LMFDB - Embedded newform 665.2.i.h.106.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(106,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("665.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.i (of order $3$, 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:	$5.31005173442$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 20 x^{18} - 43 x^{17} + 207 x^{16} - 401 x^{15} + 1351 x^{14} - 2135 x^{13} + \cdots + 1024 $ x^20 - 3x^19 + 20x^18 - 43x^17 + 207x^16 - 401x^15 + 1351x^14 - 2135x^13 + 5714x^12 - 7983x^11 + 16723x^10 - 18718x^9 + 30867x^8 - 28726x^7 + 37857x^6 - 24848x^5 + 21360x^4 - 7488x^3 + 5888x^2 - 1536*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.2
Root			$-0.994744 + 1.72295i$ of defining polynomial
Character	$\chi$	$=$	665.106
Dual form			665.2.i.h.596.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994744 + 1.72295i) q^{2} +(0.457864 - 0.793043i) q^{3} +(-0.979030 - 1.69573i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.910914 + 1.57775i) q^{6} -1.00000 q^{7} -0.0834388 q^{8} +(1.08072 + 1.87186i) q^{9} +O(q^{10})$	\(q+(-0.994744 + 1.72295i) q^{2} +(0.457864 - 0.793043i) q^{3} +(-0.979030 - 1.69573i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.910914 + 1.57775i) q^{6} -1.00000 q^{7} -0.0834388 q^{8} +(1.08072 + 1.87186i) q^{9} +(0.994744 + 1.72295i) q^{10} +4.43179 q^{11} -1.79305 q^{12} +(-0.850001 - 1.47224i) q^{13} +(0.994744 - 1.72295i) q^{14} +(-0.457864 - 0.793043i) q^{15} +(2.04106 - 3.53522i) q^{16} +(2.62241 - 4.54215i) q^{17} -4.30016 q^{18} +(-3.22913 + 2.92792i) q^{19} -1.95806 q^{20} +(-0.457864 + 0.793043i) q^{21} +(-4.40849 + 7.63574i) q^{22} +(-0.410109 - 0.710330i) q^{23} +(-0.0382036 + 0.0661706i) q^{24} +(-0.500000 - 0.866025i) q^{25} +3.38213 q^{26} +4.72648 q^{27} +(0.979030 + 1.69573i) q^{28} +(1.00317 + 1.73754i) q^{29} +1.82183 q^{30} +9.36456 q^{31} +(3.97723 + 6.88876i) q^{32} +(2.02916 - 3.51460i) q^{33} +(5.21726 + 9.03656i) q^{34} +(-0.500000 + 0.866025i) q^{35} +(2.11612 - 3.66522i) q^{36} +9.69834 q^{37} +(-1.83249 - 8.47615i) q^{38} -1.55674 q^{39} +(-0.0417194 + 0.0722601i) q^{40} +(-4.61931 + 8.00088i) q^{41} +(-0.910914 - 1.57775i) q^{42} +(2.16054 - 3.74216i) q^{43} +(-4.33886 - 7.51512i) q^{44} +2.16144 q^{45} +1.63182 q^{46} +(-2.74990 - 4.76296i) q^{47} +(-1.86906 - 3.23730i) q^{48} +1.00000 q^{49} +1.98949 q^{50} +(-2.40142 - 4.15937i) q^{51} +(-1.66435 + 2.88274i) q^{52} +(4.05494 + 7.02337i) q^{53} +(-4.70163 + 8.14346i) q^{54} +(2.21589 - 3.83804i) q^{55} +0.0834388 q^{56} +(0.843463 + 3.90143i) q^{57} -3.99158 q^{58} +(5.04415 - 8.73673i) q^{59} +(-0.896525 + 1.55283i) q^{60} +(3.79046 + 6.56527i) q^{61} +(-9.31533 + 16.1346i) q^{62} +(-1.08072 - 1.87186i) q^{63} -7.66104 q^{64} -1.70000 q^{65} +(4.03698 + 6.99225i) q^{66} +(4.13244 + 7.15760i) q^{67} -10.2697 q^{68} -0.751097 q^{69} +(-0.994744 - 1.72295i) q^{70} +(-4.31840 + 7.47968i) q^{71} +(-0.0901741 - 0.156186i) q^{72} +(5.29336 - 9.16837i) q^{73} +(-9.64736 + 16.7097i) q^{74} -0.915727 q^{75} +(8.12638 + 2.60922i) q^{76} -4.43179 q^{77} +(1.54856 - 2.68218i) q^{78} +(-4.90961 + 8.50369i) q^{79} +(-2.04106 - 3.53522i) q^{80} +(-1.07808 + 1.86729i) q^{81} +(-9.19006 - 15.9177i) q^{82} -9.69804 q^{83} +1.79305 q^{84} +(-2.62241 - 4.54215i) q^{85} +(4.29837 + 7.44499i) q^{86} +1.83726 q^{87} -0.369783 q^{88} +(-5.38917 - 9.33432i) q^{89} +(-2.15008 + 3.72405i) q^{90} +(0.850001 + 1.47224i) q^{91} +(-0.803019 + 1.39087i) q^{92} +(4.28769 - 7.42650i) q^{93} +10.9418 q^{94} +(0.921086 + 4.26047i) q^{95} +7.28411 q^{96} +(4.61200 - 7.98823i) q^{97} +(-0.994744 + 1.72295i) q^{98} +(4.78953 + 8.29571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/665\mathbb{Z}\right)^\times$.

$n$	$211$	$267$	$381$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.994744	+	1.72295i	−0.703390	+	1.21831i	0.263879	+	0.964556i	$0.414998\pi$
$2$	−0.994744	+	1.72295i	−0.703390	+	1.21831i	−0.967269	+	0.253752i	$0.918335\pi$
$3$	0.457864	−	0.793043i	0.264348	−	0.457864i	−0.703045	−	0.711146i	$-0.748177\pi$
$3$	0.457864	−	0.793043i	0.264348	−	0.457864i	0.967393	+	0.253282i	$0.0815100\pi$
$4$	−0.979030	−	1.69573i	−0.489515	−	0.847865i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.910914	+	1.57775i	0.371879	+	0.644114i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.0834388			−0.0295001
$9$	1.08072	+	1.87186i	0.360241	+	0.623955i
$10$	0.994744	+	1.72295i	0.314566	+	0.544844i
$11$	4.43179			1.33623			0.668117	−	0.744056i	$-0.267100\pi$
$11$	4.43179			1.33623			0.668117	+	0.744056i	$0.267100\pi$
$12$	−1.79305			−0.517609
$13$	−0.850001	−	1.47224i	−0.235748	−	0.408327i	0.723742	−	0.690071i	$-0.242421\pi$
$13$	−0.850001	−	1.47224i	−0.235748	−	0.408327i	−0.959490	+	0.281744i	$0.909087\pi$
$14$	0.994744	−	1.72295i	0.265856	−	0.460477i
$15$	−0.457864	−	0.793043i	−0.118220	−	0.204763i
$16$	2.04106	−	3.53522i	0.510265	−	0.883805i
$17$	2.62241	−	4.54215i	0.636029	−	1.10163i	−0.350268	−	0.936650i	$-0.613909\pi$
$17$	2.62241	−	4.54215i	0.636029	−	1.10163i	0.986296	−	0.164984i	$-0.0527573\pi$
$18$	−4.30016			−1.01356
$19$	−3.22913	+	2.92792i	−0.740814	+	0.671711i
$19$	−3.22913	+	2.92792i	−0.740814	+	0.671711i
$20$	−1.95806			−0.437836
$21$	−0.457864	+	0.793043i	−0.0999141	+	0.173056i
$22$	−4.40849	+	7.63574i	−0.939894	+	1.62794i
$23$	−0.410109	−	0.710330i	−0.0855137	−	0.148114i	0.820096	−	0.572226i	$-0.193920\pi$
$23$	−0.410109	−	0.710330i	−0.0855137	−	0.148114i	−0.905610	+	0.424111i	$0.860586\pi$
$24$	−0.0382036	+	0.0661706i	−0.00779828	+	0.0135070i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.38213			0.663291
$27$	4.72648			0.909611
$28$	0.979030	+	1.69573i	0.185019	+	0.320463i
$29$	1.00317	+	1.73754i	0.186284	+	0.322653i	0.944008	−	0.329922i	$-0.107022\pi$
$29$	1.00317	+	1.73754i	0.186284	+	0.322653i	−0.757725	+	0.652574i	$0.773689\pi$
$30$	1.82183			0.332619
$31$	9.36456			1.68192			0.840962	−	0.541094i	$-0.181990\pi$
$31$	9.36456			1.68192			0.840962	+	0.541094i	$0.181990\pi$
$32$	3.97723	+	6.88876i	0.703081	+	1.21777i
$33$	2.02916	−	3.51460i	0.353231	−	0.611813i
$34$	5.21726	+	9.03656i	0.894752	+	1.54976i
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	2.11612	−	3.66522i	0.352686	−	0.610871i
$37$	9.69834			1.59440			0.797199	−	0.603717i	$-0.206314\pi$
$37$	9.69834			1.59440			0.797199	+	0.603717i	$0.206314\pi$
$38$	−1.83249	−	8.47615i	−0.297269	−	1.37501i
$39$	−1.55674			−0.249278
$40$	−0.0417194	+	0.0722601i	−0.00659642	+	0.0114253i
$41$	−4.61931	+	8.00088i	−0.721415	+	1.24953i	0.239017	+	0.971015i	$0.423175\pi$
$41$	−4.61931	+	8.00088i	−0.721415	+	1.24953i	−0.960433	+	0.278513i	$0.910159\pi$
$42$	−0.910914	−	1.57775i	−0.140557	−	0.243452i
$43$	2.16054	−	3.74216i	0.329479	−	0.570675i	−0.652929	−	0.757419i	$-0.726460\pi$
$43$	2.16054	−	3.74216i	0.329479	−	0.570675i	0.982409	+	0.186744i	$0.0597935\pi$
$44$	−4.33886	−	7.51512i	−0.654107	−	1.13295i
$45$	2.16144			0.322209
$46$	1.63182			0.240598
$47$	−2.74990	−	4.76296i	−0.401114	−	0.694750i	0.592747	−	0.805389i	$-0.298044\pi$
$47$	−2.74990	−	4.76296i	−0.401114	−	0.694750i	−0.993861	+	0.110639i	$0.964710\pi$
$48$	−1.86906	−	3.23730i	−0.269775	−	0.467264i
$49$	1.00000			0.142857
$50$	1.98949			0.281356
$51$	−2.40142	−	4.15937i	−0.336265	−	0.582429i
$52$	−1.66435	+	2.88274i	−0.230804	+	0.399765i
$53$	4.05494	+	7.02337i	0.556989	+	0.964733i	0.997746	+	0.0671068i	$0.0213768\pi$
$53$	4.05494	+	7.02337i	0.556989	+	0.964733i	−0.440757	+	0.897627i	$0.645290\pi$
$54$	−4.70163	+	8.14346i	−0.639811	+	1.10819i
$55$	2.21589	−	3.83804i	0.298791	−	0.517522i
$56$	0.0834388			0.0111500
$57$	0.843463	+	3.90143i	0.111719	+	0.516757i
$58$	−3.99158			−0.524120
$59$	5.04415	−	8.73673i	0.656693	−	1.13743i	−0.324774	−	0.945792i	$-0.605288\pi$
$59$	5.04415	−	8.73673i	0.656693	−	1.13743i	0.981467	−	0.191633i	$-0.0613785\pi$
$60$	−0.896525	+	1.55283i	−0.115741	+	0.200469i
$61$	3.79046	+	6.56527i	0.485319	+	0.840597i	0.999858	−	0.0168700i	$-0.00537014\pi$
$61$	3.79046	+	6.56527i	0.485319	+	0.840597i	−0.514539	+	0.857467i	$0.672037\pi$
$62$	−9.31533	+	16.1346i	−1.18305	+	2.04910i
$63$	−1.08072	−	1.87186i	−0.136158	−	0.235833i
$64$	−7.66104			−0.957630
$65$	−1.70000			−0.210859
$66$	4.03698	+	6.99225i	0.496918	+	0.860687i
$67$	4.13244	+	7.15760i	0.504858	+	0.874440i	0.999984	+	0.00561904i	$0.00178861\pi$
$67$	4.13244	+	7.15760i	0.504858	+	0.874440i	−0.495126	+	0.868821i	$0.664878\pi$
