479	+	22.7030i	−1.20452	+	0.875135i	−0.209798	+	0.977745i	$0.567281\pi$
$674$	−11.0712	+	8.04367i	−0.426445	+	0.309831i
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$	4.27155			0.164290
$677$	23.0982			0.887735			0.443867	−	0.896093i	$-0.353606\pi$
$677$	23.0982			0.887735			0.443867	+	0.896093i	$0.353606\pi$
$678$	7.77068	+	5.64573i	0.298431	+	0.216823i
$679$	−4.72871	−	14.5535i	−0.181471	−	0.558511i
$680$	−0.726037	+	2.23451i	−0.0278423	+	0.0856897i
$681$	11.2664			0.431728
$682$	9.97949	+	11.5005i	0.382135	+	0.440377i
$683$	−6.45812			−0.247113			−0.123557	−	0.992338i	$-0.539430\pi$
$683$	−6.45812			−0.247113			−0.123557	+	0.992338i	$0.539430\pi$
$684$	−0.657125	+	2.02242i	−0.0251258	+	0.0773293i
$685$	5.62385	+	17.3084i	0.214876	+	0.661321i
$686$	−10.1458	−	7.37136i	−0.387369	−	0.281440i
$687$	3.04464			0.116160
$688$	−7.85742			−0.299561
$689$	6.25596	+	4.54522i	0.238333	+	0.173159i
$690$	−5.05256	+	3.67090i	−0.192348	+	0.139749i
$691$	−1.42289	+	1.03379i	−0.0541292	+	0.0393272i	−0.614521	−	0.788901i	$-0.710651\pi$
$691$	−1.42289	+	1.03379i	−0.0541292	+	0.0393272i	0.560392	+	0.828228i	$0.310651\pi$
$692$	−0.367551	+	1.13120i	−0.0139722	+	0.0430019i
$693$	2.12117	+	1.54112i	0.0805764	+	0.0585422i
$694$	−1.58760	+	4.88612i	−0.0602644	+	0.185475i
$695$	−6.11561	−	18.8219i	−0.231978	−	0.713956i
$696$	−4.57201	+	3.32176i	−0.173301	+	0.125911i
$697$	−2.53476	−	7.80118i	−0.0960108	−	0.295491i
$698$	9.26938	+	28.5282i	0.350851	+	1.07981i
$699$	−11.9642	+	8.69249i	−0.452527	+	0.328780i
$700$	−0.296261	−	0.911799i	−0.0111976	−	0.0344628i
$701$	6.49011	−	19.9745i	0.245128	−	0.754426i	−0.750487	−	0.660885i	$-0.770181\pi$
$701$	6.49011	−	19.9745i	0.245128	−	0.754426i	0.995615	−	0.0935416i	$-0.0298188\pi$
$702$	−3.36220	−	2.44278i	−0.126898	−	0.0921968i
$703$	4.50400	−	13.8619i	0.169872	−	0.522811i
$704$	−2.21249	+	1.60747i	−0.0833865	+	0.0605838i
$705$	6.31423	−	4.58756i	0.237808	−	0.172777i
$706$	16.4098	+	11.9224i	0.617592	+	0.448707i
$707$	−3.28986			−0.123728
$708$	−6.83246			−0.256780
$709$	−26.2806	−	19.0939i	−0.986987	−	0.717088i	−0.0277278	−	0.999616i	$-0.508827\pi$
$709$	−26.2806	−	19.0939i	−0.986987	−	0.717088i	−0.959259	+	0.282527i	$0.908827\pi$
$710$	0.986350	+	3.03567i	0.0370171	+	0.113927i
$711$	1.74552	−	5.37214i	0.0654619	−	0.201471i
$712$	9.36646			0.351023
$713$	22.7897	+	26.2631i	0.853480	+	0.983562i
$714$	2.25252			0.0842986
$715$	3.51214	−	10.8093i	0.131347	−	0.404244i
$716$	1.11930	+	3.44484i	0.0418301	+	0.128740i
$717$	5.02138	+	3.64824i	0.187527	+	0.136246i
$718$	19.1193			0.713528
$719$	16.5195			0.616072			0.308036	−	0.951375i	$-0.400328\pi$
$719$	16.5195			0.616072			0.308036	+	0.951375i	$0.400328\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	12.7147	−	9.23780i	0.473522	−	0.344034i
$722$	11.7129	−	8.50995i	0.435910	−	0.316707i
