LMFDB - Embedded newform 143.2.e.b.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.e (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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$1.14257 - 1.97899i$ of defining polynomial
Character	$\chi$	$=$	143.100
Dual form			143.2.e.b.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14257 - 1.97899i) q^{2} +(-0.610938 + 1.05818i) q^{3} +(-1.61094 - 2.79023i) q^{4} +2.50702 q^{5} +(1.39608 + 2.41808i) q^{6} +(-2.25351 - 3.90319i) q^{7} -2.79216 q^{8} +(0.753509 + 1.30512i) q^{9} +O(q^{10})$	\(q+(1.14257 - 1.97899i) q^{2} +(-0.610938 + 1.05818i) q^{3} +(-1.61094 - 2.79023i) q^{4} +2.50702 q^{5} +(1.39608 + 2.41808i) q^{6} +(-2.25351 - 3.90319i) q^{7} -2.79216 q^{8} +(0.753509 + 1.30512i) q^{9} +(2.86445 - 4.96137i) q^{10} +(-0.500000 + 0.866025i) q^{11} +3.93673 q^{12} +(-2.50000 + 2.59808i) q^{13} -10.2992 q^{14} +(-1.53163 + 2.65287i) q^{15} +(0.0316332 - 0.0547902i) q^{16} +(1.61094 + 2.79023i) q^{17} +3.44375 q^{18} +(1.17420 + 2.03378i) q^{19} +(-4.03865 - 6.99515i) q^{20} +5.50702 q^{21} +(1.14257 + 1.97899i) q^{22} +(-2.89608 + 5.01616i) q^{23} +(1.70584 - 2.95460i) q^{24} +1.28514 q^{25} +(2.28514 + 7.91597i) q^{26} -5.50702 q^{27} +(-7.26053 + 12.5756i) q^{28} +(0.309757 - 0.536515i) q^{29} +(3.50000 + 6.06218i) q^{30} +6.01404 q^{31} +(-2.86445 - 4.96137i) q^{32} +(-0.610938 - 1.05818i) q^{33} +7.36245 q^{34} +(-5.64959 - 9.78538i) q^{35} +(2.42771 - 4.20492i) q^{36} +(-2.53163 + 4.38492i) q^{37} +5.36645 q^{38} +(-1.22188 - 4.23270i) q^{39} -7.00000 q^{40} +(4.18122 - 7.24209i) q^{41} +(6.29216 - 10.8983i) q^{42} +(-5.54567 - 9.60538i) q^{43} +3.22188 q^{44} +(1.88906 + 3.27195i) q^{45} +(6.61796 + 11.4626i) q^{46} +6.74293 q^{47} +(0.0386518 + 0.0669469i) q^{48} +(-6.65661 + 11.5296i) q^{49} +(1.46837 - 2.54329i) q^{50} -3.93673 q^{51} +(11.2766 + 2.79023i) q^{52} -4.06327 q^{53} +(-6.29216 + 10.8983i) q^{54} +(-1.25351 + 2.17114i) q^{55} +(6.29216 + 10.8983i) q^{56} -2.86946 q^{57} +(-0.707839 - 1.22601i) q^{58} +(-5.53163 - 9.58107i) q^{59} +9.86946 q^{60} +(0.0722863 + 0.125204i) q^{61} +(6.87147 - 11.9017i) q^{62} +(3.39608 - 5.88218i) q^{63} -12.9648 q^{64} +(-6.26755 + 6.51343i) q^{65} -2.79216 q^{66} +(-4.36445 + 7.55944i) q^{67} +(5.19024 - 8.98976i) q^{68} +(-3.53865 - 6.12912i) q^{69} -25.8202 q^{70} +(0.857429 + 1.48511i) q^{71} +(-2.10392 - 3.64410i) q^{72} -2.00000 q^{73} +(5.78514 + 10.0202i) q^{74} +(-0.785142 + 1.35991i) q^{75} +(3.78314 - 6.55259i) q^{76} +4.50702 q^{77} +(-9.77256 - 2.41808i) q^{78} +1.87347 q^{79} +(0.0793049 - 0.137360i) q^{80} +(1.10392 - 1.91204i) q^{81} +(-9.55469 - 16.5492i) q^{82} -5.38049 q^{83} +(-8.87147 - 15.3658i) q^{84} +(4.03865 + 6.99515i) q^{85} -25.3453 q^{86} +(0.378485 + 0.655555i) q^{87} +(1.39608 - 2.41808i) q^{88} +(4.25351 - 7.36729i) q^{89} +8.63355 q^{90} +(15.7746 + 3.90319i) q^{91} +18.6616 q^{92} +(-3.67420 + 6.36391i) q^{93} +(7.70428 - 13.3442i) q^{94} +(2.94375 + 5.09873i) q^{95} +7.00000 q^{96} +(-0.0562477 - 0.0974238i) q^{97} +(15.2113 + 26.3467i) q^{98} -1.50702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 3 q^{11} + 30 q^{12} - 15 q^{13} - 16 q^{14} - 6 q^{15} - 3 q^{16} + 7 q^{17} + 10 q^{18} - 2 q^{19} - 4 q^{20} + 16 q^{21} + q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 21 q^{30} + 2 q^{31} - 6 q^{32} - q^{33} - 8 q^{34} - 11 q^{35} - 3 q^{36} - 12 q^{37} + 62 q^{38} - 2 q^{39} - 42 q^{40} - q^{41} + 9 q^{42} + 4 q^{43} + 14 q^{44} + 14 q^{45} + 20 q^{46} - 16 q^{47} - 20 q^{48} + 12 q^{50} - 30 q^{51} + 49 q^{52} - 18 q^{53} - 9 q^{54} + q^{55} + 9 q^{56} + 52 q^{57} - 33 q^{58} - 30 q^{59} - 10 q^{60} + 18 q^{61} + 13 q^{62} + 6 q^{63} - 16 q^{64} + 5 q^{65} + 12 q^{66} - 15 q^{67} + 29 q^{68} - q^{69} - 58 q^{70} + 11 q^{71} - 27 q^{72} - 12 q^{73} + 23 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{77} + 42 q^{78} + 24 q^{79} + q^{80} + 21 q^{81} - 44 q^{82} - 28 q^{83} - 25 q^{84} + 4 q^{85} - 86 q^{86} - 43 q^{87} - 6 q^{88} + 17 q^{89} + 22 q^{90} + 35 q^{91} + 14 q^{92} - 13 q^{93} + 10 q^{94} + 7 q^{95} + 42 q^{96} - 11 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 3 * q^11 + 30 * q^12 - 15 * q^13 - 16 * q^14 - 6 * q^15 - 3 * q^16 + 7 * q^17 + 10 * q^18 - 2 * q^19 - 4 * q^20 + 16 * q^21 + q^22 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 21 * q^30 + 2 * q^31 - 6 * q^32 - q^33 - 8 * q^34 - 11 * q^35 - 3 * q^36 - 12 * q^37 + 62 * q^38 - 2 * q^39 - 42 * q^40 - q^41 + 9 * q^42 + 4 * q^43 + 14 * q^44 + 14 * q^45 + 20 * q^46 - 16 * q^47 - 20 * q^48 + 12 * q^50 - 30 * q^51 + 49 * q^52 - 18 * q^53 - 9 * q^54 + q^55 + 9 * q^56 + 52 * q^57 - 33 * q^58 - 30 * q^59 - 10 * q^60 + 18 * q^61 + 13 * q^62 + 6 * q^63 - 16 * q^64 + 5 * q^65 + 12 * q^66 - 15 * q^67 + 29 * q^68 - q^69 - 58 * q^70 + 11 * q^71 - 27 * q^72 - 12 * q^73 + 23 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^77 + 42 * q^78 + 24 * q^79 + q^80 + 21 * q^81 - 44 * q^82 - 28 * q^83 - 25 * q^84 + 4 * q^85 - 86 * q^86 - 43 * q^87 - 6 * q^88 + 17 * q^89 + 22 * q^90 + 35 * q^91 + 14 * q^92 - 13 * q^93 + 10 * q^94 + 7 * q^95 + 42 * q^96 - 11 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	−0.106382	−	0.994325i	$-0.533927\pi$
$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	0.914302	−	0.405033i	$-0.132740\pi$
$3$	−0.610938	+	1.05818i	−0.352725	+	0.610938i	−0.986726	−	0.162394i	$-0.948078\pi$
$3$	−0.610938	+	1.05818i	−0.352725	+	0.610938i	0.634001	+	0.773333i	$0.281412\pi$
$4$	−1.61094	−	2.79023i	−0.805469	−	1.39511i
$5$	2.50702			1.12117			0.560586	−	0.828096i	$-0.310576\pi$
$5$	2.50702			1.12117			0.560586	+	0.828096i	$0.310576\pi$
$6$	1.39608	+	2.41808i	0.569948	+	0.987178i
$7$	−2.25351	−	3.90319i	−0.851746	−	1.47527i	−0.879631	−	0.475657i	$-0.842210\pi$
$7$	−2.25351	−	3.90319i	−0.851746	−	1.47527i	0.0278844	−	0.999611i	$-0.491123\pi$
$8$	−2.79216			−0.987178
$9$	0.753509	+	1.30512i	0.251170	+	0.435039i
$10$	2.86445	−	4.96137i	0.905818	−	1.56892i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	3.93673			1.13644
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−10.2992			−2.75257
$15$	−1.53163	+	2.65287i	−0.395466	+	0.684967i
$16$	0.0316332	−	0.0547902i	0.00790829	−	0.0136976i
$17$	1.61094	+	2.79023i	0.390710	+	0.676729i	0.992543	−	0.121892i	$-0.0388962\pi$
$17$	1.61094	+	2.79023i	0.390710	+	0.676729i	−0.601833	+	0.798622i	$0.705563\pi$
$18$	3.44375			0.811700
$19$	1.17420	+	2.03378i	0.269381	+	0.466582i	0.968702	−	0.248226i	$-0.0798476\pi$
$19$	1.17420	+	2.03378i	0.269381	+	0.466582i	−0.699321	+	0.714808i	$0.746514\pi$
$20$	−4.03865	−	6.99515i	−0.903070	−	1.56416i
$21$	5.50702			1.20173
$22$	1.14257	+	1.97899i	0.243597	+	0.421922i
$23$	−2.89608	+	5.01616i	−0.603875	+	1.04594i	0.388354	+	0.921510i	$0.373044\pi$
$23$	−2.89608	+	5.01616i	−0.603875	+	1.04594i	−0.992228	+	0.124431i	$0.960289\pi$
$24$	1.70584	−	2.95460i	0.348203	−	0.603105i
$25$	1.28514			0.257028
$26$	2.28514	+	7.91597i	0.448153	+	1.55245i
$27$	−5.50702			−1.05983
$28$	−7.26053	+	12.5756i	−1.37211	+	2.37657i
$29$	0.309757	−	0.536515i	0.0575204	−	0.0996283i	−0.835831	−	0.548986i	$-0.815014\pi$
$29$	0.309757	−	0.536515i	0.0575204	−	0.0996283i	0.893352	+	0.449358i	$0.148347\pi$
$30$	3.50000	+	6.06218i	0.639010	+	1.10680i
$31$	6.01404			1.08015			0.540076	−	0.841616i	$-0.318395\pi$
$31$	6.01404			1.08015			0.540076	+	0.841616i	$0.318395\pi$
$32$	−2.86445	−	4.96137i	−0.506368	−	0.877054i
$33$	−0.610938	−	1.05818i	−0.106351	−	0.184205i
$34$	7.36245			1.26265
$35$	−5.64959	−	9.78538i	−0.954955	−	1.65403i
$36$	2.42771	−	4.20492i	0.404619	−	0.700821i
$37$	−2.53163	+	4.38492i	−0.416198	+	0.720876i	−0.995553	−	0.0941990i	$-0.969971\pi$
$37$	−2.53163	+	4.38492i	−0.416198	+	0.720876i	0.579355	+	0.815075i	$0.303304\pi$
$38$	5.36645			0.870553
$39$	−1.22188	−	4.23270i	−0.195657	−	0.677775i
$40$	−7.00000			−1.10680
$41$	4.18122	−	7.24209i	0.652997	−	1.13102i	−0.329395	−	0.944192i	$-0.606845\pi$
$41$	4.18122	−	7.24209i	0.652997	−	1.13102i	0.982392	−	0.186832i	$-0.0598221\pi$
$42$	6.29216	−	10.8983i	0.970902	−	1.68165i
$43$	−5.54567	−	9.60538i	−0.845707	−	1.46481i	−0.885006	−	0.465580i	$-0.845846\pi$
$43$	−5.54567	−	9.60538i	−0.845707	−	1.46481i	0.0392992	−	0.999227i	$-0.487487\pi$
$44$	3.22188			0.485716
$45$	1.88906	+	3.27195i	0.281605	+	0.487754i
$46$	6.61796	+	11.4626i	0.975764	+	1.69007i
$47$	6.74293			0.983558			0.491779	−	0.870720i	$-0.336347\pi$
$47$	6.74293			0.983558			0.491779	+	0.870720i	$0.336347\pi$
$48$	0.0386518	+	0.0669469i	0.00557891	+	0.00966295i
$49$	−6.65661	+	11.5296i	−0.950944	+	1.64708i
$50$	1.46837	−	2.54329i	0.207658	−	0.359675i
$51$	−3.93673			−0.551253
$52$	11.2766	+	2.79023i	1.56378	+	0.386935i
$53$	−4.06327			−0.558133			−0.279066	−	0.960272i	$-0.590025\pi$
$53$	−4.06327			−0.558133			−0.279066	+	0.960272i	$0.590025\pi$