$68$	−10.2697			−1.24538
$69$	−0.751097			−0.0904215
$70$	−0.994744	−	1.72295i	−0.118895	−	0.205932i
$71$	−4.31840	+	7.47968i	−0.512499	+	0.887675i	0.487396	+	0.873181i	$0.337947\pi$
$71$	−4.31840	+	7.47968i	−0.512499	+	0.887675i	−0.999895	+	0.0144937i	$0.995386\pi$
$72$	−0.0901741	−	0.156186i	−0.0106271	−	0.0184067i
$73$	5.29336	−	9.16837i	0.619541	−	1.07308i	−0.370028	−	0.929020i	$-0.620652\pi$
$73$	5.29336	−	9.16837i	0.619541	−	1.07308i	0.989569	−	0.144056i	$-0.0460146\pi$
$74$	−9.64736	+	16.7097i	−1.12148	+	1.94247i
$75$	−0.915727			−0.105739
$76$	8.12638	+	2.60922i	0.932159	+	0.299298i
$77$	−4.43179			−0.505049
$78$	1.54856	−	2.68218i	0.175339	−	0.303697i
$79$	−4.90961	+	8.50369i	−0.552374	+	0.956740i	0.445728	+	0.895168i	$0.352945\pi$
$79$	−4.90961	+	8.50369i	−0.552374	+	0.956740i	−0.998103	+	0.0615720i	$0.980389\pi$
$80$	−2.04106	−	3.53522i	−0.228197	−	0.395250i
$81$	−1.07808	+	1.86729i	−0.119787	+	0.207477i
$82$	−9.19006	−	15.9177i	−1.01487	−	1.75781i
$83$	−9.69804			−1.06450			−0.532249	−	0.846588i	$-0.678653\pi$
$83$	−9.69804			−1.06450			−0.532249	+	0.846588i	$0.678653\pi$
$84$	1.79305			0.195638
$85$	−2.62241	−	4.54215i	−0.284441	−	0.492666i
$86$	4.29837	+	7.44499i	0.463505	+	0.802814i
$87$	1.83726			0.196975
$88$	−0.369783			−0.0394190
$89$	−5.38917	−	9.33432i	−0.571251	−	0.989436i	−0.996438	−	0.0843302i	$-0.973125\pi$
$89$	−5.38917	−	9.33432i	−0.571251	−	0.989436i	0.425187	−	0.905106i	$-0.360208\pi$
$90$	−2.15008	+	3.72405i	−0.226639	+	0.392549i
$91$	0.850001	+	1.47224i	0.0891043	+	0.154333i
$92$	−0.803019	+	1.39087i	−0.0837205	+	0.145008i
$93$	4.28769	−	7.42650i	0.444613	−	0.770092i
$94$	10.9418			1.12856
$95$	0.921086	+	4.26047i	0.0945014	+	0.437115i
$96$	7.28411			0.743431
$97$	4.61200	−	7.98823i	0.468278	−	0.811081i	−0.531065	−	0.847331i	$-0.678208\pi$
$97$	4.61200	−	7.98823i	0.468278	−	0.811081i	0.999343	+	0.0362499i	$0.0115412\pi$
$98$	−0.994744	+	1.72295i	−0.100484	+	0.174044i
$99$	4.78953	+	8.29571i	0.481366	+	0.833750i
$100$	−0.979030	+	1.69573i	−0.0979030	+	0.169573i
$101$	−2.26586	−	3.92459i	−0.225462	−	0.390511i	0.730996	−	0.682382i	$-0.239056\pi$
$101$	−2.26586	−	3.92459i	−0.225462	−	0.390511i	−0.956458	+	0.291870i	$0.905722\pi$
$102$	9.55517			0.946103
$103$	−4.38168			−0.431740			−0.215870	−	0.976422i	$-0.569259\pi$
$103$	−4.38168			−0.431740			−0.215870	+	0.976422i	$0.569259\pi$
$104$	0.0709231	+	0.122842i	0.00695458	+	0.0120457i
$105$	0.457864	+	0.793043i	0.0446829	+	0.0773931i
$106$	−16.1345			−1.56712
$107$	−15.2617			−1.47541			−0.737703	−	0.675125i	$-0.764090\pi$
$107$	−15.2617			−1.47541			−0.737703	+	0.675125i	$0.764090\pi$
$108$	−4.62736	−	8.01483i	−0.445268	−	0.771227i
$109$	6.90431	−	11.9586i	0.661313	−	1.14543i	−0.318957	−	0.947769i	$-0.603333\pi$
$109$	6.90431	−	11.9586i	0.661313	−	1.14543i	0.980271	−	0.197659i	$-0.0633340\pi$
$110$	4.40849	+	7.63574i	0.420333	+	0.728039i
$111$	4.44052	−	7.69120i	0.421475	−	0.730017i
$112$	−2.04106	+	3.53522i	−0.192862	+	0.334047i
$113$	−11.5767			−1.08905			−0.544524	−	0.838745i	$-0.683290\pi$
$113$	−11.5767			−1.08905			−0.544524	+	0.838745i	$0.683290\pi$
$114$	−7.56098	−	2.42768i	−0.708151	−	0.227373i
$115$	−0.820219			−0.0764858
$116$	1.96426	−	3.40220i	0.182377	−	0.315887i
$117$	1.83723	−	3.18217i	0.169852	−	0.294192i
$118$	10.0353	+	17.3816i	0.923822	+	1.60011i
$119$	−2.62241	+	4.54215i	−0.240396	+	0.416378i
$120$	0.0382036	+	0.0661706i	0.00348750	+	0.00604052i
$121$	8.64076			0.785523
$122$	−15.0822			−1.36547
$123$	4.23003	+	7.32663i	0.381409	+	0.660620i
$124$	−9.16818	−	15.8798i	−0.823327	−	1.42604i
$125$	−1.00000			−0.0894427
$126$	4.30016			0.383089
$127$	6.27769	+	10.8733i	0.557055	+	0.964847i	0.997740	+	0.0671859i	$0.0214021\pi$
$127$	6.27769	+	10.8733i	0.557055	+	0.964847i	−0.440686	+	0.897662i	$0.645265\pi$
$128$	−0.333682	+	0.577954i	−0.0294936	+	0.0510844i
$129$	−1.97847	−	3.42680i	−0.174194	−	0.301713i
$130$	1.69107	−	2.92901i	0.148316	−	0.256891i
$131$	5.39585	−	9.34589i	0.471438	−	0.816554i	−0.528028	−	0.849227i	$-0.677069\pi$
$131$	5.39585	−	9.34589i	0.471438	−	0.816554i	0.999466	+	0.0326726i	$0.0104019\pi$
$132$	−7.94642			−0.691647
$133$	3.22913	−	2.92792i	0.280001	−	0.253883i
$134$	−16.4429			−1.42045
$135$	2.36324	−	4.09325i	0.203395	−	0.352291i
$136$	−0.218811	+	0.378992i	−0.0187629	+	0.0324983i
$137$	−2.24151	−	3.88240i	−0.191505	−	0.331696i	0.754244	−	0.656594i	$-0.228003\pi$
$137$	−2.24151	−	3.88240i	−0.191505	−	0.331696i	−0.945749	+	0.324898i	$0.894670\pi$
$138$	0.747149	−	1.29410i	0.0636016	−	0.110161i
$139$	−2.40916	−	4.17280i	−0.204343	−	0.353932i	0.745580	−	0.666416i	$-0.232172\pi$
$139$	−2.40916	−	4.17280i	−0.204343	−	0.353932i	−0.949923	+	0.312484i	$0.898839\pi$
$140$	1.95806			0.165486
$141$	−5.03632			−0.424134
$142$	−8.59140	−	14.8807i	−0.720974	−	1.24876i
$143$	−3.76703	−	6.52468i	−0.315014	−	0.545621i
$144$	8.82327			0.735273
$145$	2.00634			0.166617
$146$	10.5311	+	18.2404i	0.871558	+	1.50958i
$147$	0.457864	−	0.793043i	0.0377640	−	0.0654091i
$148$	−9.49497	−	16.4458i	−0.780482	−	1.35183i
$149$	10.7047	−	18.5412i	0.876967	−	1.51895i	0.0223139	−	0.999751i	$-0.492897\pi$
$149$	10.7047	−	18.5412i	0.876967	−	1.51895i	0.854653	−	0.519200i	$-0.173770\pi$
$150$	0.910914	−	1.57775i	0.0743758	−	0.128823i
$151$	4.67743			0.380644			0.190322	−	0.981722i	$-0.439047\pi$
$151$	4.67743			0.380644			0.190322	+	0.981722i	$0.439047\pi$
$152$	0.269435	−	0.244302i	0.0218541	−	0.0198155i
$153$	11.3364			0.916493
$154$	4.40849	−	7.63574i	0.355247	−	0.615305i
$155$	4.68228	−	8.10994i	0.376090	−	0.651406i
$156$	1.52409	+	2.63981i	0.122025	+	0.211354i
$157$	−4.85087	+	8.40195i	−0.387142	+	0.670549i	−0.992064	−	0.125736i	$-0.959871\pi$
$157$	−4.85087	+	8.40195i	−0.387142	+	0.670549i	0.604922	+	0.796285i	$0.293204\pi$
$158$	−9.76761	−	16.9180i	−0.777069	−	1.34592i
$159$	7.42644			0.588955
$160$	7.95445			0.628855
$161$	0.410109	+	0.710330i	0.0323212	+	0.0559819i
$162$	−2.14483	−	3.71496i	−0.168514	−	0.291875i
$163$	−17.7041			−1.38669			−0.693345	−	0.720606i	$-0.743864\pi$
$163$	−17.7041			−1.38669			−0.693345	+	0.720606i	$0.743864\pi$
$164$	18.0898			1.41257
$165$	−2.02916	−	3.51460i	−0.157970	−	0.273611i
$166$	9.64706	−	16.7092i	0.748757	−	1.29689i
$167$	−2.15881	−	3.73917i	−0.167054	−	0.289346i	0.770329	−	0.637647i	$-0.220092\pi$
$167$	−2.15881	−	3.73917i	−0.167054	−	0.289346i	−0.937383	+	0.348301i	$0.886759\pi$
$168$	0.0382036	−	0.0661706i	0.00294747	−	0.00510517i
$169$	5.05500	−	8.75551i	0.388846	−	0.673501i
$170$	10.4345			0.800291
$171$	−8.97046	−	2.88023i	−0.685988	−	0.220257i
$172$	−8.46093			−0.645140
$173$	−3.59616	+	6.22873i	−0.273411	+	0.473562i	−0.969733	−	0.244168i	$-0.921485\pi$
$173$	−3.59616	+	6.22873i	−0.273411	+	0.473562i	0.696322	+	0.717730i	$0.254819\pi$
$174$	−1.82760	+	3.16549i	−0.138550	+	0.239976i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	9.04555	−	15.6674i	0.681834	−	1.18097i
$177$	−4.61907	−	8.00046i	−0.347190	−	0.601352i
$178$	21.4434			1.60725
$179$	−24.6582			−1.84304			−0.921521	−	0.388329i	$-0.873053\pi$
$179$	−24.6582			−1.84304			−0.921521	+	0.388329i	$0.873053\pi$
$180$	−2.11612	−	3.66522i	−0.157726	−	0.273190i
$181$	8.34885	+	14.4606i	0.620565	+	1.07485i	0.989381	+	0.145348i	$0.0464301\pi$
$181$	8.34885	+	14.4606i	0.620565	+	1.07485i	−0.368815	+	0.929503i	$0.620237\pi$
$182$	−3.38213			−0.250700
$183$	6.94206			0.513172
$184$	0.0342191	+	0.0592691i	0.00252266	+	0.00436938i
$185$	4.84917	−	8.39901i	0.356518	−	0.617508i
$186$	8.53031	+	14.7749i	0.625472	+	1.08335i
$187$	11.6220	−	20.1299i	0.849884	−	1.47204i
$188$	−5.38447	+	9.32617i	−0.392703	+	0.680181i
$189$	−4.72648			−0.343800
$190$	−8.25681	−	2.65109i	−0.599012	−	0.192331i
$191$	7.87328			0.569691			0.284845	−	0.958573i	$-0.408058\pi$
$191$	7.87328			0.569691			0.284845	+	0.958573i	$0.408058\pi$
$192$	−3.50771	+	6.07553i	−0.253147	+	0.438464i
$193$	−9.94073	+	17.2178i	−0.715549	+	1.23937i	0.247198	+	0.968965i	$0.420490\pi$
$193$	−9.94073	+	17.2178i	−0.715549	+	1.23937i	−0.962747	+	0.270403i	$0.912843\pi$
$194$	9.17552	+	15.8925i	0.658764	+	1.14101i
$195$	−0.778369	+	1.34818i	−0.0557402	+	0.0965448i
$196$	−0.979030	−	1.69573i	−0.0699307	−	0.121124i
$197$	8.62383			0.614422			0.307211	−	0.951641i	$-0.400604\pi$
$197$	8.62383			0.614422			0.307211	+	0.951641i	$0.400604\pi$
$198$	−19.0574			−1.35435
