LMFDB - Embedded newform 143.2.e.c.133.6

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 2x^{9} + 59x^{8} - 13x^{7} + 175x^{6} - 50x^{5} + 380x^{4} - 64x^{3} + 280x^{2} + 48x + 144 $ x^12 + 9x^10 - 2x^9 + 59x^8 - 13x^7 + 175x^6 - 50x^5 + 380x^4 - 64x^3 + 280x^2 + 48x + 144
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			133.6
Root			$-0.368446 - 0.638166i$ of defining polynomial
Character	$\chi$	$=$	143.133
Dual form			143.2.e.c.100.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22850 + 2.12782i) q^{2} +(0.332058 + 0.575141i) q^{3} +(-2.01840 + 3.49598i) q^{4} -1.73689 q^{5} +(-0.815863 + 1.41312i) q^{6} +(0.817900 - 1.41664i) q^{7} -5.00442 q^{8} +(1.27948 - 2.21612i) q^{9} +O(q^{10})$	\(q+(1.22850 + 2.12782i) q^{2} +(0.332058 + 0.575141i) q^{3} +(-2.01840 + 3.49598i) q^{4} -1.73689 q^{5} +(-0.815863 + 1.41312i) q^{6} +(0.817900 - 1.41664i) q^{7} -5.00442 q^{8} +(1.27948 - 2.21612i) q^{9} +(-2.13376 - 3.69579i) q^{10} +(0.500000 + 0.866025i) q^{11} -2.68091 q^{12} +(3.57116 + 0.496822i) q^{13} +4.01915 q^{14} +(-0.576748 - 0.998957i) q^{15} +(-2.11110 - 3.65653i) q^{16} +(-1.73733 + 3.00914i) q^{17} +6.28732 q^{18} +(-0.146891 + 0.254422i) q^{19} +(3.50575 - 6.07213i) q^{20} +1.08636 q^{21} +(-1.22850 + 2.12782i) q^{22} +(-3.73910 - 6.47631i) q^{23} +(-1.66176 - 2.87825i) q^{24} -1.98321 q^{25} +(3.33001 + 8.20911i) q^{26} +3.69179 q^{27} +(3.30171 + 5.71872i) q^{28} +(-3.30897 - 5.73130i) q^{29} +(1.41707 - 2.45443i) q^{30} +0.799011 q^{31} +(0.182534 - 0.316158i) q^{32} +(-0.332058 + 0.575141i) q^{33} -8.53719 q^{34} +(-1.42060 + 2.46056i) q^{35} +(5.16499 + 8.94603i) q^{36} +(0.810960 + 1.40462i) q^{37} -0.721818 q^{38} +(0.900088 + 2.21889i) q^{39} +8.69213 q^{40} +(-1.68855 - 2.92466i) q^{41} +(1.33459 + 2.31158i) q^{42} +(3.98379 - 6.90013i) q^{43} -4.03681 q^{44} +(-2.22231 + 3.84915i) q^{45} +(9.18694 - 15.9122i) q^{46} -5.35709 q^{47} +(1.40201 - 2.42836i) q^{48} +(2.16208 + 3.74483i) q^{49} +(-2.43636 - 4.21991i) q^{50} -2.30757 q^{51} +(-8.94492 + 11.4819i) q^{52} +9.28173 q^{53} +(4.53534 + 7.85544i) q^{54} +(-0.868446 - 1.50419i) q^{55} +(-4.09311 + 7.08948i) q^{56} -0.195105 q^{57} +(8.13011 - 14.0818i) q^{58} +(-4.75997 + 8.24452i) q^{59} +4.65644 q^{60} +(2.77904 - 4.81344i) q^{61} +(0.981582 + 1.70015i) q^{62} +(-2.09297 - 3.62512i) q^{63} -7.54743 q^{64} +(-6.20271 - 0.862926i) q^{65} -1.63173 q^{66} +(-1.00528 - 1.74119i) q^{67} +(-7.01325 - 12.1473i) q^{68} +(2.48319 - 4.30102i) q^{69} -6.98082 q^{70} +(-6.01431 + 10.4171i) q^{71} +(-6.40303 + 11.0904i) q^{72} +1.85800 q^{73} +(-1.99252 + 3.45115i) q^{74} +(-0.658540 - 1.14062i) q^{75} +(-0.592969 - 1.02705i) q^{76} +1.63580 q^{77} +(-3.61564 + 4.64112i) q^{78} -14.2951 q^{79} +(3.66675 + 6.35100i) q^{80} +(-2.61254 - 4.52505i) q^{81} +(4.14876 - 7.18587i) q^{82} -15.5910 q^{83} +(-2.19271 + 3.79789i) q^{84} +(3.01754 - 5.22654i) q^{85} +19.5763 q^{86} +(2.19754 - 3.80625i) q^{87} +(-2.50221 - 4.33395i) q^{88} +(8.17876 + 14.1660i) q^{89} -10.9204 q^{90} +(3.62467 - 4.65271i) q^{91} +30.1881 q^{92} +(0.265318 + 0.459544i) q^{93} +(-6.58117 - 11.3989i) q^{94} +(0.255133 - 0.441903i) q^{95} +0.242447 q^{96} +(-7.28238 + 12.6134i) q^{97} +(-5.31221 + 9.20101i) q^{98} +2.55895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.22850	+	2.12782i	0.868678	+	1.50459i	0.863349	+	0.504608i	$0.168363\pi$
$2$	1.22850	+	2.12782i	0.868678	+	1.50459i	0.00532913	+	0.999986i	$0.498304\pi$
$3$	0.332058	+	0.575141i	0.191714	+	0.332058i	0.945818	−	0.324697i	$-0.105262\pi$
$3$	0.332058	+	0.575141i	0.191714	+	0.332058i	−0.754105	+	0.656754i	$0.771929\pi$
$4$	−2.01840	+	3.49598i	−1.00920	+	1.74799i
$5$	−1.73689			−0.776761			−0.388381	−	0.921499i	$-0.626965\pi$
$5$	−1.73689			−0.776761			−0.388381	+	0.921499i	$0.626965\pi$
$6$	−0.815863	+	1.41312i	−0.333075	+	0.576902i
$7$	0.817900	−	1.41664i	0.309137	−	0.535441i	−0.669037	−	0.743229i	$-0.733293\pi$
$7$	0.817900	−	1.41664i	0.309137	−	0.535441i	0.978174	+	0.207788i	$0.0666264\pi$
$8$	−5.00442			−1.76933
$9$	1.27948	−	2.21612i	0.426492	−	0.738705i
$10$	−2.13376	−	3.69579i	−0.674755	−	1.16871i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−2.68091			−0.773911
$13$	3.57116	+	0.496822i	0.990461	+	0.137794i
$13$	3.57116	+	0.496822i	0.990461	+	0.137794i
$14$	4.01915			1.07416
$15$	−0.576748	−	0.998957i	−0.148916	−	0.257930i
$16$	−2.11110	−	3.65653i	−0.527775	−	0.914133i
$17$	−1.73733	+	3.00914i	−0.421363	+	0.729823i	−0.996073	−	0.0885347i	$-0.971782\pi$
$17$	−1.73733	+	3.00914i	−0.421363	+	0.729823i	0.574710	+	0.818357i	$0.305115\pi$
$18$	6.28732			1.48194
$19$	−0.146891	+	0.254422i	−0.0336990	+	0.0583684i	−0.882383	−	0.470532i	$-0.844062\pi$
$19$	−0.146891	+	0.254422i	−0.0336990	+	0.0583684i	0.848684	+	0.528900i	$0.177395\pi$
$20$	3.50575	−	6.07213i	0.783909	−	1.35777i
$21$	1.08636			0.237063
$22$	−1.22850	+	2.12782i	−0.261916	+	0.453652i
$23$	−3.73910	−	6.47631i	−0.779656	−	1.35040i	−0.932140	−	0.362098i	$-0.882060\pi$
$23$	−3.73910	−	6.47631i	−0.779656	−	1.35040i	0.152484	−	0.988306i	$-0.451273\pi$
$24$	−1.66176	−	2.87825i	−0.339204	−	0.587519i
$25$	−1.98321			−0.396642
$26$	3.33001	+	8.20911i	0.653068	+	1.60994i
$27$	3.69179			0.710484
$28$	3.30171	+	5.71872i	0.623964	+	1.08074i
$29$	−3.30897	−	5.73130i	−0.614460	−	1.06428i	−0.990479	−	0.137664i	$-0.956041\pi$
$29$	−3.30897	−	5.73130i	−0.614460	−	1.06428i	0.376019	−	0.926612i	$-0.377293\pi$
$30$	1.41707	−	2.45443i	0.258720	−	0.448115i
$31$	0.799011			0.143507			0.0717533	−	0.997422i	$-0.477141\pi$
$31$	0.799011			0.143507			0.0717533	+	0.997422i	$0.477141\pi$
$32$	0.182534	−	0.316158i	0.0322678	−	0.0558894i
$33$	−0.332058	+	0.575141i	−0.0578038	+	0.100119i
$34$	−8.53719			−1.46412
$35$	−1.42060	+	2.46056i	−0.240126	+	0.415910i
$36$	5.16499	+	8.94603i	0.860832	+	1.49101i
$37$	0.810960	+	1.40462i	0.133321	+	0.230919i	0.924955	−	0.380077i	$-0.124103\pi$
$37$	0.810960	+	1.40462i	0.133321	+	0.230919i	−0.791634	+	0.610996i	$0.790769\pi$
$38$	−0.721818			−0.117094
$39$	0.900088	+	2.21889i	0.144129	+	0.355307i
$40$	8.69213			1.37435
$41$	−1.68855	−	2.92466i	−0.263708	−	0.456756i	0.703516	−	0.710679i	$-0.251612\pi$
$41$	−1.68855	−	2.92466i	−0.263708	−	0.456756i	−0.967224	+	0.253924i	$0.918279\pi$
$42$	1.33459	+	2.31158i	0.205932	+	0.356684i
$43$	3.98379	−	6.90013i	0.607522	−	1.05226i	−0.384125	−	0.923281i	$-0.625497\pi$
$43$	3.98379	−	6.90013i	0.607522	−	1.05226i	0.991647	−	0.128978i	$-0.0411698\pi$
$44$	−4.03681			−0.608572
$45$	−2.22231	+	3.84915i	−0.331282	+	0.573798i
$46$	9.18694	−	15.9122i	1.35454	−	2.34613i
$47$	−5.35709			−0.781412			−0.390706	−	0.920515i	$-0.627769\pi$
$47$	−5.35709			−0.781412			−0.390706	+	0.920515i	$0.627769\pi$
$48$	1.40201	−	2.42836i	0.202363	−	0.350503i
$49$	2.16208	+	3.74483i	0.308868	+	0.534976i
$50$	−2.43636	−	4.21991i	−0.344554	−	0.596785i
$51$	−2.30757			−0.323124
$52$	−8.94492	+	11.4819i	−1.24044	+	1.59225i
$53$	9.28173			1.27494			0.637472	−	0.770474i	$-0.279980\pi$
$53$	9.28173			1.27494			0.637472	+	0.770474i	$0.279980\pi$
$54$	4.53534	+	7.85544i	0.617182	+	1.06899i
$55$	−0.868446	−	1.50419i	−0.117101	−	0.202825i
$56$	−4.09311	+	7.08948i	−0.546965	+	0.947372i
$57$	−0.195105			−0.0258422
$58$	8.13011	−	14.0818i	1.06754	−	1.84903i
$59$	−4.75997	+	8.24452i	−0.619696	+	1.07334i	0.369845	+	0.929093i	$0.379411\pi$
$59$	−4.75997	+	8.24452i	−0.619696	+	1.07334i	−0.989541	+	0.144251i	$0.953923\pi$
$60$	4.65644			0.601144
$61$	2.77904	−	4.81344i	0.355820	−	0.616298i	−0.631438	−	0.775426i	$-0.717535\pi$
$61$	2.77904	−	4.81344i	0.355820	−	0.616298i	0.987258	+	0.159128i	$0.0508684\pi$
$62$	0.981582	+	1.70015i	0.124661	+	0.215919i
$63$	−2.09297	−	3.62512i	−0.263689	−	0.456723i
$64$	−7.54743			−0.943428
$65$	−6.20271	−	0.862926i	−0.769352	−	0.107033i
$66$	−1.63173			−0.200852
$67$	−1.00528	−	1.74119i	−0.122814	−	0.212720i	0.798062	−	0.602575i	$-0.205859\pi$
$67$	−1.00528	−	1.74119i	−0.122814	−	0.212720i	−0.920876	+	0.389855i	$0.872525\pi$
$68$	−7.01325	−	12.1473i	−0.850481	−	1.47308i
$69$	2.48319	−	4.30102i	0.298941	−	0.517782i
$70$	−6.98082			−0.834368
$71$	−6.01431	+	10.4171i	−0.713768	+	1.23628i	0.249665	+	0.968332i	$0.419679\pi$
$71$	−6.01431	+	10.4171i	−0.713768	+	1.23628i	−0.963433	+	0.267950i	$0.913654\pi$
$72$	−6.40303	+	11.0904i	−0.754604	+	1.30701i
$73$	1.85800			0.217462			0.108731	−	0.994071i	$-0.465321\pi$