$54$	−6.29216	+	10.8983i	−0.856255	+	1.48308i
$55$	−1.25351	+	2.17114i	−0.169023	+	0.292757i
$56$	6.29216	+	10.8983i	0.840825	+	1.45635i
$57$	−2.86946			−0.380070
$58$	−0.707839	−	1.22601i	−0.0929438	−	0.160983i
$59$	−5.53163	−	9.58107i	−0.720157	−	1.24735i	−0.960936	−	0.276769i	$-0.910736\pi$
$59$	−5.53163	−	9.58107i	−0.720157	−	1.24735i	0.240779	−	0.970580i	$-0.422597\pi$
$60$	9.86946			1.27414
$61$	0.0722863	+	0.125204i	0.00925531	+	0.0160307i	0.870616	−	0.491963i	$-0.163721\pi$
$61$	0.0722863	+	0.125204i	0.00925531	+	0.0160307i	−0.861361	+	0.507994i	$0.830387\pi$
$62$	6.87147	−	11.9017i	0.872677	−	1.51152i
$63$	3.39608	−	5.88218i	0.427866	−	0.741086i
$64$	−12.9648			−1.62060
$65$	−6.26755	+	6.51343i	−0.777393	+	0.807891i
$66$	−2.79216			−0.343691
$67$	−4.36445	+	7.55944i	−0.533202	+	0.923533i	0.466046	+	0.884761i	$0.345678\pi$
$67$	−4.36445	+	7.55944i	−0.533202	+	0.923533i	−0.999248	+	0.0387726i	$0.987655\pi$
$68$	5.19024	−	8.98976i	0.629409	−	1.09017i
$69$	−3.53865	−	6.12912i	−0.426004	−	0.737860i
$70$	−25.8202			−3.08611
$71$	0.857429	+	1.48511i	0.101758	+	0.176250i	0.912409	−	0.409280i	$-0.134220\pi$
$71$	0.857429	+	1.48511i	0.101758	+	0.176250i	−0.810651	+	0.585530i	$0.800887\pi$
$72$	−2.10392	−	3.64410i	−0.247949	−	0.429461i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	5.78514	+	10.0202i	0.672509	+	1.16482i
$75$	−0.785142	+	1.35991i	−0.0906604	+	0.157028i
$76$	3.78314	−	6.55259i	0.433956	−	0.751634i
$77$	4.50702			0.513622
$78$	−9.77256	−	2.41808i	−1.10652	−	0.273794i
$79$	1.87347			0.210782			0.105391	−	0.994431i	$-0.466391\pi$
$79$	1.87347			0.210782			0.105391	+	0.994431i	$0.466391\pi$
$80$	0.0793049	−	0.137360i	0.00886656	−	0.0153573i
$81$	1.10392	−	1.91204i	0.122658	−	0.212449i
$82$	−9.55469	−	16.5492i	−1.05514	−	1.82755i
$83$	−5.38049			−0.590585			−0.295293	−	0.955407i	$-0.595417\pi$
$83$	−5.38049			−0.590585			−0.295293	+	0.955407i	$0.595417\pi$
$84$	−8.87147	−	15.3658i	−0.967956	−	1.67655i
$85$	4.03865	+	6.99515i	0.438053	+	0.758731i
$86$	−25.3453			−2.73305
$87$	0.378485	+	0.655555i	0.0405778	+	0.0702828i
$88$	1.39608	−	2.41808i	0.148823	−	0.257768i
$89$	4.25351	−	7.36729i	0.450871	−	0.780932i	−0.547569	−	0.836760i	$-0.684447\pi$
$89$	4.25351	−	7.36729i	0.450871	−	0.780932i	0.998440	+	0.0558287i	$0.0177801\pi$
$90$	8.63355			0.910056
$91$	15.7746	+	3.90319i	1.65362	+	0.409166i
$92$	18.6616			1.94561
$93$	−3.67420	+	6.36391i	−0.380997	+	0.659907i
$94$	7.70428	−	13.3442i	0.794636	−	1.37635i
$95$	2.94375	+	5.09873i	0.302023	+	0.523119i
$96$	7.00000			0.714435
$97$	−0.0562477	−	0.0974238i	−0.00571109	−	0.00989189i	0.863156	−	0.504938i	$-0.168485\pi$
$97$	−0.0562477	−	0.0974238i	−0.00571109	−	0.00989189i	−0.868867	+	0.495046i	$0.835151\pi$
$98$	15.2113	+	26.3467i	1.53657	+	2.66142i
$99$	−1.50702			−0.151461
$100$	−2.07028	−	3.58584i	−0.207028	−	0.358584i
$101$	6.37848	−	11.0479i	0.634683	−	1.09930i	−0.351899	−	0.936038i	$-0.614464\pi$
$101$	6.37848	−	11.0479i	0.634683	−	1.09930i	0.986582	−	0.163265i	$-0.0522026\pi$
$102$	−4.49800	+	7.79076i	−0.445368	+	0.771400i
$103$	15.6304			1.54011			0.770056	−	0.637976i	$-0.220228\pi$
$103$	15.6304			1.54011			0.770056	+	0.637976i	$0.220228\pi$
$104$	6.98040	−	7.25425i	0.684485	−	0.711337i
$105$	13.8062			1.34735
$106$	−4.64257	+	8.04117i	−0.450926	+	0.781027i
$107$	2.80976	−	4.86664i	0.271629	−	0.470476i	−0.697650	−	0.716439i	$-0.745771\pi$
$107$	2.80976	−	4.86664i	0.271629	−	0.470476i	0.969279	+	0.245963i	$0.0791042\pi$
$108$	8.87147	+	15.3658i	0.853657	+	1.47858i
$109$	9.90466			0.948694			0.474347	−	0.880338i	$-0.342684\pi$
$109$	9.90466			0.948694			0.474347	+	0.880338i	$0.342684\pi$
$110$	2.86445	+	4.96137i	0.273114	+	0.473048i
$111$	−3.09334	−	5.35783i	−0.293607	−	0.508542i
$112$	−0.285142			−0.0269434
$113$	−4.12498	−	7.14467i	−0.388045	−	0.672114i	0.604141	−	0.796877i	$-0.293516\pi$
$113$	−4.12498	−	7.14467i	−0.388045	−	0.672114i	−0.992187	+	0.124763i	$0.960183\pi$
$114$	−3.27857	+	5.67865i	−0.307066	+	0.531854i
$115$	−7.26053	+	12.5756i	−0.677048	+	1.17268i
$116$	−1.99600			−0.185324
$117$	−5.27457	−	1.30512i	−0.487634	−	0.120658i
$118$	−25.2811			−2.32732
$119$	7.26053	−	12.5756i	0.665572	−	1.15280i
$120$	4.27657	−	7.40723i	0.390395	−	0.676185i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.330369			0.0299102
$123$	5.10894	+	8.84894i	0.460657	+	0.797882i
$124$	−9.68824	−	16.7805i	−0.870030	−	1.50694i
$125$	−9.31322			−0.832999
$126$	−7.76053	−	13.4416i	−0.691363	−	1.19748i
$127$	3.03865	−	5.26310i	0.269637	−	0.467025i	−0.699131	−	0.714993i	$-0.746430\pi$
$127$	3.03865	−	5.26310i	0.269637	−	0.467025i	0.968768	+	0.247969i	$0.0797630\pi$
$128$	−9.08432	+	15.7345i	−0.802948	+	1.39075i
$129$	13.5522			1.19321
$130$	5.72889	+	19.8455i	0.502457	+	1.74056i
$131$	−11.9508			−1.04414			−0.522072	−	0.852902i	$-0.674841\pi$
$131$	−11.9508			−1.04414			−0.522072	+	0.852902i	$0.674841\pi$
$132$	−1.96837	+	3.40931i	−0.171324	+	0.296742i
$133$	5.29216	−	9.16629i	0.458889	−	0.794818i
$134$	9.97338	+	17.2744i	0.861569	+	1.49228i
$135$	−13.8062			−1.18825
$136$	−4.49800	−	7.79076i	−0.385700	−	0.668052i
$137$	1.13555	+	1.96683i	0.0970168	+	0.168038i	0.910449	−	0.413622i	$-0.135737\pi$
$137$	1.13555	+	1.96683i	0.0970168	+	0.168038i	−0.813432	+	0.581660i	$0.802403\pi$
$138$	−16.1726			−1.37671
$139$	5.07730	+	8.79415i	0.430651	+	0.745910i	0.996930	−	0.0783043i	$-0.0249506\pi$
$139$	5.07730	+	8.79415i	0.430651	+	0.745910i	−0.566278	+	0.824214i	$0.691617\pi$
$140$	−18.2023	+	31.5273i	−1.53837	+	2.66454i
$141$	−4.11951	+	7.13521i	−0.346926	+	0.600893i
$142$	3.91869			0.328849
$143$	−1.00000	−	3.46410i	−0.0836242	−	0.289683i
$144$	0.0953435			0.00794529
$145$	0.776567	−	1.34505i	0.0644903	−	0.111701i
$146$	−2.28514	+	3.95798i	−0.189120	+	0.327565i
$147$	−8.13355	−	14.0877i	−0.670844	−	1.16194i
$148$	16.3132			1.34094
$149$	5.48240	+	9.49580i	0.449136	+	0.777926i	0.998330	−	0.0577685i	$-0.0183985\pi$
$149$	5.48240	+	9.49580i	0.449136	+	0.777926i	−0.549194	+	0.835695i	$0.685065\pi$
$150$	1.79416	+	3.10758i	0.146493	+	0.253733i
$151$	−10.8835			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$151$	−10.8835			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$152$	−3.27857	−	5.67865i	−0.265927	−	0.460599i
$153$	−2.42771	+	4.20492i	−0.196269	+	0.339948i
$154$	5.14959	−	8.91935i	0.414966	−	0.718742i
$155$	15.0773			1.21104
$156$	−9.84183	+	10.2279i	−0.787977	+	0.818890i
$157$	13.9820			1.11588			0.557941	−	0.829881i	$-0.311592\pi$
$157$	13.9820			1.11588			0.557941	+	0.829881i	$0.311592\pi$
$158$	2.14057	−	3.70758i	0.170295	−	0.294959i
$159$	2.48240	−	4.29965i	0.196867	−	0.340984i
$160$	−7.18122	−	12.4382i	−0.567726	−	0.983329i
$161$	26.1054			2.05739
$162$	−2.52261	−	4.36929i	−0.198195	−	0.343284i
$163$	−0.697262	−	1.20769i	−0.0546137	−	0.0945938i	0.837426	−	0.546551i	$-0.184059\pi$
$163$	−0.697262	−	1.20769i	−0.0546137	−	0.0945938i	−0.892040	+	0.451957i	$0.850726\pi$
$164$	−26.9428			−2.10388
$165$	−1.53163	−	2.65287i	−0.119237	−	0.206525i
$166$	−6.14759	+	10.6479i	−0.477145	+	0.826440i
$167$	−11.9171	+	20.6411i	−0.922176	+	1.59726i	−0.126134	+	0.992013i	$0.540257\pi$
$167$	−11.9171	+	20.6411i	−0.922176	+	1.59726i	−0.796042	+	0.605242i	$0.793076\pi$
$168$	−15.3765			−1.18632
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	18.4578			1.41565
$171$	−1.76955	+	3.06495i	−0.135321	+	0.234382i
$172$	−17.8675	+	30.9474i	−1.36238	+	2.35971i
$173$	3.69882	+	6.40654i	0.281216	+	0.487080i	0.971685	−	0.236282i	$-0.0759289\pi$
$173$	3.69882	+	6.40654i	0.281216	+	0.487080i	−0.690469	+	0.723362i	$0.742596\pi$
$174$	1.72978			0.131135
$175$	−2.89608	−	5.01616i	−0.218923	−	0.379186i
$176$	0.0316332	+	0.0547902i	0.00238444	+	0.00412997i
$177$	13.5179			1.01607
$178$	−9.71987	−	16.8353i	−0.728535	−	1.26186i
$179$	−9.26053	+	16.0397i	−0.692164	+	1.19886i	0.278963	+	0.960302i	$0.410009\pi$
$179$	−9.26053	+	16.0397i	−0.692164	+	1.19886i	−0.971127	+	0.238562i	$0.923324\pi$
$180$	6.08632	−	10.5418i	0.453648	−	0.785741i
$181$	−18.0561			−1.34210			−0.671051	−	0.741411i	$-0.734157\pi$
$181$	−18.0561			−1.34210			−0.671051	+	0.741411i	$0.734157\pi$
$182$	25.7479	−	26.7581i	1.90856	−	1.98344i
$183$	−0.176650			−0.0130583
$184$	8.08632	−	14.0059i	0.596132	−	1.03253i
$185$	−6.34685	+	10.9931i	−0.466630	+	0.808227i
$186$	8.39608	+	14.5424i	0.615630	+	1.06630i
$187$	−3.22188			−0.235607
$188$	−10.8624	−	18.8143i	−0.792225	−	1.37217i
$189$	12.4101	+	21.4950i	0.902703	+	1.56353i
$190$	13.4538			0.976040
$191$	1.68122	+	2.91196i	0.121649	+	0.210702i	0.920418	−	0.390935i	$-0.127848\pi$
$191$	1.68122	+	2.91196i	0.121649	+	0.210702i	−0.798769	+	0.601638i	$0.794515\pi$
$192$	7.92070	−	13.7190i	0.571627	−	0.990087i
$193$	−7.79918	+	13.5086i	−0.561397	+	0.972369i	0.435978	+	0.899958i	$0.356403\pi$