$723$	4.74693	−	14.6096i	0.176540	−	0.543335i
$724$	−7.99806	−	5.81093i	−0.297245	−	0.215961i
$725$	−1.74635	+	5.37471i	−0.0648578	+	0.199612i
$726$	1.08802	+	3.34859i	0.0403803	+	0.124278i
$727$	−31.3699	+	22.7916i	−1.16345	+	0.845293i	−0.990210	−	0.139587i	$-0.955423\pi$
$727$	−31.3699	+	22.7916i	−1.16345	+	0.845293i	−0.173237	+	0.984880i	$0.555423\pi$
$728$	1.23123	+	3.78935i	0.0456326	+	0.140443i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.40520	−	1.02094i	0.0520087	−	0.0377866i
$731$	−5.70478	−	17.5575i	−0.210999	−	0.649388i
$732$	−2.65027	+	8.15669i	−0.0979567	+	0.301480i
$733$	−23.6961	−	17.2162i	−0.875235	−	0.635896i	0.0567512	−	0.998388i	$-0.481926\pi$
$733$	−23.6961	−	17.2162i	−0.875235	−	0.635896i	−0.931987	+	0.362493i	$0.881926\pi$
$734$	0.991126	−	3.05037i	0.0365831	−	0.112591i
$735$	4.91951	−	3.57423i	0.181459	−	0.131838i
$736$	−5.05256	+	3.67090i	−0.186240	+	0.135311i
$737$	−18.3373	−	13.3229i	−0.675464	−	0.490754i
$738$	−3.49122			−0.128514
$739$	32.3182			1.18884			0.594422	−	0.804153i	$-0.297381\pi$
$739$	32.3182			1.18884			0.594422	+	0.804153i	$0.297381\pi$
$740$	−5.54508	−	4.02874i	−0.203841	−	0.148099i
$741$	−2.73095	−	8.40500i	−0.100324	−	0.308765i
$742$	−0.551247	+	1.69656i	−0.0202369	+	0.0622828i
$743$	13.4089			0.491923			0.245962	−	0.969280i	$-0.420896\pi$
$743$	13.4089			0.491923			0.245962	+	0.969280i	$0.420896\pi$
$744$	2.87180	−	4.76998i	0.105285	−	0.174876i
$745$	5.72968			0.209919
$746$	2.87143	−	8.83736i	0.105131	−	0.323559i
$747$	−2.73614	−	8.42098i	−0.100110	−	0.308108i
$748$	−5.19826	−	3.77676i	−0.190067	−	0.138092i
$749$	4.51848			0.165102
$750$	1.00000			0.0365148
$751$	10.9431	+	7.95064i	0.399320	+	0.290123i	0.769264	−	0.638931i	$-0.220623\pi$
$751$	10.9431	+	7.95064i	0.399320	+	0.290123i	−0.369944	+	0.929054i	$0.620623\pi$
$752$	6.31423	−	4.58756i	0.230256	−	0.167291i
$753$	−15.5966	+	11.3316i	−0.568371	+	0.412946i
$754$	7.25767	−	22.3368i	0.264309	−	0.813459i
$755$	−12.6414	−	9.18453i	−0.460068	−	0.334259i
$756$	0.296261	−	0.911799i	0.0107749	−	0.0331618i
$757$	0.394272	+	1.21345i	0.0143301	+	0.0441034i	0.957966	−	0.286882i	$-0.0926188\pi$
$757$	0.394272	+	1.21345i	0.0143301	+	0.0441034i	−0.943636	+	0.330986i	$0.892619\pi$
$758$	−16.4899	+	11.9806i	−0.598940	+	0.435155i
$759$	−5.27789	−	16.2437i	−0.191575	−	0.589609i
$760$	0.657125	+	2.02242i	0.0238364	+	0.0733610i
$761$	−5.14587	+	3.73870i	−0.186538	+	0.135528i	−0.677135	−	0.735859i	$-0.736779\pi$
$761$	−5.14587	+	3.73870i	−0.186538	+	0.135528i	0.490597	+	0.871387i	$0.336779\pi$
$762$	5.50749	+	16.9503i	0.199515	+	0.614045i
$763$	−1.46663	+	4.51382i	−0.0530956	+	0.163411i
$764$	5.96226	+	4.33184i	0.215707	+	0.156720i
$765$	−0.726037	+	2.23451i	−0.0262499	+	0.0807890i
$766$	21.7816	−	15.8253i	0.787003	−	0.571791i