$73$	1.85800			0.217462			0.108731	+	0.994071i	$0.465321\pi$
$74$	−1.99252	+	3.45115i	−0.231626	+	0.401188i
$75$	−0.658540	−	1.14062i	−0.0760417	−	0.131708i
$76$	−0.592969	−	1.02705i	−0.0680182	−	0.117811i
$77$	1.63580			0.186417
$78$	−3.61564	+	4.64112i	−0.409391	+	0.525504i
$79$	−14.2951			−1.60833			−0.804164	−	0.594407i	$-0.797387\pi$
$79$	−14.2951			−1.60833			−0.804164	+	0.594407i	$0.797387\pi$
$80$	3.66675	+	6.35100i	0.409955	+	0.710063i
$81$	−2.61254	−	4.52505i	−0.290282	−	0.502784i
$82$	4.14876	−	7.18587i	0.458154	−	0.793547i
$83$	−15.5910			−1.71134			−0.855668	−	0.517526i	$-0.826853\pi$
$83$	−15.5910			−1.71134			−0.855668	+	0.517526i	$0.826853\pi$
$84$	−2.19271	+	3.79789i	−0.239245	+	0.414384i
$85$	3.01754	−	5.22654i	0.327299	−	0.566898i
$86$	19.5763			2.11096
$87$	2.19754	−	3.80625i	0.235601	−	0.408072i
$88$	−2.50221	−	4.33395i	−0.266736	−	0.462001i
$89$	8.17876	+	14.1660i	0.866947	+	1.50160i	0.865101	+	0.501599i	$0.167255\pi$
$89$	8.17876	+	14.1660i	0.866947	+	1.50160i	0.00184681	+	0.999998i	$0.499412\pi$
$90$	−10.9204			−1.15111
$91$	3.62467	−	4.65271i	0.379969	−	0.487737i
$92$	30.1881			3.14732
$93$	0.265318	+	0.459544i	0.0275122	+	0.0476525i
$94$	−6.58117	−	11.3989i	−0.678795	−	1.17571i
$95$	0.255133	−	0.441903i	0.0261761	−	0.0453383i
$96$	0.242447			0.0247447
$97$	−7.28238	+	12.6134i	−0.739413	+	1.28070i	0.213346	+	0.976977i	$0.431564\pi$
$97$	−7.28238	+	12.6134i	−0.739413	+	1.28070i	−0.952760	+	0.303725i	$0.901770\pi$
$98$	−5.31221	+	9.20101i	−0.536614	+	0.929443i
$99$	2.55895			0.257184
$100$	4.00292	−	6.93325i	0.400292	−	0.693325i
$101$	8.78324	+	15.2130i	0.873965	+	1.51375i	0.857862	+	0.513881i	$0.171793\pi$
$101$	8.78324	+	15.2130i	0.873965	+	1.51375i	0.0161030	+	0.999870i	$0.494874\pi$
$102$	−2.83484	−	4.91009i	−0.280691	−	0.486171i
$103$	9.04786			0.891512			0.445756	−	0.895155i	$-0.352935\pi$
$103$	9.04786			0.891512			0.445756	+	0.895155i	$0.352935\pi$
$104$	−17.8716	−	2.48631i	−1.75245	−	0.243802i
$105$	−1.88689			−0.184142
$106$	11.4026	+	19.7498i	1.10752	+	1.91827i
$107$	−4.77399	−	8.26879i	−0.461519	−	0.799374i	0.537518	−	0.843252i	$-0.319362\pi$
$107$	−4.77399	−	8.26879i	−0.461519	−	0.799374i	−0.999037	+	0.0438783i	$0.986029\pi$
$108$	−7.45151	+	12.9064i	−0.717022	+	1.24192i
$109$	12.8592			1.23169			0.615843	−	0.787869i	$-0.288816\pi$
$109$	12.8592			1.23169			0.615843	+	0.787869i	$0.288816\pi$
$110$	2.13376	−	3.69579i	0.203446	−	0.352379i
$111$	−0.538571	+	0.932832i	−0.0511189	+	0.0885405i
$112$	−6.90667			−0.652619
$113$	0.234273	−	0.405772i	0.0220385	−	0.0381719i	−0.854796	−	0.518964i	$-0.826318\pi$
$113$	0.234273	−	0.405772i	0.0220385	−	0.0381719i	0.876834	+	0.480793i	$0.159651\pi$
$114$	−0.239685	−	0.415147i	−0.0224486	−	0.0388821i
$115$	6.49441	+	11.2486i	0.605607	+	1.04894i
$116$	26.7153			2.48046
$117$	5.67022	−	7.27843i	0.524212	−	0.672891i
$118$	−23.3904			−2.15326
$119$	2.84192	+	4.92235i	0.260518	+	0.451231i
$120$	2.88629	+	4.99920i	0.263481	+	0.456362i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	13.6562			1.23637
$123$	1.12140	−	1.94231i	0.101113	−	0.175133i
$124$	−1.61273	+	2.79332i	−0.144827	+	0.250848i
$125$	12.1291			1.08486
$126$	5.14240	−	8.90690i	0.458121	−	0.793490i
$127$	−4.98873	−	8.64074i	−0.442678	−	0.766742i	0.555209	−	0.831711i	$-0.312638\pi$
$127$	−4.98873	−	8.64074i	−0.442678	−	0.766742i	−0.997887	+	0.0649694i	$0.979305\pi$
$128$	−9.63705	−	16.6919i	−0.851803	−	1.47537i
$129$	5.29139			0.465881
$130$	−5.78386	−	14.2583i	−0.507278	−	1.25054i
$131$	−5.28118			−0.461419			−0.230710	−	0.973023i	$-0.574105\pi$
$131$	−5.28118			−0.461419			−0.230710	+	0.973023i	$0.574105\pi$
$132$	−1.34045	−	2.32173i	−0.116671	−	0.202081i
$133$	0.240284	+	0.416183i	0.0208352	+	0.0360877i
$134$	2.46996	−	4.27809i	0.213372	−	0.369571i
$135$	−6.41223			−0.551877
$136$	8.69430	−	15.0590i	0.745530	−	1.29130i
$137$	−1.34851	+	2.33569i	−0.115211	+	0.199551i	−0.917864	−	0.396895i	$-0.870088\pi$
$137$	−1.34851	+	2.33569i	−0.115211	+	0.199551i	0.802653	+	0.596446i	$0.203421\pi$
$138$	12.2024			1.03874
$139$	0.609649	−	1.05594i	0.0517098	−	0.0895639i	−0.839012	−	0.544113i	$-0.816866\pi$
$139$	0.609649	−	1.05594i	0.0517098	−	0.0895639i	0.890722	+	0.454549i	$0.150200\pi$
$140$	−5.73470	−	9.93280i	−0.484671	−	0.839475i
$141$	−1.77886	−	3.08108i	−0.149807	−	0.259474i
$142$	−29.5542			−2.48014
$143$	1.35532	+	3.34112i	0.113337	+	0.279399i
$144$	−10.8044			−0.900366
$145$	5.74732	+	9.95465i	0.477289	+	0.826689i
$146$	2.28254	+	3.95348i	0.188905	+	0.327192i
$147$	−1.43587	+	2.48700i	−0.118429	+	0.205124i
$148$	−6.54737			−0.538191
$149$	11.0516	−	19.1419i	0.905379	−	1.56816i	0.0849707	−	0.996383i	$-0.472920\pi$
$149$	11.0516	−	19.1419i	0.905379	−	1.56816i	0.820408	−	0.571778i	$-0.193746\pi$
$150$	1.61803	−	2.80251i	0.132111	−	0.228824i
$151$	−0.270215			−0.0219898			−0.0109949	−	0.999940i	$-0.503500\pi$
$151$	−0.270215			−0.0219898			−0.0109949	+	0.999940i	$0.503500\pi$
$152$	0.735102	−	1.27323i	0.0596246	−	0.103273i
$153$	4.44573	+	7.70023i	0.359416	+	0.622527i
$154$	2.00957	+	3.48068i	0.161936	+	0.280482i
$155$	−1.38779			−0.111470
$156$	−9.57394	−	1.33193i	−0.766529	−	0.106640i
$157$	−12.2284			−0.975929			−0.487964	−	0.872864i	$-0.662260\pi$
$157$	−12.2284			−0.975929			−0.487964	+	0.872864i	$0.662260\pi$
$158$	−17.5615	−	30.4174i	−1.39712	−	2.41988i
$159$	3.08207	+	5.33830i	0.244424	+	0.423355i
$160$	−0.317042	+	0.549132i	−0.0250643	+	0.0434127i
$161$	−12.2328			−0.964083
$162$	6.41899	−	11.1180i	0.504323	−	0.873514i
$163$	0.997987	−	1.72856i	0.0781684	−	0.135392i	−0.824291	−	0.566166i	$-0.808426\pi$
$163$	0.997987	−	1.72856i	0.0781684	−	0.135392i	0.902460	+	0.430774i	$0.141759\pi$
$164$	13.6327			1.06454
$165$	0.576748	−	0.998957i	0.0448998	−	0.0777687i
$166$	−19.1535	−	33.1748i	−1.48660	−	2.57486i
$167$	7.86410	+	13.6210i	0.608542	+	1.05403i	0.991481	+	0.130252i	$0.0415786\pi$
$167$	7.86410	+	13.6210i	0.608542	+	1.05403i	−0.382939	+	0.923774i	$0.625088\pi$
$168$	−5.43660			−0.419443
$169$	12.5063	+	3.54846i	0.962026	+	0.272958i
$170$	14.8282			1.13727
$171$	0.375886	+	0.651053i	0.0287447	+	0.0497873i
$172$	16.0818	+	27.8545i	1.22623	+	2.12388i
$173$	5.34534	−	9.25840i	0.406399	−	0.703903i	−0.588084	−	0.808800i	$-0.700118\pi$
$173$	5.34534	−	9.25840i	0.406399	−	0.703903i	0.994483	+	0.104896i	$0.0334510\pi$
$174$	10.7987			0.818644
$175$	−1.62207	+	2.80950i	−0.122617	+	0.212378i
$176$	2.11110	−	3.65653i	0.159130	−	0.275621i
$177$	−6.32235			−0.475217
$178$	−20.0952	+	34.8058i	−1.50620	+	2.60881i
$179$	12.4530	+	21.5693i	0.930784	+	1.61217i	0.781984	+	0.623298i	$0.214208\pi$
$179$	12.4530	+	21.5693i	0.930784	+	1.61217i	0.148800	+	0.988867i	$0.452459\pi$
$180$	−8.97103	−	15.5383i	−0.668661	−	1.15816i
$181$	5.01445			0.372721			0.186361	−	0.982481i	$-0.440331\pi$
$181$	5.01445			0.372721			0.186361	+	0.982481i	$0.440331\pi$
$182$	14.3530	+	1.99680i	1.06392	+	0.148013i
$183$	3.69121			0.272862
$184$	18.7120	+	32.4102i	1.37947	+	2.38931i
$185$	−1.40855	−	2.43968i	−0.103559	−	0.179369i
$186$	−0.651884	+	1.12910i	−0.0477984	+	0.0827893i
$187$	−3.47465			−0.254092
$188$	10.8128	−	18.7283i	0.788603	−	1.36590i
$189$	3.01951	−	5.22995i	0.219637	−	0.380423i
$190$	1.25372			0.0909543
$191$	10.9339	−	18.9381i	0.791152	−	1.37032i	−0.134102	−	0.990968i	$-0.542815\pi$
$191$	10.9339	−	18.9381i	0.791152	−	1.37032i	0.925254	−	0.379348i	$-0.123852\pi$
$192$	−2.50618	−	4.34083i	−0.180868	−	0.313273i
$193$	9.39113	+	16.2659i	0.675988	+	1.17085i	0.976179	+	0.216967i	$0.0696163\pi$
$193$	9.39113	+	16.2659i	0.675988	+	1.17085i	−0.300191	+	0.953879i	$0.597050\pi$
$194$	−35.7855			−2.56925
$195$	−1.56335	−	3.85397i	−0.111954	−	0.275989i
$196$	−17.4558			−1.24684
$197$	−6.89782	−	11.9474i	−0.491450	−	0.851216i	0.508502	−	0.861061i	$-0.330199\pi$
$197$	−6.89782	−	11.9474i	−0.491450	−	0.851216i	−0.999952	+	0.00984508i	$0.996866\pi$
$198$	3.14366	+	5.44498i	0.223410	+	0.386958i
$199$	6.12338	−	10.6060i	0.434075	−	0.751839i	−0.563145	−	0.826358i	$-0.690409\pi$
$199$	6.12338	−	10.6060i	0.434075	−	0.751839i	0.997220	+	0.0745187i	$0.0237421\pi$
$200$	9.92481			0.701790
$201$	0.667620	−	1.15635i	0.0470903	−	0.0815627i
$202$	−21.5803	+	37.3782i	−1.51839	+	2.62992i
$203$	−10.8256			−0.759810
$204$	4.65761	−	8.06721i	0.326098	−	0.564818i
$205$	2.93284	+	5.07982i	0.204838	+	0.354790i
