LMFDB - Embedded newform 342.2.e.d.115.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(115,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.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:	$2.73088374913$
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} - 2x^{10} - 6x^{9} + 10x^{8} + 15x^{6} + 90x^{4} - 162x^{3} - 162x^{2} + 729 $ x^12 - 2x^10 - 6x^9 + 10x^8 + 15x^6 + 90x^4 - 162x^3 - 162*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			115.4
Root			$1.65241 + 0.519186i$ of defining polynomial
Character	$\chi$	$=$	342.115
Dual form			342.2.e.d.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.376574 + 1.69062i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(1.65241 + 0.519186i) q^{6} +(1.76747 - 3.06135i) q^{7} -1.00000 q^{8} +(-2.71638 + 1.27329i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.376574 + 1.69062i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(1.65241 + 0.519186i) q^{6} +(1.76747 - 3.06135i) q^{7} -1.00000 q^{8} +(-2.71638 + 1.27329i) q^{9} -2.44949 q^{10} +(2.40980 - 4.17390i) q^{11} +(1.27583 - 1.17143i) q^{12} +(1.08432 + 1.87809i) q^{13} +(-1.76747 - 3.06135i) q^{14} +(3.12514 - 2.86941i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.715332 q^{17} +(-0.255493 + 2.98910i) q^{18} +1.00000 q^{19} +(-1.22474 + 2.12132i) q^{20} +(5.84116 + 1.83529i) q^{21} +(-2.40980 - 4.17390i) q^{22} +(0.380824 + 0.659606i) q^{23} +(-0.376574 - 1.69062i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.16863 q^{26} +(-3.17556 - 4.11288i) q^{27} -3.53494 q^{28} +(0.804235 - 1.39298i) q^{29} +(-0.922415 - 4.14115i) q^{30} +(2.63455 + 4.56317i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.96395 + 2.50228i) q^{33} +(-0.357666 + 0.619496i) q^{34} -8.65880 q^{35} +(2.46089 + 1.71581i) q^{36} +9.61585 q^{37} +(0.500000 - 0.866025i) q^{38} +(-2.76681 + 2.54041i) q^{39} +(1.22474 + 2.12132i) q^{40} +(-3.79532 - 6.57368i) q^{41} +(4.50999 - 4.14094i) q^{42} +(-5.47096 + 9.47599i) q^{43} -4.81961 q^{44} +(6.02793 + 4.20287i) q^{45} +0.761648 q^{46} +(-4.81579 + 8.34120i) q^{47} +(-1.65241 - 0.519186i) q^{48} +(-2.74790 - 4.75951i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.269376 - 1.20935i) q^{51} +(1.08432 - 1.87809i) q^{52} -6.33500 q^{53} +(-5.14964 + 0.693678i) q^{54} -11.8056 q^{55} +(-1.76747 + 3.06135i) q^{56} +(0.376574 + 1.69062i) q^{57} +(-0.804235 - 1.39298i) q^{58} +(3.02721 + 5.24329i) q^{59} +(-4.04755 - 1.27174i) q^{60} +(-7.20512 + 12.4796i) q^{61} +5.26910 q^{62} +(-0.903151 + 10.5663i) q^{63} +1.00000 q^{64} +(2.65602 - 4.60037i) q^{65} +(6.14901 - 5.64584i) q^{66} +(-5.58914 - 9.68068i) q^{67} +(0.357666 + 0.619496i) q^{68} +(-0.971734 + 0.892219i) q^{69} +(-4.32940 + 7.49874i) q^{70} +4.21495 q^{71} +(2.71638 - 1.27329i) q^{72} +11.7117 q^{73} +(4.80793 - 8.32757i) q^{74} +(-1.65241 - 0.519186i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(-8.51851 - 14.7545i) q^{77} +(0.816652 + 3.66633i) q^{78} +(-4.93688 + 8.55093i) q^{79} +2.44949 q^{80} +(5.75748 - 6.91747i) q^{81} -7.59063 q^{82} +(3.51347 - 6.08550i) q^{83} +(-1.33117 - 5.97624i) q^{84} +(0.876100 + 1.51745i) q^{85} +(5.47096 + 9.47599i) q^{86} +(2.65785 + 0.835096i) q^{87} +(-2.40980 + 4.17390i) q^{88} +12.6524 q^{89} +(6.65375 - 3.11890i) q^{90} +7.66599 q^{91} +(0.380824 - 0.659606i) q^{92} +(-6.72248 + 6.17239i) q^{93} +(4.81579 + 8.34120i) q^{94} +(-1.22474 - 2.12132i) q^{95} +(-1.27583 + 1.17143i) q^{96} +(-2.32662 + 4.02983i) q^{97} -5.49581 q^{98} +(-1.23137 + 14.4063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 - 8 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} - 8 q^{9} + 4 q^{11} - 8 q^{13} + 4 q^{14} + 12 q^{15} - 6 q^{16} - 8 q^{17} - 4 q^{18} + 12 q^{19} + 14 q^{21} - 4 q^{22} + 4 q^{23} - 6 q^{25} - 16 q^{26} - 18 q^{27} + 8 q^{28} - 8 q^{31} + 6 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 44 q^{37} + 6 q^{38} - 14 q^{39} + 4 q^{41} + 10 q^{42} - 20 q^{43} - 8 q^{44} - 24 q^{45} + 8 q^{46} + 10 q^{47} - 18 q^{49} + 6 q^{50} + 28 q^{51} - 8 q^{52} + 8 q^{53} + 4 q^{56} + 16 q^{59} - 12 q^{60} - 12 q^{61} - 16 q^{62} - 12 q^{63} + 12 q^{64} - 24 q^{65} - 28 q^{66} - 20 q^{67} + 4 q^{68} + 40 q^{69} + 8 q^{71} + 8 q^{72} + 8 q^{73} + 22 q^{74} - 6 q^{76} - 20 q^{77} - 10 q^{78} - 16 q^{79} - 8 q^{81} + 8 q^{82} + 8 q^{83} - 4 q^{84} + 20 q^{86} + 42 q^{87} - 4 q^{88} - 8 q^{89} + 24 q^{90} + 68 q^{91} + 4 q^{92} + 16 q^{93} - 10 q^{94} - 24 q^{97} - 36 