$199$	0.484938	+	0.839937i	0.0343763	+	0.0595416i	0.882702	−	0.469934i	$-0.155722\pi$
$199$	0.484938	+	0.839937i	0.0343763	+	0.0595416i	−0.848325	+	0.529475i	$0.822389\pi$
$200$	0.0417194	+	0.0722601i	0.00295001	+	0.00510956i
$201$	7.56838			0.533833
$202$	9.01581			0.634350
$203$	−1.00317	−	1.73754i	−0.0704086	−	0.121951i
$204$	−4.70212	+	8.14430i	−0.329214	+	0.570215i
$205$	4.61931	+	8.00088i	0.322627	+	0.558806i
$206$	4.35865	−	7.54940i	0.303681	−	0.525992i
$207$	0.886428	−	1.53534i	0.0616110	−	0.106713i
$208$	−6.93961			−0.481176
$209$	−14.3108	+	12.9759i	−0.989901	+	0.897563i
$210$	−1.82183			−0.125718
$211$	2.92448	−	5.06535i	0.201329	−	0.348713i	−0.747628	−	0.664118i	$-0.768807\pi$
$211$	2.92448	−	5.06535i	0.201329	−	0.348713i	0.948957	+	0.315405i	$0.102140\pi$
$212$	7.93982	−	13.7522i	0.545309	−	0.944503i
$213$	3.95447	+	6.84935i	0.270956	+	0.469310i
$214$	15.1815	−	26.2951i	1.03779	−	1.79750i
$215$	−2.16054	−	3.74216i	−0.147348	−	0.255213i
$216$	−0.394372			−0.0268336
$217$	−9.36456			−0.635708
$218$	13.7360	+	23.7915i	0.930322	+	1.61137i
$219$	−4.84728	−	8.39573i	−0.327549	−	0.567331i
$220$	−8.67771			−0.585051
$221$	−8.91621			−0.599769
$222$	8.83436	+	15.3016i	0.592923	+	1.02697i
$223$	4.94545	−	8.56578i	0.331172	−	0.573607i	−0.651570	−	0.758589i	$-0.725889\pi$
$223$	4.94545	−	8.56578i	0.331172	−	0.573607i	0.982742	+	0.184982i	$0.0592226\pi$
$224$	−3.97723	−	6.88876i	−0.265740	−	0.460274i
$225$	1.08072	−	1.87186i	0.0720481	−	0.124791i
$226$	11.5159	−	19.9461i	0.766026	−	1.32680i
$227$	−26.2987			−1.74551			−0.872753	−	0.488162i	$-0.837667\pi$
$227$	−26.2987			−1.74551			−0.872753	+	0.488162i	$0.837667\pi$
$228$	5.78999	−	5.24990i	0.383452	−	0.347683i
$229$	20.9191			1.38237			0.691186	−	0.722677i	$-0.257089\pi$
$229$	20.9191			1.38237			0.691186	+	0.722677i	$0.257089\pi$
$230$	0.815908	−	1.41319i	0.0537994	−	0.0931832i
$231$	−2.02916	+	3.51460i	−0.133509	+	0.231244i
$232$	−0.0837031	−	0.144978i	−0.00549538	−	0.00951828i
$233$	2.41247	−	4.17853i	0.158046	−	0.273744i	−0.776118	−	0.630588i	$-0.782814\pi$
$233$	2.41247	−	4.17853i	0.158046	−	0.273744i	0.934164	+	0.356844i	$0.116147\pi$
$234$	3.65514	+	6.33089i	0.238944	+	0.413863i
$235$	−5.49980			−0.358767
$236$	−19.7535			−1.28584
$237$	4.49586	+	7.78707i	0.292038	+	0.505824i
$238$	−5.21726	−	9.03656i	−0.338185	−	0.585753i
$239$	−4.34456			−0.281026			−0.140513	−	0.990079i	$-0.544875\pi$
$239$	−4.34456			−0.281026			−0.140513	+	0.990079i	$0.544875\pi$
$240$	−3.73811			−0.241294
$241$	−14.0011	−	24.2507i	−0.901892	−	1.56212i	−0.825035	−	0.565081i	$-0.808845\pi$
$241$	−14.0011	−	24.2507i	−0.901892	−	1.56212i	−0.0768573	−	0.997042i	$-0.524489\pi$
$242$	−8.59534	+	14.8876i	−0.552529	+	0.957009i
$243$	8.07694	+	13.9897i	0.518136	+	0.897438i
$244$	7.42195	−	12.8552i	0.475142	−	0.822970i
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	−16.8312			−1.07312
$247$	7.05538	+	2.26534i	0.448923	+	0.144140i
$248$	−0.781368			−0.0496169
$249$	−4.44038	+	7.69096i	−0.281398	+	0.487395i
$250$	0.994744	−	1.72295i	0.0629131	−	0.108969i
$251$	7.41051	+	12.8354i	0.467748	+	0.810162i	0.999321	−	0.0368498i	$-0.0117323\pi$
$251$	7.41051	+	12.8354i	0.467748	+	0.810162i	−0.531573	+	0.847012i	$0.678399\pi$
$252$	−2.11612	+	3.66522i	−0.133303	+	0.230887i
$253$	−1.81752	−	3.14804i	−0.114266	−	0.197915i
$254$	−24.9788			−1.56731
$255$	−4.80283			−0.300765
$256$	−8.32489	−	14.4191i	−0.520306	−	0.901196i
$257$	−4.88103	−	8.45419i	−0.304470	−	0.527358i	0.672673	−	0.739940i	$-0.265146\pi$
$257$	−4.88103	−	8.45419i	−0.304470	−	0.527358i	−0.977143	+	0.212582i	$0.931813\pi$
$258$	7.87226			0.490106
$259$	−9.69834			−0.602626
$260$	1.66435	+	2.88274i	0.103219	+	0.178780i
$261$	−2.16829	+	3.75559i	−0.134214	+	0.232465i
$262$	10.7350	+	18.5935i	0.663209	+	1.14871i
$263$	−15.6522	+	27.1104i	−0.965156	+	1.67170i	−0.255962	+	0.966687i	$0.582392\pi$
$263$	−15.6522	+	27.1104i	−0.965156	+	1.67170i	−0.709195	+	0.705013i	$0.750941\pi$
$264$	−0.169310	+	0.293254i	−0.0104203	+	0.0180485i
$265$	8.10988			0.498186
$266$	1.83249	+	8.47615i	0.112357	+	0.519706i
$267$	−9.87002			−0.604036
$268$	8.09157	−	14.0150i	0.494271	−	0.856103i
$269$	−9.28129	+	16.0757i	−0.565890	+	0.980150i	0.431076	+	0.902315i	$0.358134\pi$
$269$	−9.28129	+	16.0757i	−0.565890	+	0.980150i	−0.996966	+	0.0778347i	$0.975199\pi$
$270$	4.70163	+	8.14346i	0.286132	+	0.495595i
$271$	−6.75053	+	11.6923i	−0.410065	+	0.710254i	−0.994896	−	0.100901i	$-0.967827\pi$
$271$	−6.75053	+	11.6923i	−0.410065	+	0.710254i	0.584831	+	0.811155i	$0.301161\pi$
$272$	−10.7050	−	18.5416i	−0.649086	−	1.12425i
$273$	1.55674			0.0942181
$274$	8.91890			0.538811
$275$	−2.21589	−	3.83804i	−0.133623	−	0.231443i
$276$	0.735347	+	1.27366i	0.0442627	+	0.0766652i
$277$	−28.9926			−1.74199			−0.870997	−	0.491289i	$-0.836526\pi$
$277$	−28.9926			−1.74199			−0.870997	+	0.491289i	$0.836526\pi$
$278$	9.58601			0.574930
$279$	10.1205	+	17.5292i	0.605897	+	1.04944i
$280$	0.0417194	−	0.0722601i	0.00249321	−	0.00431837i
$281$	1.42721	+	2.47200i	0.0851402	+	0.147467i	0.905451	−	0.424451i	$-0.139533\pi$
$281$	1.42721	+	2.47200i	0.0851402	+	0.147467i	−0.820311	+	0.571918i	$0.806200\pi$
$282$	5.00984	−	8.67730i	0.298332	−	0.516726i
$283$	0.695780	−	1.20513i	0.0413598	−	0.0716373i	−0.844604	−	0.535391i	$-0.820164\pi$
$283$	0.695780	−	1.20513i	0.0413598	−	0.0716373i	0.885964	+	0.463753i	$0.153498\pi$
$284$	16.9114			1.00350
$285$	3.80047	+	1.22025i	0.225120	+	0.0722816i
$286$	14.9889			0.886312
$287$	4.61931	−	8.00088i	0.272669	−	0.472277i
$288$	−8.59655	+	14.8897i	−0.506556	+	0.877381i
$289$	−5.25410	−	9.10037i	−0.309065	−	0.535316i
$290$	−1.99579	+	3.45681i	−0.117197	+	0.202991i
$291$	−4.22334	−	7.31504i	−0.247577	−	0.428815i
$292$	−20.7294			−1.21310
$293$	15.5291			0.907219			0.453609	−	0.891201i	$-0.350136\pi$
$293$	15.5291			0.907219			0.453609	+	0.891201i	$0.350136\pi$
$294$	0.910914	+	1.57775i	0.0531256	+	0.0920162i
$295$	−5.04415	−	8.73673i	−0.293682	−	0.508672i
$296$	−0.809218			−0.0470349
$297$	20.9467			1.21545
$298$	21.2970	+	36.8874i	1.23370	+	2.13683i
$299$	−0.697187	+	1.20756i	−0.0403194	+	0.0698352i
$300$	0.896525	+	1.55283i	0.0517609	+	0.0896525i
$301$	−2.16054	+	3.74216i	−0.124531	+	0.215695i
$302$	−4.65284	+	8.05896i	−0.267741	+	0.463741i
$303$	−4.14982			−0.238401
$304$	3.75998	+	17.3918i	0.215650	+	0.997485i
$305$	7.58092			0.434083
$306$	−11.2768	+	19.5320i	−0.644652	+	1.11657i
$307$	−7.66052	+	13.2684i	−0.437209	+	0.757268i	−0.997473	−	0.0710458i	$-0.977366\pi$
$307$	−7.66052	+	13.2684i	−0.437209	+	0.757268i	0.560264	+	0.828314i	$0.310700\pi$
$308$	4.33886	+	7.51512i	0.247229	+	0.428214i
$309$	−2.00621	+	3.47486i	−0.114129	+	0.197678i
$310$	9.31533	+	16.1346i	0.529075	+	0.916385i
$311$	−13.0831			−0.741873			−0.370936	−	0.928658i	$-0.620963\pi$
$311$	−13.0831			−0.741873			−0.370936	+	0.928658i	$0.620963\pi$
$312$	0.129892			0.00735371
$313$	6.42046	+	11.1206i	0.362906	+	0.628571i	0.988438	−	0.151627i	$-0.0484514\pi$
$313$	6.42046	+	11.1206i	0.362906	+	0.628571i	−0.625532	+	0.780198i	$0.715118\pi$
$314$	−9.65074	−	16.7156i	−0.544623	−	0.943315i
$315$	−2.16144			−0.121784
$316$	19.2266			1.08158
$317$	−0.658663	−	1.14084i	−0.0369942	−	0.0640758i	0.846936	−	0.531696i	$-0.178445\pi$
$317$	−0.658663	−	1.14084i	−0.0369942	−	0.0640758i	−0.883930	+	0.467620i	$0.845112\pi$
$318$	−7.38741	+	12.7954i	−0.414265	+	0.717528i
$319$	4.44583	+	7.70040i	0.248919	+	0.431140i
$320$	−3.83052	+	6.63465i	−0.214132	+	0.370888i
$321$	−6.98779	+	12.1032i	−0.390020	+	0.675535i
$322$	−1.63182			−0.0909375
$323$	4.83093	+	22.3454i	0.268800	+	1.24333i
$324$	4.22190			0.234550
$325$	−0.850001	+	1.47224i	−0.0471496	+	0.0816654i
$326$	17.6110	−	30.5032i	0.975384	−	1.68941i
$327$	−6.32247	−	10.9508i	−0.349633	−	0.605583i
$328$	0.385430	−	0.667584i	0.0212818	−	0.0368612i
$329$	2.74990	+	4.76296i	0.151607	+	0.262591i
$330$	8.07396			0.444457
$331$	−23.5737			−1.29573			−0.647865	−	0.761755i	$-0.724338\pi$
$331$	−23.5737			−1.29573			−0.647865	+	0.761755i	$0.724338\pi$
$332$	9.49467	+	16.4453i	0.521088	+	0.902550i
$333$	10.4812	+	18.1540i	0.574367	+	0.994832i
$334$	8.58986			0.470016
$335$	8.26489			0.451559
$336$	1.86906	+	3.23730i	0.101965	+	0.176609i
$337$	11.0442	−	19.1291i	0.601615	−	1.04203i	−0.390962	−	0.920407i	$-0.627858\pi$
$337$	11.0442	−	19.1291i	0.601615	−	1.04203i	0.992577	−	0.121621i	$-0.0388091\pi$
$338$	10.0569	+	17.4190i	0.547021	+	0.947468i