$206$	11.1153	+	19.2522i	0.774436	+	1.34136i
$207$	−19.1363			−1.33007
$208$	−5.72242	−	14.1069i	−0.396779	−	0.978137i
$209$	−0.293781			−0.0203213
$210$	−2.31804	−	4.01496i	−0.159960	−	0.277058i
$211$	6.90199	+	11.9546i	0.475152	+	0.822988i	0.999595	−	0.0284577i	$-0.00905958\pi$
$211$	6.90199	+	11.9546i	0.475152	+	0.822988i	−0.524443	+	0.851446i	$0.675726\pi$
$212$	−18.7343	+	32.4487i	−1.28668	+	2.22859i
$213$	−7.98840			−0.547356
$214$	11.7296	−	20.3163i	0.801822	−	1.38880i
$215$	−6.91941	+	11.9848i	−0.471900	+	0.817355i
$216$	−18.4752			−1.25708
$217$	0.653511	−	1.13191i	0.0443632	−	0.0768394i
$218$	15.7974	+	27.3620i	1.06994	+	1.85319i
$219$	0.616963	+	1.06861i	0.0416905	+	0.0722100i
$220$	7.01149			0.472715
$221$	−7.69927	+	9.88296i	−0.517909	+	0.664800i
$222$	−2.64653			−0.177623
$223$	−8.20287	−	14.2078i	−0.549305	−	0.951424i	−0.998322	−	0.0579008i	$-0.981559\pi$
$223$	−8.20287	−	14.2078i	−0.549305	−	0.951424i	0.449018	−	0.893523i	$-0.351774\pi$
$224$	−0.298589	−	0.517172i	−0.0199503	−	0.0345550i
$225$	−2.53747	+	4.39502i	−0.169164	+	0.293001i
$226$	1.15121			0.0765775
$227$	−5.00628	+	8.67114i	−0.332279	+	0.575524i	−0.982958	−	0.183829i	$-0.941151\pi$
$227$	−5.00628	+	8.67114i	−0.332279	+	0.575524i	0.650680	+	0.759352i	$0.274484\pi$
$228$	0.393800	−	0.682081i	0.0260800	−	0.0451719i
$229$	−8.46067			−0.559097			−0.279548	−	0.960132i	$-0.590185\pi$
$229$	−8.46067			−0.559097			−0.279548	+	0.960132i	$0.590185\pi$
$230$	−15.9567	+	27.6378i	−1.05215	+	1.82238i
$231$	0.543180	+	0.940816i	0.0357386	+	0.0619011i
$232$	16.5595	+	28.6818i	1.08718	+	1.88305i
$233$	−11.5661			−0.757722			−0.378861	−	0.925454i	$-0.623684\pi$
$233$	−11.5661			−0.757722			−0.378861	+	0.925454i	$0.623684\pi$
$234$	22.4530	+	3.12368i	1.46780	+	0.204201i
$235$	9.30469			0.606971
$236$	−19.2151	−	33.2815i	−1.25080	−	2.16644i
$237$	−4.74681	−	8.22172i	−0.308339	−	0.534058i
$238$	−6.98257	+	12.0942i	−0.452613	+	0.783948i
$239$	5.10653			0.330314			0.165157	−	0.986267i	$-0.447187\pi$
$239$	5.10653			0.330314			0.165157	+	0.986267i	$0.447187\pi$
$240$	−2.43514	+	4.21779i	−0.157188	+	0.272257i
$241$	13.4159	−	23.2369i	0.864191	−	1.49682i	−0.00365724	−	0.999993i	$-0.501164\pi$
$241$	13.4159	−	23.2369i	0.864191	−	1.49682i	0.867848	−	0.496829i	$-0.165503\pi$
$242$	−2.45699			−0.157941
$243$	7.27271	−	12.5967i	0.466544	−	0.808078i
$244$	11.2185	+	19.4309i	0.718188	+	1.24394i
$245$	−3.75529	−	6.50436i	−0.239917	−	0.415548i
$246$	5.51052			0.351338
$247$	−0.650972	+	0.835602i	−0.0414203	+	0.0531681i
$248$	−3.99858			−0.253910
$249$	−5.17712	−	8.96703i	−0.328086	−	0.568262i
$250$	14.9005	+	25.8085i	0.942391	+	1.63227i
$251$	0.345482	−	0.598392i	0.0218066	−	0.0377702i	−0.854916	−	0.518766i	$-0.826392\pi$
$251$	0.345482	−	0.598392i	0.0218066	−	0.0377702i	0.876723	+	0.480996i	$0.159725\pi$
$252$	16.8978			1.06446
$253$	3.73910	−	6.47631i	0.235075	−	0.407162i
$254$	12.2573	−	21.2302i	0.769090	−	1.33210i
$255$	4.00800			0.250991
$256$	16.1307	−	27.9392i	1.00817	−	1.74620i
$257$	−3.44745	−	5.97116i	−0.215046	−	0.372471i	0.738241	−	0.674537i	$-0.235657\pi$
$257$	−3.44745	−	5.97116i	−0.215046	−	0.372471i	−0.953287	+	0.302067i	$0.902323\pi$
$258$	6.50046	+	11.2591i	0.404701	+	0.700962i
$259$	2.65314			0.164858
$260$	15.5363	−	19.9428i	0.963523	−	1.23680i
$261$	−16.9350			−1.04825
$262$	−6.48791	−	11.2374i	−0.400825	−	0.694249i
$263$	−1.22321	−	2.11867i	−0.0754266	−	0.130643i	0.825845	−	0.563897i	$-0.190699\pi$
$263$	−1.22321	−	2.11867i	−0.0754266	−	0.130643i	−0.901272	+	0.433254i	$0.857365\pi$
$264$	1.66176	−	2.87825i	0.102274	−	0.177144i
$265$	−16.1214			−0.990327
$266$	−0.590375	+	1.02256i	−0.0361982	+	0.0626971i
$267$	−5.43164	+	9.40788i	−0.332411	+	0.575753i
$268$	8.11621			0.495777
$269$	−10.8109	+	18.7251i	−0.659154	+	1.14169i	0.321681	+	0.946848i	$0.395752\pi$
$269$	−10.8109	+	18.7251i	−0.659154	+	1.14169i	−0.980835	+	0.194840i	$0.937581\pi$
$270$	−7.87740	−	13.6441i	−0.479403	−	0.830350i
$271$	−0.935607	−	1.62052i	−0.0568341	−	0.0984395i	0.836209	−	0.548412i	$-0.184767\pi$
$271$	−0.935607	−	1.62052i	−0.0568341	−	0.0984395i	−0.893043	+	0.449972i	$0.851434\pi$
$272$	14.6707			0.889540
$273$	3.87956	+	0.539728i	0.234802	+	0.0326658i
$274$	−6.62656			−0.400325
$275$	−0.991605	−	1.71751i	−0.0597960	−	0.103570i
$276$	10.0242	+	17.3624i	0.603385	+	1.04509i
$277$	3.14410	−	5.44573i	0.188910	−	0.327203i	−0.755977	−	0.654598i	$-0.772838\pi$
$277$	3.14410	−	5.44573i	0.188910	−	0.327203i	0.944887	+	0.327396i	$0.106171\pi$
$278$	2.99581			0.179676
$279$	1.02231	−	1.77070i	0.0612044	−	0.106009i
$280$	7.10929	−	12.3137i	0.424862	−	0.735882i
$281$	−7.68890			−0.458681			−0.229341	−	0.973346i	$-0.573657\pi$
$281$	−7.68890			−0.458681			−0.229341	+	0.973346i	$0.573657\pi$
$282$	4.37065	−	7.57020i	0.260269	−	0.450799i
$283$	−13.8569	−	24.0009i	−0.823707	−	1.42670i	−0.902903	−	0.429844i	$-0.858569\pi$
$283$	−13.8569	−	24.0009i	−0.823707	−	1.42670i	0.0791961	−	0.996859i	$-0.474765\pi$
$284$	−24.2786	−	42.0518i	−1.44067	−	2.49532i
$285$	0.338875			0.0200732
$286$	−5.44430	+	6.98843i	−0.321928	+	0.413234i
$287$	−5.52428			−0.326088
$288$	−0.467095	−	0.809033i	−0.0275239	−	0.0476727i
$289$	2.46340	+	4.26674i	0.144906	+	0.250984i
$290$	−14.1211	+	24.4585i	−0.829220	+	1.43625i
$291$	−9.67268			−0.567022
$292$	−3.75019	+	6.49552i	−0.219463	+	0.380122i
$293$	8.11955	−	14.0635i	0.474349	−	0.821597i	−0.525219	−	0.850967i	$-0.676017\pi$
$293$	8.11955	−	14.0635i	0.474349	−	0.821597i	0.999569	+	0.0293698i	$0.00935003\pi$
$294$	−7.05584			−0.411505
$295$	8.26756	−	14.3198i	0.481356	−	0.833733i
$296$	−4.05838	−	7.02932i	−0.235889	−	0.408571i
$297$	1.84589	+	3.19718i	0.107110	+	0.185519i
$298$	54.3072			3.14593
$299$	−10.1353	−	24.9856i	−0.586142	−	1.44495i
$300$	5.31680			0.306965
$301$	−6.51669	−	11.2872i	−0.375616	−	0.650585i
$302$	−0.331958	−	0.574969i	−0.0191021	−	0.0330857i
$303$	−5.83308	+	10.1032i	−0.335102	+	0.580413i
$304$	1.24040			0.0711419
$305$	−4.82689	+	8.36042i	−0.276387	+	0.478716i
$306$	−10.9231	+	18.9194i	−0.624433	+	1.08155i
$307$	−5.80030			−0.331041			−0.165520	−	0.986206i	$-0.552930\pi$
$307$	−5.80030			−0.331041			−0.165520	+	0.986206i	$0.552930\pi$
$308$	−3.30171	+	5.71872i	−0.188132	+	0.325854i
$309$	3.00441	+	5.20379i	0.170915	+	0.296033i
$310$	−1.70490	−	2.95297i	−0.0968318	−	0.167718i
$311$	−8.39017			−0.475763			−0.237881	−	0.971294i	$-0.576453\pi$
$311$	−8.39017			−0.475763			−0.237881	+	0.971294i	$0.576453\pi$
$312$	−4.50442	−	11.1043i	−0.255012	−	0.628655i
$313$	2.73695			0.154702			0.0773508	−	0.997004i	$-0.475354\pi$
$313$	2.73695			0.154702			0.0773508	+	0.997004i	$0.475354\pi$
$314$	−15.0225	−	26.0197i	−0.847768	−	1.46838i
$315$	3.63525	+	6.29645i	0.204823	+	0.354765i
$316$	28.8534	−	49.9755i	1.62313	−	2.81134i
$317$	9.07707			0.509819			0.254910	−	0.966965i	$-0.417954\pi$
$317$	9.07707			0.509819			0.254910	+	0.966965i	$0.417954\pi$
$318$	−7.57262	+	13.1162i	−0.424652	+	0.735518i
$319$	3.30897	−	5.73130i	0.185267	−	0.320891i
$320$	13.1091			0.732819
$321$	3.17048	−	5.49143i	0.176959	−	0.306502i
$322$	−15.0280	−	26.0293i	−0.837477	−	1.45055i
$323$	−0.510393	−	0.884027i	−0.0283990	−	0.0491886i
$324$	21.0926			1.17181
$325$	−7.08235	−	0.985302i	−0.392858	−	0.0546547i
$326$	4.90409			0.271613
$327$	4.26999	+	7.39584i	0.236131	+	0.408991i
$328$	8.45023	+	14.6362i	0.466586	+	0.808151i
$329$	−4.38157	+	7.58910i	−0.241564	+	0.418401i
$330$	2.83413			0.156014
$331$	−9.02953	+	15.6396i	−0.496308	+	0.859630i	−0.999991	−	0.00425828i	$-0.998645\pi$
$331$	−9.02953	+	15.6396i	−0.496308	+	0.859630i	0.503683	+	0.863888i	$0.331978\pi$
$332$	31.4689	−	54.5058i	1.72708	−	2.99140i
$333$	4.15041			0.227441
$334$	−19.3220	+	33.4667i	−1.05725	+	1.83122i
$335$	1.74606	+	3.02426i	0.0953972	+	0.165233i
$336$	−2.29341	−	3.97231i	−0.125116	−	0.216707i
$337$	−14.4529			−0.787298			−0.393649	−	0.919261i	$-0.628788\pi$
$337$	−14.4529			−0.787298			−0.393649	+	0.919261i	$0.628788\pi$
$338$	7.81351	+	30.9705i	0.424999	+	1.68457i
$339$	0.311168			0.0169003
$340$	12.1812	+	21.0985i	0.660621	+	1.14423i
$341$	0.399505	+	0.691964i	0.0216344	+	0.0374719i
$342$	−0.923548	+	1.59963i	−0.0499397	+	0.0864982i
$343$	18.5241			1.00021
$344$	−19.9366	+	34.5311i	−1.07491	+	1.86179i
$345$	−4.31304	+	7.47040i	−0.232206	+	0.402193i
$346$	26.2669			1.41212