q^{98} - 4 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 - 8 * q^9 + 4 * q^11 - 8 * q^13 + 4 * q^14 + 12 * q^15 - 6 * q^16 - 8 * q^17 - 4 * q^18 + 12 * q^19 + 14 * q^21 - 4 * q^22 + 4 * q^23 - 6 * q^25 - 16 * q^26 - 18 * q^27 + 8 * q^28 - 8 * q^31 + 6 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 44 * q^37 + 6 * q^38 - 14 * q^39 + 4 * q^41 + 10 * q^42 - 20 * q^43 - 8 * q^44 - 24 * q^45 + 8 * q^46 + 10 * q^47 - 18 * q^49 + 6 * q^50 + 28 * q^51 - 8 * q^52 + 8 * q^53 + 4 * q^56 + 16 * q^59 - 12 * q^60 - 12 * q^61 - 16 * q^62 - 12 * q^63 + 12 * q^64 - 24 * q^65 - 28 * q^66 - 20 * q^67 + 4 * q^68 + 40 * q^69 + 8 * q^71 + 8 * q^72 + 8 * q^73 + 22 * q^74 - 6 * q^76 - 20 * q^77 - 10 * q^78 - 16 * q^79 - 8 * q^81 + 8 * q^82 + 8 * q^83 - 4 * q^84 + 20 * q^86 + 42 * q^87 - 4 * q^88 - 8 * q^89 + 24 * q^90 + 68 * q^91 + 4 * q^92 + 16 * q^93 - 10 * q^94 - 24 * q^97 - 36 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.376574	+	1.69062i	0.217415	+	0.976079i
$3$	0.376574	+	1.69062i	0.217415	+	0.976079i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	−0.998430	−	0.0560116i	$-0.982162\pi$
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	0.450708	−	0.892672i	$-0.351172\pi$
$6$	1.65241	+	0.519186i	0.674592	+	0.211957i
$7$	1.76747	−	3.06135i	0.668041	−	1.15708i	−0.310410	−	0.950603i	$-0.600466\pi$
$7$	1.76747	−	3.06135i	0.668041	−	1.15708i	0.978451	−	0.206478i	$-0.0662003\pi$
$8$	−1.00000			−0.353553
$9$	−2.71638	+	1.27329i	−0.905461	+	0.424429i
$10$	−2.44949			−0.774597
$11$	2.40980	−	4.17390i	0.726583	−	1.25848i	−0.231736	−	0.972779i	$-0.574440\pi$
$11$	2.40980	−	4.17390i	0.726583	−	1.25848i	0.958319	−	0.285700i	$-0.0922262\pi$
$12$	1.27583	−	1.17143i	0.368301	−	0.338163i
$13$	1.08432	+	1.87809i	0.300735	+	0.520889i	0.976303	−	0.216409i	$-0.0694346\pi$
$13$	1.08432	+	1.87809i	0.300735	+	0.520889i	−0.675567	+	0.737298i	$0.736101\pi$
$14$	−1.76747	−	3.06135i	−0.472376	−	0.818180i
$15$	3.12514	−	2.86941i	0.806907	−	0.740879i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.715332			−0.173494			−0.0867468	−	0.996230i	$-0.527647\pi$
$17$	−0.715332			−0.173494			−0.0867468	+	0.996230i	$0.527647\pi$
$18$	−0.255493	+	2.98910i	−0.0602202	+	0.704538i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−1.22474	+	2.12132i	−0.273861	+	0.474342i
$21$	5.84116	+	1.83529i	1.27464	+	0.400494i
$22$	−2.40980	−	4.17390i	−0.513772	−	0.889879i
$23$	0.380824	+	0.659606i	0.0794073	+	0.137537i	0.902994	−	0.429652i	$-0.141364\pi$
$23$	0.380824	+	0.659606i	0.0794073	+	0.137537i	−0.823587	+	0.567190i	$0.808031\pi$
$24$	−0.376574	−	1.69062i	−0.0768679	−	0.345096i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.16863			0.425304
$27$	−3.17556	−	4.11288i	−0.611138	−	0.791524i
$28$	−3.53494			−0.668041
$29$	0.804235	−	1.39298i	0.149343	−	0.258669i	−0.781642	−	0.623727i	$-0.785618\pi$
$29$	0.804235	−	1.39298i	0.149343	−	0.258669i	0.930985	+	0.365058i	$0.118951\pi$
$30$	−0.922415	−	4.14115i	−0.168409	−	0.756068i
$31$	2.63455	+	4.56317i	0.473179	+	0.819570i	0.999529	−	0.0306982i	$-0.00977306\pi$
$31$	2.63455	+	4.56317i	0.473179	+	0.819570i	−0.526350	+	0.850268i	$0.676440\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	7.96395	+	2.50228i	1.38635	+	0.435590i
$34$	−0.357666	+	0.619496i	−0.0613392	+	0.106243i
$35$	−8.65880			−1.46360
$36$	2.46089	+	1.71581i	0.410148	+	0.285969i
$37$	9.61585			1.58084			0.790418	−	0.612567i	$-0.209863\pi$
$37$	9.61585			1.58084			0.790418	+	0.612567i	$0.209863\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$	−2.76681	+	2.54041i	−0.443044	+	0.406791i
$40$	1.22474	+	2.12132i	0.193649	+	0.335410i
$41$	−3.79532	−	6.57368i	−0.592729	−	1.02664i	−0.993863	−	0.110617i	$-0.964717\pi$
$41$	−3.79532	−	6.57368i	−0.592729	−	1.02664i	0.401134	−	0.916019i	$-0.368616\pi$
$42$	4.50999	−	4.14094i	0.695906	−	0.638961i
$43$	−5.47096	+	9.47599i	−0.834314	+	1.44507i	0.0602737	+	0.998182i	$0.480803\pi$
$43$	−5.47096	+	9.47599i	−0.834314	+	1.44507i	−0.894588	+	0.446892i	$0.852531\pi$
$44$	−4.81961			−0.726583
$45$	6.02793	+	4.20287i	0.898590	+	0.626527i
$46$	0.761648			0.112299
$47$	−4.81579	+	8.34120i	−0.702456	+	1.21669i	0.265146	+	0.964208i	$0.414580\pi$
$47$	−4.81579	+	8.34120i	−0.702456	+	1.21669i	−0.967602	+	0.252481i	$0.918754\pi$
$48$	−1.65241	−	0.519186i	−0.238504	−	0.0749381i
$49$	−2.74790	−	4.75951i	−0.392558	−	0.679930i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.269376	−	1.20935i	−0.0377202	−	0.169343i