$339$	−5.30057	+	9.18086i	−0.287888	+	0.498636i
$340$	−5.13484	+	8.89381i	−0.278476	+	0.482334i
$341$	41.5017			2.24745
$342$	13.8858	−	12.5905i	0.750858	−	0.680818i
$343$	−1.00000			−0.0539949
$344$	−0.180273	+	0.312242i	−0.00971966	+	0.0168349i
$345$	−0.375549	+	0.650469i	−0.0202189	+	0.0350201i
$346$	−7.15452	−	12.3920i	−0.384629	−	0.666197i
$347$	13.5125	−	23.4044i	0.725390	−	1.25641i	−0.233424	−	0.972375i	$-0.574993\pi$
$347$	13.5125	−	23.4044i	0.725390	−	1.25641i	0.958813	−	0.284037i	$-0.0916738\pi$
$348$	−1.79873	−	3.11549i	−0.0964220	−	0.167008i
$349$	−20.6428			−1.10498			−0.552491	−	0.833519i	$-0.686323\pi$
$349$	−20.6428			−1.10498			−0.552491	+	0.833519i	$0.686323\pi$
$350$	−1.98949			−0.106343
$351$	−4.01751	−	6.95853i	−0.214439	−	0.371419i
$352$	17.6262	+	30.5295i	0.939481	+	1.62723i
$353$	23.3170			1.24104			0.620520	−	0.784191i	$-0.286922\pi$
$353$	23.3170			1.24104			0.620520	+	0.784191i	$0.286922\pi$
$354$	18.3792			0.976841
$355$	4.31840	+	7.47968i	0.229197	+	0.396980i
$356$	−10.5523	+	18.2772i	−0.559272	+	0.968687i
$357$	2.40142	+	4.15937i	0.127096	+	0.220137i
$358$	24.5286	−	42.4848i	1.29638	−	2.24539i
$359$	−12.9639	+	22.4541i	−0.684206	+	1.18508i	0.289480	+	0.957184i	$0.406518\pi$
$359$	−12.9639	+	22.4541i	−0.684206	+	1.18508i	−0.973686	+	0.227895i	$0.926816\pi$
$360$	−0.180348			−0.00950519
$361$	1.85459	−	18.9093i	0.0976099	−	0.995225i
$362$	−33.2199			−1.74600
$363$	3.95629	−	6.85249i	0.207651	−	0.359663i
$364$	1.66435	−	2.88274i	0.0872358	−	0.151097i
$365$	−5.29336	−	9.16837i	−0.277067	−	0.479895i
$366$	−6.90557	+	11.9608i	−0.360960	+	0.625201i
$367$	0.551085	+	0.954508i	0.0287664	+	0.0498249i	0.880050	−	0.474881i	$-0.157509\pi$
$367$	0.551085	+	0.954508i	0.0287664	+	0.0498249i	−0.851284	+	0.524706i	$0.824175\pi$
$368$	−3.34823			−0.174539
$369$	−19.9688			−1.03953
$370$	9.64736	+	16.7097i	0.501543	+	0.868697i
$371$	−4.05494	−	7.02337i	−0.210522	−	0.364635i
$372$	−16.7911			−0.870579
$373$	−15.4671			−0.800856			−0.400428	−	0.916328i	$-0.631138\pi$
$373$	−15.4671			−0.800856			−0.400428	+	0.916328i	$0.631138\pi$
$374$	23.1218	+	40.0481i	1.19560	+	2.07084i
$375$	−0.457864	+	0.793043i	−0.0236440	+	0.0409526i
$376$	0.229448	+	0.397416i	0.0118329	+	0.0204952i
$377$	1.70539	−	2.95382i	0.0878319	−	0.152129i
$378$	4.70163	−	8.14346i	0.241826	−	0.418855i
$379$	3.94751			0.202770			0.101385	−	0.994847i	$-0.467673\pi$
$379$	3.94751			0.202770			0.101385	+	0.994847i	$0.467673\pi$
$380$	6.32283	−	5.73304i	0.324355	−	0.294099i
$381$	11.4973			0.589025
$382$	−7.83190	+	13.5652i	−0.400715	+	0.694058i
$383$	−0.804839	+	1.39402i	−0.0411253	+	0.0712312i	−0.885855	−	0.463961i	$-0.846428\pi$
$383$	−0.804839	+	1.39402i	−0.0411253	+	0.0712312i	0.844730	+	0.535193i	$0.179761\pi$
$384$	0.305562	+	0.529248i	0.0155931	+	0.0270081i
$385$	−2.21589	+	3.83804i	−0.112932	+	0.195605i
$386$	−19.7770	−	34.2547i	−1.00662	−	1.74352i
$387$	9.33977			0.474767
$388$	−18.0612			−0.916917
$389$	17.1776	+	29.7525i	0.870941	+	1.50851i	0.861025	+	0.508563i	$0.169823\pi$
$389$	17.1776	+	29.7525i	0.870941	+	1.50851i	0.00991602	+	0.999951i	$0.496844\pi$
$390$	−1.54856	−	2.68218i	−0.0784142	−	0.135817i
$391$	−4.30191			−0.217557
$392$	−0.0834388			−0.00421430
$393$	−4.94113	−	8.55829i	−0.249247	−	0.431709i
$394$	−8.57850	+	14.8584i	−0.432179	+	0.748555i
$395$	4.90961	+	8.50369i	0.247029	+	0.427867i
$396$	9.37819	−	16.2435i	0.471272	−	0.816267i
$397$	−5.82735	+	10.0933i	−0.292466	+	0.506566i	−0.974392	−	0.224855i	$-0.927809\pi$
$397$	−5.82735	+	10.0933i	−0.292466	+	0.506566i	0.681926	+	0.731421i	$0.261143\pi$
$398$	−1.92956			−0.0967199
$399$	−0.843463	−	3.90143i	−0.0422260	−	0.195316i
$400$	−4.08212			−0.204106
$401$	7.50609	−	13.0009i	0.374836	−	0.649235i	−0.615466	−	0.788163i	$-0.711032\pi$
$401$	7.50609	−	13.0009i	0.374836	−	0.649235i	0.990303	+	0.138928i	$0.0443656\pi$
$402$	−7.52860	+	13.0399i	−0.375493	+	0.650372i
$403$	−7.95988	−	13.7869i	−0.396510	−	0.686775i
$404$	−4.43669	+	7.68458i	−0.220734	+	0.382322i
$405$	1.07808	+	1.86729i	0.0535704	+	0.0927866i
$406$	3.99158			0.198099
$407$	42.9810			2.13049
$408$	0.200371	+	0.347053i	0.00991986	+	0.0171817i
$409$	5.36662	+	9.29526i	0.265362	+	0.459621i	0.967658	−	0.252264i	$-0.0811751\pi$
$409$	5.36662	+	9.29526i	0.265362	+	0.459621i	−0.702296	+	0.711885i	$0.747842\pi$
$410$	−18.3801			−0.907730
$411$	−4.10522			−0.202496
$412$	4.28980	+	7.43014i	0.211343	+	0.366057i
$413$	−5.04415	+	8.73673i	−0.248207	+	0.429906i
$414$	1.76354	+	3.05454i	0.0866732	+	0.150122i
$415$	−4.84902	+	8.39875i	−0.238029	+	0.412278i
$416$	6.76129	−	11.7109i	0.331500	−	0.574174i
$417$	−4.41228			−0.216070
$418$	−8.12120	−	37.5645i	−0.397221	−	1.83734i
$419$	−34.3950			−1.68031			−0.840153	−	0.542350i	$-0.817535\pi$
$419$	−34.3950			−1.68031			−0.840153	+	0.542350i	$0.817535\pi$
$420$	0.896525	−	1.55283i	0.0437459	−	0.0757702i
$421$	1.85549	−	3.21380i	0.0904310	−	0.156631i	−0.817262	−	0.576267i	$-0.804509\pi$
$421$	1.85549	−	3.21380i	0.0904310	−	0.156631i	0.907693	+	0.419636i	$0.137842\pi$
$422$	5.81821	+	10.0774i	0.283226	+	0.490562i
$423$	5.94375	−	10.2949i	0.288995	−	0.500554i
$424$	−0.338340	−	0.586021i	−0.0164312	−	0.0284597i
$425$	−5.24483			−0.254411
$426$	−15.7348			−0.762351
$427$	−3.79046	−	6.56527i	−0.183433	−	0.317716i
$428$	14.9417	+	25.8798i	0.722234	+	1.25095i
$429$	−6.89914			−0.333093
$430$	8.59673			0.414571
$431$	5.58733	+	9.67755i	0.269132	+	0.466151i	0.968638	−	0.248476i	$-0.0799297\pi$
$431$	5.58733	+	9.67755i	0.269132	+	0.466151i	−0.699506	+	0.714627i	$0.746596\pi$
$432$	9.64702	−	16.7091i	0.464143	−	0.803918i
$433$	6.30928	+	10.9280i	0.303205	+	0.525166i	0.976860	−	0.213880i	$-0.0686101\pi$
$433$	6.30928	+	10.9280i	0.303205	+	0.525166i	−0.673655	+	0.739046i	$0.735277\pi$
$434$	9.31533	−	16.1346i	0.447150	−	0.774487i
$435$	0.918628	−	1.59111i	0.0440448	−	0.0762879i
$436$	−27.0381			−1.29489
$437$	3.40409	+	1.09298i	0.162840	+	0.0522845i
$438$	19.2872			0.921578
$439$	13.3176	−	23.0668i	0.635616	−	1.10092i	−0.350768	−	0.936462i	$-0.614079\pi$
$439$	13.3176	−	23.0668i	0.635616	−	1.10092i	0.986384	−	0.164457i	$-0.0525872\pi$
$440$	−0.184892	+	0.320242i	−0.00881436	+	0.0152669i
$441$	1.08072	+	1.87186i	0.0514629	+	0.0891364i
$442$	8.86935	−	15.3622i	0.421872	−	0.730703i
$443$	−7.45064	−	12.9049i	−0.353991	−	0.613130i	0.632954	−	0.774189i	$-0.281842\pi$
$443$	−7.45064	−	12.9049i	−0.353991	−	0.613130i	−0.986945	+	0.161059i	$0.948509\pi$
$444$	−17.3896			−0.825274
$445$	−10.7783			−0.510942
$446$	9.83892	+	17.0415i	0.465886	+	0.806939i
$447$	−9.80263	−	16.9786i	−0.463648	−	0.803063i
$448$	7.66104			0.361950
$449$	8.48319			0.400347			0.200173	−	0.979761i	$-0.435849\pi$
$449$	8.48319			0.400347			0.200173	+	0.979761i	$0.435849\pi$
$450$	2.15008	+	3.72405i	0.101356	+	0.175553i
$451$	−20.4718	+	35.4582i	−0.963980	+	1.66966i
$452$	11.3340	+	19.6310i	0.533106	+	0.923366i
$453$	2.14162	−	3.70940i	0.100622	−	0.174283i
$454$	26.1605	−	45.3112i	1.22777	−	2.12656i
$455$	1.70000			0.0796973
$456$	−0.0703776	−	0.325531i	−0.00329573	−	0.0152444i
$457$	1.54588			0.0723133			0.0361566	−	0.999346i	$-0.488488\pi$
$457$	1.54588			0.0723133			0.0361566	+	0.999346i	$0.488488\pi$
$458$	−20.8091	+	36.0424i	−0.972346	+	1.68415i
$459$	12.3948	−	21.4684i	0.578538	−	1.00206i
$460$	0.803019	+	1.39087i	0.0374410	+	0.0648496i
$461$	−0.914453	+	1.58388i	−0.0425903	+	0.0737686i	−0.886535	−	0.462662i	$-0.846894\pi$
$461$	−0.914453	+	1.58388i	−0.0425903	+	0.0737686i	0.843944	+	0.536431i	$0.180228\pi$
$462$	−4.03698	−	6.99225i	−0.187817	−	0.325309i
$463$	0.969451			0.0450542			0.0225271	−	0.999746i	$-0.492829\pi$
$463$	0.969451			0.0450542			0.0225271	+	0.999746i	$0.492829\pi$
$464$	8.19010			0.380216
$465$	−4.28769	−	7.42650i	−0.198837	−	0.344396i
$466$	4.79958	+	8.31312i	0.222336	+	0.385098i
$467$	−7.10205			−0.328643			−0.164322	−	0.986407i	$-0.552544\pi$
$467$	−7.10205			−0.328643			−0.164322	+	0.986407i	$0.552544\pi$
$468$	−7.19481			−0.332580
$469$	−4.13244	−	7.15760i	−0.190819	−	0.330507i
$470$	5.47089	−	9.47586i	0.252353	−	0.437089i
$471$	4.44207	+	7.69390i	0.204680	+	0.354516i
$472$	−0.420878	+	0.728982i	−0.0193725	+	0.0335541i
$473$	9.57506	−	16.5845i	0.440262	−	0.762555i
$474$	−17.8889			−0.821666
$475$	4.15022	+	1.33255i	0.190425	+	0.0611416i
$476$	10.2697			0.470710
$477$	−8.76453	+	15.1806i	−0.401300	+	0.695072i