$767$	22.9721	−	16.6902i	0.829474	−	0.602648i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	−27.8849			−1.00556			−0.502778	−	0.864416i	$-0.667689\pi$
$769$	−27.8849			−1.00556			−0.502778	+	0.864416i	$0.667689\pi$
$770$	2.62191			0.0944869
$771$	−18.6851	−	13.5755i	−0.672927	−	0.488910i
$772$	8.27605	+	25.4711i	0.297862	+	0.916724i
$773$	13.8815	−	42.7228i	0.499282	−	1.53663i	−0.310894	−	0.950445i	$-0.600628\pi$
$773$	13.8815	−	42.7228i	0.499282	−	1.53663i	0.810176	−	0.586187i	$-0.199372\pi$
$774$	−7.85742			−0.282429
$775$	−0.480387	−	5.54700i	−0.0172560	−	0.199254i
$776$	15.9613			0.572977
$777$	−2.03061	+	6.24956i	−0.0728476	+	0.224202i
$778$	−7.61965	−	23.4509i	−0.273178	−	0.840754i
$779$	−6.00622	−	4.36377i	−0.215195	−	0.156348i
$780$	−4.15591			−0.148805
$781$	−8.72917			−0.312354
$782$	−11.8710	−	8.62481i	−0.424507	−	0.308422i
$783$	−4.57201	+	3.32176i	−0.163390	+	0.118710i
$784$	4.91951	−	3.57423i	0.175697	−	0.127651i
$785$	−5.64572	+	17.3757i	−0.201504	+	0.620167i
$786$	13.2592	+	9.63337i	0.472940	+	0.343611i
$787$	13.0027	−	40.0181i	0.463495	−	1.42649i	−0.397370	−	0.917659i	$-0.630077\pi$
$787$	13.0027	−	40.0181i	0.463495	−	1.42649i	0.860865	−	0.508833i	$-0.169923\pi$
$788$	0.888488	+	2.73448i	0.0316511	+	0.0974120i
$789$	4.65217	−	3.38000i	0.165622	−	0.120331i
$790$	−1.74552	−	5.37214i	−0.0621027	−	0.191132i
$791$	−2.84562	−	8.75791i	−0.101178	−	0.311395i
$792$	−2.21249	+	1.60747i	−0.0786175	+	0.0571190i
$793$	−11.0143	−	33.8984i	−0.391128	−	1.20377i
$794$	2.97140	−	9.14504i	0.105451	−	0.324545i
$795$	−1.50532	−	1.09368i	−0.0533882	−	0.0387888i
$796$	4.28910	−	13.2005i	0.152023	−	0.467880i
$797$	−27.2543	+	19.8014i	−0.965397	+	0.701402i	−0.954398	−	0.298537i	$-0.903501\pi$
$797$	−27.2543	+	19.8014i	−0.965397	+	0.701402i	−0.0109995	+	0.999940i	$0.503501\pi$
$798$	1.64936	−	1.19833i	0.0583868	−	0.0424205i
$799$	14.8353	+	10.7785i	0.524836	+	0.381316i
$800$	1.00000			0.0353553
$801$	9.36646			0.330948
$802$	−25.3543	−	18.4210i	−0.895290	−	0.650467i
$803$	1.46787	+	4.51763i	0.0517999	+	0.159424i
$804$	−2.56116	+	7.88244i	−0.0903252	+	0.277992i
$805$	5.98752			0.211032
$806$	1.99644	+	23.0528i	0.0703217	+	0.812001i
$807$	−12.5665			−0.442361
$808$	1.06039	−	3.26356i	0.0373046	−	0.114812i
$809$	−2.84875	−	8.76756i	−0.100157	−	0.308251i	0.888406	−	0.459058i	$-0.151813\pi$
$809$	−2.84875	−	8.76756i	−0.100157	−	0.308251i	−0.988563	+	0.150807i	$0.951813\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	40.0169			1.40518			0.702592	−	0.711593i	$-0.252026\pi$
$811$	40.0169			1.40518			0.702592	+	0.711593i	$0.252026\pi$
$812$	5.41804			0.190136
$813$	−14.1964	−	10.3143i	−0.497888	−	0.361737i
$814$	15.1647	−	11.0178i	0.531521	−	0.386172i
$815$	−5.31217	+	3.85952i	−0.186077	+	0.135193i
$816$	−0.726037	+	2.23451i	−0.0254164	+	0.0782236i
$817$	−13.5177	−	9.82120i	−0.472925	−	0.343600i
$818$	−7.35450	+	22.6348i	−0.257144	+	0.791408i