$52$	1.08432	−	1.87809i	0.150368	−	0.260444i
$53$	−6.33500			−0.870179			−0.435089	−	0.900387i	$-0.643283\pi$
$53$	−6.33500			−0.870179			−0.435089	+	0.900387i	$0.643283\pi$
$54$	−5.14964	+	0.693678i	−0.700777	+	0.0943976i
$55$	−11.8056			−1.59186
$56$	−1.76747	+	3.06135i	−0.236188	+	0.409090i
$57$	0.376574	+	1.69062i	0.0498785	+	0.223928i
$58$	−0.804235	−	1.39298i	−0.105601	−	0.182907i
$59$	3.02721	+	5.24329i	0.394109	+	0.682618i	0.992987	−	0.118223i	$-0.0377197\pi$
$59$	3.02721	+	5.24329i	0.394109	+	0.682618i	−0.598878	+	0.800841i	$0.704386\pi$
$60$	−4.04755	−	1.27174i	−0.522537	−	0.164181i
$61$	−7.20512	+	12.4796i	−0.922521	+	1.59785i	−0.127021	+	0.991900i	$0.540542\pi$
$61$	−7.20512	+	12.4796i	−0.922521	+	1.59785i	−0.795500	+	0.605953i	$0.792792\pi$
$62$	5.26910			0.669176
$63$	−0.903151	+	10.5663i	−0.113786	+	1.33123i
$64$	1.00000			0.125000
$65$	2.65602	−	4.60037i	0.329439	−	0.570605i
$66$	6.14901	−	5.64584i	0.756891	−	0.694955i
$67$	−5.58914	−	9.68068i	−0.682822	−	1.18268i	−0.974116	−	0.226049i	$-0.927419\pi$
$67$	−5.58914	−	9.68068i	−0.682822	−	1.18268i	0.291293	−	0.956634i	$-0.405914\pi$
$68$	0.357666	+	0.619496i	0.0433734	+	0.0751249i
$69$	−0.971734	+	0.892219i	−0.116983	+	0.107411i
$70$	−4.32940	+	7.49874i	−0.517462	+	0.896271i
$71$	4.21495			0.500222			0.250111	−	0.968217i	$-0.419533\pi$
$71$	4.21495			0.500222			0.250111	+	0.968217i	$0.419533\pi$
$72$	2.71638	−	1.27329i	0.320129	−	0.150058i
$73$	11.7117			1.37075			0.685374	−	0.728191i	$-0.259639\pi$
$73$	11.7117			1.37075			0.685374	+	0.728191i	$0.259639\pi$
$74$	4.80793	−	8.32757i	0.558910	−	0.968061i
$75$	−1.65241	−	0.519186i	−0.190803	−	0.0599505i
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$	−8.51851	−	14.7545i	−0.970775	−	1.68143i
$78$	0.816652	+	3.66633i	0.0924676	+	0.415130i
$79$	−4.93688	+	8.55093i	−0.555442	+	0.962054i	0.442427	+	0.896805i	$0.354118\pi$
$79$	−4.93688	+	8.55093i	−0.555442	+	0.962054i	−0.997869	+	0.0652496i	$0.979216\pi$
$80$	2.44949			0.273861
$81$	5.75748	−	6.91747i	0.639720	−	0.768608i
$82$	−7.59063			−0.838245
$83$	3.51347	−	6.08550i	0.385653	−	0.667971i	−0.606206	−	0.795307i	$-0.707309\pi$
$83$	3.51347	−	6.08550i	0.385653	−	0.667971i	0.991860	+	0.127337i	$0.0406428\pi$
$84$	−1.33117	−	5.97624i	−0.145242	−	0.652061i
$85$	0.876100	+	1.51745i	0.0950263	+	0.164590i
$86$	5.47096	+	9.47599i	0.589949	+	1.02182i
$87$	2.65785	+	0.835096i	0.284951	+	0.0895317i
$88$	−2.40980	+	4.17390i	−0.256886	+	0.444940i
$89$	12.6524			1.34115			0.670576	−	0.741841i	$-0.266047\pi$
$89$	12.6524			1.34115			0.670576	+	0.741841i	$0.266047\pi$
$90$	6.65375	−	3.11890i	0.701367	−	0.328761i
$91$	7.66599			0.803614
$92$	0.380824	−	0.659606i	0.0397036	−	0.0687687i
$93$	−6.72248	+	6.17239i	−0.697089	+	0.640047i
$94$	4.81579	+	8.34120i	0.496711	+	0.860329i
$95$	−1.22474	−	2.12132i	−0.125656	−	0.217643i
$96$	−1.27583	+	1.17143i	−0.130214	+	0.119559i
$97$	−2.32662	+	4.02983i	−0.236233	+	0.409167i	−0.959630	−	0.281265i	$-0.909246\pi$
$97$	−2.32662	+	4.02983i	−0.236233	+	0.409167i	0.723398	+	0.690432i	$0.242579\pi$
$98$	−5.49581			−0.555160
$99$	−1.23137	+	14.4063i	−0.123758	+	1.44789i
$100$	1.00000			0.100000
$101$	2.63548	−	4.56478i	0.262240	−	0.454213i	−0.704597	−	0.709608i	$-0.748872\pi$
$101$	2.63548	−	4.56478i	0.262240	−	0.454213i	0.966837	+	0.255395i	$0.0822055\pi$
$102$	−1.18202	−	0.371391i	−0.117037	−	0.0367732i
$103$	1.00560	+	1.74175i	0.0990844	+	0.171619i	0.911306	−	0.411730i	$-0.135075\pi$
$103$	1.00560	+	1.74175i	0.0990844	+	0.171619i	−0.812222	+	0.583349i	$0.801742\pi$
$104$	−1.08432	−	1.87809i	−0.106326	−	0.184162i
$105$	−3.26068	−	14.6387i	−0.318210	−	1.42859i
$106$	−3.16750	+	5.48627i	−0.307655	+	0.532874i
$107$	−1.89160			−0.182867			−0.0914337	−	0.995811i	$-0.529145\pi$
$107$	−1.89160			−0.182867			−0.0914337	+	0.995811i	$0.529145\pi$
$108$	−1.97408	+	4.80656i	−0.189956	+	0.462511i
$109$	14.1121			1.35169			0.675847	−	0.737042i	$-0.263778\pi$
$109$	14.1121			1.35169			0.675847	+	0.737042i	$0.263778\pi$
$110$	−5.90279	+	10.2239i	−0.562809	+	0.974814i
$111$	3.62108	+	16.2567i	0.343698	+	1.54302i
$112$	1.76747	+	3.06135i	0.167010	+	0.289270i
$113$	5.48979	+	9.50859i	0.516436	+	0.894493i	0.999818	+	0.0190836i	$0.00607486\pi$
$113$	5.48979	+	9.50859i	0.516436	+	0.894493i	−0.483382	+	0.875409i	$0.660592\pi$
$114$	1.65241	+	0.519186i	0.154762	+	0.0486263i
$115$	0.932824	−	1.61570i	0.0869863	−	0.150665i
$116$	−1.60847			−0.149343
$117$	−5.33677	−	3.72097i	−0.493385	−	0.344004i