$347$	1.75882	−	3.04636i	0.0944182	−	0.163537i	−0.814947	−	0.579535i	$-0.803234\pi$
$347$	1.75882	−	3.04636i	0.0944182	−	0.163537i	0.909366	+	0.415998i	$0.136568\pi$
$348$	8.87104	+	15.3651i	0.475537	+	0.823655i
$349$	12.1521	+	21.0480i	0.650484	+	1.12667i	0.983005	+	0.183576i	$0.0587674\pi$
$349$	12.1521	+	21.0480i	0.650484	+	1.12667i	−0.332521	+	0.943096i	$0.607899\pi$
$350$	−7.97081			−0.426058
$351$	13.1839	+	1.83416i	0.703707	+	0.0979002i
$352$	0.365068			0.0194582
$353$	5.07014	+	8.78173i	0.269856	+	0.467404i	0.968824	−	0.247748i	$-0.0796905\pi$
$353$	5.07014	+	8.78173i	0.269856	+	0.467404i	−0.698968	+	0.715153i	$0.746357\pi$
$354$	−7.76698	−	13.4528i	−0.412810	−	0.715008i
$355$	10.4462	−	18.0934i	0.554427	−	0.960296i
$356$	−66.0322			−3.49970
$357$	−1.88736	+	3.26901i	−0.0998898	+	0.173014i
$358$	−30.5970	+	52.9956i	−1.61710	+	2.80090i
$359$	4.78700			0.252648			0.126324	−	0.991989i	$-0.459682\pi$
$359$	4.78700			0.252648			0.126324	+	0.991989i	$0.459682\pi$
$360$	11.1214	−	19.2628i	0.586147	−	1.01524i
$361$	9.45685	+	16.3797i	0.497729	+	0.862091i
$362$	6.16023	+	10.6698i	0.323775	+	0.560794i
$363$	−0.664116			−0.0348570
$364$	8.94972	+	22.0628i	0.469093	+	1.15641i
$365$	−3.22714			−0.168916
$366$	4.53463	+	7.85422i	0.237029	+	0.410546i
$367$	−4.87417	−	8.44230i	−0.254429	−	0.440685i	0.710311	−	0.703888i	$-0.248554\pi$
$367$	−4.87417	−	8.44230i	−0.254429	−	0.440685i	−0.964740	+	0.263203i	$0.915221\pi$
$368$	−15.7872	+	27.3443i	−0.822966	+	1.42542i
$369$	−8.64186			−0.449877
$370$	3.46079	−	5.99427i	0.179918	−	0.311627i
$371$	7.59153	−	13.1489i	0.394133	−	0.682658i
$372$	−2.14207			−0.111061
$373$	−0.291858	+	0.505513i	−0.0151118	+	0.0261745i	−0.873482	−	0.486856i	$-0.838144\pi$
$373$	−0.291858	+	0.505513i	−0.0151118	+	0.0261745i	0.858371	+	0.513030i	$0.171477\pi$
$374$	−4.26859	−	7.39342i	−0.220724	−	0.382305i
$375$	4.02755	+	6.97593i	0.207982	+	0.360235i
$376$	26.8091			1.38258
$377$	−8.96941	−	22.1114i	−0.461948	−	1.13879i
$378$	14.8378			0.763176
$379$	15.7241	+	27.2349i	0.807691	+	1.39896i	0.914459	+	0.404677i	$0.132616\pi$
$379$	15.7241	+	27.2349i	0.807691	+	1.39896i	−0.106769	+	0.994284i	$0.534050\pi$
$380$	1.02992	+	1.78388i	0.0528339	+	0.0915110i
$381$	3.31310	−	5.73845i	0.169735	−	0.293990i
$382$	53.7292			2.74902
$383$	−2.60574	+	4.51327i	−0.133147	+	0.230617i	−0.924888	−	0.380240i	$-0.875842\pi$
$383$	−2.60574	+	4.51327i	−0.133147	+	0.230617i	0.791741	+	0.610857i	$0.209175\pi$
$384$	6.40011	−	11.0853i	0.326604	−	0.565695i
$385$	−2.84121			−0.144801
$386$	−23.0739	+	39.9652i	−1.17443	+	2.03418i
$387$	−10.1943	−	17.6571i	−0.518207	−	0.897560i
$388$	−29.3976	−	50.9181i	−1.49243	−	2.58497i
$389$	−2.19164			−0.111121			−0.0555603	−	0.998455i	$-0.517695\pi$
$389$	−2.19164			−0.111121			−0.0555603	+	0.998455i	$0.517695\pi$
$390$	6.27998	−	8.06112i	0.317999	−	0.408191i
$391$	25.9841			1.31407
$392$	−10.8199	−	18.7407i	−0.546490	−	0.946548i
$393$	−1.75366	−	3.03743i	−0.0884604	−	0.153218i
$394$	16.9479	−	29.3546i	0.853823	−	1.47886i
$395$	24.8291			1.24929
$396$	−5.16499	+	8.94603i	−0.259551	+	0.449555i
$397$	−2.08684	+	3.61452i	−0.104736	+	0.181408i	−0.913630	−	0.406546i	$-0.866733\pi$
$397$	−2.08684	+	3.61452i	−0.104736	+	0.181408i	0.808894	+	0.587954i	$0.200066\pi$
$398$	30.0902			1.50828
$399$	−0.159576	+	0.276394i	−0.00798880	+	0.0138370i
$400$	4.18675	+	7.25166i	0.209338	+	0.362583i
$401$	−11.2165	−	19.4276i	−0.560125	−	0.970166i	−0.997485	−	0.0708790i	$-0.977420\pi$
$401$	−11.2165	−	19.4276i	−0.560125	−	0.970166i	0.437359	−	0.899287i	$-0.355914\pi$
$402$	3.28067			0.163625
$403$	2.85339	+	0.396966i	0.142138	+	0.0197743i
$404$	−70.9125			−3.52803
$405$	4.53770	+	7.85952i	0.225480	+	0.390543i
$406$	−13.2992	−	23.0350i	−0.660030	−	1.14321i
$407$	−0.810960	+	1.40462i	−0.0401978	+	0.0696246i
$408$	11.5480			0.571713
$409$	−6.49060	+	11.2420i	−0.320939	+	0.555883i	−0.980682	−	0.195608i	$-0.937332\pi$
$409$	−6.49060	+	11.2420i	−0.320939	+	0.555883i	0.659743	+	0.751491i	$0.270665\pi$
$410$	−7.20595	+	12.4811i	−0.355877	+	0.616396i
$411$	−1.79113			−0.0883501
$412$	−18.2622	+	31.6311i	−0.899715	+	1.55835i
$413$	7.78637	+	13.4864i	0.383142	+	0.663622i
$414$	−23.5089	−	40.7186i	−1.15540	−	2.00121i
$415$	27.0799			1.32930
$416$	0.808932	−	1.03836i	0.0396612	−	0.0509100i
$417$	0.809755			0.0396539
$418$	−0.360909	−	0.625112i	−0.0176526	−	0.0305752i
$419$	−5.82053	−	10.0815i	−0.284351	−	0.492511i	0.688100	−	0.725616i	$-0.258445\pi$
$419$	−5.82053	−	10.0815i	−0.284351	−	0.492511i	−0.972452	+	0.233105i	$0.925112\pi$
$420$	3.80851	−	6.59652i	0.185836	−	0.321877i
$421$	−14.7033			−0.716594			−0.358297	−	0.933608i	$-0.616642\pi$
$421$	−14.7033			−0.716594			−0.358297	+	0.933608i	$0.616642\pi$
$422$	−16.9581	+	29.3723i	−0.825509	+	1.42982i
$423$	−6.85427	+	11.8719i	−0.333266	+	0.577234i
$424$	−46.4497			−2.25580
$425$	3.44548	−	5.96775i	0.167130	−	0.289478i
$426$	−9.81371	−	16.9979i	−0.475476	−	0.823549i
$427$	−4.54596	−	7.87383i	−0.219994	−	0.381041i
$428$	38.5433			1.86306
$429$	−1.47157	+	1.88895i	−0.0710482	+	0.0911991i
$430$	−34.0019			−1.63972
$431$	−15.5760	−	26.9784i	−0.750268	−	1.29950i	−0.947693	−	0.319185i	$-0.896591\pi$
$431$	−15.5760	−	26.9784i	−0.750268	−	1.29950i	0.197424	−	0.980318i	$-0.436742\pi$
$432$	−7.79372	−	13.4991i	−0.374976	−	0.649477i
$433$	−17.0243	+	29.4869i	−0.818135	+	1.41705i	0.0889205	+	0.996039i	$0.471658\pi$
$433$	−17.0243	+	29.4869i	−0.818135	+	1.41705i	−0.907055	+	0.421012i	$0.861675\pi$
$434$	3.21134			0.154149
$435$	−3.81688	+	6.61104i	−0.183006	+	0.316975i
$436$	−25.9550	+	44.9554i	−1.24302	+	2.15297i
$437$	2.19695			0.105095
$438$	−1.51587	+	2.62557i	−0.0724312	+	0.125454i
$439$	13.0458	+	22.5960i	0.622642	+	1.07845i	0.988992	+	0.147971i	$0.0472741\pi$
$439$	13.0458	+	22.5960i	0.622642	+	1.07845i	−0.366349	+	0.930477i	$0.619393\pi$
$440$	4.34606	+	7.52760i	0.207190	+	0.358864i
$441$	11.0653			0.526919
$442$	−30.4876	−	4.24146i	−1.45015	−	0.201746i
$443$	26.8402			1.27522			0.637608	−	0.770361i	$-0.279924\pi$
$443$	26.8402			1.27522			0.637608	+	0.770361i	$0.279924\pi$
$444$	−2.17411	−	3.76566i	−0.103179	−	0.178710i
$445$	−14.2056	−	24.6049i	−0.673411	−	1.16638i
$446$	20.1544	−	34.9084i	0.954338	−	1.65296i
$447$	14.6790			0.694294
$448$	−6.17304	+	10.6920i	−0.291649	+	0.505151i
$449$	9.35994	−	16.2119i	0.441723	−	0.765087i	−0.556094	−	0.831119i	$-0.687701\pi$
$449$	9.35994	−	16.2119i	0.441723	−	0.765087i	0.997817	+	0.0660324i	$0.0210341\pi$
$450$	−12.4691			−0.587798
$451$	1.68855	−	2.92466i	0.0795109	−	0.137717i
$452$	0.945714	+	1.63802i	0.0444826	+	0.0770462i
$453$	−0.0897271	−	0.155412i	−0.00421575	−	0.00730189i
$454$	−24.6008			−1.15457
$455$	−6.29566	+	8.08125i	−0.295145	+	0.378855i
$456$	0.976385			0.0457234
$457$	3.69400	+	6.39819i	0.172798	+	0.299295i	0.939397	−	0.342831i	$-0.111386\pi$
$457$	3.69400	+	6.39819i	0.172798	+	0.299295i	−0.766599	+	0.642126i	$0.778053\pi$
$458$	−10.3939	−	18.0028i	−0.485675	−	0.841214i
$459$	−6.41383	+	11.1091i	−0.299372	+	0.518528i
$460$	−52.4334			−2.44472
$461$	10.4437	−	18.0890i	0.486411	−	0.842488i	−0.513467	−	0.858109i	$-0.671639\pi$
$461$	10.4437	−	18.0890i	0.486411	−	0.842488i	0.999878	+	0.0156208i	$0.00497247\pi$
$462$	−1.33459	+	2.31158i	−0.0620907	+	0.107544i
$463$	−26.4800			−1.23063			−0.615315	−	0.788281i	$-0.710971\pi$
$463$	−26.4800			−1.23063			−0.615315	+	0.788281i	$0.710971\pi$
$464$	−13.9711	+	24.1987i	−0.648593	+	1.12340i
$465$	−0.460828	−	0.798178i	−0.0213704	−	0.0370146i
$466$	−14.2089	−	24.6106i	−0.658216	−	1.14006i
$467$	23.2677			1.07670			0.538351	−	0.842721i	$-0.319047\pi$
$467$	23.2677			1.07670			0.538351	+	0.842721i	$0.319047\pi$
$468$	14.0004	+	34.5138i	0.647170	+	1.59540i
$469$	−3.28886			−0.151866
$470$	11.4308	+	19.7987i	0.527262	+	0.913245i
$471$	−4.06052	−	7.03303i	−0.187099	−	0.324065i
$472$	23.8209	−	41.2590i	1.09645	−	1.89910i
$473$	7.96758			0.366350
$474$	11.6629	−	20.2007i	0.535694	−	0.927848i
$475$	0.291315	−	0.504572i	0.0133664	−	0.0231513i
$476$	−22.9445			−1.05166
$477$	11.8757	−	20.5694i	0.543753	−	0.941808i
$478$	6.27335	+	10.8658i	0.286936	+	0.496989i
$479$	−5.16822	−	8.95162i	−0.236142	−	0.409010i	0.723462	−	0.690364i	$-0.242550\pi$
$479$	−5.16822	−	8.95162i	−0.236142	−	0.409010i	−0.959604	+	0.281354i	$0.909216\pi$
$480$	−0.421105			−0.0192207
$481$	2.19822	+	5.41903i	0.100230	+	0.247087i