$193$	−7.79918	+	13.5086i	−0.561397	+	0.972369i	−0.997375	+	0.0724110i	$0.976931\pi$
$194$	−0.257068			−0.0184564
$195$	−3.06327	−	10.6115i	−0.219365	−	0.759903i
$196$	42.8935			3.06382
$197$	10.5140	−	18.2108i	0.749094	−	1.29747i	−0.199163	−	0.979966i	$-0.563822\pi$
$197$	10.5140	−	18.2108i	0.749094	−	1.29747i	0.948257	−	0.317503i	$-0.102844\pi$
$198$	−1.72188	+	2.98238i	−0.122368	+	0.211948i
$199$	11.3062	+	19.5829i	0.801475	+	1.38820i	0.918645	+	0.395084i	$0.129284\pi$
$199$	11.3062	+	19.5829i	0.801475	+	1.38820i	−0.117170	+	0.993112i	$0.537382\pi$
$200$	−3.58832			−0.253733
$201$	−5.33281	−	9.23671i	−0.376148	−	0.651507i
$202$	−14.5757	−	25.2459i	−1.02555	−	1.77630i
$203$	−2.79216			−0.195971
$204$	6.34183	+	10.9844i	0.444017	+	0.769060i
$205$	10.4824	−	18.1561i	0.732123	−	1.26807i
$206$	17.8589	−	30.9325i	1.24429	−	2.15517i
$207$	−8.72889			−0.606700
$208$	0.0632663	+	0.219161i	0.00438673	+	0.0151961i
$209$	−2.34841			−0.162443
$210$	15.7746	−	27.3223i	1.08855	−	1.88542i
$211$	−10.1882	+	17.6466i	−0.701387	+	1.21484i	0.266592	+	0.963809i	$0.414102\pi$
$211$	−10.1882	+	17.6466i	−0.701387	+	1.21484i	−0.967979	+	0.251029i	$0.919231\pi$
$212$	6.54567	+	11.3374i	0.449558	+	0.778658i
$213$	−2.09534			−0.143571
$214$	−6.42070	−	11.1210i	−0.438910	−	0.760214i
$215$	−13.9031	−	24.0809i	−0.948183	−	1.64230i
$216$	15.3765			1.04624
$217$	−13.5527	−	23.4739i	−0.920016	−	1.59352i
$218$	11.3168	−	19.6012i	0.766469	−	1.32756i
$219$	1.22188	−	2.11635i	0.0825667	−	0.143010i
$220$	8.07730			0.544572
$221$	−11.2766	−	2.79023i	−0.758544	−	0.187691i
$222$	−14.1375			−0.948844
$223$	8.88706	−	15.3928i	0.595122	−	1.03078i	−0.398408	−	0.917208i	$-0.630437\pi$
$223$	8.88706	−	15.3928i	0.595122	−	1.03078i	0.993530	−	0.113573i	$-0.0362294\pi$
$224$	−12.9101	+	22.3610i	−0.862594	+	1.49406i
$225$	0.968367	+	1.67726i	0.0645578	+	0.111817i
$226$	−18.8523			−1.25404
$227$	−2.91012	−	5.04047i	−0.193151	−	0.334548i	0.753142	−	0.657858i	$-0.228537\pi$
$227$	−2.91012	−	5.04047i	−0.193151	−	0.334548i	−0.946293	+	0.323311i	$0.895204\pi$
$228$	4.62253	+	8.00646i	0.306135	+	0.530241i
$229$	23.6656			1.56387			0.781934	−	0.623361i	$-0.214233\pi$
$229$	23.6656			1.56387			0.781934	+	0.623361i	$0.214233\pi$
$230$	16.5913	+	28.7370i	1.09400	+	1.89486i
$231$	−2.75351	+	4.76922i	−0.181168	+	0.313792i
$232$	−0.864891	+	1.49804i	−0.0567829	+	0.0983509i
$233$	−22.8875			−1.49941			−0.749705	−	0.661772i	$-0.769805\pi$
$233$	−22.8875			−1.49941			−0.749705	+	0.661772i	$0.769805\pi$
$234$	−8.60938	+	8.94713i	−0.562813	+	0.584892i
$235$	16.9047			1.10274
$236$	−17.8222	+	30.8690i	−1.16013	+	2.00940i
$237$	−1.14457	+	1.98246i	−0.0743480	+	0.128774i
$238$	−16.5913	−	28.7370i	−1.07546	−	1.86275i
$239$	16.2007			1.04794			0.523969	−	0.851737i	$-0.324451\pi$
$239$	16.2007			1.04794			0.523969	+	0.851737i	$0.324451\pi$
$240$	0.0969008	+	0.167837i	0.00625492	+	0.0108338i
$241$	−0.0969008	−	0.167837i	−0.00624193	−	0.0108113i	0.862888	−	0.505396i	$-0.168654\pi$
$241$	−0.0969008	−	0.167837i	−0.00624193	−	0.0108113i	−0.869129	+	0.494585i	$0.835320\pi$
$242$	−2.28514			−0.146895
$243$	−6.91168	−	11.9714i	−0.443384	−	0.767964i
$244$	0.232897	−	0.403390i	0.0149097	−	0.0258244i
$245$	−16.6882	+	28.9049i	−1.06617	+	1.84667i
$246$	23.3493			1.48870
$247$	−8.21943	−	2.03378i	−0.522990	−	0.129406i
$248$	−16.7922			−1.06630
$249$	3.28714	−	5.69350i	0.208314	−	0.360811i
$250$	−10.6410	+	18.4308i	−0.672997	+	1.16566i
$251$	−4.07028	−	7.04994i	−0.256914	−	0.444988i	0.708500	−	0.705711i	$-0.249372\pi$
$251$	−4.07028	−	7.04994i	−0.256914	−	0.444988i	−0.965414	+	0.260723i	$0.916039\pi$
$252$	−21.8835			−1.37853
$253$	−2.89608	−	5.01616i	−0.182075	−	0.315363i
$254$	−6.94375	−	12.0269i	−0.435690	−	0.754637i
$255$	−9.86946			−0.618050
$256$	7.79416	+	13.4999i	0.487135	+	0.843743i
$257$	8.94877	−	15.4997i	0.558209	−	0.966846i	−0.439437	−	0.898273i	$-0.644822\pi$
$257$	8.94877	−	15.4997i	0.558209	−	0.966846i	0.997646	−	0.0685729i	$-0.0218446\pi$
$258$	15.4844	−	26.8198i	0.964017	−	1.66973i
$259$	22.8202			1.41798
$260$	28.2706	+	6.99515i	1.75327	+	0.433821i
$261$	0.933619			0.0577896
$262$	−13.6546	+	23.6505i	−0.843584	+	1.46113i
$263$	7.78359	−	13.4816i	0.479956	−	0.831309i	−0.519779	−	0.854301i	$-0.673986\pi$
$263$	7.78359	−	13.4816i	0.479956	−	0.831309i	0.999736	+	0.0229917i	$0.00731913\pi$
$264$	1.70584	+	2.95460i	0.104987	+	0.181843i
$265$	−10.1867			−0.625763
$266$	−12.0933	−	20.9463i	−0.741490	−	1.28430i
$267$	5.19726	+	9.00192i	0.318067	+	0.550909i
$268$	28.1234			1.71791
$269$	0.746491	+	1.29296i	0.0455143	+	0.0788331i	0.887885	−	0.460065i	$-0.152174\pi$
$269$	0.746491	+	1.29296i	0.0455143	+	0.0788331i	−0.842371	+	0.538898i	$0.818841\pi$
$270$	−15.7746	+	27.3223i	−0.960009	+	1.66279i
$271$	−11.6356	+	20.1534i	−0.706809	+	1.22423i	0.259225	+	0.965817i	$0.416533\pi$
$271$	−11.6356	+	20.1534i	−0.706809	+	1.22423i	−0.966035	+	0.258413i	$0.916800\pi$
$272$	0.203836			0.0123594
$273$	−13.7675	+	14.3077i	−0.833250	+	0.865939i
$274$	5.18980			0.313527
$275$	−0.642571	+	1.11297i	−0.0387485	+	0.0671144i
$276$	−11.4011	+	19.7473i	−0.686265	+	1.18865i
$277$	7.03008	+	12.1764i	0.422396	+	0.731612i	0.996173	−	0.0873997i	$-0.0278557\pi$
$277$	7.03008	+	12.1764i	0.422396	+	0.731612i	−0.573777	+	0.819012i	$0.694522\pi$
$278$	23.2047			1.39173
$279$	4.53163	+	7.84902i	0.271302	+	0.469908i
$280$	15.7746	+	27.3223i	0.942711	+	1.63282i
$281$	11.6797			0.696750			0.348375	−	0.937355i	$-0.386734\pi$
$281$	11.6797			0.696750			0.348375	+	0.937355i	$0.386734\pi$
$282$	9.41368	+	16.3050i	0.560576	+	0.970947i
$283$	1.73591	−	3.00669i	0.103189	−	0.178729i	−0.809808	−	0.586695i	$-0.800429\pi$
$283$	1.73591	−	3.00669i	0.103189	−	0.178729i	0.912997	+	0.407966i	$0.133762\pi$
$284$	2.76253	−	4.78484i	0.163926	−	0.283928i
$285$	−7.19380			−0.426124
$286$	−7.99800	−	1.97899i	−0.472932	−	0.117020i
$287$	−37.6897			−2.22475
$288$	4.31678	−	7.47687i	0.254368	−	0.440579i
$289$	3.30976	−	5.73267i	0.194692	−	0.337216i
$290$	−1.77457	−	3.07364i	−0.104206	−	0.180490i
$291$	0.137455			0.00805778
$292$	3.22188	+	5.58045i	0.188546	+	0.326571i
$293$	−3.18980	−	5.52489i	−0.186350	−	0.322768i	0.757681	−	0.652626i	$-0.226333\pi$
$293$	−3.18980	−	5.52489i	−0.186350	−	0.322768i	−0.944031	+	0.329858i	$0.892999\pi$
$294$	−37.1726			−2.16795
$295$	−13.8679	−	24.0199i	−0.807421	−	1.39849i
$296$	7.06873	−	12.2434i	0.410861	−	0.711633i
$297$	2.75351	−	4.76922i	0.159775	−	0.276738i
$298$	25.0561			1.45146
$299$	−5.79216	−	20.0646i	−0.334969	−	1.16037i
$300$	5.05926			0.292097
$301$	−24.9944	+	43.2916i	−1.44066	+	2.49529i
$302$	−12.4352	+	21.5384i	−0.715564	+	1.23939i
$303$	7.79372	+	13.4991i	0.447737	+	0.775504i
$304$	0.148575			0.00852137
$305$	0.181223	+	0.313888i	0.0103768	+	0.0179731i
$306$	5.54767	+	9.60885i	0.317139	+	0.549301i
$307$	5.06327			0.288976			0.144488	−	0.989507i	$-0.453847\pi$
$307$	5.06327			0.288976			0.144488	+	0.989507i	$0.453847\pi$
$308$	−7.26053	−	12.5756i	−0.413707	−	0.716562i
$309$	−9.54923	+	16.5397i	−0.543237	+	0.940913i
$310$	17.2269	−	29.8379i	0.978422	−	1.69468i
$311$	2.91958			0.165554			0.0827771	−	0.996568i	$-0.473621\pi$
$311$	2.91958			0.165554			0.0827771	+	0.996568i	$0.473621\pi$
$312$	3.41168	+	11.8184i	0.193148	+	0.669085i
$313$	15.7882			0.892399			0.446200	−	0.894933i	$-0.352777\pi$
$313$	15.7882			0.892399			0.446200	+	0.894933i	$0.352777\pi$
$314$	15.9754	−	27.6702i	0.901543	−	1.56152i
$315$	8.51404	−	14.7467i	0.479712	−	0.830885i
$316$	−3.01804	−	5.22740i	−0.169778	−	0.294064i
$317$	−20.4397			−1.14801			−0.574005	−	0.818852i	$-0.694611\pi$
$317$	−20.4397			−1.14801			−0.574005	+	0.818852i	$0.694611\pi$
$318$	−5.67265	−	9.82531i	−0.318106	−	0.550976i
$319$	0.309757	+	0.536515i	0.0173431	+	0.0300391i
$320$	−32.5030			−1.81697
$321$	3.43318	+	5.94643i	0.191621	+	0.331898i
$322$	29.8273	−	51.6623i	1.66221	−	2.87903i
$323$	−3.78314	+	6.55259i	−0.210500	+	0.364596i
$324$	−7.11338			−0.395188
$325$	−3.21286	+	3.33890i	−0.178217	+	0.185209i
$326$	−3.18668			−0.176494
$327$	−6.05113	+	10.4809i	−0.334628	+	0.579593i
$328$	−11.6746	+	20.2211i	−0.644625	+	1.11652i
$329$	−15.1953	−	26.3190i	−0.837742	−	1.45101i
$330$	−7.00000			−0.385337
$331$	14.1406	+	24.4922i	0.777236	+	1.34621i	0.933529	+	0.358502i	$0.116712\pi$
$331$	14.1406	+	24.4922i	0.777236	+	1.34621i	−0.156293	+	0.987711i	$0.549954\pi$
$332$	8.66763	+	15.0128i	0.475698	+	0.823933i
$333$	−7.63044			−0.418145
$334$	27.2324	+	47.1678i	1.49009	+	2.58091i
$335$	−10.9418	+	18.9517i	−0.597812	+	1.03544i
$336$	0.174204	−	0.301731i	0.00950363	−	0.0164608i
$337$	−31.9256			−1.73910			−0.869550	−	0.493846i	$-0.835591\pi$
$337$	−31.9256			−1.73910			−0.869550	+	0.493846i	$0.835591\pi$
$338$	−26.2791	−	13.8529i	−1.42940	−	0.753501i
$339$	10.0804			0.547493