$118$	6.05442			0.557355
$119$	−1.26433	+	2.18988i	−0.115901	+	0.200746i
$120$	−3.12514	+	2.86941i	−0.285285	+	0.261940i
$121$	−6.11431	−	10.5903i	−0.555847	−	0.962754i
$122$	7.20512	+	12.4796i	0.652321	+	1.12985i
$123$	9.68437	−	8.89191i	0.873210	−	0.801757i
$124$	2.63455	−	4.56317i	0.236589	−	0.409785i
$125$	−9.79796			−0.876356
$126$	8.69910	+	6.06530i	0.774978	+	0.540340i
$127$	9.81198			0.870672			0.435336	−	0.900268i	$-0.356630\pi$
$127$	9.81198			0.870672			0.435336	+	0.900268i	$0.356630\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−18.0805	−	5.68090i	−1.59190	−	0.500175i
$130$	−2.65602	−	4.60037i	−0.232949	−	0.403479i
$131$	−1.94671	−	3.37180i	−0.170085	−	0.294595i	0.768365	−	0.640012i	$-0.221071\pi$
$131$	−1.94671	−	3.37180i	−0.170085	−	0.294595i	−0.938449	+	0.345417i	$0.887737\pi$
$132$	−1.81494	−	8.14812i	−0.157970	−	0.709203i
$133$	1.76747	−	3.06135i	0.153259	−	0.265453i
$134$	−11.1783			−0.965657
$135$	−4.83548	+	11.7736i	−0.416172	+	1.01331i
$136$	0.715332			0.0613392
$137$	5.30586	−	9.19002i	0.453310	−	0.785157i	−0.545279	−	0.838255i	$-0.683576\pi$
$137$	5.30586	−	9.19002i	0.453310	−	0.785157i	0.998589	+	0.0530980i	$0.0169096\pi$
$138$	0.286817	+	1.28766i	0.0244155	+	0.109613i
$139$	0.593871	+	1.02861i	0.0503715	+	0.0872460i	0.890112	−	0.455742i	$-0.150626\pi$
$139$	0.593871	+	1.02861i	0.0503715	+	0.0872460i	−0.839740	+	0.542988i	$0.817293\pi$
$140$	4.32940	+	7.49874i	0.365901	+	0.633759i
$141$	−15.9153	−	5.00059i	−1.34031	−	0.421126i
$142$	2.10747	−	3.65025i	0.176855	−	0.306322i
$143$	10.4520			0.874037
$144$	0.255493	−	2.98910i	0.0212911	−	0.249092i
$145$	−3.93993			−0.327194
$146$	5.85584	−	10.1426i	0.484633	−	0.839409i
$147$	7.01172	−	6.43796i	0.578317	−	0.530994i
$148$	−4.80793	−	8.32757i	−0.395209	−	0.684522i
$149$	−1.75883	−	3.04638i	−0.144089	−	0.249569i	0.784944	−	0.619567i	$-0.212692\pi$
$149$	−1.75883	−	3.04638i	−0.144089	−	0.249569i	−0.929033	+	0.369998i	$0.879358\pi$
$150$	−1.27583	+	1.17143i	−0.104171	+	0.0956470i
$151$	11.9484	−	20.6952i	0.972345	−	1.68415i	0.283914	−	0.958850i	$-0.408367\pi$
$151$	11.9484	−	20.6952i	0.972345	−	1.68415i	0.688431	−	0.725302i	$-0.258300\pi$
$152$	−1.00000			−0.0811107
$153$	1.94312	−	0.910824i	0.157092	−	0.0736357i
$154$	−17.0370			−1.37288
$155$	6.45330	−	11.1774i	0.518342	−	0.897794i
$156$	3.58346	+	1.12592i	0.286907	+	0.0901461i
$157$	2.18403	+	3.78285i	0.174304	+	0.301904i	0.939920	−	0.341394i	$-0.110899\pi$
$157$	2.18403	+	3.78285i	0.174304	+	0.301904i	−0.765616	+	0.643298i	$0.777566\pi$
$158$	4.93688	+	8.55093i	0.392757	+	0.680275i
$159$	−2.38560	−	10.7101i	−0.189190	−	0.849363i
$160$	1.22474	−	2.12132i	0.0968246	−	0.167705i
$161$	2.69238			0.212189
$162$	−3.11197	−	8.44486i	−0.244499	−	0.663491i
$163$	−15.8931			−1.24484			−0.622420	−	0.782683i	$-0.713851\pi$
$163$	−15.8931			−1.24484			−0.622420	+	0.782683i	$0.713851\pi$
$164$	−3.79532	+	6.57368i	−0.296364	+	0.513318i
$165$	−4.44568	−	19.9587i	−0.346096	−	1.55379i
$166$	−3.51347	−	6.08550i	−0.272698	−	0.472327i
$167$	10.8469	+	18.7874i	0.839360	+	1.45381i	0.890431	+	0.455119i	$0.150403\pi$
$167$	10.8469	+	18.7874i	0.839360	+	1.45381i	−0.0510704	+	0.998695i	$0.516263\pi$
$168$	−5.84116	−	1.83529i	−0.450655	−	0.141596i
$169$	4.14852	−	7.18544i	0.319117	−	0.552726i
$170$	1.75220			0.134388
$171$	−2.71638	+	1.27329i	−0.207727	+	0.0973707i
$172$	10.9419			0.834314
$173$	−8.37036	+	14.4979i	−0.636387	+	1.10225i	0.349833	+	0.936812i	$0.386238\pi$
$173$	−8.37036	+	14.4979i	−0.636387	+	1.10225i	−0.986220	+	0.165442i	$0.947095\pi$
$174$	2.05214	−	1.88421i	0.155572	−	0.142842i
$175$	1.76747	+	3.06135i	0.133608	+	0.231416i
$176$	2.40980	+	4.17390i	0.181646	+	0.314620i
$177$	−7.72443	+	7.09235i	−0.580603	+	0.533094i
$178$	6.32620	−	10.9573i	0.474169	−	0.821285i
$179$	−22.6162			−1.69041			−0.845207	−	0.534440i	$-0.820523\pi$
$179$	−22.6162			−1.69041			−0.845207	+	0.534440i	$0.820523\pi$
$180$	0.625827	−	7.32177i	0.0466464	−	0.545733i
$181$	−3.73702			−0.277770			−0.138885	−	0.990308i	$-0.544352\pi$
$181$	−3.73702			−0.277770			−0.138885	+	0.990308i	$0.544352\pi$
$182$	3.83299	−	6.63894i	0.284120	−	0.492111i
$183$	−23.8116	−	7.48160i	−1.76020	−	0.553056i
$184$	−0.380824	−	0.659606i	−0.0280747	−	0.0486268i
$185$	−11.7770	−	20.3983i	−0.865860	−	1.49971i
$186$	1.98421	+	8.90804i	0.145489	+	0.653169i
$187$	−1.72381	+	2.98573i	−0.126058	+	0.218338i
$188$	9.63159			0.702456
$189$	−18.2037	+	2.45211i	−1.32412	+	0.178365i
$190$	−2.44949			−0.177705