$819$	1.23123	+	3.78935i	0.0430228	+	0.132411i
$820$	−2.82446	+	2.05209i	−0.0986344	+	0.0716621i
$821$	7.00787	+	21.5680i	0.244576	+	0.752728i	0.995706	+	0.0925735i	$0.0295093\pi$
$821$	7.00787	+	21.5680i	0.244576	+	0.752728i	−0.751130	+	0.660155i	$0.770491\pi$
$822$	5.62385	+	17.3084i	0.196154	+	0.603701i
$823$	6.41939	−	4.66396i	0.223766	−	0.162575i	−0.470254	−	0.882531i	$-0.655838\pi$
$823$	6.41939	−	4.66396i	0.223766	−	0.162575i	0.694020	+	0.719955i	$0.255838\pi$
$824$	5.06570	+	15.5906i	0.176472	+	0.543125i
$825$	−0.845097	+	2.60094i	−0.0294225	+	0.0905532i
$826$	5.29941	+	3.85025i	0.184390	+	0.133967i
$827$	−9.22805	+	28.4010i	−0.320891	+	0.987600i	0.652371	+	0.757900i	$0.273775\pi$
$827$	−9.22805	+	28.4010i	−0.320891	+	0.987600i	−0.973261	+	0.229700i	$0.926225\pi$
$828$	−5.05256	+	3.67090i	−0.175589	+	0.127573i
$829$	28.1119	−	20.4245i	0.976368	−	0.709373i	0.0194742	−	0.999810i	$-0.493801\pi$
$829$	28.1119	−	20.4245i	0.976368	−	0.709373i	0.956894	+	0.290437i	$0.0938008\pi$
$830$	−7.16332	−	5.20445i	−0.248642	−	0.180649i
$831$	−13.7835			−0.478145
$832$	−4.15591			−0.144080
$833$	11.5584	+	8.39769i	0.400476	+	0.290963i
$834$	−6.11561	−	18.8219i	−0.211766	−	0.651750i
$835$	2.83336	−	8.72018i	0.0980524	−	0.301774i
$836$	−5.81554			−0.201135
$837$	2.87180	−	4.76998i	0.0992641	−	0.164875i
$838$	28.9253			0.999209
$839$	10.8438	−	33.3738i	0.374370	−	1.15219i	−0.569533	−	0.821968i	$-0.692876\pi$
$839$	10.8438	−	33.3738i	0.374370	−	1.15219i	0.943903	−	0.330223i	$-0.107124\pi$
$840$	−0.296261	−	0.911799i	−0.0102220	−	0.0314601i
$841$	−2.37632	−	1.72650i	−0.0819422	−	0.0595345i
$842$	−17.2289			−0.593747
$843$	−6.24533			−0.215101
$844$	−2.84313	−	2.06566i	−0.0978647	−	0.0711029i
$845$	3.45576	−	2.51075i	0.118882	−	0.0863726i
$846$	6.31423	−	4.58756i	0.217088	−	0.157724i
$847$	1.04311	−	3.21037i	0.0358417	−	0.110310i
$848$	−1.50532	−	1.09368i	−0.0516929	−	0.0375571i
$849$	6.58553	−	20.2682i	0.226015	−	0.695602i
$850$	0.726037	+	2.23451i	0.0249029	+	0.0766432i
$851$	34.6308	−	25.1607i	1.18713	−	0.862499i
$852$	0.986350	+	3.03567i	0.0337918	+	0.104000i
$853$	3.80335	+	11.7055i	0.130224	+	0.400789i	0.994817	−	0.101685i	$-0.0324234\pi$
$853$	3.80335	+	11.7055i	0.130224	+	0.400789i	−0.864593	+	0.502474i	$0.832423\pi$
$854$	6.65209	−	4.83302i	0.227630	−	0.165383i
$855$	0.657125	+	2.02242i	0.0224732	+	0.0691654i
$856$	−1.45640	+	4.48235i	−0.0497789	+	0.153204i
$857$	9.57069	+	6.95351i	0.326928	+	0.237527i	0.739126	−	0.673567i	$-0.235239\pi$
$857$	9.57069	+	6.95351i	0.326928	+	0.237527i	−0.412198	+	0.911094i	$0.635239\pi$
$858$	3.51214	−	10.8093i	0.119903	−	0.369022i
$859$	−37.5353	+	27.2710i	−1.28069	+	0.930473i	−0.999574	−	0.0292012i	$-0.990704\pi$
$859$	−37.5353	+	27.2710i	−1.28069	+	0.930473i	−0.281113	+	0.959675i	$0.590704\pi$
$860$	−6.35679	+	4.61848i	−0.216765	+	0.157489i