$478$	4.32173	−	7.48545i	0.197671	−	0.342376i
$479$	−17.6042	−	30.4914i	−0.804357	−	1.39319i	−0.916724	−	0.399520i	$-0.869177\pi$
$479$	−17.6042	−	30.4914i	−0.804357	−	1.39319i	0.112368	−	0.993667i	$-0.464157\pi$
$480$	3.64205	−	6.30822i	0.166236	−	0.287930i
$481$	−8.24360	−	14.2783i	−0.375876	−	0.651036i
$482$	55.7102			2.53753
$483$	0.751097			0.0341761
$484$	−8.45956	−	14.6524i	−0.384526	−	0.666018i
$485$	−4.61200	−	7.98823i	−0.209420	−	0.362727i
$486$	−32.1380			−1.45781
$487$	−29.4396			−1.33403			−0.667017	−	0.745042i	$-0.732429\pi$
$487$	−29.4396			−1.33403			−0.667017	+	0.745042i	$0.732429\pi$
$488$	−0.316272	−	0.547799i	−0.0143170	−	0.0247977i
$489$	−8.10605	+	14.0401i	−0.366568	+	0.634915i
$490$	0.994744	+	1.72295i	0.0449379	+	0.0778348i
$491$	−2.38240	+	4.12644i	−0.107516	+	0.186224i	−0.914763	−	0.403990i	$-0.867623\pi$
$491$	−2.38240	+	4.12644i	−0.107516	+	0.186224i	0.807247	+	0.590213i	$0.200956\pi$
$492$	8.28265	−	14.3460i	0.373411	−	0.646767i
$493$	10.5229			0.473927
$494$	−10.9214	+	9.90261i	−0.491375	+	0.445539i
$495$	9.57906			0.430547
$496$	19.1136	−	33.1058i	0.858227	−	1.48649i
$497$	4.31840	−	7.47968i	0.193707	−	0.335510i
$498$	−8.83408	−	15.3011i	−0.395865	−	0.685658i
$499$	−7.45072	+	12.9050i	−0.333540	+	0.577708i	−0.983203	−	0.182514i	$-0.941577\pi$
$499$	−7.45072	+	12.9050i	−0.333540	+	0.577708i	0.649663	+	0.760222i	$0.274910\pi$
$500$	0.979030	+	1.69573i	0.0437836	+	0.0758353i
$501$	−3.95377			−0.176641
$502$	−29.4862			−1.31604
$503$	4.12274	+	7.14079i	0.183824	+	0.318392i	0.943180	−	0.332284i	$-0.107819\pi$
$503$	4.12274	+	7.14079i	0.183824	+	0.318392i	−0.759356	+	0.650676i	$0.774486\pi$
$504$	0.0901741	+	0.156186i	0.00401668	+	0.00695709i
$505$	−4.53172			−0.201659
$506$	7.23186			0.321495
$507$	−4.62900	−	8.01766i	−0.205581	−	0.356077i
$508$	12.2921	−	21.2905i	0.545374	−	0.944615i
$509$	−11.3564	−	19.6698i	−0.503363	−	0.871850i	−0.999992	−	0.00388766i	$-0.998763\pi$
$509$	−11.3564	−	19.6698i	−0.503363	−	0.871850i	0.496629	−	0.867963i	$-0.334571\pi$
$510$	4.77759	−	8.27502i	0.211555	−	0.366424i
$511$	−5.29336	+	9.16837i	−0.234165	+	0.405585i
$512$	31.7898			1.40492
$513$	−15.2624	+	13.8387i	−0.673852	+	0.610995i
$514$	19.4215			0.856645
$515$	−2.19084	+	3.79465i	−0.0965399	+	0.167212i
$516$	−3.87395	+	6.70989i	−0.170541	+	0.295386i
$517$	−12.1870	−	21.1085i	−0.535982	−	0.928349i
$518$	9.64736	−	16.7097i	0.423881	−	0.734183i
$519$	3.29310	+	5.70382i	0.144551	+	0.250370i
$520$	0.141846			0.00622037
$521$	9.20220			0.403156			0.201578	−	0.979473i	$-0.435393\pi$
$521$	9.20220			0.403156			0.201578	+	0.979473i	$0.435393\pi$
$522$	−4.31379	−	7.47170i	−0.188809	−	0.327027i
$523$	16.0678	+	27.8303i	0.702597	+	1.21693i	0.967552	+	0.252672i	$0.0813095\pi$
$523$	16.0678	+	27.8303i	0.702597	+	1.21693i	−0.264955	+	0.964261i	$0.585357\pi$
$524$	−21.1308			−0.923103
$525$	0.915727			0.0399656
$526$	−31.1399	−	53.9358i	−1.35776	−	2.35171i
$527$	24.5577	−	42.5352i	1.06975	−	1.85286i
$528$	−8.28326	−	14.3470i	−0.360483	−	0.624374i
$529$	11.1636	−	19.3360i	0.485375	−	0.840694i
$530$	−8.06726	+	13.9729i	−0.350419	+	0.606944i
$531$	21.8053			0.946269
$532$	−8.12638	−	2.60922i	−0.352323	−	0.113124i
$533$	15.7057			0.680288
$534$	9.81814	−	17.0055i	0.424873	−	0.735901i
$535$	−7.63086	+	13.2170i	−0.329911	+	0.571423i
$536$	−0.344806	−	0.597222i	−0.0148934	−	0.0257961i
$537$	−11.2901	+	19.5550i	−0.487204	+	0.843862i
$538$	−18.4650	−	31.9823i	−0.796083	−	1.37886i
$539$	4.43179			0.190891
$540$	−9.25472			−0.398260
$541$	6.27803	+	10.8739i	0.269914	+	0.467504i	0.968839	−	0.247690i	$-0.0796715\pi$
$541$	6.27803	+	10.8739i	0.269914	+	0.467504i	−0.698926	+	0.715194i	$0.746338\pi$
$542$	−13.4301	−	23.2616i	−0.576872	−	0.999171i
$543$	15.2905			0.656180
$544$	41.7197			1.78872
$545$	−6.90431	−	11.9586i	−0.295748	−	0.512251i
$546$	−1.54856	+	2.68218i	−0.0662721	+	0.114787i
$547$	19.8411	+	34.3658i	0.848344	+	1.46938i	0.882685	+	0.469965i	$0.155733\pi$
$547$	19.8411	+	34.3658i	0.848344	+	1.46938i	−0.0343409	+	0.999410i	$0.510933\pi$
$548$	−4.38901	+	7.60198i	−0.187489	+	0.324741i
$549$	−8.19287	+	14.1905i	−0.349663	+	0.605634i
$550$	8.81699			0.375958
$551$	−8.32673	−	2.67354i	−0.354731	−	0.113897i
$552$	0.0626707			0.00266744
$553$	4.90961	−	8.50369i	0.208778	−	0.361614i
$554$	28.8402	−	49.9526i	1.22530	−	2.12228i
$555$	−4.44052	−	7.69120i	−0.188490	−	0.326473i
$556$	−4.71729	+	8.17059i	−0.200058	+	0.346510i
$557$	−9.21381	−	15.9588i	−0.390402	−	0.676195i	0.602101	−	0.798420i	$-0.294330\pi$
$557$	−9.21381	−	15.9588i	−0.390402	−	0.676195i	−0.992502	+	0.122225i	$0.960997\pi$
$558$	−40.2691			−1.70473
$559$	−7.34584			−0.310696
$560$	2.04106	+	3.53522i	0.0862505	+	0.149390i
$561$	−10.6426	−	18.4335i	−0.449330	−	0.778262i
$562$	−5.67883			−0.239547
$563$	13.2602			0.558852			0.279426	−	0.960167i	$-0.409856\pi$
$563$	13.2602			0.558852			0.279426	+	0.960167i	$0.409856\pi$
$564$	4.93071	+	8.54023i	0.207620	+	0.359609i
$565$	−5.78837	+	10.0258i	−0.243519	+	0.421787i
$566$	1.38425	+	2.39758i	0.0581842	+	0.100778i
$567$	1.07808	−	1.86729i	0.0452752	−	0.0784190i
$568$	0.360322	−	0.624096i	0.0151188	−	0.0261865i
$569$	−13.5316			−0.567274			−0.283637	−	0.958932i	$-0.591541\pi$
$569$	−13.5316			−0.567274			−0.283637	+	0.958932i	$0.591541\pi$
$570$	−5.88292	+	5.33416i	−0.246409	+	0.223424i
$571$	−7.53858			−0.315480			−0.157740	−	0.987481i	$-0.550421\pi$
$571$	−7.53858			−0.315480			−0.157740	+	0.987481i	$0.550421\pi$
$572$	−7.37606	+	12.7757i	−0.308409	+	0.534179i
$573$	3.60489	−	6.24385i	0.150596	−	0.260841i
$574$	9.19006	+	15.9177i	0.383586	+	0.664390i
$575$	−0.410109	+	0.710330i	−0.0171027	+	0.0296228i
$576$	−8.27945	−	14.3404i	−0.344977	−	0.597518i
$577$	24.0460			1.00105			0.500524	−	0.865722i	$-0.333141\pi$
$577$	24.0460			1.00105			0.500524	+	0.865722i	$0.333141\pi$
$578$	20.9059			0.869572
$579$	9.10300	+	15.7669i	0.378308	+	0.655248i
$580$	−1.96426	−	3.40220i	−0.0815616	−	0.141269i
$581$	9.69804			0.402342
$582$	16.8046			0.696571
$583$	17.9706	+	31.1261i	0.744268	+	1.28911i
$584$	−0.441672	+	0.764998i	−0.0182765	+	0.0316559i
$585$	−1.83723	−	3.18217i	−0.0759601	−	0.131567i
$586$	−15.4475	+	26.7558i	−0.638129	+	1.10527i
$587$	−14.8607	+	25.7394i	−0.613366	+	1.06238i	0.377303	+	0.926090i	$0.376852\pi$
$587$	−14.8607	+	25.7394i	−0.613366	+	1.06238i	−0.990669	+	0.136291i	$0.956482\pi$
$588$	−1.79305			−0.0739441
$589$	−30.2394	+	27.4187i	−1.24599	+	1.12977i
$590$	20.0706			0.826292
$591$	3.94854	−	6.83907i	0.162421	−	0.281322i
$592$	19.7949	−	34.2858i	0.813565	−	1.40914i
$593$	19.9132	+	34.4907i	0.817737	+	1.41636i	0.907346	+	0.420385i	$0.138105\pi$
$593$	19.9132	+	34.4907i	0.817737	+	1.41636i	−0.0896089	+	0.995977i	$0.528562\pi$
$594$	−20.8366	+	36.0901i	−0.854938	+	1.48080i
$595$	2.62241	+	4.54215i	0.107508	+	0.186210i
$596$	−41.9211			−1.71715
$597$	0.888142			0.0363492
$598$	−1.38704	−	2.40243i	−0.0567205	−	0.0982427i
$599$	−11.7753	−	20.3955i	−0.481127	−	0.833337i	0.518638	−	0.854994i	$-0.326439\pi$
$599$	−11.7753	−	20.3955i	−0.481127	−	0.833337i	−0.999765	+	0.0216567i	$0.993106\pi$
$600$	0.0764072			0.00311931
$601$	−6.97902			−0.284680			−0.142340	−	0.989818i	$-0.545463\pi$
$601$	−6.97902			−0.284680			−0.142340	+	0.989818i	$0.545463\pi$
$602$	−4.29837	−	7.44499i	−0.175188	−	0.303435i
$603$	−8.93204	+	15.4708i	−0.363741	+	0.630018i
$604$	−4.57934	−	7.93165i	−0.186331	−	0.322734i
$605$	4.32038	−	7.48312i	0.175648	−	0.304232i
$606$	4.12801	−	7.14993i	0.167689	−	0.290446i
$607$	17.5841			0.713717			0.356859	−	0.934158i	$-0.383848\pi$
$607$	17.5841			0.713717			0.356859	+	0.934158i	$0.383848\pi$
$608$	−33.0127	−	10.5997i	−1.33884	−	0.429875i
$609$	−1.83726			−0.0744494
$610$	−7.54108	+	13.0615i	−0.305329	+	0.528846i
$611$	−4.67483	+	8.09705i	−0.189124	+	0.327572i
$612$	−11.0987	−	19.2235i	−0.448637	−	0.777062i
$613$	−1.44371	+	2.50058i	−0.0583109	+	0.100997i	−0.893707	−	0.448651i	$-0.851905\pi$
$613$	−1.44371	+	2.50058i	−0.0583109	+	0.100997i	0.835396	+	0.549648i	$0.185238\pi$
$614$	−15.2405	−	26.3973i	−0.615057	−	1.06531i
$615$	8.46006			0.341143
$616$	0.369783			0.0148990
$617$	16.0617	+	27.8196i	0.646619	+	1.11998i	0.983925	+	0.178581i	$0.0571507\pi$
$617$	16.0617	+	27.8196i	0.646619	+	1.11998i	−0.337307	+	0.941395i	$0.609516\pi$
$618$	−3.99133	−	6.91319i	−0.160555	−	0.278089i
$619$	17.7856			0.714864			0.357432	−	0.933939i	$-0.383652\pi$