$191$	−6.82543	+	11.8220i	−0.493871	+	0.855409i	−0.999975	−	0.00706294i	$-0.997752\pi$
$191$	−6.82543	+	11.8220i	−0.493871	+	0.855409i	0.506104	+	0.862472i	$0.331085\pi$
$192$	0.376574	+	1.69062i	0.0271769	+	0.122010i
$193$	−4.76570	−	8.25444i	−0.343043	−	0.594168i	0.641953	−	0.766744i	$-0.278124\pi$
$193$	−4.76570	−	8.25444i	−0.343043	−	0.594168i	−0.984996	+	0.172576i	$0.944791\pi$
$194$	2.32662	+	4.02983i	0.167042	+	0.289325i
$195$	8.77765	+	2.75794i	0.628581	+	0.197500i
$196$	−2.74790	+	4.75951i	−0.196279	+	0.339965i
$197$	4.94021			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$197$	4.94021			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$198$	11.8605	+	8.26955i	0.842891	+	0.587691i
$199$	−8.30823			−0.588955			−0.294478	−	0.955658i	$-0.595146\pi$
$199$	−8.30823			−0.588955			−0.294478	+	0.955658i	$0.595146\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	14.2616	−	13.0946i	1.00594	−	0.923622i
$202$	−2.63548	−	4.56478i	−0.185432	−	0.321177i
$203$	−2.84292	−	4.92409i	−0.199534	−	0.345603i
$204$	−0.912644	+	0.837963i	−0.0638978	+	0.0586692i
$205$	−9.29659	+	16.1022i	−0.649302	+	1.12462i
$206$	2.01119			0.140127
$207$	−1.87433	−	1.30685i	−0.130275	−	0.0908320i
$208$	−2.16863			−0.150368
$209$	2.40980	−	4.17390i	0.166690	−	0.288715i
$210$	−14.3079	−	4.49553i	−0.987336	−	0.310221i
$211$	−7.81375	−	13.5338i	−0.537920	−	0.931705i	−0.999016	−	0.0443549i	$-0.985877\pi$
$211$	−7.81375	−	13.5338i	−0.537920	−	0.931705i	0.461095	−	0.887351i	$-0.347457\pi$
$212$	3.16750	+	5.48627i	0.217545	+	0.376798i
$213$	1.58724	+	7.12587i	0.108756	+	0.488257i
$214$	−0.945798	+	1.63817i	−0.0646534	+	0.111983i
$215$	26.8021			1.82789
$216$	3.17556	+	4.11288i	0.216070	+	0.279846i
$217$	18.6259			1.26441
$218$	7.05605	−	12.2214i	0.477896	−	0.827740i
$219$	4.41032	+	19.8000i	0.298022	+	1.33796i
$220$	5.90279	+	10.2239i	0.397966	+	0.689297i
$221$	−0.775647	−	1.34346i	−0.0521756	−	0.0903709i
$222$	15.8893	+	4.99242i	1.06642	+	0.335069i
$223$	1.73262	−	3.00098i	0.116024	−	0.200960i	−0.802164	−	0.597103i	$-0.796318\pi$
$223$	1.73262	−	3.00098i	0.116024	−	0.200960i	0.918189	+	0.396143i	$0.129652\pi$
$224$	3.53494			0.236188
$225$	0.255493	−	2.98910i	0.0170328	−	0.199273i
$226$	10.9796			0.730351
$227$	−7.36581	+	12.7580i	−0.488886	+	0.846775i	−0.999918	−	0.0127864i	$-0.995930\pi$
$227$	−7.36581	+	12.7580i	−0.488886	+	0.846775i	0.511032	+	0.859561i	$0.329263\pi$
$228$	1.27583	−	1.17143i	0.0844940	−	0.0775800i
$229$	−5.51065	−	9.54472i	−0.364154	−	0.630733i	0.624486	−	0.781036i	$-0.285308\pi$
$229$	−5.51065	−	9.54472i	−0.364154	−	0.630733i	−0.988640	+	0.150303i	$0.951975\pi$
$230$	−0.932824	−	1.61570i	−0.0615086	−	0.106536i
$231$	21.7364	−	19.9577i	1.43015	−	1.31312i
$232$	−0.804235	+	1.39298i	−0.0528006	+	0.0914534i
$233$	29.9139			1.95972			0.979862	−	0.199677i	$-0.0639894\pi$
$233$	29.9139			1.95972			0.979862	+	0.199677i	$0.0639894\pi$
$234$	−5.89084	+	2.76129i	−0.385096	+	0.180511i
$235$	23.5925			1.53900
$236$	3.02721	−	5.24329i	0.197055	−	0.341309i
$237$	−16.3155	−	5.12632i	−1.05980	−	0.332990i
$238$	1.26433	+	2.18988i	0.0819543	+	0.141949i
$239$	1.14603	+	1.98497i	0.0741302	+	0.128397i	0.900708	−	0.434426i	$-0.143049\pi$
$239$	1.14603	+	1.98497i	0.0741302	+	0.128397i	−0.826577	+	0.562823i	$0.809715\pi$
$240$	0.922415	+	4.14115i	0.0595416	+	0.267310i
$241$	6.39565	−	11.0776i	0.411980	−	0.713570i	−0.583126	−	0.812381i	$-0.698171\pi$
$241$	6.39565	−	11.0776i	0.411980	−	0.713570i	0.995106	+	0.0988115i	$0.0315041\pi$
$242$	−12.2286			−0.786086
$243$	13.8629	+	7.12876i	0.889307	+	0.457310i
$244$	14.4102			0.922521
$245$	−6.73096	+	11.6584i	−0.430025	+	0.744825i
$246$	−2.85844	−	12.8329i	−0.182247	−	0.818194i
$247$	1.08432	+	1.87809i	0.0689934	+	0.119500i
$248$	−2.63455	−	4.56317i	−0.167294	−	0.289762i
$249$	11.6113	+	3.64829i	0.735839	+	0.231201i
$250$	−4.89898	+	8.48528i	−0.309839	+	0.536656i
$251$	−23.5887			−1.48891			−0.744453	−	0.667675i	$-0.767289\pi$
$251$	−23.5887			−1.48891			−0.744453	+	0.667675i	$0.767289\pi$
$252$	9.60225	−	4.50099i	0.604885	−	0.283536i
$253$	3.67084			0.230784
$254$	4.90599	−	8.49742i	0.307829	−	0.533176i
$255$	−2.23551	+	2.05258i	−0.139993	+	0.128538i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.23360	+	7.33282i	0.264085	+	0.457408i	0.967323	−	0.253545i	$-0.0815968\pi$
$257$	4.23360	+	7.33282i	0.264085	+	0.457408i	−0.703239	+	0.710954i	$0.748263\pi$
$258$	−13.9601	+	12.8177i	−0.869115	+	0.797997i