$861$	2.70787	+	1.96738i	0.0922840	+	0.0670483i
$862$	16.6048			0.565561
$863$	−43.7536			−1.48939			−0.744695	−	0.667405i	$-0.767405\pi$
$863$	−43.7536			−1.48939			−0.744695	+	0.667405i	$0.767405\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	0.367551	+	1.13120i	0.0124971	+	0.0384621i
$866$	−4.14005	+	12.7418i	−0.140685	+	0.432982i
$867$	11.4798			0.389875
$868$	−4.91543	+	2.08138i	−0.166841	+	0.0706466i
$869$	15.4478			0.524029
$870$	−1.74635	+	5.37471i	−0.0592068	+	0.182220i
$871$	−10.6439	−	32.7587i	−0.360656	−	1.10999i
$872$	−4.00500	−	2.90981i	−0.135627	−	0.0985385i
$873$	15.9613			0.540207
$874$	−13.2807			−0.449225
$875$	−0.775623	−	0.563523i	−0.0262208	−	0.0190505i
$876$	1.40520	−	1.02094i	0.0474773	−	0.0344943i
$877$	23.9829	−	17.4246i	0.809846	−	0.588387i	−0.103940	−	0.994584i	$-0.533145\pi$
$877$	23.9829	−	17.4246i	0.809846	−	0.588387i	0.913786	+	0.406196i	$0.133145\pi$
$878$	8.26020	−	25.4223i	0.278768	−	0.857960i
$879$	−1.17626	−	0.854606i	−0.0396744	−	0.0288251i
$880$	−0.845097	+	2.60094i	−0.0284882	+	0.0876777i
$881$	−5.64452	−	17.3721i	−0.190169	−	0.585280i	0.809830	−	0.586664i	$-0.199559\pi$
$881$	−5.64452	−	17.3721i	−0.190169	−	0.585280i	−0.999999	+	0.00138481i	$0.999559\pi$
$882$	4.91951	−	3.57423i	0.165649	−	0.120351i
$883$	−3.10007	−	9.54104i	−0.104326	−	0.321082i	0.885246	−	0.465123i	$-0.153990\pi$
$883$	−3.10007	−	9.54104i	−0.104326	−	0.321082i	−0.989572	+	0.144042i	$0.953990\pi$
$884$	−3.01734	−	9.28642i	−0.101484	−	0.312336i
$885$	−5.52758	+	4.01602i	−0.185808	+	0.134997i
$886$	3.38251	+	10.4103i	0.113637	+	0.349740i
$887$	−1.78131	+	5.48232i	−0.0598107	+	0.184078i	−0.976498	−	0.215527i	$-0.930853\pi$
$887$	−1.78131	+	5.48232i	−0.0598107	+	0.184078i	0.916687	+	0.399606i	$0.130853\pi$
$888$	−5.54508	−	4.02874i	−0.186081	−	0.135196i
$889$	5.28016	−	16.2506i	0.177091	−	0.545029i
$890$	7.57763	−	5.50547i	0.254003	−	0.184544i
$891$	−2.21249	+	1.60747i	−0.0741213	+	0.0538523i
$892$	13.9402	+	10.1282i	0.466753	+	0.339116i
$893$	16.5970			0.555396
$894$	5.72968			0.191629
$895$	2.93035	+	2.12903i	0.0979510	+	0.0711655i
$896$	−0.296261	−	0.911799i	−0.00989740	−	0.0304611i
$897$	8.02051	−	24.6846i	0.267797	−	0.824195i
$898$	22.9541			0.765989
$899$	30.6525	+	7.10507i	1.02232	+	0.236967i
$900$	1.00000			0.0333333
$901$	1.35092	−	4.15771i	0.0450057	−	0.138513i
$902$	−2.95042	−	9.08046i	−0.0982383	−	0.302346i
$903$	6.09439	+	4.42784i	0.202809	+	0.147349i
$904$	9.60509			0.319460
$905$	−9.88614			−0.328626
$906$	−12.6414	−	9.18453i	−0.419983	−	0.305136i
$907$	−44.6260	+	32.4227i	−1.48178	+	1.07658i	−0.504805	+	0.863233i	$0.668436\pi$
$907$	−44.6260	+	32.4227i	−1.48178	+	1.07658i	−0.976977	+	0.213344i	$0.931564\pi$
$908$	9.11469	−	6.62221i	0.302481	−	0.219766i
$909$	1.06039	−	3.26356i	0.0351711	−	0.108245i