$619$	17.7856			0.714864			0.357432	+	0.933939i	$0.383652\pi$
$620$	−18.3364			−0.736406
$621$	−1.93837	−	3.35736i	−0.0777842	−	0.134726i
$622$	13.0143	−	22.5414i	0.521826	−	0.903829i
$623$	5.38917	+	9.33432i	0.215913	+	0.373972i
$624$	−3.17740	+	5.50341i	−0.127198	+	0.220313i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−25.5468			−1.02106
$627$	3.73805	+	17.2903i	0.149283	+	0.690509i
$628$	18.9966			0.758046
$629$	25.4331	−	44.0514i	1.01408	−	1.75644i
$630$	2.15008	−	3.72405i	0.0856613	−	0.148370i
$631$	−8.71029	−	15.0867i	−0.346751	−	0.600591i	0.638919	−	0.769274i	$-0.279382\pi$
$631$	−8.71029	−	15.0867i	−0.346751	−	0.600591i	−0.985670	+	0.168683i	$0.946049\pi$
$632$	0.409652	−	0.709538i	0.0162951	−	0.0282239i
$633$	−2.67803	−	4.63848i	−0.106442	−	0.184363i
$634$	2.62080			0.104085
$635$	12.5554			0.498245
$636$	−7.27071	−	12.5932i	−0.288302	−	0.499355i
$637$	−0.850001	−	1.47224i	−0.0336783	−	0.0583325i
$638$	−17.6898			−0.700347
$639$	−18.6679			−0.738492
$640$	0.333682	+	0.577954i	0.0131899	+	0.0228456i
$641$	−12.0488	+	20.8691i	−0.475898	+	0.824279i	−0.999619	−	0.0276106i	$-0.991210\pi$
$641$	−12.0488	+	20.8691i	−0.475898	+	0.824279i	0.523721	+	0.851890i	$0.324543\pi$
$642$	−13.9021	−	24.0792i	−0.548673	−	0.950329i
$643$	3.50148	−	6.06475i	0.138085	−	0.239170i	−0.788687	−	0.614795i	$-0.789239\pi$
$643$	3.50148	−	6.06475i	0.138085	−	0.239170i	0.926772	+	0.375625i	$0.122572\pi$
$644$	0.803019	−	1.39087i	0.0316434	−	0.0548079i
$645$	−3.95693			−0.155804
$646$	−43.3055	−	13.9045i	−1.70383	−	0.547066i
$647$	8.12854			0.319566			0.159783	−	0.987152i	$-0.448921\pi$
$647$	8.12854			0.319566			0.159783	+	0.987152i	$0.448921\pi$
$648$	0.0899540	−	0.155805i	0.00353373	−	0.00612059i
$649$	22.3546	−	38.7193i	0.877496	−	1.51987i
$650$	−1.69107	−	2.92901i	−0.0663291	−	0.114885i
$651$	−4.28769	+	7.42650i	−0.168048	+	0.291067i
$652$	17.3328	+	30.0213i	0.678805	+	1.17573i
$653$	41.7308			1.63305			0.816527	−	0.577308i	$-0.195897\pi$
$653$	41.7308			1.63305			0.816527	+	0.577308i	$0.195897\pi$
$654$	25.1570			0.983715
$655$	−5.39585	−	9.34589i	−0.210833	−	0.365174i
$656$	18.8566	+	32.6606i	0.736226	+	1.27518i
$657$	22.8826			0.892735
$658$	−10.9418			−0.426555
$659$	−4.11320	−	7.12428i	−0.160228	−	0.277522i	0.774723	−	0.632301i	$-0.217889\pi$
$659$	−4.11320	−	7.12428i	−0.160228	−	0.277522i	−0.934950	+	0.354779i	$0.884556\pi$
$660$	−3.97321	+	6.88180i	−0.154657	+	0.267874i
$661$	17.0862	+	29.5941i	0.664575	+	1.15108i	0.979400	+	0.201928i	$0.0647206\pi$
$661$	17.0862	+	29.5941i	0.664575	+	1.15108i	−0.314826	+	0.949149i	$0.601946\pi$
$662$	23.4498	−	40.6163i	0.911403	−	1.57860i
$663$	−4.08241	+	7.07094i	−0.158548	+	0.274613i
$664$	0.809193			0.0314028
$665$	−0.921086	−	4.26047i	−0.0357182	−	0.165214i
$666$	−41.7045			−1.61602
$667$	0.822817	−	1.42516i	0.0318596	−	0.0551825i
$668$	−4.22708	+	7.32153i	−0.163551	+	0.283278i
$669$	−4.52869	−	7.84392i	−0.175089	−	0.303263i
$670$	−8.22144	+	14.2400i	−0.317622	+	0.550138i
$671$	16.7985	+	29.0959i	0.648500	+	1.12324i
$672$	−7.28411			−0.280991
$673$	−1.60931			−0.0620342			−0.0310171	−	0.999519i	$-0.509875\pi$
$673$	−1.60931			−0.0620342			−0.0310171	+	0.999519i	$0.509875\pi$
$674$	21.9723	+	38.0571i	0.846340	+	1.46590i
$675$	−2.36324	−	4.09325i	−0.0909611	−	0.157549i
$676$	−19.7960			−0.761384
$677$	−38.3610			−1.47433			−0.737167	−	0.675711i	$-0.763837\pi$
$677$	−38.3610			−1.47433			−0.737167	+	0.675711i	$0.763837\pi$
$678$	−10.5454	−	18.2652i	−0.404994	−	0.701471i
$679$	−4.61200	+	7.98823i	−0.176992	+	0.306560i
$680$	0.218811	+	0.378992i	0.00839102	+	0.0145337i
$681$	−12.0412	+	20.8560i	−0.461421	+	0.799204i
$682$	−41.2836	+	71.5053i	−1.58083	+	2.73808i
$683$	−44.3981			−1.69884			−0.849422	−	0.527714i	$-0.823049\pi$
$683$	−44.3981			−1.69884			−0.849422	+	0.527714i	$0.823049\pi$
$684$	3.89825	+	18.0313i	0.149053	+	0.689444i
$685$	−4.48301			−0.171287
$686$	0.994744	−	1.72295i	0.0379795	−	0.0657824i
$687$	9.57808	−	16.5897i	0.365427	−	0.632938i
$688$	−8.81958	−	15.2760i	−0.336243	−	0.582391i
$689$	6.89341	−	11.9397i	0.262618	−	0.454868i
$690$	−0.747149	−	1.29410i	−0.0284435	−	0.0492656i
$691$	−7.38244			−0.280841			−0.140421	−	0.990092i	$-0.544845\pi$
$691$	−7.38244			−0.280841			−0.140421	+	0.990092i	$0.544845\pi$
$692$	14.0830			0.535355
$693$	−4.78953	−	8.29571i	−0.181939	−	0.315128i
$694$	26.8830	+	46.5627i	1.02046	+	1.76750i
$695$	−4.81833			−0.182770
$696$	−0.153299			−0.00581077
$697$	24.2275	+	41.9632i	0.917681	+	1.58947i
$698$	20.5343	−	35.5664i	0.777233	−	1.34621i
$699$	−2.20917	−	3.82639i	−0.0835584	−	0.144727i
$700$	0.979030	−	1.69573i	0.0370039	−	0.0640926i
$701$	16.3209	−	28.2686i	0.616431	−	1.06769i	−0.373701	−	0.927549i	$-0.621911\pi$
$701$	16.3209	−	28.2686i	0.616431	−	1.06769i	0.990132	−	0.140140i	$-0.0447554\pi$
$702$	15.9856			0.603336
$703$	−31.3172	+	28.3960i	−1.18115	+	1.07097i
$704$	−33.9521			−1.27962
$705$	−2.51816	+	4.36158i	−0.0948393	+	0.164267i
$706$	−23.1944	+	40.1740i	−0.872935	+	1.51197i
$707$	2.26586	+	3.92459i	0.0852165	+	0.147599i
$708$	−9.04441	+	15.6654i	−0.339910	+	0.588741i
$709$	−5.12172	−	8.87107i	−0.192350	−	0.333160i	0.753679	−	0.657243i	$-0.228278\pi$
$709$	−5.12172	−	8.87107i	−0.192350	−	0.333160i	−0.946029	+	0.324083i	$0.894944\pi$
$710$	−17.1828			−0.644859
$711$	−21.2237			−0.795950
$712$	0.449666	+	0.778845i	0.0168520	+	0.0291884i
$713$	−3.84049	−	6.65193i	−0.143828	−	0.249117i
$714$	−9.55517			−0.357593
$715$	−7.53405			−0.281758
$716$	24.1411	+	41.8137i	0.902197	+	1.56265i
$717$	−1.98922	+	3.44543i	−0.0742887	+	0.128672i
$718$	−25.7914	−	44.6721i	−0.962527	−	1.66715i
$719$	−10.3004	+	17.8408i	−0.384141	+	0.665351i	−0.991650	−	0.128962i	$-0.958836\pi$
$719$	−10.3004	+	17.8408i	−0.384141	+	0.665351i	0.607509	+	0.794313i	$0.292169\pi$
$720$	4.41164	−	7.64118i	0.164412	−	0.284770i
$721$	4.38168			0.163182
$722$	30.7348	+	22.0052i	1.14383	+	0.818950i
$723$	−25.6425			−0.953653
$724$	16.3476	−	28.3148i	0.607552	−	1.05231i
$725$	1.00317	−	1.73754i	0.0372567	−	0.0645305i
$726$	7.87099	+	13.6330i	0.292120	+	0.505966i
$727$	4.00462	−	6.93620i	0.148523	−	0.257249i	−0.782159	−	0.623079i	$-0.785881\pi$
$727$	4.00462	−	6.93620i	0.148523	−	0.257249i	0.930682	+	0.365830i	$0.119215\pi$
$728$	−0.0709231	−	0.122842i	−0.00262858	−	0.00455284i
$729$	8.32406			0.308299
$730$	21.0622			0.779545
$731$	−11.3317	−	19.6270i	−0.419116	−	0.725931i
$732$	−6.79649	−	11.7719i	−0.251205	−	0.435100i
$733$	−32.0241			−1.18284			−0.591418	−	0.806365i	$-0.701432\pi$
$733$	−32.0241			−1.18284			−0.591418	+	0.806365i	$0.701432\pi$
$734$	−2.19275			−0.0809361
$735$	−0.457864	−	0.793043i	−0.0168886	−	0.0292518i
$736$	3.26220	−	5.65029i	0.120246	−	0.208272i
$737$	18.3141	+	31.7210i	0.674609	+	1.16846i
$738$	19.8638	−	34.4051i	0.731196	−	1.26647i
$739$	13.0855	−	22.6648i	0.481358	−	0.833737i	−0.518413	−	0.855131i	$-0.673477\pi$
$739$	13.0855	−	22.6648i	0.481358	−	0.833737i	0.999771	+	0.0213934i	$0.00681025\pi$
$740$	−18.9899			−0.698084
$741$	5.02691	−	4.55800i	0.184668	−	0.167442i
$742$	16.1345			0.592317
$743$	−0.536635	+	0.929479i	−0.0196872	+	0.0340993i	−0.875701	−	0.482853i	$-0.839600\pi$
$743$	−0.536635	+	0.929479i	−0.0196872	+	0.0340993i	0.856014	+	0.516953i	$0.172934\pi$
$744$	−0.357760	+	0.619658i	−0.0131161	+	0.0227178i
$745$	−10.7047	−	18.5412i	−0.392191	−	0.679296i
$746$	15.3858	−	26.6490i	0.563314	−	0.975688i
$747$	−10.4809	−	18.1534i	−0.383475	−	0.664199i
$748$	−45.5131			−1.66412
$749$	15.2617			0.557651
$750$	−0.910914	−	1.57775i	−0.0332619	−	0.0576113i
$751$	15.8616	+	27.4731i	0.578799	+	1.00251i	0.995617	+	0.0935195i	$0.0298117\pi$
$751$	15.8616	+	27.4731i	0.578799	+	1.00251i	−0.416818	+	0.908990i	$0.636855\pi$
$752$	−22.4508			−0.818698
$753$	13.5720			0.494592
$754$	3.39285	+	5.87658i	0.123560	+	0.214012i
$755$	2.33871	−	4.05077i	0.0851145	−	0.147423i
$756$	4.62736	+	8.01483i	0.168296	+	0.291496i
$757$	−1.03789	+	1.79768i	−0.0377229	+	0.0653379i	−0.884270	−	0.466975i	$-0.845344\pi$
$757$	−1.03789	+	1.79768i	−0.0377229	+	0.0653379i	0.846548	+	0.532313i	$0.178677\pi$
$758$	−3.92676	+	6.80135i	−0.142626	+	0.247036i
$759$	−3.32870			−0.120824
$760$	−0.0768543	−	0.355489i	−0.00278780	−	0.0128949i
$761$	35.2240			1.27687			0.638434	−	0.769677i	$-0.279583\pi$
$761$	35.2240			1.27687			0.638434	+	0.769677i	$0.279583\pi$
$762$	−11.4369	+	19.8092i	−0.414314	+	0.717613i
$763$	−6.90431	+	11.9586i	−0.249953	+	0.432931i