$259$	16.9957	−	29.4375i	1.05606	−	1.82916i
$260$	−5.31204			−0.329439
$261$	−0.410953	+	4.80788i	−0.0254373	+	0.297600i
$262$	−3.89341			−0.240536
$263$	−14.4087	+	24.9566i	−0.888478	+	1.53889i	−0.0468036	+	0.998904i	$0.514903\pi$
$263$	−14.4087	+	24.9566i	−0.888478	+	1.53889i	−0.841675	+	0.539985i	$0.818430\pi$
$264$	−7.96395	−	2.50228i	−0.490147	−	0.154004i
$265$	7.75876	+	13.4386i	0.476617	+	0.825524i
$266$	−1.76747	−	3.06135i	−0.108371	−	0.187703i
$267$	4.76457	+	21.3904i	0.291587	+	1.30907i
$268$	−5.58914	+	9.68068i	−0.341411	+	0.591342i
$269$	12.5148			0.763043			0.381521	−	0.924360i	$-0.375400\pi$
$269$	12.5148			0.763043			0.381521	+	0.924360i	$0.375400\pi$
$270$	7.77851	+	10.0745i	0.473385	+	0.613112i
$271$	−11.5323			−0.700536			−0.350268	−	0.936649i	$-0.613910\pi$
$271$	−11.5323			−0.700536			−0.350268	+	0.936649i	$0.613910\pi$
$272$	0.357666	−	0.619496i	0.0216867	−	0.0375625i
$273$	2.88681	+	12.9603i	0.174718	+	0.784391i
$274$	−5.30586	−	9.19002i	−0.320539	−	0.555190i
$275$	2.40980	+	4.17390i	0.145317	+	0.251696i
$276$	1.25855	+	0.395437i	0.0757559	+	0.0238025i
$277$	9.61011	−	16.6452i	0.577416	−	1.00011i	−0.418359	−	0.908282i	$-0.637395\pi$
$277$	9.61011	−	16.6452i	0.577416	−	1.00011i	0.995775	−	0.0918315i	$-0.0292721\pi$
$278$	1.18774			0.0712360
$279$	−12.9667	−	9.04079i	−0.776295	−	0.541258i
$280$	8.65880			0.517462
$281$	−14.0494	+	24.3343i	−0.838117	+	1.45166i	0.0533502	+	0.998576i	$0.483010\pi$
$281$	−14.0494	+	24.3343i	−0.838117	+	1.45166i	−0.891467	+	0.453085i	$0.850323\pi$
$282$	−12.2883	+	11.2828i	−0.731757	+	0.671878i
$283$	−2.31453	−	4.00888i	−0.137584	−	0.238303i	0.788997	−	0.614396i	$-0.210600\pi$
$283$	−2.31453	−	4.00888i	−0.137584	−	0.238303i	−0.926582	+	0.376094i	$0.877267\pi$
$284$	−2.10747	−	3.65025i	−0.125056	−	0.216603i
$285$	3.12514	−	2.86941i	0.185117	−	0.169969i
$286$	5.22598	−	9.05166i	0.309019	−	0.535236i
$287$	−26.8324			−1.58387
$288$	−2.46089	−	1.71581i	−0.145009	−	0.101105i
$289$	−16.4883			−0.969900
$290$	−1.96997	+	3.41208i	−0.115680	+	0.200364i
$291$	−7.68905	−	2.41590i	−0.450740	−	0.141623i
$292$	−5.85584	−	10.1426i	−0.342687	−	0.593552i
$293$	−13.6871	−	23.7067i	−0.799607	−	1.38496i	−0.919872	−	0.392218i	$-0.871708\pi$
$293$	−13.6871	−	23.7067i	−0.799607	−	1.38496i	0.120265	−	0.992742i	$-0.461625\pi$
$294$	−2.06958	−	9.29131i	−0.120700	−	0.541880i
$295$	7.41513	−	12.8434i	0.431725	−	0.747770i
$296$	−9.61585			−0.558910
$297$	−24.8193	+	3.34326i	−1.44016	+	0.193995i
$298$	−3.51766			−0.203772
$299$	−0.825867	+	1.43044i	−0.0477611	+	0.0827247i
$300$	0.376574	+	1.69062i	0.0217415	+	0.0976079i
$301$	19.3395	+	33.4970i	1.11471	+	1.93074i
$302$	−11.9484	−	20.6952i	−0.687552	−	1.19087i
$303$	8.70976	+	2.73661i	0.500363	+	0.157214i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	35.2977			2.02114
$306$	0.182762	−	2.13820i	0.0104478	−	0.122233i
$307$	15.0895			0.861201			0.430601	−	0.902543i	$-0.358302\pi$
$307$	15.0895			0.861201			0.430601	+	0.902543i	$0.358302\pi$
$308$	−8.51851	+	14.7545i	−0.485387	+	0.840716i
$309$	−2.56595	+	2.35598i	−0.145972	+	0.134027i
$310$	−6.45330	−	11.1774i	−0.366523	−	0.634836i
$311$	8.94548	+	15.4940i	0.507252	+	0.878586i	0.999965	+	0.00839381i	$0.00267186\pi$
$311$	8.94548	+	15.4940i	0.507252	+	0.878586i	−0.492713	+	0.870192i	$0.663995\pi$
$312$	2.76681	−	2.54041i	0.156640	−	0.143822i
$313$	−6.93392	+	12.0099i	−0.391928	+	0.678840i	−0.992704	−	0.120578i	$-0.961525\pi$
$313$	−6.93392	+	12.0099i	−0.391928	+	0.678840i	0.600776	+	0.799418i	$0.294859\pi$
$314$	4.36805			0.246504
$315$	23.5206	−	11.0251i	1.32524	−	0.621196i
$316$	9.87376			0.555442
$317$	−2.49313	+	4.31823i	−0.140028	+	0.242536i	−0.927507	−	0.373806i	$-0.878053\pi$
$317$	−2.49313	+	4.31823i	−0.140028	+	0.242536i	0.787479	+	0.616342i	$0.211386\pi$
$318$	−10.4680	−	3.28904i	−0.587016	−	0.184440i
$319$	−3.87610	−	6.71360i	−0.217020	−	0.375890i
$320$	−1.22474	−	2.12132i	−0.0684653	−	0.118585i
$321$	−0.712327	−	3.19797i	−0.0397582	−	0.178493i
$322$	1.34619	−	2.33167i	0.0750202	−	0.129939i
$323$	−0.715332			−0.0398022
$324$	−8.86945	−	1.52739i	−0.492747	−	0.0848548i
$325$	−2.16863			−0.120294
$326$	−7.94653	+	13.7638i	−0.440118	+	0.762306i
$327$	5.31426	+	23.8582i	0.293879	+	1.31936i
$328$	3.79532	+	6.57368i	0.209561	+	0.362971i
$329$	17.0235	+	29.4856i	0.938538	+	1.62560i
$330$	−19.5076	−	6.12930i	−1.07386	−	0.337407i
$331$	−1.65709	+	2.87017i	−0.0910821	+	0.157759i	−0.907967	−	0.419042i	$-0.862366\pi$