$910$	3.22341	+	2.34195i	0.106855	+	0.0776348i
$911$	0.273166	−	0.840717i	0.00905038	−	0.0278542i	−0.946429	−	0.322911i	$-0.895339\pi$
$911$	0.273166	−	0.840717i	0.00905038	−	0.0278542i	0.955480	+	0.295057i	$0.0953386\pi$
$912$	0.657125	+	2.02242i	0.0217596	+	0.0669691i
$913$	19.5902	−	14.2331i	0.648340	−	0.471047i
$914$	5.86916	+	18.0634i	0.194135	+	0.597485i
$915$	2.65027	+	8.15669i	0.0876152	+	0.269652i
$916$	2.46317	−	1.78960i	0.0813854	−	0.0591299i
$917$	−4.85551	−	14.9437i	−0.160343	−	0.493485i
$918$	−0.726037	+	2.23451i	−0.0239628	+	0.0737499i
$919$	6.25791	+	4.54664i	0.206429	+	0.149980i	0.686197	−	0.727416i	$-0.259279\pi$
$919$	6.25791	+	4.54664i	0.206429	+	0.149980i	−0.479767	+	0.877396i	$0.659279\pi$
$920$	−1.92991	+	5.93964i	−0.0636272	+	0.195824i
$921$	4.84561	−	3.52054i	0.159668	−	0.116006i
$922$	−20.5772	+	14.9502i	−0.677675	+	0.492360i
$923$	−10.7318	−	7.79710i	−0.353241	−	0.256645i
$924$	2.62191			0.0862544
$925$	−6.85410			−0.225361
$926$	5.83033	+	4.23598i	0.191597	+	0.139203i
$927$	5.06570	+	15.5906i	0.166379	+	0.512063i
$928$	−1.74635	+	5.37471i	−0.0573268	+	0.176434i
$929$	19.5028			0.639868			0.319934	−	0.947440i	$-0.396339\pi$
$929$	19.5028			0.639868			0.319934	+	0.947440i	$0.396339\pi$
$930$	−0.480387	−	5.54700i	−0.0157525	−	0.181893i
$931$	12.9309			0.423795
$932$	−4.56991	+	14.0648i	−0.149693	+	0.460706i
$933$	−3.40246	−	10.4717i	−0.111392	−	0.342828i
$934$	25.3597	+	18.4249i	0.829794	+	0.602881i
$935$	−6.42541			−0.210133
$936$	−4.15591			−0.135840
$937$	14.9591	+	10.8684i	0.488693	+	0.355056i	0.804681	−	0.593707i	$-0.202336\pi$
$937$	14.9591	+	10.8684i	0.488693	+	0.355056i	−0.315989	+	0.948763i	$0.602336\pi$
$938$	6.42843	−	4.67053i	0.209896	−	0.152498i
$939$	8.74489	−	6.35354i	0.285379	−	0.207340i
$940$	2.41182	−	7.42283i	0.0786650	−	0.242106i
$941$	−12.0218	−	8.73434i	−0.391899	−	0.284731i	0.374334	−	0.927294i	$-0.377871\pi$
$941$	−12.0218	−	8.73434i	−0.391899	−	0.284731i	−0.766233	+	0.642563i	$0.777871\pi$
$942$	−5.64572	+	17.3757i	−0.183947	+	0.566132i
$943$	−6.73774	−	20.7366i	−0.219411	−	0.675277i
$944$	−5.52758	+	4.01602i	−0.179907	+	0.130710i
$945$	−0.296261	−	0.911799i	−0.00963739	−	0.0296608i
$946$	−6.64028	−	20.4367i	−0.215894	−	0.664454i
$947$	−25.8444	+	18.7771i	−0.839831	+	0.610173i	−0.922324	−	0.386418i	$-0.873712\pi$
$947$	−25.8444	+	18.7771i	−0.839831	+	0.610173i	0.0824921	+	0.996592i	$0.473712\pi$
$948$	−1.74552	−	5.37214i	−0.0566917	−	0.174479i
$949$	−2.23063	+	6.86518i	−0.0724094	+	0.222853i
$950$	1.72038	+	1.24993i	0.0558164	+	0.0405530i
$951$	−2.25291	+	6.93374i	−0.0730556	+	0.224842i
$952$	1.82233	−	1.32400i	0.0590621	−	0.0429111i
$953$	48.7216	−	35.3983i	1.57825	−	1.14666i	0.659576	−	0.751637i	$-0.270736\pi$
$953$	48.7216	−	35.3983i	1.57825	−	1.14666i	0.918670	−	0.395026i	$-0.129264\pi$
$954$	−1.50532	−	1.09368i	−0.0487365	−	0.0354091i