$340$	13.0120	−	22.5375i	0.705677	−	1.22227i
$341$	−3.00702	+	5.20831i	−0.162839	+	0.282046i
$342$	4.04367	+	7.00384i	0.218657	+	0.378724i
$343$	28.4538			1.53636
$344$	15.4844	+	26.8198i	0.834863	+	1.44603i
$345$	−8.87147	−	15.3658i	−0.477624	−	0.827268i
$346$	16.9047			0.908800
$347$	0.959347	+	1.66164i	0.0515004	+	0.0892014i	0.890626	−	0.454736i	$-0.150266\pi$
$347$	0.959347	+	1.66164i	0.0515004	+	0.0892014i	−0.839126	+	0.543937i	$0.816933\pi$
$348$	1.21943	−	2.11212i	0.0653684	−	0.113221i
$349$	0.0948995	−	0.164371i	0.00507985	−	0.00879856i	−0.863474	−	0.504393i	$-0.831716\pi$
$349$	0.0948995	−	0.164371i	0.00507985	−	0.00879856i	0.868554	+	0.495594i	$0.165050\pi$
$350$	−13.2359			−0.707489
$351$	13.7675	−	14.3077i	0.734857	−	0.763686i
$352$	5.72889			0.305351
$353$	5.47494	−	9.48288i	0.291402	−	0.504723i	−0.682740	−	0.730662i	$-0.739212\pi$
$353$	5.47494	−	9.48288i	0.291402	−	0.504723i	0.974141	+	0.225939i	$0.0725450\pi$
$354$	15.4452	−	26.7519i	0.820904	−	1.42185i
$355$	2.14959	+	3.72320i	0.114088	+	0.197607i
$356$	−27.4086			−1.45265
$357$	8.87147	+	15.3658i	0.469528	+	0.813246i
$358$	21.1616	+	36.6530i	1.11843	+	1.93717i
$359$	3.79216			0.200143			0.100071	−	0.994980i	$-0.468093\pi$
$359$	3.79216			0.200143			0.100071	+	0.994980i	$0.468093\pi$
$360$	−5.27457	−	9.13582i	−0.277994	−	0.481500i
$361$	6.74249	−	11.6783i	0.354868	−	0.614649i
$362$	−20.6304	+	35.7330i	−1.08431	+	1.87808i
$363$	1.22188			0.0641319
$364$	−14.5211	−	50.3024i	−0.761110	−	2.63656i
$365$	−5.01404			−0.262447
$366$	−0.201835	+	0.349588i	−0.0105501	+	0.0182733i
$367$	12.5035	−	21.6566i	0.652675	−	1.13047i	−0.329796	−	0.944052i	$-0.606980\pi$
$367$	12.5035	−	21.6566i	0.652675	−	1.13047i	0.982471	−	0.186415i	$-0.0596867\pi$
$368$	0.183224	+	0.317354i	0.00955123	+	0.0165432i
$369$	12.6024			0.656053
$370$	14.5035	+	25.1207i	0.753999	+	1.30596i
$371$	9.15661	+	15.8597i	0.475387	+	0.823395i
$372$	23.6757			1.22753
$373$	4.33983	+	7.51681i	0.224708	+	0.389206i	0.956232	−	0.292610i	$-0.0945238\pi$
$373$	4.33983	+	7.51681i	0.224708	+	0.389206i	−0.731524	+	0.681816i	$0.761191\pi$
$374$	−3.68122	+	6.37607i	−0.190352	+	0.329698i
$375$	5.68980	−	9.85502i	0.293820	−	0.508911i
$376$	−18.8274			−0.970947
$377$	0.619514	+	2.14606i	0.0319066	+	0.110528i
$378$	56.7178			2.91725
$379$	−7.35743	+	12.7434i	−0.377926	+	0.654587i	−0.990760	−	0.135625i	$-0.956696\pi$
$379$	−7.35743	+	12.7434i	−0.377926	+	0.654587i	0.612835	+	0.790211i	$0.290029\pi$
$380$	9.48441	−	16.4275i	0.486540	−	0.842712i
$381$	3.71286	+	6.43086i	0.190215	+	0.329463i
$382$	7.68367			0.393131
$383$	2.69526	+	4.66833i	0.137721	+	0.238540i	0.926634	−	0.375965i	$-0.122689\pi$
$383$	2.69526	+	4.66833i	0.137721	+	0.238540i	−0.788912	+	0.614506i	$0.789355\pi$
$384$	−11.0999	−	19.2256i	−0.566440	−	0.981103i
$385$	11.2992			0.575860
$386$	17.8222	+	30.8690i	0.907128	+	1.57119i
$387$	8.35743	−	14.4755i	0.424832	−	0.735831i
$388$	−0.181223	+	0.313888i	−0.00920021	+	0.0159352i
$389$	−21.5531			−1.09279			−0.546394	−	0.837529i	$-0.684000\pi$
$389$	−21.5531			−1.09279			−0.546394	+	0.837529i	$0.684000\pi$
$390$	−24.5000	−	6.06218i	−1.24061	−	0.306970i
$391$	−18.6616			−0.943759
$392$	18.5863	−	32.1925i	0.938751	−	1.62596i
$393$	7.30118	−	12.6460i	0.368296	−	0.637907i
$394$	−24.0261	−	41.6144i	−1.21042	−	2.09650i
$395$	4.69682			0.236323
$396$	2.42771	+	4.20492i	0.121997	+	0.211305i
$397$	8.76555	+	15.1824i	0.439930	+	0.761981i	0.997684	−	0.0680254i	$-0.0216699\pi$
$397$	8.76555	+	15.1824i	0.439930	+	0.761981i	−0.557753	+	0.830007i	$0.688337\pi$
$398$	51.6725			2.59011
$399$	6.46637	+	11.2001i	0.323723	+	0.560705i
$400$	0.0406531	−	0.0704133i	0.00203266	−	0.00352066i
$401$	18.2183	−	31.5551i	0.909779	−	1.57578i	0.0954093	−	0.995438i	$-0.469584\pi$
$401$	18.2183	−	31.5551i	0.909779	−	1.57578i	0.814370	−	0.580346i	$-0.197083\pi$
$402$	−24.3725			−1.21559
$403$	−15.0351	+	15.6249i	−0.748951	+	0.778333i
$404$	−41.1014			−2.04487
$405$	2.76755	−	4.79353i	0.137520	−	0.238192i
$406$	−3.19024	+	5.52566i	−0.158329	+	0.274234i
$407$	−2.53163	−	4.38492i	−0.125488	−	0.217352i
$408$	10.9920			0.544185
$409$	−14.4332	−	24.9990i	−0.713675	−	1.23612i	−0.963469	−	0.267822i	$-0.913696\pi$
$409$	−14.4332	−	24.9990i	−0.713675	−	1.23612i	0.249794	−	0.968299i	$-0.419637\pi$
$410$	−23.9538	−	41.4892i	−1.18299	−	2.04900i
$411$	−2.77501			−0.136881
$412$	−25.1797	−	43.6125i	−1.24051	−	2.14863i
$413$	−24.9312	+	43.1821i	−1.22678	+	2.12485i
$414$	−9.97338	+	17.2744i	−0.490165	+	0.848991i
$415$	−13.4890			−0.662148
$416$	20.0511	+	4.96137i	0.983088	+	0.243251i
$417$	−12.4077			−0.607606
$418$	−2.68322	+	4.64748i	−0.131241	+	0.227316i
$419$	2.10236	−	3.64140i	0.102707	−	0.177894i	−0.810092	−	0.586303i	$-0.800583\pi$
$419$	2.10236	−	3.64140i	0.102707	−	0.177894i	0.912799	+	0.408409i	$0.133916\pi$
$420$	−22.2409	−	38.5224i	−1.08525	−	1.87970i
$421$	13.5843			0.662059			0.331030	−	0.943620i	$-0.392604\pi$
$421$	13.5843			0.662059			0.331030	+	0.943620i	$0.392604\pi$
$422$	23.2816	+	40.3249i	1.13333	+	1.96298i
$423$	5.08086	+	8.80031i	0.247040	+	0.427886i
$424$	11.3453			0.550976
$425$	2.07028	+	3.58584i	0.100424	+	0.173939i
$426$	−2.39408	+	4.14667i	−0.115994	+	0.200907i
$427$	0.325796	−	0.564295i	0.0157664	−	0.0273081i
$428$	−18.1054			−0.875156
$429$	4.27657	+	1.05818i	0.206475	+	0.0510892i
$430$	−63.5411			−3.06423
$431$	15.0191	−	26.0138i	0.723442	−	1.25304i	−0.236170	−	0.971712i	$-0.575892\pi$
$431$	15.0191	−	26.0138i	0.723442	−	1.25304i	0.959612	−	0.281327i	$-0.0907746\pi$
$432$	−0.174204	+	0.301731i	−0.00838141	+	0.0145170i
$433$	−2.12853	−	3.68673i	−0.102291	−	0.177173i	0.810337	−	0.585964i	$-0.199284\pi$
$433$	−2.12853	−	3.68673i	−0.102291	−	0.177173i	−0.912628	+	0.408791i	$0.865951\pi$
$434$	−61.9397			−2.97320
$435$	0.948868	+	1.64349i	0.0454947	+	0.0787992i
$436$	−15.9558	−	27.6362i	−0.764144	−	1.32354i
$437$	−13.6024			−0.650689
$438$	−2.79216	−	4.83616i	−0.133415	−	0.231081i
$439$	2.50156	−	4.33282i	0.119393	−	0.206794i	−0.800134	−	0.599821i	$-0.795239\pi$
$439$	2.50156	−	4.33282i	0.119393	−	0.206794i	0.919527	+	0.393026i	$0.128572\pi$
$440$	3.50000	−	6.06218i	0.166856	−	0.289003i
$441$	−20.0633			−0.955394
$442$	−18.4061	+	19.1282i	−0.875490	+	0.909836i
$443$	28.3101			1.34505			0.672527	−	0.740073i	$-0.265209\pi$
$443$	28.3101			1.34505			0.672527	+	0.740073i	$0.265209\pi$
$444$	−9.96637	+	17.2623i	−0.472983	+	0.819230i
$445$	10.6636	−	18.4699i	0.505504	−	0.875559i
$446$	−20.3082	−	35.1748i	−0.961621	−	1.66558i
$447$	−13.3976			−0.633687
$448$	29.2163	+	50.6041i	1.38034	+	2.39082i
$449$	2.86289	+	4.95867i	0.135108	+	0.234014i	0.925639	−	0.378408i	$-0.123528\pi$
$449$	2.86289	+	4.95867i	0.135108	+	0.234014i	−0.790531	+	0.612423i	$0.790195\pi$
$450$	4.42571			0.208630
$451$	4.18122	+	7.24209i	0.196886	+	0.341017i
$452$	−13.2902	+	23.0192i	−0.625117	+	1.08273i
$453$	6.64915	−	11.5167i	0.312404	−	0.541100i
$454$	−13.3001			−0.624203
$455$	39.5471	+	9.78538i	1.85400	+	0.458746i
$456$	8.01201			0.375197
$457$	6.24493	−	10.8165i	0.292126	−	0.505976i	−0.682186	−	0.731178i	$-0.738971\pi$
$457$	6.24493	−	10.8165i	0.292126	−	0.505976i	0.974312	+	0.225202i	$0.0723041\pi$
$458$	27.0397	−	46.8341i	1.26348	−	2.18841i
$459$	−8.87147	−	15.3658i	−0.414085	−	0.717216i
$460$	46.7850			2.18136
$461$	6.58632	+	11.4078i	0.306756	+	0.531316i	0.977651	−	0.210236i	$-0.0674232\pi$
$461$	6.58632	+	11.4078i	0.306756	+	0.531316i	−0.670895	+	0.741552i	$0.734090\pi$
$462$	6.29216	+	10.8983i	0.292738	+	0.507037i
$463$	−10.4086			−0.483727			−0.241863	−	0.970310i	$-0.577759\pi$
$463$	−10.4086			−0.483727			−0.241863	+	0.970310i	$0.577759\pi$
$464$	−0.0195972	−	0.0339433i	−0.000909776	−	0.00157578i
$465$	−9.21130	+	15.9544i	−0.427164	+	0.739869i
$466$	−26.1506	+	45.2942i	−1.21140	+	2.09821i
$467$	23.3553			1.08076			0.540378	−	0.841422i	$-0.318281\pi$
$467$	23.3553			1.08076			0.540378	+	0.841422i	$0.318281\pi$
$468$	4.85543	+	16.8197i	0.224442	+	0.777491i
$469$	39.3413			1.81661
$470$	19.3148	−	33.4542i	0.890924	−	1.54313i
$471$	−8.54211	+	14.7954i	−0.393600	+	0.681735i
$472$	15.4452	+	26.7519i	0.710923	+	1.23136i
$473$	11.0913			0.509980
$474$	2.61551	+	4.53020i	0.120134	+	0.208079i
$475$	1.50902	+	2.61370i	0.0692386	+	0.119925i
$476$	−46.7850			−2.14439
$477$	−3.06171	−	5.30304i	−0.140186	−	0.242809i
$478$	18.5105	−	32.0611i	0.846650	−	1.46644i
$479$	−4.11094	+	7.12035i	−0.187834	+	0.325337i	−0.944528	−	0.328432i	$-0.893480\pi$
$479$	−4.11094	+	7.12035i	−0.187834	+	0.325337i	0.756694	+	0.653769i	$0.226813\pi$
$480$	17.5491			0.801005
$481$	−5.06327	−	17.5397i	−0.230865	−	0.799740i
$482$	−0.442864			−0.0201719
$483$	−15.9488	+	27.6241i	−0.725694	+	1.25694i
$484$	−1.61094	+	2.79023i	−0.0732245	+	0.126828i
$485$	−0.141014	−	0.244243i	−0.00640311	−	0.0110905i