$482$	65.9253			3.00281
$483$	−4.06201	−	7.03561i	−0.184828	−	0.320131i
$484$	−2.01840	−	3.49598i	−0.0917456	−	0.158908i
$485$	12.6487	−	21.9082i	0.574348	−	0.994799i
$486$	35.7380			1.62111
$487$	−13.6825	+	23.6988i	−0.620014	+	1.07390i	0.369469	+	0.929243i	$0.379540\pi$
$487$	−13.6825	+	23.6988i	−0.620014	+	1.07390i	−0.989483	+	0.144652i	$0.953794\pi$
$488$	−13.9075	+	24.0885i	−0.629562	+	1.09043i
$489$	1.32556			0.0599438
$490$	9.22673	−	15.9812i	0.416821	−	0.721955i
$491$	12.4644	+	21.5890i	0.562512	+	0.974299i	0.997276	+	0.0737551i	$0.0234983\pi$
$491$	12.4644	+	21.5890i	0.562512	+	0.974299i	−0.434764	+	0.900544i	$0.643168\pi$
$492$	4.52686	+	7.84075i	0.204086	+	0.353488i
$493$	22.9950			1.03564
$494$	−2.57772	−	0.358615i	−0.115977	−	0.0161348i
$495$	−4.44462			−0.199771
$496$	−1.68679	−	2.92161i	−0.0757392	−	0.131184i
$497$	9.83822	+	17.0403i	0.441304	+	0.764362i
$498$	12.7201	−	22.0319i	0.570003	−	0.987273i
$499$	11.7972			0.528117			0.264058	−	0.964507i	$-0.414939\pi$
$499$	11.7972			0.528117			0.264058	+	0.964507i	$0.414939\pi$
$500$	−24.4814	+	42.4030i	−1.09484	+	1.89632i
$501$	−5.22267	+	9.04593i	−0.233332	+	0.404142i
$502$	1.69769			0.0757717
$503$	1.19351	−	2.06721i	0.0532158	−	0.0921724i	−0.838190	−	0.545378i	$-0.816386\pi$
$503$	1.19351	−	2.06721i	0.0532158	−	0.0921724i	0.891406	+	0.453205i	$0.149720\pi$
$504$	10.4741	+	18.1416i	0.466553	+	0.808093i
$505$	−15.2555	−	26.4233i	−0.678862	−	1.17582i
$506$	18.3739			0.816818
$507$	2.11196	+	8.37120i	0.0937955	+	0.371778i
$508$	40.2771			1.78701
$509$	15.8359	+	27.4286i	0.701914	+	1.21575i	0.967794	+	0.251745i	$0.0810044\pi$
$509$	15.8359	+	27.4286i	0.701914	+	1.21575i	−0.265879	+	0.964006i	$0.585662\pi$
$510$	4.92381	+	8.52828i	0.218030	+	0.377639i
$511$	1.51966	−	2.63212i	0.0672257	−	0.116438i
$512$	40.7179			1.79949
$513$	−0.542288	+	0.939271i	−0.0239426	+	0.0414698i
$514$	8.47036	−	14.6711i	0.373611	−	0.647114i
$515$	−15.7151			−0.692492
$516$	−10.6802	+	18.4986i	−0.470168	+	0.814355i
$517$	−2.67855	−	4.63938i	−0.117802	−	0.204040i
$518$	3.25937	+	5.64539i	0.143208	+	0.248044i
$519$	7.09985			0.311649
$520$	31.0410	+	4.31844i	1.36124	+	0.189376i
$521$	16.5505			0.725091			0.362546	−	0.931966i	$-0.381908\pi$
$521$	16.5505			0.725091			0.362546	+	0.931966i	$0.381908\pi$
$522$	−20.8045	−	36.0345i	−0.910590	−	1.57719i
$523$	15.2491	+	26.4123i	0.666798	+	1.15493i	0.978794	+	0.204845i	$0.0656691\pi$
$523$	15.2491	+	26.4123i	0.666798	+	1.15493i	−0.311996	+	0.950083i	$0.600998\pi$
$524$	10.6596	−	18.4629i	0.465665	−	0.806556i
$525$	−2.15448			−0.0940292
$526$	3.00543	−	5.20555i	0.131043	−	0.226973i
$527$	−1.38814	+	2.40433i	−0.0604684	+	0.104734i
$528$	2.80403			0.122030
$529$	−16.4617	+	28.5126i	−0.715728	+	1.23968i
$530$	−19.8050	−	34.3033i	−0.860275	−	1.49004i
$531$	12.1805	+	21.0973i	0.528590	+	0.915546i
$532$	−1.93996			−0.0841078
$533$	−4.57706	−	11.2833i	−0.198254	−	0.488736i
$534$	−26.6910			−1.15503
$535$	8.29189	+	14.3620i	0.358490	+	0.620923i
$536$	5.03082	+	8.71364i	0.217298	+	0.376372i
$537$	−8.27026	+	14.3245i	−0.356888	+	0.618148i
$538$	−53.1247			−2.29037
$539$	−2.16208	+	3.74483i	−0.0931273	+	0.161301i
$540$	12.9425	−	22.4170i	0.556955	−	0.964674i
$541$	−12.2536			−0.526824			−0.263412	−	0.964683i	$-0.584848\pi$
$541$	−12.2536			−0.526824			−0.263412	+	0.964683i	$0.584848\pi$
$542$	2.29878	−	3.98160i	0.0987410	−	0.171024i
$543$	1.66509	+	2.88402i	0.0714558	+	0.123765i
$544$	0.634242	+	1.09854i	0.0271929	+	0.0470995i
$545$	−22.3350			−0.956726
$546$	3.61759	+	8.91806i	0.154818	+	0.381658i
$547$	−19.1291			−0.817903			−0.408952	−	0.912556i	$-0.634106\pi$
$547$	−19.1291			−0.817903			−0.408952	+	0.912556i	$0.634106\pi$
$548$	−5.44368	−	9.42873i	−0.232542	−	0.402775i
$549$	−7.11143	−	12.3174i	−0.303508	−	0.525692i
$550$	2.43636	−	4.21991i	0.103887	−	0.179937i
$551$	1.94422			0.0828268
$552$	−12.4269	+	21.5241i	−0.528926	+	0.916126i
$553$	−11.6920	+	20.2511i	−0.497194	+	0.861166i
$554$	15.4500			0.656409
$555$	0.935439	−	1.62023i	0.0397072	−	0.0687748i
$556$	2.46104	+	4.26264i	0.104371	+	0.180776i
$557$	2.06926	+	3.58406i	0.0876773	+	0.151862i	0.906529	−	0.422144i	$-0.138722\pi$
$557$	2.06926	+	3.58406i	0.0876773	+	0.151862i	−0.818852	+	0.574005i	$0.805389\pi$
$558$	5.02364			0.212668
$559$	17.6549	−	22.6622i	0.746722	−	0.958509i
$560$	11.9961			0.506929
$561$	−1.15378	−	1.99841i	−0.0487128	−	0.0843731i
$562$	−9.44578	−	16.3606i	−0.398446	−	0.690129i
$563$	−3.61813	+	6.26678i	−0.152486	+	0.264113i	−0.932141	−	0.362096i	$-0.882061\pi$
$563$	−3.61813	+	6.26678i	−0.152486	+	0.264113i	0.779655	+	0.626210i	$0.215395\pi$
$564$	14.3619			0.604744
$565$	−0.406906	+	0.704782i	−0.0171187	+	0.0296504i
$566$	34.0463	−	58.9699i	1.43107	−	2.47869i
$567$	−8.54719			−0.358948
$568$	30.0981	−	52.1315i	1.26289	−	2.18739i
$569$	3.08684	+	5.34657i	0.129407	+	0.224140i	0.923447	−	0.383726i	$-0.125359\pi$
$569$	3.08684	+	5.34657i	0.129407	+	0.224140i	−0.794040	+	0.607866i	$0.792026\pi$
$570$	0.416307	+	0.721065i	0.0174372	+	0.0302021i
$571$	5.47725			0.229216			0.114608	−	0.993411i	$-0.463439\pi$
$571$	5.47725			0.229216			0.114608	+	0.993411i	$0.463439\pi$
$572$	−14.4161	−	2.00557i	−0.602766	−	0.0838573i
$573$	14.5228			0.606698
$574$	−6.78655	−	11.7547i	−0.283265	−	0.490630i
$575$	7.41542	+	12.8439i	0.309244	+	0.535627i
$576$	−9.65675	+	16.7260i	−0.402364	+	0.696916i
$577$	−36.9750			−1.53929			−0.769644	−	0.638473i	$-0.779566\pi$
$577$	−36.9750			−1.53929			−0.769644	+	0.638473i	$0.779566\pi$
$578$	−6.05256	+	10.4833i	−0.251753	+	0.436049i
$579$	−6.23679	+	10.8024i	−0.259192	+	0.448934i
$580$	−46.4016			−1.92672
$581$	−12.7519	+	22.0869i	−0.529038	+	0.916320i
$582$	−11.8828	−	20.5817i	−0.492560	−	0.853139i
$583$	4.64087	+	8.03822i	0.192205	+	0.332909i
$584$	−9.29820			−0.384762
$585$	−9.84856	+	12.6418i	−0.407188	+	0.522676i
$586$	39.8993			1.64823
$587$	−15.4908	−	26.8309i	−0.639374	−	1.10743i	−0.985570	−	0.169266i	$-0.945860\pi$
$587$	−15.4908	−	26.8309i	−0.639374	−	1.10743i	0.346197	−	0.938162i	$-0.387473\pi$
$588$	−5.79633	−	10.0395i	−0.239037	−	0.414024i
$589$	−0.117367	+	0.203286i	−0.00483603	+	0.00837625i
$590$	40.6266			1.67257
$591$	4.58095	−	7.93444i	0.188435	−	0.326379i
$592$	3.42403	−	5.93060i	0.140727	−	0.243746i
$593$	−30.0100			−1.23236			−0.616181	−	0.787604i	$-0.711321\pi$
$593$	−30.0100			−1.23236			−0.616181	+	0.787604i	$0.711321\pi$
$594$	−4.53534	+	7.85544i	−0.186087	+	0.322313i
$595$	−4.93610	−	8.54958i	−0.202360	−	0.350499i
$596$	44.6130	+	77.2720i	1.82742	+	3.16518i
$597$	8.13326			0.332872
$598$	40.7136	−	52.2609i	1.66490	−	2.13711i
$599$	−10.2955			−0.420664			−0.210332	−	0.977630i	$-0.567455\pi$
$599$	−10.2955			−0.420664			−0.210332	+	0.977630i	$0.567455\pi$
$600$	3.29561	+	5.70816i	0.134543	+	0.233035i
$601$	−13.7628	−	23.8379i	−0.561398	−	0.972370i	−0.997375	−	0.0724117i	$-0.976930\pi$
$601$	−13.7628	−	23.8379i	−0.561398	−	0.972370i	0.435977	−	0.899958i	$-0.356403\pi$
$602$	16.0114	−	27.7326i	0.652578	−	1.13030i
$603$	−5.14491			−0.209517
$604$	0.545404	−	0.944667i	0.0221922	−	0.0384379i
$605$	0.868446	−	1.50419i	0.0353073	−	0.0611541i
$606$	−28.6637			−1.16438
$607$	3.47162	−	6.01302i	0.140909	−	0.244061i	−0.786930	−	0.617042i	$-0.788331\pi$
$607$	3.47162	−	6.01302i	0.140909	−	0.244061i	0.927839	+	0.372981i	$0.121664\pi$
$608$	0.0536250	+	0.0928813i	0.00217478	+	0.00376683i
$609$	−3.59473	−	6.22626i	−0.145666	−	0.252301i
$610$	−23.7193			−0.960365
$611$	−19.1310	−	2.66152i	−0.773958	−	0.107674i
$612$	−35.8931			−1.45089
$613$	7.38122	+	12.7846i	0.298125	+	0.516367i	0.975707	−	0.219080i	$-0.0703056\pi$
$613$	7.38122	+	12.7846i	0.298125	+	0.516367i	−0.677582	+	0.735447i	$0.736972\pi$
$614$	−7.12565	−	12.3420i	−0.287568	−	0.498082i
$615$	−1.94774	+	3.37359i	−0.0785405	+	0.136036i
$616$	−8.18623			−0.329833
$617$	16.1119	−	27.9067i	0.648642	−	1.12348i	−0.334806	−	0.942287i	$-0.608671\pi$
$617$	16.1119	−	27.9067i	0.648642	−	1.12348i	0.983448	−	0.181193i	$-0.0579959\pi$
$618$	−7.38181	+	12.7857i	−0.296940	+	0.514315i
$619$	16.4101			0.659579			0.329789	−	0.944055i	$-0.393022\pi$
$619$	16.4101			0.659579			0.329789	+	0.944055i	$0.393022\pi$
$620$	2.80113	−	4.85170i	0.112496	−	0.194849i
$621$	−13.8040	−	23.9092i	−0.553934	−	0.959441i
$622$	−10.3073	−	17.8527i	−0.413285	−	0.715830i
$623$	26.7577			1.07202