$955$	7.36976			0.238480
$956$	6.20676			0.200741
$957$	−12.5035	−	9.08431i	−0.404180	−	0.293654i
$958$	−1.69595	−	5.21961i	−0.0547938	−	0.168638i
$959$	5.39171	−	16.5940i	0.174107	−	0.535848i
$960$	1.00000			0.0322749
$961$	−30.5385	+	5.32942i	−0.985112	+	0.171917i
$962$	28.4850			0.918393
$963$	−1.45640	+	4.48235i	−0.0469320	+	0.144442i
$964$	−4.74693	−	14.6096i	−0.152888	−	0.470542i
$965$	21.6670	+	15.7420i	0.697485	+	0.506753i
$966$	5.98752			0.192645
$967$	−44.4691			−1.43003			−0.715015	−	0.699109i	$-0.753580\pi$
$967$	−44.4691			−1.43003			−0.715015	+	0.699109i	$0.753580\pi$
$968$	2.84848	+	2.06954i	0.0915536	+	0.0665176i
$969$	−4.04203	+	2.93671i	−0.129849	+	0.0943407i
$970$	12.9129	−	9.38180i	0.414610	−	0.301232i
$971$	12.4707	−	38.3810i	0.400205	−	1.23170i	−0.524628	−	0.851331i	$-0.675796\pi$
$971$	12.4707	−	38.3810i	0.400205	−	1.23170i	0.924833	−	0.380373i	$-0.124204\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−5.86317	+	18.0450i	−0.187965	+	0.578496i
$974$	7.76754	+	23.9060i	0.248888	+	0.765998i
$975$	−3.36220	+	2.44278i	−0.107677	+	0.0782316i
$976$	2.65027	+	8.15669i	0.0848330	+	0.261089i
$977$	−15.3094	−	47.1174i	−0.489791	−	1.50742i	−0.824921	−	0.565249i	$-0.808780\pi$
$977$	−15.3094	−	47.1174i	−0.489791	−	1.50742i	0.335130	−	0.942172i	$-0.391220\pi$
$978$	−5.31217	+	3.85952i	−0.169864	+	0.123414i
$979$	7.91557	+	24.3616i	0.252983	+	0.778601i
$980$	1.87909	−	5.78323i	0.0600252	−	0.184739i
$981$	−4.00500	−	2.90981i	−0.127870	−	0.0929029i
$982$	−0.977575	+	3.00867i	−0.0311957	+	0.0960104i
$983$	15.5496	−	11.2974i	0.495954	−	0.360332i	−0.311516	−	0.950241i	$-0.600837\pi$
$983$	15.5496	−	11.2974i	0.495954	−	0.360332i	0.807469	+	0.589909i	$0.200837\pi$
$984$	−2.82446	+	2.05209i	−0.0900404	+	0.0654182i
$985$	2.32609	+	1.69000i	0.0741154	+	0.0538480i
$986$	−13.2778			−0.422851
$987$	−7.48266			−0.238176
$988$	−7.14972	−	5.19458i	−0.227463	−	0.165261i
$989$	−15.1641	−	46.6703i	−0.482190	−	1.48403i
$990$	−0.845097	+	2.60094i	−0.0268589	+	0.0826633i
$991$	21.2175			0.673998			0.336999	−	0.941505i	$-0.390588\pi$
$991$	21.2175			0.673998			0.336999	+	0.941505i	$0.390588\pi$
$992$	−0.480387	−	5.54700i	−0.0152523	−	0.176117i
$993$	20.8732			0.662392
$994$	0.945636	−	2.91037i	0.0299938	−	0.0923113i
$995$	−4.28910	−	13.2005i	−0.135974	−	0.418484i
$996$	−7.16332	−	5.20445i	−0.226978	−	0.164909i
$997$	−37.5234			−1.18838			−0.594188	−	0.804326i	$-0.702527\pi$
$997$	−37.5234			−1.18838			−0.594188	+	0.804326i	$0.702527\pi$
$998$	8.95462			0.283454
$999$	−5.54508	−	4.02874i	−0.175439	−	0.127464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.d.721.2	✓	12
31.4	even	5	inner	930.2.n.d.841.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.721.2	✓	12	1.1	even	1	trivial