$486$	−31.5883			−1.43288
$487$	−1.86946	−	3.23801i	−0.0847135	−	0.146728i	0.820556	−	0.571567i	$-0.193664\pi$
$487$	−1.86946	−	3.23801i	−0.0847135	−	0.146728i	−0.905269	+	0.424839i	$0.860331\pi$
$488$	−0.201835	−	0.349588i	−0.00913664	−	0.0158251i
$489$	1.70393			0.0770546
$490$	38.1350	+	66.0518i	1.72276	+	2.98392i
$491$	4.08832	−	7.08119i	0.184504	−	0.319569i	−0.758906	−	0.651201i	$-0.774266\pi$
$491$	4.08832	−	7.08119i	0.184504	−	0.319569i	0.943409	+	0.331631i	$0.107599\pi$
$492$	16.4604	−	28.5102i	0.742090	−	1.28534i
$493$	1.99600			0.0898952
$494$	−13.4161	+	13.9424i	−0.603620	+	0.627300i
$495$	−3.77812			−0.169814
$496$	0.190243	−	0.329511i	0.00854216	−	0.0147955i
$497$	3.86445	−	6.69342i	0.173344	−	0.300241i
$498$	−7.51159	−	13.0105i	−0.336602	−	0.583013i
$499$	−0.918694			−0.0411264			−0.0205632	−	0.999789i	$-0.506546\pi$
$499$	−0.918694			−0.0411264			−0.0205632	+	0.999789i	$0.506546\pi$
$500$	15.0030	+	25.9860i	0.670955	+	1.16213i
$501$	−14.5613	−	25.2209i	−0.650549	−	1.12678i
$502$	−18.6024			−0.830264
$503$	9.05425	+	15.6824i	0.403709	+	0.699244i	0.994170	−	0.107822i	$-0.0343875\pi$
$503$	9.05425	+	15.6824i	0.403709	+	0.699244i	−0.590461	+	0.807066i	$0.701054\pi$
$504$	−9.48240	+	16.4240i	−0.422380	+	0.731583i
$505$	15.9910	−	27.6972i	0.711589	−	1.23251i
$506$	−13.2359			−0.588408
$507$	14.0516	+	7.40723i	0.624052	+	0.328967i
$508$	−19.5803			−0.868736
$509$	−10.2043	+	17.6743i	−0.452297	+	0.783401i	−0.998528	−	0.0542333i	$-0.982729\pi$
$509$	−10.2043	+	17.6743i	−0.452297	+	0.783401i	0.546232	+	0.837634i	$0.316062\pi$
$510$	−11.2766	+	19.5316i	−0.499335	+	0.864873i
$511$	4.50702	+	7.80639i	0.199379	+	0.345334i
$512$	−0.715746			−0.0316318
$513$	−6.46637	−	11.2001i	−0.285497	−	0.494495i
$514$	−20.4492	−	35.4191i	−0.901976	−	1.56227i
$515$	39.1858			1.72673
$516$	−21.8318	−	37.8138i	−0.961093	−	1.66466i
$517$	−3.37147	+	5.83955i	−0.148277	+	0.256823i
$518$	26.0737	−	45.1611i	1.14561	−	1.98426i
$519$	−9.03900			−0.396768
$520$	17.5000	−	18.1865i	0.767426	−	0.797532i
$521$	−12.0069			−0.526033			−0.263016	−	0.964791i	$-0.584717\pi$
$521$	−12.0069			−0.526033			−0.263016	+	0.964791i	$0.584717\pi$
$522$	1.06673	−	1.84762i	0.0466893	−	0.0808683i
$523$	−8.92070	+	15.4511i	−0.390075	+	0.675629i	−0.992459	−	0.122577i	$-0.960884\pi$
$523$	−8.92070	+	15.4511i	−0.390075	+	0.675629i	0.602384	+	0.798206i	$0.294218\pi$
$524$	19.2520	+	33.3454i	0.841025	+	1.45670i
$525$	7.07730			0.308879
$526$	−17.7866	−	30.8073i	−0.775533	−	1.34326i
$527$	9.68824	+	16.7805i	0.422026	+	0.730971i
$528$	−0.0773036			−0.00336421
$529$	−5.27457	−	9.13582i	−0.229329	−	0.397209i
$530$	−11.6390	+	20.1594i	−0.505566	+	0.875667i
$531$	8.33627	−	14.4389i	0.361763	−	0.626593i
$532$	−34.1014			−1.47848
$533$	8.36245	+	28.9684i	0.362218	+	1.25476i
$534$	23.7530			1.02789
$535$	7.04411	−	12.2008i	0.304544	−	0.527485i
$536$	12.1862	−	21.1072i	0.526365	−	0.911692i
$537$	−11.3152	−	19.5985i	−0.488288	−	0.845739i
$538$	3.41168			0.147088
$539$	−6.65661	−	11.5296i	−0.286720	−	0.496614i
$540$	22.2409	+	38.5224i	0.957097	+	1.65774i
$541$	−19.1234			−0.822180			−0.411090	−	0.911595i	$-0.634852\pi$
$541$	−19.1234			−0.822180			−0.411090	+	0.911595i	$0.634852\pi$
$542$	26.5889	+	46.0533i	1.14209	+	1.97816i
$543$	11.0312	−	19.1066i	0.473394	−	0.819942i
$544$	9.22889	−	15.9849i	0.395686	−	0.685348i
$545$	24.8312			1.06365
$546$	12.5843	+	43.5934i	0.538559	+	1.86562i
$547$	−44.1225			−1.88654			−0.943272	−	0.332022i	$-0.892269\pi$
$547$	−44.1225			−1.88654			−0.943272	+	0.332022i	$0.892269\pi$
$548$	3.65861	−	6.33690i	0.156288	−	0.270699i
$549$	−0.108937	+	0.188684i	−0.00464931	+	0.00805284i
$550$	1.46837	+	2.54329i	0.0626114	+	0.108446i
$551$	1.45487			0.0619796
$552$	9.88049	+	17.1135i	0.420541	+	0.728399i
$553$	−4.22188	−	7.31250i	−0.179532	−	0.310959i
$554$	32.1295			1.36505
$555$	−7.75507	−	13.4322i	−0.329184	−	0.570164i
$556$	16.3584	−	28.3337i	0.693753	−	1.20161i
$557$	10.6726	−	18.4856i	0.452215	−	0.783259i	−0.546309	−	0.837584i	$-0.683967\pi$
$557$	10.6726	−	18.4856i	0.452215	−	0.783259i	0.998523	+	0.0543253i	$0.0173008\pi$
$558$	20.7109			0.876760
$559$	38.8197	+	9.60538i	1.64190	+	0.406264i
$560$	−0.714858			−0.0302082
$561$	1.96837	−	3.40931i	0.0831045	−	0.143941i
$562$	13.3449	−	23.1140i	0.562919	−	0.975003i
$563$	9.95935	+	17.2501i	0.419736	+	0.727005i	0.995913	−	0.0903206i	$-0.0287892\pi$
$563$	9.95935	+	17.2501i	0.419736	+	0.727005i	−0.576176	+	0.817325i	$0.695456\pi$
$564$	26.5451			1.11775
$565$	−10.3414	−	17.9118i	−0.435066	−	0.753556i
$566$	−3.96681	−	6.87072i	−0.166737	−	0.288798i
$567$	−9.95077			−0.417893
$568$	−2.39408	−	4.14667i	−0.100453	−	0.173990i
$569$	−23.2109	+	40.2024i	−0.973050	+	1.68537i	−0.286823	+	0.957984i	$0.592599\pi$
$569$	−23.2109	+	40.2024i	−0.973050	+	1.68537i	−0.686227	+	0.727388i	$0.740734\pi$
$570$	−8.21943	+	14.2365i	−0.344274	+	0.596300i
$571$	−5.67878			−0.237649			−0.118825	−	0.992915i	$-0.537913\pi$
$571$	−5.67878			−0.237649			−0.118825	+	0.992915i	$0.537913\pi$
$572$	−8.05469	+	8.37068i	−0.336784	+	0.349996i
$573$	−4.10849			−0.171635
$574$	−43.0632	+	74.5876i	−1.79742	+	3.11323i
$575$	−3.72188	+	6.44648i	−0.155213	+	0.268837i
$576$	−9.76910	−	16.9206i	−0.407046	−	0.705024i
$577$	−6.37648			−0.265456			−0.132728	−	0.991152i	$-0.542374\pi$
$577$	−6.37648			−0.265456			−0.132728	+	0.991152i	$0.542374\pi$
$578$	−7.56327	−	13.1000i	−0.314590	−	0.544887i
$579$	−9.52963	−	16.5058i	−0.396038	−	0.685958i
$580$	−5.00400			−0.207780
$581$	12.1250	+	21.0011i	0.503029	+	0.871271i
$582$	0.157053	−	0.272023i	0.00651004	−	0.0112757i
$583$	2.03163	−	3.51889i	0.0841416	−	0.145738i
$584$	5.58432			0.231081
$585$	−13.2234	−	3.27195i	−0.546722	−	0.135279i
$586$	−14.5783			−0.602224
$587$	0.436734	−	0.756445i	0.0180259	−	0.0312218i	−0.856872	−	0.515530i	$-0.827595\pi$
$587$	0.436734	−	0.756445i	0.0180259	−	0.0312218i	0.874898	+	0.484308i	$0.160929\pi$
$588$	−26.2053	+	45.3889i	−1.08069	+	1.87181i
$589$	7.06171	+	12.2312i	0.290973	+	0.503979i
$590$	−63.3803			−2.60933
$591$	12.8469	+	22.2514i	0.528449	+	0.915300i
$592$	0.160167	+	0.277418i	0.00658283	+	0.0114018i
$593$	18.7850			0.771409			0.385705	−	0.922622i	$-0.373958\pi$
$593$	18.7850			0.771409			0.385705	+	0.922622i	$0.373958\pi$
$594$	−6.29216	−	10.8983i	−0.258170	−	0.447164i
$595$	18.2023	−	31.5273i	0.746221	−	1.29249i
$596$	17.6636	−	30.5943i	0.723530	−	1.25319i
$597$	−27.6295			−1.13080
$598$	−46.3257	−	11.4626i	−1.89440	−	0.468742i
$599$	11.7601			0.480504			0.240252	−	0.970711i	$-0.422770\pi$
$599$	11.7601			0.480504			0.240252	+	0.970711i	$0.422770\pi$
$600$	2.19224	−	3.79708i	0.0894980	−	0.155015i
$601$	−14.2585	+	24.6965i	−0.581617	+	1.00739i	0.413670	+	0.910427i	$0.364247\pi$
$601$	−14.2585	+	24.6965i	−0.581617	+	1.00739i	−0.995288	+	0.0969642i	$0.969087\pi$
$602$	57.1159	+	98.9276i	2.32787	+	4.03199i
$603$	−13.1546			−0.535697
$604$	17.5326	+	30.3674i	0.713393	+	1.23563i
$605$	−1.25351	−	2.17114i	−0.0509624	−	0.0882695i
$606$	35.6195			1.44694
$607$	−7.73591	−	13.3990i	−0.313991	−	0.543848i	0.665231	−	0.746637i	$-0.268333\pi$
$607$	−7.73591	−	13.3990i	−0.313991	−	0.543848i	−0.979223	+	0.202789i	$0.935000\pi$
$608$	6.72689	−	11.6513i	0.272812	−	0.472523i
$609$	1.70584	−	2.95460i	0.0691240	−	0.119726i
$610$	0.828241			0.0335345
$611$	−16.8573	+	17.5187i	−0.681975	+	0.708729i
$612$	15.6436			0.632354
$613$	9.79416	−	16.9640i	0.395582	−	0.685169i	−0.597593	−	0.801800i	$-0.703876\pi$
$613$	9.79416	−	16.9640i	0.395582	−	0.685169i	0.993175	+	0.116631i	$0.0372094\pi$
$614$	5.78514	−	10.0202i	0.233469	−	0.404381i
$615$	12.8082	+	22.1845i	0.516476	+	0.894563i
$616$	−12.5843			−0.507037
$617$	14.6551	+	25.3833i	0.589990	+	1.02189i	0.994233	+	0.107241i	$0.0342017\pi$
$617$	14.6551	+	25.3833i	0.589990	+	1.02189i	−0.404243	+	0.914652i	$0.632465\pi$
$618$	21.8213	+	37.7957i	0.877783	+	1.52037i
$619$	−3.74293			−0.150441			−0.0752206	−	0.997167i	$-0.523966\pi$
$619$	−3.74293			−0.150441			−0.0752206	+	0.997167i	$0.523966\pi$
$620$	−24.2886	−	42.0691i	−0.975454	−	1.68954i
$621$	15.9488	−	27.6241i	0.640002	−	1.10852i
$622$	3.33583	−	5.77783i	0.133755	−	0.231670i
$623$	−38.3413			−1.53611
$624$	−0.270563	−	0.0669469i	−0.0108312	−	0.00268002i
$625$	−29.7741			−1.19096
$626$	18.0391	−	31.2446i	0.720987	−	1.24879i
$627$	1.43473	−	2.48503i	0.0572977	−	0.0992425i
$628$	−22.5241	−	39.0128i	−0.898808	−	1.55678i
$629$	−16.3132			−0.650451
$630$	−19.4558	−	33.6984i	−0.775137	−	1.34258i
$631$	11.2590	+	19.5011i	0.448213	+	0.776327i	0.998270	−	0.0588001i	$-0.0187274\pi$
$631$	11.2590	+	19.5011i	0.448213	+	0.776327i	−0.550057	+	0.835127i	$0.685394\pi$
$632$	−5.23102			−0.208079
$633$	−12.4488	−	21.5619i	−0.494794	−	0.857009i
$634$	−23.3539	+	40.4501i	−0.927501	+	1.60648i
$635$	7.61796	−	13.1947i	0.302309	−	0.523615i