$624$	6.21327	−	7.97550i	0.248730	−	0.319276i
$625$	−11.1508			−0.446033
$626$	3.36233	+	5.82373i	0.134386	+	0.232763i
$627$	−0.0975523	−	0.168966i	−0.00389586	−	0.00674783i
$628$	24.6818	−	42.7500i	0.984909	−	1.70591i
$629$	−5.63560			−0.224706
$630$	−8.93179	+	15.4703i	−0.355851	+	0.616352i
$631$	7.23956	−	12.5393i	0.288202	−	0.499181i	−0.685178	−	0.728375i	$-0.740276\pi$
$631$	7.23956	−	12.5393i	0.288202	−	0.499181i	0.973381	+	0.229194i	$0.0736091\pi$
$632$	71.5388			2.84566
$633$	−4.58372	+	7.93923i	−0.182186	+	0.315556i
$634$	11.1511	+	19.3143i	0.442868	+	0.767071i
$635$	8.66489	+	15.0080i	0.343856	+	0.595575i
$636$	−24.8835			−0.986693
$637$	5.86061	+	14.4475i	0.232206	+	0.572433i
$638$	16.2602			0.643748
$639$	15.3903	+	26.6568i	0.608832	+	1.05453i
$640$	16.7385	+	28.9919i	0.661648	+	1.14601i
$641$	−23.8430	+	41.2973i	−0.941742	+	1.63115i	−0.179596	+	0.983740i	$0.557479\pi$
$641$	−23.8430	+	41.2973i	−0.941742	+	1.63115i	−0.762146	+	0.647405i	$0.775854\pi$
$642$	15.5797			0.614881
$643$	20.9279	−	36.2481i	0.825315	−	1.42949i	−0.0763634	−	0.997080i	$-0.524331\pi$
$643$	20.9279	−	36.2481i	0.825315	−	1.42949i	0.901678	−	0.432407i	$-0.142336\pi$
$644$	24.6908	−	42.7657i	0.972954	−	1.68521i
$645$	−9.19058			−0.361879
$646$	1.25403	−	2.17205i	0.0493392	−	0.0854580i
$647$	−19.0009	−	32.9105i	−0.747002	−	1.29384i	−0.949254	−	0.314511i	$-0.898159\pi$
$647$	−19.0009	−	32.9105i	−0.747002	−	1.29384i	0.202252	−	0.979334i	$-0.435174\pi$
$648$	13.0742	+	22.6452i	0.513605	+	0.889589i
$649$	−9.51995			−0.373691
$650$	−6.60410	−	16.2804i	−0.259034	−	0.638569i
$651$	0.868014			0.0340201
$652$	4.02868	+	6.97788i	0.157775	+	0.273275i
$653$	−17.3946	−	30.1283i	−0.680704	−	1.17901i	−0.974766	−	0.223227i	$-0.928341\pi$
$653$	−17.3946	−	30.1283i	−0.680704	−	1.17901i	0.294063	−	0.955786i	$-0.404992\pi$
$654$	−10.4913	+	18.1715i	−0.410243	+	0.710563i
$655$	9.17284			0.358413
$656$	−7.12941	+	12.3485i	−0.278357	+	0.482128i
$657$	2.37726	−	4.11754i	0.0927459	−	0.160641i
$658$	−21.5309			−0.839364
$659$	10.2476	−	17.7494i	0.399190	−	0.691418i	−0.594436	−	0.804143i	$-0.702625\pi$
$659$	10.2476	−	17.7494i	0.399190	−	0.691418i	0.993626	+	0.112725i	$0.0359579\pi$
$660$	2.32822	+	4.03260i	0.0906259	+	0.156969i
$661$	0.970913	+	1.68167i	0.0377642	+	0.0654094i	0.884290	−	0.466939i	$-0.154643\pi$
$661$	0.970913	+	1.68167i	0.0377642	+	0.0654094i	−0.846526	+	0.532348i	$0.821310\pi$
$662$	−44.3709			−1.72453
$663$	−8.24069	−	1.14645i	−0.320042	−	0.0445245i
$664$	78.0239			3.02792
$665$	−0.417346	−	0.722865i	−0.0161840	−	0.0280315i
$666$	5.09876	+	8.83131i	0.197573	+	0.342206i
$667$	−24.7451	+	42.8598i	−0.958135	+	1.65954i
$668$	−63.4917			−2.45657
$669$	5.44765	−	9.43561i	0.210618	−	0.364802i
$670$	−4.29004	+	7.43057i	−0.165739	+	0.287068i
$671$	5.55808			0.214567
$672$	0.198298	−	0.343462i	0.00764950	−	0.0132493i
$673$	−16.1773	−	28.0200i	−0.623591	−	1.08009i	−0.988812	−	0.149170i	$-0.952340\pi$
$673$	−16.1773	−	28.0200i	−0.623591	−	1.08009i	0.365221	−	0.930921i	$-0.380994\pi$
$674$	−17.7553	−	30.7531i	−0.683909	−	1.18456i
$675$	−7.32158			−0.281808
$676$	−37.6482	+	36.5596i	−1.44801	+	1.40614i
$677$	17.5181			0.673274			0.336637	−	0.941634i	$-0.390710\pi$
$677$	17.5181			0.673274			0.336637	+	0.941634i	$0.390710\pi$
$678$	0.382269	+	0.662109i	0.0146810	+	0.0254282i
$679$	11.9125	+	20.6331i	0.457160	+	0.791825i
$680$	−15.1011	+	26.1558i	−0.579099	+	1.00303i
$681$	−6.64950			−0.254809
$682$	−0.981582	+	1.70015i	−0.0375867	+	0.0651021i
$683$	10.2286	−	17.7165i	0.391388	−	0.677904i	−0.601245	−	0.799065i	$-0.705328\pi$
$683$	10.2286	−	17.7165i	0.391388	−	0.677904i	0.992633	+	0.121161i	$0.0386618\pi$
$684$	−3.03476			−0.116037
$685$	2.34222	−	4.05684i	0.0894915	−	0.155004i
$686$	22.7567	+	39.4158i	0.868856	+	1.50490i
$687$	−2.80943	−	4.86608i	−0.107186	−	0.185652i
$688$	−33.6407			−1.28254
$689$	33.1465	+	4.61137i	1.26278	+	0.175679i
$690$	−21.1942			−0.806849
$691$	−9.06307	−	15.6977i	−0.344775	−	0.597168i	0.640538	−	0.767927i	$-0.278712\pi$
$691$	−9.06307	−	15.6977i	−0.344775	−	0.597168i	−0.985313	+	0.170758i	$0.945378\pi$
$692$	21.5781	+	37.3744i	0.820277	+	1.42076i
$693$	2.09297	−	3.62512i	0.0795052	−	0.137707i
$694$	8.64279			0.328076
$695$	−1.05889	+	1.83406i	−0.0401661	+	0.0695698i
$696$	−10.9974	+	19.0480i	−0.416855	+	0.722014i
$697$	11.7343			0.444467
$698$	−29.8575	+	51.7147i	−1.13012	+	1.95743i
$699$	−3.84062	−	6.65215i	−0.145266	−	0.251607i
$700$	−6.54797	−	11.3414i	−0.247490	−	0.428665i
$701$	9.99654			0.377564			0.188782	−	0.982019i	$-0.439546\pi$
$701$	9.99654			0.377564			0.188782	+	0.982019i	$0.439546\pi$
$702$	12.2937	+	30.3063i	0.463995	+	1.14384i
$703$	−0.476489			−0.0179711
$704$	−3.77371	−	6.53626i	−0.142227	−	0.246345i
$705$	3.08969	+	5.35151i	0.116365	+	0.201549i
$706$	−12.4573	+	21.5766i	−0.468836	+	0.812048i
$707$	28.7352			1.08070
$708$	12.7610	−	22.1028i	0.479590	−	0.830673i
$709$	11.6777	−	20.2264i	0.438565	−	0.759617i	−0.559014	−	0.829158i	$-0.688820\pi$
$709$	11.6777	−	20.2264i	0.438565	−	0.759617i	0.997579	+	0.0695409i	$0.0221534\pi$
$710$	51.3325			1.92647
$711$	−18.2903	+	31.6797i	−0.685939	+	1.18808i
$712$	−40.9300	−	70.8928i	−1.53391	−	2.65682i
$713$	−2.98758	−	5.17464i	−0.111886	−	0.193792i
$714$	−9.27446			−0.347088
$715$	−2.35404	−	5.80317i	−0.0880361	−	0.217026i
$716$	−100.541			−3.75740
$717$	1.69566	+	2.93698i	0.0633257	+	0.109683i
$718$	5.88081	+	10.1859i	0.219470	+	0.380133i
$719$	−4.44260	+	7.69481i	−0.165681	+	0.286968i	−0.936897	−	0.349606i	$-0.886316\pi$
$719$	−4.44260	+	7.69481i	−0.165681	+	0.286968i	0.771216	+	0.636574i	$0.219649\pi$
$720$	18.7661			0.699370
$721$	7.40024	−	12.8176i	0.275599	−	0.477352i
$722$	−23.2354	+	40.2449i	−0.864732	+	1.49776i
$723$	17.8194			0.662709
$724$	−10.1212	+	17.5304i	−0.376151	+	0.651513i
$725$	6.56238	+	11.3664i	0.243721	+	0.422136i
$726$	−0.815863	−	1.41312i	−0.0302795	−	0.0524457i
$727$	−22.6584			−0.840353			−0.420177	−	0.907442i	$-0.638032\pi$
$727$	−22.6584			−0.840353			−0.420177	+	0.907442i	$0.638032\pi$
$728$	−18.1394	+	23.2841i	−0.672290	+	0.862967i
$729$	−6.01541			−0.222793
$730$	−3.96453	−	6.86676i	−0.146734	−	0.254150i
$731$	13.8423	+	23.9755i	0.511975	+	0.886767i
$732$	−7.45035	+	12.9044i	−0.275373	+	0.476960i
$733$	−40.9147			−1.51122			−0.755609	−	0.655023i	$-0.772659\pi$
$733$	−40.9147			−1.51122			−0.755609	+	0.655023i	$0.772659\pi$
$734$	11.9758	−	20.7427i	0.442034	−	0.765626i
$735$	2.49395	−	4.31965i	0.0919907	−	0.159333i
$736$	−2.73005			−0.100631
$737$	1.00528	−	1.74119i	0.0370298	−	0.0641375i
$738$	−10.6165	−	18.3883i	−0.390798	−	0.676882i
$739$	−6.61084	−	11.4503i	−0.243184	−	0.421207i	0.718436	−	0.695593i	$-0.244858\pi$
$739$	−6.61084	−	11.4503i	−0.243184	−	0.421207i	−0.961619	+	0.274387i	$0.911525\pi$
$740$	11.3721			0.418046
$741$	−0.696749	−	0.0969322i	−0.0255957	−	0.00356089i
$742$	37.3047			1.36950
$743$	11.2790	+	19.5358i	0.413787	+	0.716700i	0.995300	−	0.0968370i	$-0.0308725\pi$
$743$	11.2790	+	19.5358i	0.413787	+	0.716700i	−0.581513	+	0.813537i	$0.697539\pi$
$744$	−1.32776	−	2.29975i	−0.0486781	−	0.0843129i
$745$	−19.1953	+	33.2473i	−0.703263	+	1.21809i
$746$	−1.43419			−0.0525093
$747$	−19.9483	+	34.5515i	−0.729870	+	1.26417i
$748$	7.01325	−	12.1473i	0.256430	−	0.444149i
$749$	−15.6186			−0.570690
$750$	−9.89566	+	17.1398i	−0.361339	+	0.625857i
$751$	−19.9760	−	34.5995i	−0.728935	−	1.26255i	−0.957333	−	0.288985i	$-0.906682\pi$
$751$	−19.9760	−	34.5995i	−0.728935	−	1.26255i	0.228398	−	0.973568i	$-0.426651\pi$
$752$	11.3094	+	19.5884i	0.412410	+	0.714314i
$753$	0.458880			0.0167225
$754$	36.0300	−	46.2490i	1.31214	−	1.68429i
$755$	0.469335			0.0170808
$756$	12.1892	+	21.1123i	0.443316	+	0.767847i
$757$	24.1796	+	41.8803i	0.878822	+	1.52216i	0.852635	+	0.522507i	$0.175003\pi$
$757$	24.1796	+	41.8803i	0.878822	+	1.52216i	0.0261863	+	0.999657i	$0.491664\pi$
$758$	−38.6339	+	66.9158i	−1.40325	+	2.43049i
$759$	4.96639			0.180268
$760$	−1.27679	+	2.21147i	−0.0463141	+	0.0802184i
$761$	−10.8964	+	18.8732i	−0.394995	+	0.684152i	−0.993101	−	0.117266i	$-0.962587\pi$
$761$	−10.8964	+	18.8732i	−0.394995	+	0.684152i	0.598105	+	0.801417i	$0.295920\pi$
$762$	16.2805			0.589780
$763$	10.5175	−	18.2169i	0.380760	−	0.659496i
$764$	44.1382	+	76.4496i	1.59686	+	2.76585i
$765$	−7.72175	−	13.3745i	−0.279180	−	0.483555i