930.2.n.d.841.2	yes	12	31.4	even	5	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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.775623 + 0.563523i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.775623 + 0.563523i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-2.21249 - 1.60747i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-1.28425 - 3.95250i) q^{13} +(0.775623 - 0.563523i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.90079 + 1.38100i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-0.657125 + 2.02242i) q^{19} +(0.809017 + 0.587785i) q^{20} +(0.296261 - 0.911799i) q^{21} +(-2.21249 + 1.60747i) q^{22} +(-5.05256 + 3.67090i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -4.15591 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.296261 - 0.911799i) q^{28} +(-1.74635 + 5.37471i) q^{29} +1.00000 q^{30} +(-0.480387 - 5.54700i) q^{31} +1.00000 q^{32} +(-0.845097 + 2.60094i) q^{33} +(0.726037 + 2.23451i) q^{34} +(-0.775623 - 0.563523i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(1.72038 + 1.24993i) q^{38} +(-3.36220 + 2.44278i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.07885 + 3.32035i) q^{41} +(-0.775623 - 0.563523i) q^{42} +(-2.42808 + 7.47285i) q^{43} +(0.845097 + 2.60094i) q^{44} +(0.809017 - 0.587785i) q^{45} +(1.92991 + 5.93964i) q^{46} +(-2.41182 - 7.42283i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.87909 - 5.78323i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.90079 + 1.38100i) q^{51} +(-1.28425 + 3.95250i) q^{52} +(-1.50532 + 1.09368i) q^{53} +(0.809017 - 0.587785i) q^{54} +(2.21249 + 1.60747i) q^{55} -0.958722 q^{56} +2.12650 q^{57} +(4.57201 + 3.32176i) q^{58} +(2.11135 + 6.49806i) q^{59} +(0.309017 - 0.951057i) q^{60} +8.57645 q^{61} +(-5.42396 - 1.25724i) q^{62} -0.958722 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.28425 + 3.95250i) q^{65} +(2.21249 + 1.60747i) q^{66} +8.28809 q^{67} +2.34951 q^{68} +(5.05256 + 3.67090i) q^{69} +(-0.775623 + 0.563523i) q^{70} +(2.58230 - 1.87615i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-1.40520 - 1.02094i) q^{73} +(-2.11803 + 6.51864i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(1.72038 - 1.24993i) q^{76} +(-0.810213 - 2.49358i) q^{77} +(1.28425 + 3.95250i) q^{78} +(-4.56982 + 3.32017i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.82446 + 2.05209i) q^{82} +(-2.73614 + 8.42098i) q^{83} +(-0.775623 + 0.563523i) q^{84} +(1.90079 - 1.38100i) q^{85} +(6.35679 + 4.61848i) q^{86} +5.65131 q^{87} +2.73479 q^{88} +(-7.57763 - 5.50547i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(1.23123 - 3.78935i) q^{91} +6.24531 q^{92} +(-5.12706 + 2.17099i) q^{93} -7.80482 q^{94} +(0.657125 - 2.02242i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-12.9129 - 9.38180i) q^{97} -6.08085 q^{98} +2.73479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

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