$636$	−15.9960			−0.634283
$637$	−13.3132	−	46.1183i	−0.527489	−	1.82728i
$638$	1.41568			0.0560472
$639$	−1.29216	+	2.23809i	−0.0511171	+	0.0885374i
$640$	−22.7746	+	39.4467i	−0.900244	+	1.55927i
$641$	−13.2906	−	23.0200i	−0.524947	−	0.909235i	−0.999578	−	0.0290503i	$-0.990752\pi$
$641$	−13.2906	−	23.0200i	−0.524947	−	0.909235i	0.474631	−	0.880185i	$-0.342582\pi$
$642$	15.6906			0.619258
$643$	−0.642571	−	1.11297i	−0.0253405	−	0.0438911i	0.853077	−	0.521785i	$-0.174734\pi$
$643$	−0.642571	−	1.11297i	−0.0253405	−	0.0438911i	−0.878418	+	0.477894i	$0.841400\pi$
$644$	−42.0541	−	72.8399i	−1.65717	−	2.87029i
$645$	33.9757			1.33779
$646$	8.64502	+	14.9736i	0.340134	+	0.589129i
$647$	6.88706	−	11.9287i	0.270758	−	0.468967i	−0.698298	−	0.715807i	$-0.746059\pi$
$647$	6.88706	−	11.9287i	0.270758	−	0.468967i	0.969056	+	0.246840i	$0.0793923\pi$
$648$	−3.08232	+	5.33874i	−0.121085	+	0.209725i
$649$	11.0633			0.434271
$650$	2.93673	+	10.1731i	0.115188	+	0.399024i
$651$	33.1194			1.29805
$652$	−2.24649	+	3.89104i	−0.0879794	+	0.152385i
$653$	−7.76910	+	13.4565i	−0.304029	+	0.526593i	−0.977045	−	0.213035i	$-0.931665\pi$
$653$	−7.76910	+	13.4565i	−0.304029	+	0.526593i	0.673016	+	0.739628i	$0.264998\pi$
$654$	13.8277	+	23.9503i	0.540706	+	0.936530i
$655$	−29.9608			−1.17067
$656$	−0.264531	−	0.458180i	−0.0103282	−	0.0178889i
$657$	−1.50702	−	2.61023i	−0.0587944	−	0.101835i
$658$	−69.4467			−2.70731
$659$	−10.1867	−	17.6439i	−0.396817	−	0.687307i	0.596514	−	0.802602i	$-0.296552\pi$
$659$	−10.1867	−	17.6439i	−0.396817	−	0.687307i	−0.993331	+	0.115295i	$0.963219\pi$
$660$	−4.93473	+	8.54721i	−0.192084	+	0.332700i
$661$	−0.494539	+	0.856566i	−0.0192353	+	0.0333166i	−0.875483	−	0.483249i	$-0.839457\pi$
$661$	−0.494539	+	0.856566i	−0.0192353	+	0.0333166i	0.856248	+	0.516566i	$0.172790\pi$
$662$	64.6264			2.51178
$663$	9.84183	−	10.2279i	0.382225	−	0.397220i
$664$	15.0232			0.583013
$665$	13.2675	−	22.9801i	0.514493	−	0.891129i
$666$	−8.71832	+	15.1006i	−0.337828	+	0.585135i
$667$	1.79416	+	3.10758i	0.0694702	+	0.120326i
$668$	76.7911			2.97114
$669$	10.8589	+	18.8081i	0.419829	+	0.727165i
$670$	25.0035	+	43.3073i	0.965968	+	1.67311i
$671$	−0.144573			−0.00558116
$672$	−15.7746	−	27.3223i	−0.608517	−	1.05398i
$673$	−15.1496	+	26.2399i	−0.583974	+	1.01147i	0.411029	+	0.911622i	$0.365170\pi$
$673$	−15.1496	+	26.2399i	−0.583974	+	1.01147i	−0.995003	+	0.0998499i	$0.968164\pi$
$674$	−36.4773	+	63.1805i	−1.40505	+	2.43362i
$675$	−7.07730			−0.272406
$676$	−35.4406	+	22.3218i	−1.36310	+	0.858531i
$677$	20.6788			0.794750			0.397375	−	0.917656i	$-0.369921\pi$
$677$	20.6788			0.794750			0.397375	+	0.917656i	$0.369921\pi$
$678$	11.5176	−	19.9491i	0.442331	−	0.766139i
$679$	−0.253509	+	0.439091i	−0.00972879	+	0.0168508i
$680$	−11.2766	−	19.5316i	−0.432437	−	0.749002i
$681$	7.11161			0.272517
$682$	6.87147	+	11.9017i	0.263122	+	0.455741i
$683$	0.219875	+	0.380834i	0.00841328	+	0.0145722i	0.870201	−	0.492696i	$-0.163989\pi$
$683$	0.219875	+	0.380834i	0.00841328	+	0.0145722i	−0.861788	+	0.507268i	$0.830655\pi$
$684$	11.4025			0.435987
$685$	2.84685	+	4.93089i	0.108773	+	0.188400i
$686$	32.5105	−	56.3098i	1.24126	−	2.14992i
$687$	−14.4582	+	25.0424i	−0.551616	+	0.955427i
$688$	−0.701708			−0.0267524
$689$	10.1582	−	10.5567i	0.386995	−	0.402177i
$690$	−40.5451			−1.54353
$691$	−10.0211	+	17.3570i	−0.381219	+	0.660291i	−0.991237	−	0.132097i	$-0.957829\pi$
$691$	−10.0211	+	17.3570i	−0.381219	+	0.660291i	0.610018	+	0.792388i	$0.291162\pi$
$692$	11.9171	−	20.6411i	0.453022	−	0.784656i
$693$	3.39608	+	5.88218i	0.129006	+	0.223446i
$694$	4.38449			0.166433
$695$	12.7289	+	22.0471i	0.482835	+	0.836294i
$696$	−1.05679	−	1.83041i	−0.0400575	−	0.0693817i
$697$	26.9428			1.02053
$698$	−0.216859	−	0.375611i	−0.00820823	−	0.0142171i
$699$	13.9828	−	24.2190i	0.528880	−	0.916047i
$700$	−9.33081	+	16.1614i	−0.352672	+	0.610845i
$701$	−36.9898			−1.39708			−0.698542	−	0.715569i	$-0.746168\pi$
$701$	−36.9898			−1.39708			−0.698542	+	0.715569i	$0.746168\pi$
$702$	−12.5843	−	43.5934i	−0.474965	−	1.64533i
$703$	−11.8906			−0.448463
$704$	6.48240	−	11.2279i	0.244315	−	0.423166i
$705$	−10.3277	+	17.8881i	−0.388964	+	0.673705i
$706$	−12.5110	−	21.6697i	−0.470858	−	0.815551i
$707$	−57.4959			−2.16236
$708$	−21.7766	−	37.7181i	−0.818413	−	1.41753i
$709$	−16.9011	−	29.2736i	−0.634734	−	1.09939i	−0.986571	−	0.163330i	$-0.947776\pi$
$709$	−16.9011	−	29.2736i	−0.634734	−	1.09939i	0.351837	−	0.936061i	$-0.385557\pi$
$710$	9.82424			0.368697
$711$	1.41168	+	2.44509i	0.0529420	+	0.0916982i
$712$	−11.8765	+	20.5707i	−0.445090	+	0.770919i
$713$	−17.4171	+	30.1674i	−0.652277	+	1.12978i
$714$	40.5451			1.51736
$715$	−2.50702	−	8.68457i	−0.0937572	−	0.324784i
$716$	59.6725			2.23007
$717$	−9.89764	+	17.1432i	−0.369634	+	0.640225i
$718$	4.33281	−	7.50465i	0.161699	−	0.280071i
$719$	−6.11049	−	10.5837i	−0.227883	−	0.394705i	0.729298	−	0.684197i	$-0.239847\pi$
$719$	−6.11049	−	10.5837i	−0.227883	−	0.394705i	−0.957180	+	0.289492i	$0.906514\pi$
$720$	0.239028			0.00890805
$721$	−35.2233	−	61.0086i	−1.31179	−	2.27208i
$722$	−15.4075	−	26.6867i	−0.573409	−	0.993174i
$723$	0.236802			0.00880674
$724$	29.0873	+	50.3807i	1.08102	+	1.87239i
$725$	0.398082	−	0.689498i	0.0147844	−	0.0256073i
$726$	1.39608	−	2.41808i	0.0518134	−	0.0897435i
$727$	35.2771			1.30836			0.654178	−	0.756340i	$-0.273015\pi$
$727$	35.2771			1.30836			0.654178	+	0.756340i	$0.273015\pi$
$728$	−44.0451	−	10.8983i	−1.63242	−	0.403919i
$729$	23.5139			0.870887
$730$	−5.72889	+	9.92274i	−0.212036	+	0.367257i
$731$	17.8675	−	30.9474i	0.660852	−	1.14463i
$732$	0.284572	+	0.492893i	0.0105181	+	0.0182178i
$733$	17.0953			0.631431			0.315715	−	0.948854i	$-0.397755\pi$
$733$	17.0953			0.631431			0.315715	+	0.948854i	$0.397755\pi$
$734$	−28.5722	−	49.4885i	−1.05462	−	1.82665i
$735$	−20.3910	−	35.3182i	−0.752132	−	1.30273i
$736$	33.1827			1.22313
$737$	−4.36445	−	7.55944i	−0.160766	−	0.278456i
$738$	14.3991	−	24.9400i	0.530038	−	0.918053i
$739$	21.6140	−	37.4365i	0.795082	−	1.37712i	−0.127705	−	0.991812i	$-0.540761\pi$
$739$	21.6140	−	37.4365i	0.795082	−	1.37712i	0.922787	−	0.385310i	$-0.125906\pi$
$740$	40.8975			1.50342
$741$	7.17366	−	7.45509i	0.263531	−	0.273870i
$742$	41.8483			1.53630
$743$	−0.729339	+	1.26325i	−0.0267568	+	0.0463442i	−0.879094	−	0.476649i	$-0.841851\pi$
$743$	−0.729339	+	1.26325i	−0.0267568	+	0.0463442i	0.852337	+	0.522993i	$0.175185\pi$
$744$	10.2590	−	17.7691i	0.376112	−	0.651445i
$745$	13.7445	+	23.8062i	0.503559	+	0.872190i
$746$	19.8343			0.726184
$747$	−4.05425	−	7.02216i	−0.148337	−	0.256927i
$748$	5.19024	+	8.98976i	0.189774	+	0.328698i
$749$	−25.3273			−0.925438
$750$	−13.0020	−	22.5201i	−0.474766	−	0.822319i
$751$	−7.67967	+	13.3016i	−0.280235	+	0.485381i	−0.971442	−	0.237275i	$-0.923746\pi$
$751$	−7.67967	+	13.3016i	−0.280235	+	0.485381i	0.691208	+	0.722656i	$0.257079\pi$
$752$	0.213300	−	0.369447i	0.00777826	−	0.0134723i
$753$	9.94677			0.362480
$754$	4.95487	+	1.22601i	0.180446	+	0.0446488i
$755$	−27.2851			−0.993008
$756$	39.9839	−	69.2541i	1.45420	−	2.51875i
$757$	−17.1898	+	29.7736i	−0.624774	+	1.08214i	0.363811	+	0.931473i	$0.381476\pi$
$757$	−17.1898	+	29.7736i	−0.624774	+	1.08214i	−0.988585	+	0.150667i	$0.951858\pi$
$758$	16.8128	+	29.1206i	0.610667	+	1.05771i
$759$	7.07730			0.256890
$760$	−8.21943	−	14.2365i	−0.298150	−	0.516411i
$761$	1.94331	+	3.36591i	0.0704449	+	0.122014i	0.899096	−	0.437751i	$-0.144225\pi$
$761$	1.94331	+	3.36591i	0.0704449	+	0.122014i	−0.828651	+	0.559765i	$0.810891\pi$
$762$	16.9688			0.614715
$763$	−22.3202	−	38.6598i	−0.808047	−	1.39958i
$764$	5.41669	−	9.38199i	0.195969	−	0.339428i
$765$	−6.08632	+	10.5418i	−0.220051	+	0.381140i
$766$	12.3181			0.445071
$767$	38.7214	+	9.58107i	1.39815	+	0.345952i
$768$	−19.0470			−0.687300
$769$	−19.7129	+	34.1437i	−0.710864	+	1.23125i	0.253670	+	0.967291i	$0.418362\pi$
$769$	−19.7129	+	34.1437i	−0.710864	+	1.23125i	−0.964533	+	0.263961i	$0.914971\pi$
$770$	12.9101	−	22.3610i	0.465248	−	0.805834i
$771$	10.9343	+	18.9387i	0.393789	+	0.682062i
$772$	50.2560			1.80875
$773$	12.2203	+	21.1662i	0.439534	+	0.761296i	0.997654	−	0.0684650i	$-0.0218102\pi$
$773$	12.2203	+	21.1662i	0.439534	+	0.761296i	−0.558119	+	0.829761i	$0.688477\pi$
$774$	−19.0979	−	33.0786i	−0.686460	−	1.18898i
$775$	7.72889			0.277630
$776$	0.157053	+	0.272023i	0.00563786	+	0.00976506i
$777$	−13.9418	+	24.1478i	−0.500158	+	0.866298i
$778$	−24.6260	+	42.6535i	−0.882885	+	1.52920i
$779$	19.6384			0.703620
$780$	−24.6737	+	25.6416i	−0.883459	+	0.918117i
$781$	−1.71486			−0.0613624
$782$	−21.3222	+	36.9312i	−0.762482	+	1.32066i
$783$	−1.70584	+	2.95460i	−0.0609617	+	0.105589i
$784$	0.421139	+	0.729434i	0.0150407	+	0.0260512i
$785$	35.0530			1.25110
$786$	−16.6842	−	28.8979i	−0.595107	−	1.03076i