$764$	−7.70818	−	13.3510i	−0.278872	−	0.483021i
$765$	5.66820	−	9.81760i	0.204934	−	0.354956i
$766$	−1.60122	−	2.77339i	−0.0578543	−	0.100207i
$767$	−17.1501			−0.619256
$768$	−15.2467			−0.550167
$769$	15.8421	+	27.4393i	0.571281	+	0.989487i	0.996435	+	0.0843663i	$0.0268866\pi$
$769$	15.8421	+	27.4393i	0.571281	+	0.989487i	−0.425154	+	0.905121i	$0.639780\pi$
$770$	−4.40849	−	7.63574i	−0.158871	−	0.275173i
$771$	−8.93938			−0.321944
$772$	38.9291			1.40109
$773$	−15.9641	−	27.6506i	−0.574189	−	0.994524i	−0.996129	−	0.0879007i	$-0.971984\pi$
$773$	−15.9641	−	27.6506i	−0.574189	−	0.994524i	0.421940	−	0.906624i	$-0.361349\pi$
$774$	−9.29067	+	16.0919i	−0.333946	+	0.578412i
$775$	−4.68228	−	8.10994i	−0.168192	−	0.291318i
$776$	−0.384820	+	0.666528i	−0.0138142	+	0.0239270i
$777$	−4.44052	+	7.69120i	−0.159303	+	0.275920i
$778$	−68.3494			−2.45044
$779$	−8.50956	−	39.3609i	−0.304887	−	1.41025i
$780$	3.04819			0.109143
$781$	−19.1382	+	33.1484i	−0.684820	+	1.18614i
$782$	4.27929	−	7.41195i	0.153027	−	0.265051i
$783$	4.74145	+	8.21243i	0.169445	+	0.293488i
$784$	2.04106	−	3.53522i	0.0728950	−	0.126258i
$785$	4.85087	+	8.40195i	0.173135	+	0.299879i
$786$	19.6606			0.701271
$787$	13.2143			0.471038			0.235519	−	0.971870i	$-0.424321\pi$
$787$	13.2143			0.471038			0.235519	+	0.971870i	$0.424321\pi$
$788$	−8.44299	−	14.6237i	−0.300769	−	0.520947i
$789$	14.3332	+	24.8258i	0.510274	+	0.883820i
$790$	−19.5352			−0.695032
$791$	11.5767			0.411622
$792$	−0.399633	−	0.692184i	−0.0142003	−	0.0245957i
$793$	6.44379	−	11.1610i	0.228826	−	0.396338i
$794$	−11.5934	−	20.0804i	−0.411435	−	0.712627i
$795$	3.71322	−	6.43149i	0.131694	−	0.228101i
$796$	0.949538	−	1.64465i	0.0336555	−	0.0582930i
$797$	3.04000			0.107682			0.0538412	−	0.998550i	$-0.482854\pi$
$797$	3.04000			0.107682			0.0538412	+	0.998550i	$0.482854\pi$
$798$	7.56098	+	2.42768i	0.267656	+	0.0859389i
$799$	−28.8455			−1.02048
$800$	3.97723	−	6.88876i	0.140616	−	0.243554i
$801$	11.6484	−	20.1756i	0.411576	−	0.712870i
$802$	14.9333	+	25.8652i	0.527312	+	0.913331i
$803$	23.4591	−	40.6323i	0.827852	−	1.43388i
$804$	−7.40968	−	12.8339i	−0.261319	−	0.452618i
$805$	0.820219			0.0289089
$806$	31.6722			1.11560
$807$	8.49913	+	14.7209i	0.299183	+	0.518201i
$808$	0.189061	+	0.327463i	0.00665114	+	0.0115201i
$809$	52.5428			1.84731			0.923653	−	0.383229i	$-0.125188\pi$
$809$	52.5428			1.84731			0.923653	+	0.383229i	$0.125188\pi$
$810$	−4.28966			−0.150723
$811$	−14.2754	−	24.7257i	−0.501277	−	0.868237i	−0.999999	−	0.00147505i	$-0.999530\pi$
$811$	−14.2754	−	24.7257i	−0.501277	−	0.868237i	0.498722	−	0.866762i	$-0.333803\pi$
$812$	−1.96426	+	3.40220i	−0.0689321	+	0.119394i
$813$	6.18164	+	10.7069i	0.216800	+	0.375508i
$814$	−42.7551	+	74.0540i	−1.49857	+	2.59559i
$815$	−8.85203	+	15.3322i	−0.310073	+	0.537063i
$816$	−19.6057			−0.686338
$817$	3.98008	+	18.4098i	0.139245	+	0.644078i
$818$	−21.3536			−0.746613
$819$	−1.83723	+	3.18217i	−0.0641980	+	0.111194i
$820$	9.04489	−	15.6662i	0.315861	−	0.547088i
$821$	6.70285	+	11.6097i	0.233931	+	0.405181i	0.958962	−	0.283536i	$-0.0915076\pi$
$821$	6.70285	+	11.6097i	0.233931	+	0.405181i	−0.725030	+	0.688717i	$0.758174\pi$
$822$	4.08364	−	7.07308i	0.142433	−	0.246702i
$823$	20.5697	+	35.6278i	0.717015	+	1.24191i	0.962177	+	0.272424i	$0.0878253\pi$
$823$	20.5697	+	35.6278i	0.717015	+	1.24191i	−0.245163	+	0.969482i	$0.578841\pi$
$824$	0.365602			0.0127364
$825$	−4.05831			−0.141292
$826$	−10.0353	−	17.3816i	−0.349172	−	0.604784i
$827$	13.5065	+	23.3940i	0.469668	+	0.813490i	0.999399	−	0.0346766i	$-0.0110401\pi$
$827$	13.5065	+	23.3940i	0.469668	+	0.813490i	−0.529730	+	0.848166i	$0.677707\pi$
$828$	−3.47136			−0.120638
$829$	25.5080			0.885929			0.442964	−	0.896539i	$-0.353927\pi$
$829$	25.5080			0.885929			0.442964	+	0.896539i	$0.353927\pi$
$830$	−9.64706	−	16.7092i	−0.334854	−	0.579985i
$831$	−13.2746	+	22.9923i	−0.460492	+	0.797596i
$832$	6.51189	+	11.2789i	0.225759	+	0.391026i
$833$	2.62241	−	4.54215i	0.0908612	−	0.157376i
$834$	4.38909	−	7.60212i	0.151982	−	0.263240i
$835$	−4.31762			−0.149418
$836$	36.0144	+	11.5635i	1.24558	+	0.399932i
$837$	44.2613			1.52990
$838$	34.2142	−	59.2607i	1.18191	−	2.04713i
$839$	6.28182	−	10.8804i	0.216872	−	0.375634i	−0.736978	−	0.675917i	$-0.763748\pi$
$839$	6.28182	−	10.8804i	0.216872	−	0.375634i	0.953850	+	0.300283i	$0.0970811\pi$
$840$	−0.0382036	−	0.0661706i	−0.00131815	−	0.00228310i
$841$	12.4873	−	21.6287i	0.430597	−	0.745816i
$842$	3.69147	+	6.39381i	0.127216	+	0.220345i
$843$	2.61387			0.0900265
$844$	−11.4526			−0.394215
$845$	−5.05500	−	8.75551i	−0.173897	−	0.301199i
$846$	11.8250	+	20.4815i	0.406552	+	0.704169i
$847$	−8.64076			−0.296900
$848$	33.1055			1.13685
$849$	−0.637145	−	1.10357i	−0.0218668	−	0.0378743i
$850$	5.21726	−	9.03656i	0.178950	−	0.309951i
$851$	−3.97738	−	6.88903i	−0.136343	−	0.236153i
$852$	7.74310	−	13.4114i	0.265274	−	0.459468i
$853$	−6.02203	+	10.4305i	−0.206191	+	0.357132i	−0.950511	−	0.310690i	$-0.899440\pi$
$853$	−6.02203	+	10.4305i	−0.206191	+	0.357132i	0.744321	+	0.667822i	$0.232773\pi$
$854$	15.0822			0.516101
$855$	−6.97959	+	6.32853i	−0.238697	+	0.216431i
$856$	1.27342			0.0435246
$857$	−6.92524	+	11.9949i	−0.236562	+	0.409737i	−0.959725	−	0.280940i	$-0.909354\pi$
$857$	−6.92524	+	11.9949i	−0.236562	+	0.409737i	0.723164	+	0.690677i	$0.242687\pi$
$858$	6.86287	−	11.8868i	0.234295	−	0.405810i
$859$	−20.0329	−	34.6980i	−0.683513	−	1.18388i	−0.973902	−	0.226971i	$-0.927118\pi$
$859$	−20.0329	−	34.6980i	−0.683513	−	1.18388i	0.290388	−	0.956909i	$-0.406216\pi$
$860$	−4.23047	+	7.32738i	−0.144258	+	0.249862i
$861$	−4.23003	−	7.32663i	−0.144159	−	0.249691i
$862$	−22.2319			−0.757220
$863$	−38.2543			−1.30219			−0.651097	−	0.758995i	$-0.725691\pi$
$863$	−38.2543			−1.30219			−0.651097	+	0.758995i	$0.725691\pi$
$864$	18.7983	+	32.5595i	0.639530	+	1.10770i
$865$	3.59616	+	6.22873i	0.122273	+	0.211783i
$866$	−25.1045			−0.853085
$867$	−9.62265			−0.326802
$868$	9.16818	+	15.8798i	0.311188	+	0.538994i
$869$	−21.7584	+	37.6866i	−0.738102	+	1.27843i
$870$	1.82760	+	3.16549i	0.0619614	+	0.107320i
$871$	7.02516	−	12.1679i	0.238039	−	0.412295i
$872$	−0.576088	+	0.997814i	−0.0195088	+	0.0337902i
$873$	19.9372			0.674771
$874$	−5.26935	+	4.77782i	−0.178238	+	0.161612i
$875$	1.00000			0.0338062
$876$	−9.49126	+	16.4393i	−0.320680	+	0.555434i
$877$	4.08313	−	7.07220i	0.137878	−	0.238811i	−0.788815	−	0.614630i	$-0.789305\pi$
$877$	4.08313	−	7.07220i	0.137878	−	0.238811i	0.926693	+	0.375819i	$0.122639\pi$
$878$	26.4953	+	45.8912i	0.894172	+	1.54875i
$879$	7.11020	−	12.3152i	0.239821	−	0.415383i
$880$	−9.04555	−	15.6674i	−0.304925	−	0.528146i
$881$	−51.0192			−1.71888			−0.859440	−	0.511236i	$-0.829188\pi$
$881$	−51.0192			−1.71888			−0.859440	+	0.511236i	$0.829188\pi$
$882$	−4.30016			−0.144794
$883$	−11.6612	−	20.1978i	−0.392431	−	0.679710i	0.600339	−	0.799746i	$-0.295032\pi$
$883$	−11.6612	−	20.1978i	−0.392431	−	0.679710i	−0.992770	+	0.120036i	$0.961699\pi$
$884$	8.72924	+	15.1195i	0.293596	+	0.508523i
$885$	−9.23814			−0.310537
$886$	29.6459			0.995974
$887$	−7.60047	−	13.1644i	−0.255199	−	0.442017i	0.709751	−	0.704453i	$-0.248808\pi$
$887$	−7.60047	−	13.1644i	−0.255199	−	0.442017i	−0.964949	+	0.262436i	$0.915474\pi$
$888$	−0.370512	+	0.641745i	−0.0124336	+	0.0215356i
$889$	−6.27769	−	10.8733i	−0.210547	−	0.364678i
$890$	10.7217	−	18.5705i	0.359392	−	0.622485i
$891$	−4.77784	+	8.27546i	−0.160064	+	0.277238i
$892$	−19.3670			−0.648455
$893$	22.8254	+	7.32876i	0.763822	+	0.245248i
$894$	39.0044			1.30450
$895$	−12.3291	+	21.3546i	−0.412117	+	0.713807i
$896$	0.333682	−	0.577954i	0.0111475	−	0.0193081i
$897$	0.638433	+	1.10580i	0.0213167	+	0.0369215i
$898$	−8.43860	+	14.6161i	−0.281600	+	0.487745i
$899$	9.39422	+	16.2713i	0.313315	+	0.542677i
$900$	−4.23224			−0.141075
$901$	42.5349			1.41704
$902$	−40.7284	−	70.5437i	−1.35611	−	2.34885i
$903$	1.97847	+	3.42680i	0.0658392	+	0.114037i
$904$	0.965950			0.0321270
$905$	16.6977			0.555050
$906$	4.26074	+	7.37981i	0.141553	+	0.245178i
$907$	−11.7396	+	20.3335i	−0.389806	+	0.675164i	−0.992423	−	0.122866i	$-0.960791\pi$
$907$	−11.7396	+	20.3335i	−0.389806	+	0.675164i	0.602617	+	0.798031i	$0.294125\pi$
$908$	25.7472	+	44.5955i	0.854451	+	1.47995i
$909$	4.89753	−	8.48277i	0.162441	−	0.281356i
$910$	−1.69107	+	2.92901i	−0.0560583	+	0.0970958i