$766$	−12.8045			−0.462647
$767$	−21.0947	+	27.0776i	−0.761685	+	0.977716i
$768$	21.4253			0.773120
$769$	−3.21280	−	5.56473i	−0.115856	−	0.200669i	0.802265	−	0.596968i	$-0.203628\pi$
$769$	−3.21280	−	5.56473i	−0.115856	−	0.200669i	−0.918122	+	0.396298i	$0.870295\pi$
$770$	−3.49041	−	6.04557i	−0.125786	−	0.217867i
$771$	2.28951	−	3.96554i	0.0824545	−	0.142815i
$772$	−75.8203			−2.72883
$773$	18.1476	−	31.4326i	0.652725	−	1.13055i	−0.329734	−	0.944074i	$-0.606959\pi$
$773$	18.1476	−	31.4326i	0.652725	−	1.13055i	0.982459	−	0.186479i	$-0.0597076\pi$
$774$	25.0474	−	43.3833i	0.900309	−	1.55938i
$775$	−1.58461			−0.0569207
$776$	36.4441	−	63.1230i	1.30827	−	2.26598i
$777$	0.880994	+	1.52593i	0.0316055	+	0.0547423i
$778$	−2.69242	−	4.66341i	−0.0965280	−	0.167191i
$779$	0.992131			0.0355468
$780$	16.6289	+	2.31342i	0.595410	+	0.0828338i
$781$	−12.0286			−0.430418
$782$	31.9214	+	55.2895i	1.14151	+	1.97715i
$783$	−12.2160	−	21.1587i	−0.436564	−	0.756152i
$784$	9.12872	−	15.8114i	0.326026	−	0.564693i
$785$	21.2393			0.758064
$786$	4.30872	−	7.46293i	0.153687	−	0.266194i
$787$	16.8664	−	29.2135i	0.601223	−	1.04135i	−0.391413	−	0.920215i	$-0.628014\pi$
$787$	16.8664	−	29.2135i	0.601223	−	1.04135i	0.992636	−	0.121134i	$-0.0386530\pi$
$788$	55.6904			1.98389
$789$	0.812356	−	1.40704i	0.0289206	−	0.0500920i
$790$	30.5024	+	52.8318i	1.08523	+	1.87967i
$791$	−0.383224	−	0.663763i	−0.0136259	−	0.0236007i
$792$	−12.8061			−0.455043
$793$	12.3158	−	15.8089i	0.437347	−	0.561389i
$794$	−10.2547			−0.363926
$795$	−5.35322	−	9.27205i	−0.189859	−	0.328846i
$796$	24.7189	+	42.8144i	0.876138	+	1.51752i
$797$	25.1675	−	43.5913i	0.891478	−	1.54408i	0.0533733	−	0.998575i	$-0.483003\pi$
$797$	25.1675	−	43.5913i	0.891478	−	1.54408i	0.838104	−	0.545510i	$-0.183664\pi$
$798$	−0.784154			−0.0277588
$799$	9.30701	−	16.1202i	0.329258	−	0.570292i
$800$	−0.362003	+	0.627008i	−0.0127987	+	0.0221681i
$801$	41.8581			1.47898
$802$	27.5589	−	47.7333i	0.973137	−	1.68552i
$803$	0.928999	+	1.60907i	0.0327837	+	0.0567830i
$804$	2.69505	+	4.66797i	0.0950471	+	0.164626i
$805$	21.2471			0.748862
$806$	2.66071	+	6.55917i	0.0937195	+	0.231037i
$807$	−14.3594			−0.505475
$808$	−43.9550	−	76.1323i	−1.54633	−	2.67832i
$809$	19.9767	+	34.6007i	0.702345	+	1.21650i	0.967641	+	0.252330i	$0.0811969\pi$
$809$	19.9767	+	34.6007i	0.702345	+	1.21650i	−0.265296	+	0.964167i	$0.585470\pi$
$810$	−11.1491	+	19.3108i	−0.391739	+	0.678512i
$811$	36.4511			1.27997			0.639986	−	0.768386i	$-0.278940\pi$
$811$	36.4511			1.27997			0.639986	+	0.768386i	$0.278940\pi$
$812$	21.8505	−	37.8461i	0.766802	−	1.32814i
$813$	0.621351	−	1.07621i	0.0217917	−	0.0377444i
$814$	−3.98504			−0.139676
$815$	−1.73340	+	3.00233i	−0.0607182	+	0.105167i
$816$	4.87151	+	8.43770i	0.170537	+	0.295379i
$817$	1.17036	+	2.02713i	0.0409458	+	0.0709202i
$818$	−31.8947			−1.11517
$819$	−5.67327	−	13.9857i	−0.198240	−	0.488701i
$820$	−23.6786			−0.826892
$821$	−13.9977	−	24.2447i	−0.488523	−	0.846147i	0.511389	−	0.859349i	$-0.329131\pi$
$821$	−13.9977	−	24.2447i	−0.488523	−	0.846147i	−0.999913	+	0.0132017i	$0.995798\pi$
$822$	−2.20040	−	3.81121i	−0.0767478	−	0.132931i
$823$	−8.25588	+	14.2996i	−0.287782	+	0.498453i	−0.973280	−	0.229622i	$-0.926251\pi$
$823$	−8.25588	+	14.2996i	−0.287782	+	0.498453i	0.685498	+	0.728074i	$0.259584\pi$
$824$	−45.2792			−1.57738
$825$	0.658540	−	1.14062i	0.0229274	−	0.0397115i
$826$	−19.1310	+	33.1359i	−0.665654	+	1.15295i
$827$	−17.9889			−0.625534			−0.312767	−	0.949830i	$-0.601256\pi$
$827$	−17.9889			−0.625534			−0.312767	+	0.949830i	$0.601256\pi$
$828$	38.6249	−	66.9002i	1.34231	−	2.32494i
$829$	22.6273	+	39.1917i	0.785879	+	1.36118i	0.928472	+	0.371401i	$0.121123\pi$
$829$	22.6273	+	39.1917i	0.785879	+	1.36118i	−0.142593	+	0.989781i	$0.545544\pi$
$830$	33.2675	+	57.6210i	1.15473	+	2.00006i
$831$	4.17609			0.144867
$832$	−26.9531	−	3.74973i	−0.934429	−	0.129998i
$833$	−15.0249			−0.520583
$834$	0.994780	+	1.72301i	0.0344464	+	0.0596630i
$835$	−13.6591	−	23.6582i	−0.472692	−	0.818726i
$836$	0.592969	−	1.02705i	0.0205083	−	0.0355213i
$837$	2.94978			0.101959
$838$	14.3010	−	24.7700i	0.494019	−	0.855667i
$839$	−3.57953	+	6.19993i	−0.123579	+	0.214046i	−0.921177	−	0.389145i	$-0.872771\pi$
$839$	−3.57953	+	6.19993i	−0.123579	+	0.214046i	0.797597	+	0.603190i	$0.206104\pi$
$840$	9.44279			0.325807
$841$	−7.39855	+	12.8147i	−0.255122	+	0.441885i
$842$	−18.0629	−	31.2859i	−0.622489	−	1.07818i
$843$	−2.55316	−	4.42220i	−0.0879355	−	0.152309i
$844$	−55.7240			−1.91810
$845$	−21.7221	−	6.16329i	−0.747264	−	0.212024i
$846$	−33.6818			−1.15800
$847$	0.817900	+	1.41664i	0.0281034	+	0.0486765i
$848$	−19.5947	−	33.9389i	−0.672883	−	1.16547i
$849$	9.20258	−	15.9393i	0.315832	−	0.547037i
$850$	16.9310			0.580729
$851$	6.06452	−	10.5041i	0.207889	−	0.360074i
$852$	16.1238	−	27.9273i	0.552393	−	0.956772i
$853$	−36.2660			−1.24172			−0.620862	−	0.783920i	$-0.713217\pi$
$853$	−36.2660			−1.24172			−0.620862	+	0.783920i	$0.713217\pi$
$854$	11.1694	−	19.3459i	0.382208	−	0.662004i
$855$	−0.652872	−	1.13081i	−0.0223278	−	0.0386728i
$856$	23.8910	+	41.3805i	0.816578	+	1.41436i
$857$	52.3196			1.78720			0.893601	−	0.448861i	$-0.148170\pi$
$857$	52.3196			1.78720			0.893601	+	0.448861i	$0.148170\pi$
$858$	−5.82715	−	0.810678i	−0.198936	−	0.0276761i
$859$	17.1259			0.584329			0.292165	−	0.956368i	$-0.405625\pi$
$859$	17.1259			0.584329			0.292165	+	0.956368i	$0.405625\pi$
$860$	−27.9323	−	48.3802i	−0.952484	−	1.64975i
$861$	−1.83438	−	3.17724i	−0.0625155	−	0.108280i
$862$	38.2700	−	66.2856i	1.30348	−	2.25770i
$863$	−15.4074			−0.524473			−0.262236	−	0.965004i	$-0.584460\pi$
$863$	−15.4074			−0.524473			−0.262236	+	0.965004i	$0.584460\pi$
$864$	0.673876	−	1.16719i	0.0229257	−	0.0397085i
$865$	−9.28428	+	16.0808i	−0.315675	+	0.546765i
$866$	−83.6570			−2.84278
$867$	−1.63598	+	2.83361i	−0.0555609	+	0.0962343i
$868$	2.63810	+	4.56932i	0.0895429	+	0.155093i
$869$	−7.14757	−	12.3800i	−0.242465	−	0.419961i
$870$	−18.7561			−0.635891
$871$	−2.72494	−	6.71751i	−0.0923310	−	0.227614i
$872$	−64.3527			−2.17926
$873$	18.6352	+	32.2772i	0.630707	+	1.09242i
$874$	2.69895	+	4.67472i	0.0912933	+	0.158125i
$875$	9.92037	−	17.1826i	0.335370	−	0.580878i
$876$	−4.98112			−0.168296
$877$	8.75784	−	15.1690i	0.295731	−	0.512222i	−0.679423	−	0.733746i	$-0.737770\pi$
$877$	8.75784	−	15.1690i	0.295731	−	0.512222i	0.975155	+	0.221525i	$0.0711033\pi$
$878$	−32.0534	+	55.5182i	−1.08175	+	1.87365i
$879$	10.7846			0.363757
$880$	−3.66675	+	6.35100i	−0.123606	+	0.214092i
$881$	1.69079	+	2.92854i	0.0569643	+	0.0986651i	0.893101	−	0.449856i	$-0.148525\pi$
$881$	1.69079	+	2.92854i	0.0569643	+	0.0986651i	−0.836137	+	0.548521i	$0.815191\pi$
$882$	13.5937	+	23.5449i	0.457723	+	0.792799i
$883$	−27.7476			−0.933780			−0.466890	−	0.884315i	$-0.654626\pi$
$883$	−27.7476			−0.933780			−0.466890	+	0.884315i	$0.654626\pi$
$884$	−19.0104	−	46.8643i	−0.639388	−	1.57622i
$885$	10.9812			0.369130
$886$	32.9731	+	57.1110i	1.10775	+	1.91868i
$887$	20.3207	+	35.1964i	0.682301	+	1.18178i	0.974277	+	0.225355i	$0.0723541\pi$
$887$	20.3207	+	35.1964i	0.682301	+	1.18178i	−0.291976	+	0.956426i	$0.594313\pi$
$888$	2.69523	−	4.66828i	0.0904461	−	0.156657i
$889$	−16.3211			−0.547394
$890$	34.9031	−	60.4539i	1.16995	−	2.02642i
$891$	2.61254	−	4.52505i	0.0875234	−	0.151595i
$892$	66.2268			2.21744
$893$	0.786906	−	1.36296i	0.0263328	−	0.0456098i
$894$	18.0331	+	31.2343i	0.603118	+	1.04463i
$895$	−21.6296	−	37.4635i	−0.722997	−	1.25227i
$896$	−31.5286			−1.05330
$897$	11.0047	−	14.1259i	0.367437	−	0.471650i
$898$	45.9946			1.53486
$899$	−2.64390	−	4.57937i	−0.0881791	−	0.152731i
$900$	−10.2433	−	17.7419i	−0.341442	−	0.591395i
$901$	−16.1254	+	27.9300i	−0.537215	+	0.930483i
$902$	8.29753			0.276277
$903$	4.32783	−	7.49603i	0.144021	−	0.249452i
$904$	−1.17240	+	2.03065i	−0.0389934	+	0.0675386i
$905$	−8.70956			−0.289516
$906$	0.220459	−	0.381846i	0.00732425	−	0.0126860i
$907$	0.261763	+	0.453387i	0.00869171	+	0.0150545i	0.870339	−	0.492454i	$-0.163900\pi$
$907$	0.261763	+	0.453387i	0.00869171	+	0.0150545i	−0.861647	+	0.507508i	$0.830567\pi$
$908$	−20.2094	−	35.0037i	−0.670672	−	1.16164i
$909$	44.9517			1.49095
$910$	−24.9296	−	3.46823i	−0.826409	−	0.114971i
$911$	11.1021			0.367828			0.183914	−	0.982942i	$-0.441123\pi$
$911$	11.1021			0.367828			0.183914	+	0.982942i	$0.441123\pi$