$787$	18.4086	+	31.8846i	0.656194	+	1.13656i	0.981593	+	0.190985i	$0.0611682\pi$
$787$	18.4086	+	31.8846i	0.656194	+	1.13656i	−0.325399	+	0.945577i	$0.605498\pi$
$788$	−67.7499			−2.41349
$789$	9.51058	+	16.4728i	0.338586	+	0.586447i
$790$	5.36645	−	9.29496i	0.190930	−	0.330700i
$791$	−18.5913	+	32.2011i	−0.661032	+	1.14494i
$792$	4.20784			0.149519
$793$	−0.506004	−	0.125204i	−0.0179687	−	0.00444611i
$794$	40.0610			1.42171
$795$	6.22343	−	10.7793i	0.220722	−	0.382302i
$796$	36.4272	−	63.0937i	1.29113	−	2.23630i
$797$	−5.76097	−	9.97830i	−0.204064	−	0.353449i	0.745770	−	0.666203i	$-0.232082\pi$
$797$	−5.76097	−	9.97830i	−0.204064	−	0.353449i	−0.949834	+	0.312754i	$0.898748\pi$
$798$	29.5531			1.04617
$799$	10.8624	+	18.8143i	0.384286	+	0.665602i
$800$	−3.68122	−	6.37607i	−0.130151	−	0.225428i
$801$	12.8202			0.452981
$802$	−41.6315	−	72.1078i	−1.47006	−	2.54621i
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$	−17.1817	+	29.7595i	−0.605951	+	1.04954i
$805$	65.4467			2.30669
$806$	13.7429	+	47.6069i	0.484074	+	1.67688i
$807$	−1.82424			−0.0642162
$808$	−17.8098	+	30.8474i	−0.626545	+	1.08521i
$809$	12.2325	−	21.1872i	0.430070	−	0.744903i	−0.566809	−	0.823849i	$-0.691822\pi$
$809$	12.2325	−	21.1872i	0.430070	−	0.744903i	0.996879	+	0.0789461i	$0.0251555\pi$
$810$	−6.32424	−	10.9539i	−0.222211	−	0.384881i
$811$	9.19291			0.322807			0.161403	−	0.986889i	$-0.448398\pi$
$811$	9.19291			0.322807			0.161403	+	0.986889i	$0.448398\pi$
$812$	4.49800	+	7.79076i	0.157849	+	0.273402i
$813$	−14.2172	−	24.6249i	−0.498619	−	0.863634i
$814$	−11.5703			−0.405538
$815$	−1.74805	−	3.02771i	−0.0612314	−	0.106056i
$816$	−0.124531	+	0.215695i	−0.00435947	+	0.00755082i
$817$	13.0235	−	22.5574i	0.455635	−	0.789182i
$818$	−65.9637			−2.30637
$819$	6.79216	+	23.5287i	0.237337	+	0.822161i
$820$	−67.5460			−2.35881
$821$	−15.2976	+	26.4963i	−0.533891	+	0.924726i	0.465325	+	0.885140i	$0.345937\pi$
$821$	−15.2976	+	26.4963i	−0.533891	+	0.924726i	−0.999216	+	0.0395862i	$0.987396\pi$
$822$	−3.17065	+	5.49172i	−0.110589	+	0.191546i
$823$	9.60738	+	16.6405i	0.334892	+	0.580050i	0.983464	−	0.181103i	$-0.0579668\pi$
$823$	9.60738	+	16.6405i	0.334892	+	0.580050i	−0.648572	+	0.761153i	$0.724633\pi$
$824$	−43.6427			−1.52037
$825$	−0.785142	−	1.35991i	−0.0273352	−	0.0473459i
$826$	56.9713	+	98.6772i	1.98228	+	3.43342i
$827$	28.4990			0.991008			0.495504	−	0.868606i	$-0.334983\pi$
$827$	28.4990			0.991008			0.495504	+	0.868606i	$0.334983\pi$
$828$	14.0617	+	24.3556i	0.488678	+	0.846415i
$829$	3.34139	−	5.78746i	0.116051	−	0.201007i	−0.802148	−	0.597125i	$-0.796310\pi$
$829$	3.34139	−	5.78746i	0.116051	−	0.201007i	0.918200	+	0.396118i	$0.129643\pi$
$830$	−15.4121	+	26.6946i	−0.534962	+	0.926582i
$831$	−17.1798			−0.595959
$832$	32.4120	−	33.6836i	1.12368	−	1.16777i
$833$	−42.8935			−1.48617
$834$	−14.1766	+	24.5547i	−0.490897	+	0.850259i
$835$	−29.8765	+	51.7476i	−1.03392	+	1.79080i
$836$	3.78314	+	6.55259i	0.130843	+	0.226626i
$837$	−33.1194			−1.14477
$838$	−4.80420	−	8.32111i	−0.165958	−	0.287448i
$839$	−4.31522	−	7.47418i	−0.148978	−	0.258037i	0.781872	−	0.623439i	$-0.214265\pi$
$839$	−4.31522	−	7.47418i	−0.148978	−	0.258037i	−0.930850	+	0.365402i	$0.880932\pi$
$840$	−38.5491			−1.33007
$841$	14.3081	+	24.7824i	0.493383	+	0.854564i
$842$	15.5211	−	26.8833i	0.534891	−	0.926458i
$843$	−7.13555	+	12.3591i	−0.245761	+	0.425671i
$844$	65.6505			2.25978
$845$	−1.25351	−	32.5671i	−0.0431220	−	1.12034i
$846$	23.2210			0.798354
$847$	−2.25351	+	3.90319i	−0.0774315	+	0.134115i
$848$	−0.128534	+	0.222627i	−0.00441387	+	0.00764505i
$849$	2.12107	+	3.67380i	0.0727950	+	0.126085i
$850$	9.46179			0.324537
$851$	−14.6636	−	25.3981i	−0.502663	−	0.870637i
$852$	3.37547	+	5.84648i	0.115642	+	0.200297i
$853$	−18.2631			−0.625317			−0.312658	−	0.949866i	$-0.601219\pi$
$853$	−18.2631			−0.625317			−0.312658	+	0.949866i	$0.601219\pi$
$854$	−0.744489	−	1.28949i	−0.0254759	−	0.0441256i
$855$	−4.43629	+	7.68388i	−0.151718	+	0.262783i
$856$	−7.84529	+	13.5884i	−0.268147	+	0.464444i
$857$	1.22899			0.0419816			0.0209908	−	0.999780i	$-0.493318\pi$
$857$	1.22899			0.0419816			0.0209908	+	0.999780i	$0.493318\pi$
$858$	6.98040	−	7.25425i	0.238307	−	0.247656i
$859$	4.15772			0.141860			0.0709298	−	0.997481i	$-0.477403\pi$
$859$	4.15772			0.141860			0.0709298	+	0.997481i	$0.477403\pi$
$860$	−44.7941	+	77.5856i	−1.52746	+	2.64565i
$861$	23.0261	−	39.8823i	0.784726	−	1.35919i
$862$	−34.3207	−	59.4452i	−1.16897	−	2.02471i
$863$	−30.0633			−1.02337			−0.511683	−	0.859174i	$-0.670978\pi$
$863$	−30.0633			−1.02337			−0.511683	+	0.859174i	$0.670978\pi$
$864$	15.7746	+	27.3223i	0.536662	+	0.929525i
$865$	9.27301	+	16.0613i	0.315292	+	0.546101i
$866$	−9.72801			−0.330571
$867$	4.04411	+	7.00461i	0.137345	+	0.237889i
$868$	−43.6651	+	75.6301i	−1.48209	+	2.56705i
$869$	−0.936734	+	1.62247i	−0.0317765	+	0.0550385i
$870$	4.33660			0.147024
$871$	−8.72889	−	30.2378i	−0.295767	−	1.02457i
$872$	−27.6554			−0.936530
$873$	0.0847663	−	0.146820i	0.00286890	−	0.00496909i
$874$	−15.5417	+	26.9190i	−0.525705	+	0.910547i
$875$	20.9874	+	36.3513i	0.709504	+	1.22890i
$876$	−7.87347			−0.266020
$877$	−27.1546	−	47.0332i	−0.916946	−	1.58820i	−0.804027	−	0.594593i	$-0.797313\pi$
$877$	−27.1546	−	47.0332i	−0.916946	−	1.58820i	−0.112919	−	0.993604i	$-0.536020\pi$
$878$	−5.71641	−	9.90112i	−0.192920	−	0.334147i
$879$	7.79508			0.262921
$880$	0.0793049	+	0.137360i	0.00267337	+	0.00463041i
$881$	−16.4081	+	28.4197i	−0.552803	+	0.957484i	0.445267	+	0.895398i	$0.353109\pi$
$881$	−16.4081	+	28.4197i	−0.552803	+	0.957484i	−0.998071	+	0.0620860i	$0.980225\pi$
$882$	−22.9237	+	39.7050i	−0.771882	+	1.33694i
$883$	−38.3444			−1.29039			−0.645196	−	0.764017i	$-0.723224\pi$
$883$	−38.3444			−1.29039			−0.645196	+	0.764017i	$0.723224\pi$
$884$	10.3805	+	35.9591i	0.349134	+	1.20943i
$885$	33.8897			1.13919
$886$	32.3463	−	56.0255i	1.08670	−	1.88221i
$887$	−9.76910	+	16.9206i	−0.328014	+	0.568138i	−0.982118	−	0.188268i	$-0.939713\pi$
$887$	−9.76910	+	16.9206i	−0.328014	+	0.568138i	0.654103	+	0.756405i	$0.273046\pi$
$888$	8.63711	+	14.9599i	0.289842	+	0.502022i
$889$	−27.3905			−0.918649
$890$	−24.3679	−	42.2065i	−0.816814	−	1.41476i
$891$	1.10392	+	1.91204i	0.0369827	+	0.0640559i
$892$	−57.2660			−1.91741
$893$	7.91758	+	13.7137i	0.264952	+	0.458910i
$894$	−15.3078	+	26.5138i	−0.511968	+	0.886754i
$895$	−23.2163	+	40.2118i	−0.776036	+	1.34413i
$896$	81.8864			2.73563
$897$	24.7706	+	6.12912i	0.827065	+	0.204646i
$898$	13.0842			0.436626
$899$	1.86289	−	3.22662i	0.0621309	−	0.107614i
$900$	3.11996	−	5.40393i	0.103999	−	0.180131i
$901$	−6.54567	−	11.3374i	−0.218068	−	0.377705i
$902$	19.1094			0.636273
$903$	−30.5401	−	52.8970i	−1.01631	−	1.76030i
$904$	11.5176	+	19.9491i	0.383070	+	0.663496i
$905$	−45.2671			−1.50473
$906$	−15.1942	−	26.3172i	−0.504795	−	0.874331i
$907$	−19.6300	+	34.0001i	−0.651803	+	1.12896i	0.330882	+	0.943672i	$0.392654\pi$
$907$	−19.6300	+	34.0001i	−0.651803	+	1.12896i	−0.982685	+	0.185284i	$0.940679\pi$
$908$	−9.37604	+	16.2398i	−0.311155	+	0.538936i
$909$	19.2250			0.637653
$910$	64.5506	−	67.0829i	2.13983	−	2.22378i
$911$	−11.1194			−0.368403			−0.184201	−	0.982889i	$-0.558970\pi$
$911$	−11.1194			−0.368403			−0.184201	+	0.982889i	$0.558970\pi$
$912$	−0.0907702	+	0.157219i	−0.00300570	+	0.00520603i
$913$	2.69024	−	4.65964i	0.0890340	−	0.154211i
$914$	−14.2706	−	24.7173i	−0.472028	−	0.817577i
$915$	−0.442864			−0.0146406
$916$	−38.1239	−	66.0325i	−1.25965	−	2.18177i
$917$	26.9312	+	46.6462i	0.889346	+	1.54039i
$918$	−40.5451			−1.33819
$919$	−4.38750	−	7.59938i	−0.144730	−	0.250680i	0.784542	−	0.620076i	$-0.212898\pi$
$919$	−4.38750	−	7.59938i	−0.144730	−	0.250680i	−0.929272	+	0.369395i	$0.879565\pi$
$920$	20.2726	−	35.1131i	0.668367	−	1.15764i
$921$	−3.09334	+	5.35783i	−0.101929	+	0.176546i
$922$	30.1014			0.991336
$923$	−6.00200	−	1.48511i	−0.197558	−	0.0488830i
$924$	17.7429			0.583700
$925$	−3.25351	+	5.63524i	−0.106975	+	0.185286i
$926$	−11.8925	+	20.5985i	−0.390813	+	0.676907i
$927$	11.7777	+	20.3995i	0.386830	+	0.670009i
$928$	−3.54913			−0.116506
$929$	−12.6140	−	21.8480i	−0.413850	−	0.716810i	0.581457	−	0.813577i	$-0.302483\pi$
$929$	−12.6140	−	21.8480i	−0.413850	−	0.716810i	−0.995307	+	0.0967675i	$0.969150\pi$
$930$	21.0491	+	36.4582i	0.690228	+	1.19551i
$931$	−31.2649			−1.02466
$932$	36.8704	+	63.8613i	1.20773	+	2.09185i
$933$	−1.78368	+	3.08943i	−0.0583952	+	0.101143i
$934$	26.6851	−	46.2200i	0.873164	−	1.51236i
$935$	−8.07730			−0.264156
$936$	14.7274	+	3.64410i	0.481381	+	0.119111i
$937$	5.68589			0.185750			0.0928750	−	0.995678i	$-0.470394\pi$
$937$	5.68589			0.185750			0.0928750	+	0.995678i	$0.470394\pi$
$938$	44.9502	−	77.8561i	1.46768	−	2.54209i
$939$	−9.64559	+	16.7066i	−0.314772	+	0.545201i