$911$	−20.4737			−0.678325			−0.339162	−	0.940728i	$-0.610144\pi$
$911$	−20.4737			−0.678325			−0.339162	+	0.940728i	$0.610144\pi$
$912$	15.5140	+	4.98122i	0.513719	+	0.164945i
$913$	−42.9797			−1.42242
$914$	−1.53776	+	2.66347i	−0.0508644	+	0.0880998i
$915$	3.47103	−	6.01200i	0.114749	−	0.198751i
$916$	−20.4804	−	35.4731i	−0.676691	−	1.17206i
$917$	−5.39585	+	9.34589i	−0.178187	+	0.308628i
$918$	24.6592	+	42.7111i	0.813876	+	1.40967i
$919$	−7.65707			−0.252583			−0.126292	−	0.991993i	$-0.540308\pi$
$919$	−7.65707			−0.252583			−0.126292	+	0.991993i	$0.540308\pi$
$920$	0.0684381			0.00225634
$921$	7.01495	+	12.1502i	0.231150	+	0.400364i
$922$	−1.81929	−	3.15111i	−0.0599152	−	0.103776i
$923$	14.6826			0.483283
$924$	7.94642			0.261418
$925$	−4.84917	−	8.39901i	−0.159440	−	0.276158i
$926$	−0.964355	+	1.67031i	−0.0316907	+	0.0548898i
$927$	−4.73537	−	8.20191i	−0.155530	−	0.269386i
$928$	−7.97965	+	13.8212i	−0.261945	+	0.453702i
$929$	13.9411	−	24.1467i	0.457393	−	0.792228i	−0.541429	−	0.840746i	$-0.682117\pi$
$929$	13.9411	−	24.1467i	0.457393	−	0.792228i	0.998822	+	0.0485181i	$0.0154499\pi$
$930$	17.0606			0.559440
$931$	−3.22913	+	2.92792i	−0.105831	+	0.0959586i
$932$	−9.44753			−0.309464
$933$	−5.99026	+	10.3754i	−0.196112	+	0.339677i
$934$	7.06472	−	12.2364i	0.231165	−	0.400389i
$935$	−11.6220	−	20.1299i	−0.380079	−	0.658317i
$936$	−0.153296	+	0.265517i	−0.00501064	+	0.00867869i
$937$	−9.80967	−	16.9908i	−0.320468	−	0.555067i	0.660117	−	0.751163i	$-0.270507\pi$
$937$	−9.80967	−	16.9908i	−0.320468	−	0.555067i	−0.980585	+	0.196096i	$0.937173\pi$
$938$	16.4429			0.536879
$939$	11.7588			0.383733
$940$	5.38447	+	9.32617i	0.175622	+	0.304186i
$941$	−20.7714	−	35.9771i	−0.677128	−	1.17282i	−0.975842	−	0.218477i	$-0.929891\pi$
$941$	−20.7714	−	35.9771i	−0.677128	−	1.17282i	0.298714	−	0.954343i	$-0.403442\pi$
$942$	−17.6749			−0.575879
$943$	7.57769			0.246764
$944$	−20.5908	−	35.6644i	−0.670175	−	1.16078i
$945$	−2.36324	+	4.09325i	−0.0768761	+	0.133153i
$946$	19.0495	+	32.9946i	0.619351	+	1.07275i
$947$	24.0110	−	41.5882i	0.780252	−	1.35144i	−0.151543	−	0.988451i	$-0.548424\pi$
$947$	24.0110	−	41.5882i	0.780252	−	1.35144i	0.931795	−	0.362985i	$-0.118242\pi$
$948$	8.80317	−	15.2475i	0.285914	−	0.495217i
$949$	−17.9975			−0.584222
$950$	−6.42432	+	5.82506i	−0.208432	+	0.188990i
$951$	−1.20631			−0.0391173
$952$	0.218811	−	0.378992i	0.00709171	−	0.0122832i
$953$	−10.0380	+	17.3864i	−0.325164	+	0.563200i	−0.981545	−	0.191229i	$-0.938753\pi$
$953$	−10.0380	+	17.3864i	−0.325164	+	0.563200i	0.656382	+	0.754429i	$0.272086\pi$
$954$	−17.4369	−	30.2016i	−0.564541	−	0.977814i
$955$	3.93664	−	6.81846i	0.127387	−	0.220640i
$956$	4.25346	+	7.36720i	0.137567	+	0.238272i
$957$	8.14233			0.263204
$958$	70.0467			2.26311
$959$	2.24151	+	3.88240i	0.0723821	+	0.125369i
$960$	3.50771	+	6.07553i	0.113211	+	0.196087i
$961$	56.6949			1.82887
$962$	32.8011			1.05755
$963$	−16.4937	−	28.5679i	−0.531501	−	0.920587i
$964$	−27.4151	+	47.4843i	−0.882980	+	1.52937i
$965$	9.94073	+	17.2178i	0.320003	+	0.554262i
$966$	−0.747149	+	1.29410i	−0.0240391	+	0.0416370i
$967$	−20.8798	+	36.1649i	−0.671450	+	1.16299i	0.306043	+	0.952018i	$0.400995\pi$
$967$	−20.8798	+	36.1649i	−0.671450	+	1.16299i	−0.977493	+	0.210968i	$0.932338\pi$
$968$	−0.720975			−0.0231730
$969$	19.9328	+	6.40002i	0.640334	+	0.205598i
$970$	18.3510			0.589217
$971$	−13.6915	+	23.7144i	−0.439382	+	0.761031i	−0.997642	−	0.0686346i	$-0.978136\pi$
$971$	−13.6915	+	23.7144i	−0.439382	+	0.761031i	0.558260	+	0.829666i	$0.311469\pi$
$972$	15.8151	−	27.3926i	0.507271	−	0.878619i
$973$	2.40916	+	4.17280i	0.0772343	+	0.133774i
$974$	29.2848	−	50.7228i	0.938346	−	1.62526i
$975$	0.778369	+	1.34818i	0.0249278	+	0.0431762i
$976$	30.9463			0.990565
$977$	−1.38519			−0.0443161			−0.0221581	−	0.999754i	$-0.507054\pi$
$977$	−1.38519			−0.0443161			−0.0221581	+	0.999754i	$0.507054\pi$
$978$	−16.1269	−	27.9326i	−0.515681	−	0.893186i
$979$	−23.8837	−	41.3677i	−0.763325	−	1.32212i
$980$	−1.95806			−0.0625479
$981$	29.8466			0.952927
$982$	−4.73976	−	8.20950i	−0.151252	−	0.261976i
$983$	18.8451	−	32.6406i	0.601064	−	1.04107i	−0.391596	−	0.920137i	$-0.628077\pi$
$983$	18.8451	−	32.6406i	0.601064	−	1.04107i	0.992660	−	0.120936i	$-0.0385897\pi$
$984$	−0.352949	−	0.611325i	−0.0112516	−	0.0194883i
$985$	4.31191	−	7.46845i	0.137389	−	0.237965i
$986$	−10.4676	+	18.1304i	−0.333355	+	0.577388i
$987$	5.03632			0.160308
$988$	−3.06602	−	14.1819i	−0.0975432	−	0.451185i
$989$	−3.54423			−0.112700
$990$	−9.52871	+	16.5042i	−0.302842	+	0.524538i
$991$	−4.19856	+	7.27213i	−0.133372	+	0.231007i	−0.924974	−	0.380030i	$-0.875914\pi$
$991$	−4.19856	+	7.27213i	−0.133372	+	0.231007i	0.791603	+	0.611036i	$0.209247\pi$
$992$	37.2450	+	64.5101i	1.18253	+	2.04820i
$993$	−10.7936	+	18.6950i	−0.342523	+	0.593268i
$994$	8.59140	+	14.8807i	0.272503	+	0.471988i
$995$	0.969876			0.0307471
$996$	17.3891			0.550993
$997$	−24.0947	−	41.7333i	−0.763087	−	1.32171i	−0.941252	−	0.337705i	$-0.890349\pi$
$997$	−24.0947	−	41.7333i	−0.763087	−	1.32171i	0.178165	−	0.984001i	$-0.442984\pi$
$998$	−14.8231	−	25.6744i	−0.469217	−	0.812708i
$999$	45.8390			1.45028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.i.h.106.2	✓	20
19.7	even	3	inner	665.2.i.h.596.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.i.h.106.2	✓	20	1.1	even	1	trivial
665.2.i.h.596.2	yes	20	19.7	even	3	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:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994744 + 1.72295i) q^{2} +(0.457864 - 0.793043i) q^{3} +(-0.979030 - 1.69573i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.910914 + 1.57775i) q^{6} -1.00000 q^{7} -0.0834388 q^{8} +(1.08072 + 1.87186i) q^{9} +O(q^{10})\)	\(q+(-0.994744 + 1.72295i) q^{2} +(0.457864 - 0.793043i) q^{3} +(-0.979030 - 1.69573i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.910914 + 1.57775i) q^{6} -1.00000 q^{7} -0.0834388 q^{8} +(1.08072 + 1.87186i) q^{9} +(0.994744 + 1.72295i) q^{10} +4.43179 q^{11} -1.79305 q^{12} +(-0.850001 - 1.47224i) q^{13} +(0.994744 - 1.72295i) q^{14} +(-0.457864 - 0.793043i) q^{15} +(2.04106 - 3.53522i) q^{16} +(2.62241 - 4.54215i) q^{17} -4.30016 q^{18} +(-3.22913 + 2.92792i) q^{19} -1.95806 q^{20} +(-0.457864 + 0.793043i) q^{21} +(-4.40849 + 7.63574i) q^{22} +(-0.410109 - 0.710330i) q^{23} +(-0.0382036 + 0.0661706i) q^{24} +(-0.500000 - 0.866025i) q^{25} +3.38213 q^{26} +4.72648 q^{27} +(0.979030 + 1.69573i) q^{28} +(1.00317 + 1.73754i) q^{29} +1.82183 q^{30} +9.36456 q^{31} +(3.97723 + 6.88876i) q^{32} +(2.02916 - 3.51460i) q^{33} +(5.21726 + 9.03656i) q^{34} +(-0.500000 + 0.866025i) q^{35} +(2.11612 - 3.66522i) q^{36} +9.69834 q^{37} +(-1.83249 - 8.47615i) q^{38} -1.55674 q^{39} +(-0.0417194 + 0.0722601i) q^{40} +(-4.61931 + 8.00088i) q^{41} +(-0.910914 - 1.57775i) q^{42} +(2.16054 - 3.74216i) q^{43} +(-4.33886 - 7.51512i) q^{44} +2.16144 q^{45} +1.63182 q^{46} +(-2.74990 - 4.76296i) q^{47} +(-1.86906 - 3.23730i) q^{48} +1.00000 q^{49} +1.98949 q^{50} +(-2.40142 - 4.15937i) q^{51} +(-1.66435 + 2.88274i) q^{52} +(4.05494 + 7.02337i) q^{53} +(-4.70163 + 8.14346i) q^{54} +(2.21589 - 3.83804i) q^{55} +0.0834388 q^{56} +(0.843463 + 3.90143i) q^{57} -3.99158 q^{58} +(5.04415 - 8.73673i) q^{59} +(-0.896525 + 1.55283i) q^{60} +(3.79046 + 6.56527i) q^{61} +(-9.31533 + 16.1346i) q^{62} +(-1.08072 - 1.87186i) q^{63} -7.66104 q^{64} -1.70000 q^{65} +(4.03698 + 6.99225i) q^{66} +(4.13244 + 7.15760i) q^{67} -10.2697 q^{68} -0.751097 q^{69} +(-0.994744 - 1.72295i) q^{70} +(-4.31840 + 7.47968i) q^{71} +(-0.0901741 - 0.156186i) q^{72} +(5.29336 - 9.16837i) q^{73} +(-9.64736 + 16.7097i) q^{74} -0.915727 q^{75} +(8.12638 + 2.60922i) q^{76} -4.43179 q^{77} +(1.54856 - 2.68218i) q^{78} +(-4.90961 + 8.50369i) q^{79} +(-2.04106 - 3.53522i) q^{80} +(-1.07808 + 1.86729i) q^{81} +(-9.19006 - 15.9177i) q^{82} -9.69804 q^{83} +1.79305 q^{84} +(-2.62241 - 4.54215i) q^{85} +(4.29837 + 7.44499i) q^{86} +1.83726 q^{87} -0.369783 q^{88} +(-5.38917 - 9.33432i) q^{89} +(-2.15008 + 3.72405i) q^{90} +(0.850001 + 1.47224i) q^{91} +(-0.803019 + 1.39087i) q^{92} +(4.28769 - 7.42650i) q^{93} +10.9418 q^{94} +(0.921086 + 4.26047i) q^{95} +7.28411 q^{96} +(4.61200 - 7.98823i) q^{97} +(-0.994744 + 1.72295i) q^{98} +(4.78953 + 8.29571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

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