$331$	−1.65709	+	2.87017i	−0.0910821	+	0.157759i	0.816885	+	0.576801i	$0.195699\pi$
$332$	−7.02693			−0.385653
$333$	−26.1203	+	12.2437i	−1.43139	+	0.670953i
$334$	21.6938			1.18703
$335$	−13.6905	+	23.7127i	−0.747995	+	1.29556i
$336$	−4.50999	+	4.14094i	−0.246040	+	0.225907i
$337$	−0.820028	−	1.42033i	−0.0446698	−	0.0773703i	0.842826	−	0.538186i	$-0.180890\pi$
$337$	−0.820028	−	1.42033i	−0.0446698	−	0.0773703i	−0.887496	+	0.460816i	$0.847557\pi$
$338$	−4.14852	−	7.18544i	−0.225649	−	0.390836i
$339$	−14.0081	+	12.8618i	−0.760815	+	0.698559i
$340$	0.876100	−	1.51745i	0.0475132	−	0.0822952i
$341$	25.3950			1.37522
$342$	−0.255493	+	2.98910i	−0.0138155	+	0.161632i
$343$	5.31724			0.287104
$344$	5.47096	−	9.47599i	0.294975	−	0.510911i
$345$	3.08281	+	0.968619i	0.165973	+	0.0521487i
$346$	8.37036	+	14.4979i	0.449993	+	0.779411i
$347$	−7.59259	−	13.1508i	−0.407592	−	0.705970i	0.587027	−	0.809567i	$-0.300298\pi$
$347$	−7.59259	−	13.1508i	−0.407592	−	0.705970i	−0.994619	+	0.103597i	$0.966965\pi$
$348$	−0.605709	−	2.71931i	−0.0324694	−	0.145770i
$349$	4.84775	−	8.39655i	0.259494	−	0.449457i	−0.706612	−	0.707601i	$-0.749777\pi$
$349$	4.84775	−	8.39655i	0.259494	−	0.449457i	0.966107	+	0.258144i	$0.0831108\pi$
$350$	3.53494			0.188951
$351$	4.28105	−	10.4237i	0.228506	−	0.556374i
$352$	4.81961			0.256886
$353$	9.07862	−	15.7246i	0.483206	−	0.836938i	−0.516608	−	0.856222i	$-0.672805\pi$
$353$	9.07862	−	15.7246i	0.483206	−	0.836938i	0.999814	+	0.0192842i	$0.00613873\pi$
$354$	2.27994	+	10.2357i	0.121177	+	0.544023i
$355$	−5.16224	−	8.94126i	−0.273983	−	0.474553i
$356$	−6.32620	−	10.9573i	−0.335288	−	0.580736i
$357$	−4.17837	−	1.31284i	−0.221143	−	0.0694831i
$358$	−11.3081	+	19.5862i	−0.597651	+	1.03516i
$359$	−9.88348			−0.521630			−0.260815	−	0.965389i	$-0.583991\pi$
$359$	−9.88348			−0.521630			−0.260815	+	0.965389i	$0.583991\pi$
$360$	−6.02793	−	4.20287i	−0.317700	−	0.221511i
$361$	1.00000			0.0526316
$362$	−1.86851	+	3.23635i	−0.0982067	+	0.170099i
$363$	15.6017	−	14.3250i	0.818875	−	0.751868i
$364$	−3.83299	−	6.63894i	−0.200904	−	0.347975i
$365$	−14.3438	−	24.8442i	−0.750790	−	1.30041i
$366$	−18.3850	+	16.8806i	−0.961001	+	0.882364i
$367$	−17.9144	+	31.0287i	−0.935126	+	1.61969i	−0.160716	+	0.987001i	$0.551380\pi$
$367$	−17.9144	+	31.0287i	−0.935126	+	1.61969i	−0.774410	+	0.632685i	$0.781953\pi$
$368$	−0.761648			−0.0397036
$369$	18.6797	+	13.0241i	0.972427	+	0.678008i
$370$	−23.5539			−1.22451
$371$	−11.1969	+	19.3936i	−0.581315	+	1.00687i
$372$	8.70669	+	2.73564i	0.451421	+	0.141837i
$373$	−4.10962	−	7.11807i	−0.212788	−	0.368560i	0.739798	−	0.672829i	$-0.234921\pi$
$373$	−4.10962	−	7.11807i	−0.212788	−	0.368560i	−0.952586	+	0.304269i	$0.901588\pi$
$374$	1.72381	+	2.98573i	0.0891361	+	0.154388i
$375$	−3.68966	−	16.5646i	−0.190533	−	0.855393i
$376$	4.81579	−	8.34120i	0.248356	−	0.430164i
$377$	3.48818			0.179651
$378$	−6.97825	+	16.9909i	−0.358922	+	0.873918i
$379$	−36.2903			−1.86411			−0.932054	−	0.362319i	$-0.881985\pi$
$379$	−36.2903			−1.86411			−0.932054	+	0.362319i	$0.881985\pi$
$380$	−1.22474	+	2.12132i	−0.0628281	+	0.108821i
$381$	3.69494	+	16.5883i	0.189297	+	0.849845i
$382$	6.82543	+	11.8220i	0.349219	+	0.604866i
$383$	4.30209	+	7.45143i	0.219826	+	0.380750i	0.954755	−	0.297394i	$-0.0961176\pi$
$383$	4.30209	+	7.45143i	0.219826	+	0.380750i	−0.734928	+	0.678145i	$0.762784\pi$
$384$	1.65241	+	0.519186i	0.0843240	+	0.0264946i
$385$	−20.8660	+	36.1410i	−1.06343	+	1.84192i
$386$	−9.53140			−0.485136
$387$	2.79558	−	32.7065i	0.142107	−	1.66257i
$388$	4.65324			0.236233
$389$	14.3782	−	24.9039i	0.729006	−	1.26268i	−0.228298	−	0.973591i	$-0.573316\pi$
$389$	14.3782	−	24.9039i	0.729006	−	1.26268i	0.957304	−	0.289084i	$-0.0933507\pi$
$390$	6.77727	−	6.22270i	0.343181	−	0.315099i
$391$	−0.272416	−	0.471838i	−0.0137766	−	0.0238619i
$392$	2.74790	+	4.75951i	0.138790	+	0.240391i
$393$	4.96734	−	4.56087i	0.250569	−	0.230065i
$394$	2.47011	−	4.27835i	0.124442	−	0.215540i
$395$	24.1857			1.21691
$396$	13.0919	−	6.13675i	0.657893	−	0.308383i
$397$	−4.38614			−0.220134			−0.110067	−	0.993924i	$-0.535107\pi$
$397$	−4.38614			−0.220134			−0.110067	+	0.993924i	$0.535107\pi$
$398$	−4.15412	+	7.19514i	−0.208227	+	0.360660i
$399$	5.84116	+	1.83529i	0.292424	+	0.0918796i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−9.06301	−	15.6976i	−0.452585	−	0.783900i	0.545961	−	0.837811i	$-0.316165\pi$
$401$	−9.06301	−	15.6976i	−0.452585	−	0.783900i	−0.998546	+	0.0539105i	$0.982831\pi$