$940$	−27.2324	−	47.1678i	−0.888221	−	1.53844i
$941$	12.2468			0.399235			0.199618	−	0.979874i	$-0.436030\pi$
$941$	12.2468			0.399235			0.199618	+	0.979874i	$0.436030\pi$
$942$	19.5199	+	33.8095i	0.635994	+	1.10157i
$943$	24.2183	+	41.9474i	0.788657	+	1.36599i
$944$	−0.699932			−0.0227809
$945$	31.1124	+	53.8883i	1.01209	+	1.75298i
$946$	12.6726	−	21.9497i	0.412023	−	0.713645i
$947$	13.7831	−	23.8731i	0.447892	−	0.775772i	−0.550357	−	0.834930i	$-0.685508\pi$
$947$	13.7831	−	23.8731i	0.447892	−	0.775772i	0.998249	+	0.0591581i	$0.0188416\pi$
$948$	7.37534			0.239540
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$	6.89665			0.223757
$951$	12.4874	−	21.6288i	0.404932	−	0.701363i
$952$	−20.2726	+	35.1131i	−0.657038	+	1.13802i
$953$	−6.17220	−	10.6906i	−0.199937	−	0.346302i	0.748571	−	0.663055i	$-0.230741\pi$
$953$	−6.17220	−	10.6906i	−0.199937	−	0.346302i	−0.948508	+	0.316754i	$0.897407\pi$
$954$	−13.9929			−0.453036
$955$	4.21486	+	7.30035i	0.136390	+	0.236234i
$956$	−26.0984	−	45.2037i	−0.844081	−	1.46199i
$957$	−0.756969			−0.0244693
$958$	9.39408	+	16.2710i	0.303509	+	0.525693i
$959$	5.11796	−	8.86456i	0.165267	−	0.286252i
$960$	19.8573	−	34.3939i	0.640893	−	1.11006i
$961$	5.16864			0.166730
$962$	−40.4960	−	10.0202i	−1.30564	−	0.323063i
$963$	8.46871			0.272900
$964$	−0.312202	+	0.540750i	−0.0100554	+	0.0174164i
$965$	−19.5527	+	33.8663i	−0.629423	+	1.09019i
$966$	36.4452	+	63.1250i	1.17261	+	2.03101i
$967$	13.5451			0.435582			0.217791	−	0.975995i	$-0.430115\pi$
$967$	13.5451			0.435582			0.217791	+	0.975995i	$0.430115\pi$
$968$	1.39608	+	2.41808i	0.0448717	+	0.0777201i
$969$	−4.62253	−	8.00646i	−0.148497	−	0.257204i
$970$	−0.644474			−0.0206928
$971$	0.744933	+	1.29026i	0.0239061	+	0.0414065i	0.877731	−	0.479154i	$-0.159056\pi$
$971$	0.744933	+	1.29026i	0.0239061	+	0.0414065i	−0.853825	+	0.520560i	$0.825723\pi$
$972$	−22.2686	+	38.5703i	−0.714264	+	1.23714i
$973$	22.8835	−	39.6354i	0.733611	−	1.27065i
$974$	−8.54399			−0.273767
$975$	−1.57028	−	5.43963i	−0.0502894	−	0.174207i
$976$	0.00914657			0.000292775
$977$	20.0913	−	34.7992i	0.642779	−	1.11333i	−0.342031	−	0.939689i	$-0.611115\pi$
$977$	20.0913	−	34.7992i	0.642779	−	1.11333i	0.984810	−	0.173637i	$-0.0555520\pi$
$978$	1.94687	−	3.37207i	0.0622539	−	0.107827i
$979$	4.25351	+	7.36729i	0.135943	+	0.235460i
$980$	107.535			3.43508
$981$	7.46325	+	12.9267i	0.238283	+	0.412719i
$982$	−9.34240	−	16.1815i	−0.298128	−	0.516373i
$983$	26.9617			0.859944			0.429972	−	0.902842i	$-0.358523\pi$
$983$	26.9617			0.859944			0.429972	+	0.902842i	$0.358523\pi$
$984$	−14.2650	−	24.7077i	−0.454751	−	0.787651i
$985$	26.3589	−	45.6549i	0.839864	−	1.45469i
$986$	2.28057	−	3.95006i	0.0726281	−	0.125796i
$987$	37.1335			1.18197
$988$	7.56628	+	26.2104i	0.240716	+	0.833863i
$989$	64.2428			2.04280
$990$	−4.31678	+	7.47687i	−0.137196	+	0.237631i
$991$	20.9612	−	36.3059i	0.665856	−	1.15330i	−0.313196	−	0.949688i	$-0.601400\pi$
$991$	20.9612	−	36.3059i	0.665856	−	1.15330i	0.979052	−	0.203608i	$-0.0652668\pi$
$992$	−17.2269	−	29.8379i	−0.546954	−	0.947353i
$993$	−34.5561			−1.09660
$994$	−8.83081	−	15.2954i	−0.280096	−	0.485141i
$995$	28.3449	+	49.0947i	0.898592	+	1.55641i
$996$	−21.1815			−0.671163
$997$	19.7018	+	34.1246i	0.623963	+	1.08074i	0.988740	+	0.149641i	$0.0478119\pi$
$997$	19.7018	+	34.1246i	0.623963	+	1.08074i	−0.364777	+	0.931095i	$0.618855\pi$
$998$	−1.04967	+	1.81809i	−0.0332268	+	0.0575505i
$999$	13.9418	−	24.1478i	0.441097	−	0.764003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.b.100.3	✓	6
13.3	even	3	inner	143.2.e.b.133.3	yes	6
13.4	even	6		1859.2.a.g.1.3		3
13.9	even	3		1859.2.a.f.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.b.100.3	✓	6	1.1	even	1	trivial
143.2.e.b.133.3	yes	6	13.3	even	3	inner
1859.2.a.f.1.1		3	13.9	even	3
1859.2.a.g.1.3		3	13.4	even	6

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14257 - 1.97899i) q^{2} +(-0.610938 + 1.05818i) q^{3} +(-1.61094 - 2.79023i) q^{4} +2.50702 q^{5} +(1.39608 + 2.41808i) q^{6} +(-2.25351 - 3.90319i) q^{7} -2.79216 q^{8} +(0.753509 + 1.30512i) q^{9} +O(q^{10})\)	\(q+(1.14257 - 1.97899i) q^{2} +(-0.610938 + 1.05818i) q^{3} +(-1.61094 - 2.79023i) q^{4} +2.50702 q^{5} +(1.39608 + 2.41808i) q^{6} +(-2.25351 - 3.90319i) q^{7} -2.79216 q^{8} +(0.753509 + 1.30512i) q^{9} +(2.86445 - 4.96137i) q^{10} +(-0.500000 + 0.866025i) q^{11} +3.93673 q^{12} +(-2.50000 + 2.59808i) q^{13} -10.2992 q^{14} +(-1.53163 + 2.65287i) q^{15} +(0.0316332 - 0.0547902i) q^{16} +(1.61094 + 2.79023i) q^{17} +3.44375 q^{18} +(1.17420 + 2.03378i) q^{19} +(-4.03865 - 6.99515i) q^{20} +5.50702 q^{21} +(1.14257 + 1.97899i) q^{22} +(-2.89608 + 5.01616i) q^{23} +(1.70584 - 2.95460i) q^{24} +1.28514 q^{25} +(2.28514 + 7.91597i) q^{26} -5.50702 q^{27} +(-7.26053 + 12.5756i) q^{28} +(0.309757 - 0.536515i) q^{29} +(3.50000 + 6.06218i) q^{30} +6.01404 q^{31} +(-2.86445 - 4.96137i) q^{32} +(-0.610938 - 1.05818i) q^{33} +7.36245 q^{34} +(-5.64959 - 9.78538i) q^{35} +(2.42771 - 4.20492i) q^{36} +(-2.53163 + 4.38492i) q^{37} +5.36645 q^{38} +(-1.22188 - 4.23270i) q^{39} -7.00000 q^{40} +(4.18122 - 7.24209i) q^{41} +(6.29216 - 10.8983i) q^{42} +(-5.54567 - 9.60538i) q^{43} +3.22188 q^{44} +(1.88906 + 3.27195i) q^{45} +(6.61796 + 11.4626i) q^{46} +6.74293 q^{47} +(0.0386518 + 0.0669469i) q^{48} +(-6.65661 + 11.5296i) q^{49} +(1.46837 - 2.54329i) q^{50} -3.93673 q^{51} +(11.2766 + 2.79023i) q^{52} -4.06327 q^{53} +(-6.29216 + 10.8983i) q^{54} +(-1.25351 + 2.17114i) q^{55} +(6.29216 + 10.8983i) q^{56} -2.86946 q^{57} +(-0.707839 - 1.22601i) q^{58} +(-5.53163 - 9.58107i) q^{59} +9.86946 q^{60} +(0.0722863 + 0.125204i) q^{61} +(6.87147 - 11.9017i) q^{62} +(3.39608 - 5.88218i) q^{63} -12.9648 q^{64} +(-6.26755 + 6.51343i) q^{65} -2.79216 q^{66} +(-4.36445 + 7.55944i) q^{67} +(5.19024 - 8.98976i) q^{68} +(-3.53865 - 6.12912i) q^{69} -25.8202 q^{70} +(0.857429 + 1.48511i) q^{71} +(-2.10392 - 3.64410i) q^{72} -2.00000 q^{73} +(5.78514 + 10.0202i) q^{74} +(-0.785142 + 1.35991i) q^{75} +(3.78314 - 6.55259i) q^{76} +4.50702 q^{77} +(-9.77256 - 2.41808i) q^{78} +1.87347 q^{79} +(0.0793049 - 0.137360i) q^{80} +(1.10392 - 1.91204i) q^{81} +(-9.55469 - 16.5492i) q^{82} -5.38049 q^{83} +(-8.87147 - 15.3658i) q^{84} +(4.03865 + 6.99515i) q^{85} -25.3453 q^{86} +(0.378485 + 0.655555i) q^{87} +(1.39608 - 2.41808i) q^{88} +(4.25351 - 7.36729i) q^{89} +8.63355 q^{90} +(15.7746 + 3.90319i) q^{91} +18.6616 q^{92} +(-3.67420 + 6.36391i) q^{93} +(7.70428 - 13.3442i) q^{94} +(2.94375 + 5.09873i) q^{95} +7.00000 q^{96} +(-0.0562477 - 0.0974238i) q^{97} +(15.2113 + 26.3467i) q^{98} -1.50702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 3 q^{11} + 30 q^{12} - 15 q^{13} - 16 q^{14} - 6 q^{15} - 3 q^{16} + 7 q^{17} + 10 q^{18} - 2 q^{19} - 4 q^{20} + 16 q^{21} + q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 21 q^{30} + 2 q^{31} - 6 q^{32} - q^{33} - 8 q^{34} - 11 q^{35} - 3 q^{36} - 12 q^{37} + 62 q^{38} - 2 q^{39} - 42 q^{40} - q^{41} + 9 q^{42} + 4 q^{43} + 14 q^{44} + 14 q^{45} + 20 q^{46} - 16 q^{47} - 20 q^{48} + 12 q^{50} - 30 q^{51} + 49 q^{52} - 18 q^{53} - 9 q^{54} + q^{55} + 9 q^{56} + 52 q^{57} - 33 q^{58} - 30 q^{59} - 10 q^{60} + 18 q^{61} + 13 q^{62} + 6 q^{63} - 16 q^{64} + 5 q^{65} + 12 q^{66} - 15 q^{67} + 29 q^{68} - q^{69} - 58 q^{70} + 11 q^{71} - 27 q^{72} - 12 q^{73} + 23 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{77} + 42 q^{78} + 24 q^{79} + q^{80} + 21 q^{81} - 44 q^{82} - 28 q^{83} - 25 q^{84} + 4 q^{85} - 86 q^{86} - 43 q^{87} - 6 q^{88} + 17 q^{89} + 22 q^{90} + 35 q^{91} + 14 q^{92} - 13 q^{93} + 10 q^{94} + 7 q^{95} + 42 q^{96} - 11 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 3 * q^11 + 30 * q^12 - 15 * q^13 - 16 * q^14 - 6 * q^15 - 3 * q^16 + 7 * q^17 + 10 * q^18 - 2 * q^19 - 4 * q^20 + 16 * q^21 + q^22 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 21 * q^30 + 2 * q^31 - 6 * q^32 - q^33 - 8 * q^34 - 11 * q^35 - 3 * q^36 - 12 * q^37 + 62 * q^38 - 2 * q^39 - 42 * q^40 - q^41 + 9 * q^42 + 4 * q^43 + 14 * q^44 + 14 * q^45 + 20 * q^46 - 16 * q^47 - 20 * q^48 + 12 * q^50 - 30 * q^51 + 49 * q^52 - 18 * q^53 - 9 * q^54 + q^55 + 9 * q^56 + 52 * q^57 - 33 * q^58 - 30 * q^59 - 10 * q^60 + 18 * q^61 + 13 * q^62 + 6 * q^63 - 16 * q^64 + 5 * q^65 + 12 * q^66 - 15 * q^67 + 29 * q^68 - q^69 - 58 * q^70 + 11 * q^71 - 27 * q^72 - 12 * q^73 + 23 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^77 + 42 * q^78 + 24 * q^79 + q^80 + 21 * q^81 - 44 * q^82 - 28 * q^83 - 25 * q^84 + 4 * q^85 - 86 * q^86 - 43 * q^87 - 6 * q^88 + 17 * q^89 + 22 * q^90 + 35 * q^91 + 14 * q^92 - 13 * q^93 + 10 * q^94 + 7 * q^95 + 42 * q^96 - 11 * q^97 + 38 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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