$912$	0.411885	+	0.713406i	0.0136389	+	0.0236232i
$913$	−7.79550	−	13.5022i	−0.257994	−	0.446858i
$914$	−9.07612	+	15.7203i	−0.300211	+	0.519981i
$915$	−6.41123			−0.211949
$916$	17.0770	−	29.5783i	0.564242	−	0.977295i
$917$	−4.31948	+	7.48156i	−0.142642	+	0.247063i
$918$	−31.5175			−1.04023
$919$	−1.84142	+	3.18943i	−0.0607429	+	0.105210i	−0.894798	−	0.446472i	$-0.852680\pi$
$919$	−1.84142	+	3.18943i	−0.0607429	+	0.105210i	0.834055	+	0.551682i	$0.186014\pi$
$920$	−32.5007	−	56.2929i	−1.07152	−	1.85592i
$921$	−1.92604	−	3.33599i	−0.0634650	−	0.109925i
$922$	51.3201			1.69014
$923$	−26.6535	+	34.2131i	−0.877311	+	1.12614i
$924$	−4.38543			−0.144270
$925$	−1.60830	−	2.78566i	−0.0528807	−	0.0915920i
$926$	−32.5306	−	56.3446i	−1.06902	−	1.85160i
$927$	11.5765	−	20.0511i	0.380222	−	0.658564i
$928$	−2.41600			−0.0793090
$929$	16.6282	−	28.8008i	0.545552	−	0.944924i	−0.453020	−	0.891500i	$-0.649653\pi$
$929$	16.6282	−	28.8008i	0.545552	−	0.944924i	0.998572	−	0.0534233i	$-0.0170133\pi$
$930$	1.13225	−	1.96112i	0.0371280	−	0.0643075i
$931$	−1.27036			−0.0416342
$932$	23.3451	−	40.4349i	0.764694	−	1.32449i
$933$	−2.78602	−	4.82553i	−0.0912102	−	0.157981i
$934$	28.5843	+	49.5095i	0.935307	+	1.62000i
$935$	6.03509			0.197369
$936$	−28.3762	+	36.4243i	−0.927504	+	1.19057i
$937$	0.0211062			0.000689510			0.000344755	−	1.00000i	$-0.499890\pi$
$937$	0.0211062			0.000689510			0.000344755		1.00000i	$0.499890\pi$
$938$	−4.04035	−	6.99810i	−0.131922	−	0.228496i
$939$	0.908826	+	1.57413i	0.0296584	+	0.0513699i
$940$	−18.7806	+	32.5290i	−0.612556	+	1.06098i
$941$	27.4643			0.895310			0.447655	−	0.894206i	$-0.352259\pi$
$941$	27.4643			0.895310			0.447655	+	0.894206i	$0.352259\pi$
$942$	9.97666	−	17.2801i	0.325057	−	0.563016i
$943$	−12.6273	+	21.8712i	−0.411203	+	0.712225i
$944$	40.1951			1.30824
$945$	−5.24456	+	9.08385i	−0.170606	+	0.295498i
$946$	9.78814	+	16.9536i	0.318240	+	0.551208i
$947$	−5.39918	−	9.35166i	−0.175450	−	0.303888i	0.764867	−	0.644188i	$-0.222805\pi$
$947$	−5.39918	−	9.35166i	−0.175450	−	0.303888i	−0.940317	+	0.340300i	$0.889471\pi$
$948$	38.3239			1.24470
$949$	6.63520	+	0.923094i	0.215388	+	0.0299649i
$950$	1.43152			0.0464445
$951$	3.01411	+	5.22059i	0.0977393	+	0.169289i
$952$	−14.2221	−	24.6335i	−0.460942	−	0.798376i
$953$	17.8773	−	30.9644i	0.579102	−	1.00303i	−0.416480	−	0.909145i	$-0.636737\pi$
$953$	17.8773	−	30.9644i	0.579102	−	1.00303i	0.995583	−	0.0938897i	$-0.0299301\pi$
$954$	58.3572			1.88938
$955$	−18.9911	+	32.8935i	−0.614536	+	1.06441i
$956$	−10.3070	+	17.8523i	−0.333354	+	0.577385i
$957$	4.39508			0.142073
$958$	12.6983	−	21.9941i	0.410263	−	0.710596i
$959$	2.20590	+	3.82072i	0.0712321	+	0.123378i
$960$	4.35296	+	7.53956i	0.140491	+	0.243338i
$961$	−30.3616			−0.979406
$962$	−8.83021	+	11.3347i	−0.284697	+	0.365444i
$963$	−24.4328			−0.787336
$964$	54.1572	+	93.8030i	1.74429	+	3.02119i
$965$	−16.3114	−	28.2521i	−0.525081	−	0.909468i
$966$	9.98033	−	17.2864i	0.321112	−	0.556182i
$967$	48.5134			1.56009			0.780043	−	0.625726i	$-0.215197\pi$
$967$	48.5134			1.56009			0.780043	+	0.625726i	$0.215197\pi$
$968$	2.50221	−	4.33395i	0.0804240	−	0.139299i
$969$	0.338960	−	0.587096i	0.0108890	−	0.0188602i
$970$	62.1555			1.99569
$971$	−8.97805	+	15.5504i	−0.288119	+	0.499037i	−0.973361	−	0.229279i	$-0.926363\pi$
$971$	−8.97805	+	15.5504i	−0.288119	+	0.499037i	0.685241	+	0.728316i	$0.259697\pi$
$972$	29.3585	+	50.8504i	0.941675	+	1.63103i
$973$	−0.997264	−	1.72731i	−0.0319708	−	0.0553751i
$974$	−67.2356			−2.15437
$975$	−1.78506	−	4.40053i	−0.0571678	−	0.140930i
$976$	−23.4673			−0.751171
$977$	−6.95892	−	12.0532i	−0.222636	−	0.385616i	0.732972	−	0.680259i	$-0.238133\pi$
$977$	−6.95892	−	12.0532i	−0.222636	−	0.385616i	−0.955607	+	0.294643i	$0.904799\pi$
$978$	1.62844	+	2.82054i	0.0520718	+	0.0901911i
$979$	−8.17876	+	14.1660i	−0.261394	+	0.452748i
$980$	30.3188			0.968499
$981$	16.4530	−	28.4974i	0.525304	−	0.909853i
$982$	−30.6250	+	53.0441i	−0.977283	+	1.69270i
$983$	11.1702			0.356275			0.178137	−	0.984006i	$-0.442993\pi$
$983$	11.1702			0.356275			0.178137	+	0.984006i	$0.442993\pi$
$984$	−5.61193	+	9.72015i	−0.178902	+	0.309867i
$985$	11.9808	+	20.7513i	0.381739	+	0.661192i
$986$	28.2493	+	48.9292i	0.899641	+	1.55822i
$987$	−5.81973			−0.185244
$988$	−1.60732	−	3.96236i	−0.0511358	−	0.126060i
$989$	−59.5832			−1.89463
$990$	−5.46019	−	9.45734i	−0.173536	−	0.300574i
$991$	8.05767	+	13.9563i	0.255960	+	0.443337i	0.965156	−	0.261675i	$-0.0842750\pi$
$991$	8.05767	+	13.9563i	0.255960	+	0.443337i	−0.709195	+	0.705012i	$0.750942\pi$
$992$	0.145847	−	0.252614i	0.00463064	−	0.00802050i
$993$	−11.9933			−0.380596
$994$	−24.1724	+	41.8679i	−0.766703	+	1.32797i
$995$	−10.6356	+	18.4215i	−0.337172	+	0.584000i
$996$	41.7980			1.32442
$997$	21.9949	−	38.0963i	0.696586	−	1.20652i	−0.273058	−	0.961998i	$-0.588035\pi$
$997$	21.9949	−	38.0963i	0.696586	−	1.20652i	0.969643	−	0.244524i	$-0.0786317\pi$
$998$	14.4929	+	25.1024i	0.458763	+	0.794602i
$999$	2.99389	+	5.18557i	0.0947224	+	0.164064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.c.133.6	yes	12
13.3	even	3		1859.2.a.k.1.1		6
13.9	even	3	inner	143.2.e.c.100.6	✓	12
13.10	even	6		1859.2.a.l.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.6	✓	12	13.9	even	3	inner
143.2.e.c.133.6	yes	12	1.1	even	1	trivial
1859.2.a.k.1.1		6	13.3	even	3
1859.2.a.l.1.6		6	13.10	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)

\(f(q)\)	\(=\)	\(q+(1.22850 + 2.12782i) q^{2} +(0.332058 + 0.575141i) q^{3} +(-2.01840 + 3.49598i) q^{4} -1.73689 q^{5} +(-0.815863 + 1.41312i) q^{6} +(0.817900 - 1.41664i) q^{7} -5.00442 q^{8} +(1.27948 - 2.21612i) q^{9} +O(q^{10})\)	\(q+(1.22850 + 2.12782i) q^{2} +(0.332058 + 0.575141i) q^{3} +(-2.01840 + 3.49598i) q^{4} -1.73689 q^{5} +(-0.815863 + 1.41312i) q^{6} +(0.817900 - 1.41664i) q^{7} -5.00442 q^{8} +(1.27948 - 2.21612i) q^{9} +(-2.13376 - 3.69579i) q^{10} +(0.500000 + 0.866025i) q^{11} -2.68091 q^{12} +(3.57116 + 0.496822i) q^{13} +4.01915 q^{14} +(-0.576748 - 0.998957i) q^{15} +(-2.11110 - 3.65653i) q^{16} +(-1.73733 + 3.00914i) q^{17} +6.28732 q^{18} +(-0.146891 + 0.254422i) q^{19} +(3.50575 - 6.07213i) q^{20} +1.08636 q^{21} +(-1.22850 + 2.12782i) q^{22} +(-3.73910 - 6.47631i) q^{23} +(-1.66176 - 2.87825i) q^{24} -1.98321 q^{25} +(3.33001 + 8.20911i) q^{26} +3.69179 q^{27} +(3.30171 + 5.71872i) q^{28} +(-3.30897 - 5.73130i) q^{29} +(1.41707 - 2.45443i) q^{30} +0.799011 q^{31} +(0.182534 - 0.316158i) q^{32} +(-0.332058 + 0.575141i) q^{33} -8.53719 q^{34} +(-1.42060 + 2.46056i) q^{35} +(5.16499 + 8.94603i) q^{36} +(0.810960 + 1.40462i) q^{37} -0.721818 q^{38} +(0.900088 + 2.21889i) q^{39} +8.69213 q^{40} +(-1.68855 - 2.92466i) q^{41} +(1.33459 + 2.31158i) q^{42} +(3.98379 - 6.90013i) q^{43} -4.03681 q^{44} +(-2.22231 + 3.84915i) q^{45} +(9.18694 - 15.9122i) q^{46} -5.35709 q^{47} +(1.40201 - 2.42836i) q^{48} +(2.16208 + 3.74483i) q^{49} +(-2.43636 - 4.21991i) q^{50} -2.30757 q^{51} +(-8.94492 + 11.4819i) q^{52} +9.28173 q^{53} +(4.53534 + 7.85544i) q^{54} +(-0.868446 - 1.50419i) q^{55} +(-4.09311 + 7.08948i) q^{56} -0.195105 q^{57} +(8.13011 - 14.0818i) q^{58} +(-4.75997 + 8.24452i) q^{59} +4.65644 q^{60} +(2.77904 - 4.81344i) q^{61} +(0.981582 + 1.70015i) q^{62} +(-2.09297 - 3.62512i) q^{63} -7.54743 q^{64} +(-6.20271 - 0.862926i) q^{65} -1.63173 q^{66} +(-1.00528 - 1.74119i) q^{67} +(-7.01325 - 12.1473i) q^{68} +(2.48319 - 4.30102i) q^{69} -6.98082 q^{70} +(-6.01431 + 10.4171i) q^{71} +(-6.40303 + 11.0904i) q^{72} +1.85800 q^{73} +(-1.99252 + 3.45115i) q^{74} +(-0.658540 - 1.14062i) q^{75} +(-0.592969 - 1.02705i) q^{76} +1.63580 q^{77} +(-3.61564 + 4.64112i) q^{78} -14.2951 q^{79} +(3.66675 + 6.35100i) q^{80} +(-2.61254 - 4.52505i) q^{81} +(4.14876 - 7.18587i) q^{82} -15.5910 q^{83} +(-2.19271 + 3.79789i) q^{84} +(3.01754 - 5.22654i) q^{85} +19.5763 q^{86} +(2.19754 - 3.80625i) q^{87} +(-2.50221 - 4.33395i) q^{88} +(8.17876 + 14.1660i) q^{89} -10.9204 q^{90} +(3.62467 - 4.65271i) q^{91} +30.1881 q^{92} +(0.265318 + 0.459544i) q^{93} +(-6.58117 - 11.3989i) q^{94} +(0.255133 - 0.441903i) q^{95} +0.242447 q^{96} +(-7.28238 + 12.6134i) q^{97} +(-5.31221 + 9.20101i) q^{98} +2.55895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

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