$402$	−4.20946	−	18.8982i	−0.209949	−	0.942557i
$403$	−5.71337	+	9.89585i	−0.284603	+	0.492947i
$404$	−5.27096			−0.262240
$405$	−21.7256	−	3.74132i	−1.07955	−	0.185908i
$406$	−5.68585			−0.282184
$407$	23.1723	−	40.1356i	1.14861	−	1.98945i
$408$	0.269376	+	1.20935i	0.0133361	+	0.0598720i
$409$	−10.6898	−	18.5153i	−0.528576	−	0.915521i	−0.999445	−	0.0333174i	$-0.989393\pi$
$409$	−10.6898	−	18.5153i	−0.528576	−	0.915521i	0.470869	−	0.882203i	$-0.343941\pi$
$410$	9.29659	+	16.1022i	0.459126	+	0.795229i
$411$	17.5349	+	5.50946i	0.864932	+	0.271762i
$412$	1.00560	−	1.74175i	0.0495422	−	0.0858096i
$413$	21.4020			1.05313
$414$	−2.06893	+	0.969796i	−0.101682	+	0.0476629i
$415$	−17.2124			−0.844924
$416$	−1.08432	+	1.87809i	−0.0531630	+	0.0920810i
$417$	−1.51536	+	1.39136i	−0.0742075	+	0.0681352i
$418$	−2.40980	−	4.17390i	−0.117867	−	0.204152i
$419$	1.60084	+	2.77274i	0.0782062	+	0.135457i	0.902476	−	0.430740i	$-0.141747\pi$
$419$	1.60084	+	2.77274i	0.0782062	+	0.135457i	−0.824270	+	0.566197i	$0.808414\pi$
$420$	−11.0472	+	10.1432i	−0.539047	+	0.494937i
$421$	−13.5458	+	23.4620i	−0.660182	+	1.14347i	0.320385	+	0.947287i	$0.396188\pi$
$421$	−13.5458	+	23.4620i	−0.660182	+	1.14347i	−0.980567	+	0.196182i	$0.937146\pi$
$422$	−15.6275			−0.760734
$423$	2.46080	−	28.7898i	0.119648	−	1.39981i
$424$	6.33500			0.307655
$425$	0.357666	−	0.619496i	0.0173494	−	0.0300500i
$426$	6.96481	+	2.18834i	0.337446	+	0.106026i
$427$	25.4697	+	44.1148i	1.23256	+	2.13486i
$428$	0.945798	+	1.63817i	0.0457169	+	0.0791839i
$429$	3.93594	+	17.6703i	0.190029	+	0.853129i
$430$	13.4011	−	23.2113i	0.646257	−	1.11935i
$431$	−16.8794			−0.813051			−0.406526	−	0.913639i	$-0.633260\pi$
$431$	−16.8794			−0.813051			−0.406526	+	0.913639i	$0.633260\pi$
$432$	5.14964	−	0.693678i	0.247762	−	0.0333746i
$433$	27.5368			1.32333			0.661667	−	0.749797i	$-0.269849\pi$
$433$	27.5368			1.32333			0.661667	+	0.749797i	$0.269849\pi$
$434$	9.31297	−	16.1305i	0.447037	−	0.774291i
$435$	−1.48368	−	6.66092i	−0.0711369	−	0.319367i
$436$	−7.05605	−	12.2214i	−0.337924	−	0.585301i
$437$	0.380824	+	0.659606i	0.0182173	+	0.0315532i
$438$	19.3525	+	6.08055i	0.924696	+	0.290540i
$439$	0.716365	−	1.24078i	0.0341902	−	0.0592192i	−0.848424	−	0.529317i	$-0.822448\pi$
$439$	0.716365	−	1.24078i	0.0341902	−	0.0592192i	0.882614	+	0.470098i	$0.155781\pi$
$440$	11.8056			0.562809
$441$	13.5246	+	9.42978i	0.644027	+	0.449037i
$442$	−1.55129			−0.0737875
$443$	−1.48941	+	2.57974i	−0.0707642	+	0.122567i	−0.899236	−	0.437463i	$-0.855877\pi$
$443$	−1.48941	+	2.57974i	−0.0707642	+	0.122567i	0.828472	+	0.560030i	$0.189210\pi$
$444$	12.2682	−	11.2643i	0.582224	−	0.534581i
$445$	−15.4960	−	26.8398i	−0.734579	−	1.27233i
$446$	−1.73262	−	3.00098i	−0.0820417	−	0.142100i
$447$	4.48794	−	4.12070i	0.212272	−	0.194902i
$448$	1.76747	−	3.06135i	0.0835051	−	0.144635i
$449$	−7.31129			−0.345041			−0.172520	−	0.985006i	$-0.555191\pi$
$449$	−7.31129			−0.345041			−0.172520	+	0.985006i	$0.555191\pi$
$450$	−2.46089	−	1.71581i	−0.116008	−	0.0808842i
$451$	−36.5839			−1.72267
$452$	5.48979	−	9.50859i	0.258218	−	0.447247i
$453$	39.4871	+	12.4069i	1.85527	+	0.582926i
$454$	7.36581	+	12.7580i	0.345694	+	0.598760i
$455$	−9.38888	−	16.2620i	−0.440158	−	0.762375i
$456$	−0.376574	−	1.69062i	−0.0176347	−	0.0791705i
$457$	−14.0894	+	24.4036i	−0.659076	+	1.14155i	0.321779	+	0.946815i	$0.395719\pi$
$457$	−14.0894	+	24.4036i	−0.659076	+	1.14155i	−0.980855	+	0.194739i	$0.937614\pi$
$458$	−11.0213			−0.514991
$459$	2.27158	+	2.94208i	0.106028	+	0.137324i
$460$	−1.86565			−0.0869863
$461$	−14.4021	+	24.9452i	−0.670773	+	1.16181i	0.306913	+	0.951738i	$0.400704\pi$
$461$	−14.4021	+	24.9452i	−0.670773	+	1.16181i	−0.977685	+	0.210075i	$0.932629\pi$
$462$	−6.41571	−	28.8031i	−0.298486	−	1.34004i
$463$	−10.7750	−	18.6629i	−0.500757	−	0.867336i	−1.00000		0.000874088i	$-0.999722\pi$
$463$	−10.7750	−	18.6629i	−0.500757	−	0.867336i	0.499243	−	0.866462i	$-0.333612\pi$
$464$	0.804235	+	1.39298i	0.0373357	+	0.0646673i
$465$	21.3269	+	6.70093i	0.989013	+	0.310748i
$466$	14.9569	−	25.9062i	0.692867	−	1.20008i
$467$	−9.63407			−0.445811			−0.222906	−	0.974840i	$-0.571554\pi$
$467$	−9.63407			−0.445811			−0.222906	+	0.974840i	$0.571554\pi$
$468$	−0.554070	+	6.48226i	−0.0256119	+	0.299643i
$469$	−39.5146			−1.82461
$470$	11.7962	−	20.4317i	0.544120	−	0.942443i
$471$	−5.57290	+	5.11688i	−0.256786	+	0.235773i
$472$	−3.02721	−	5.24329i	−0.139339	−	0.241342i
$473$	26.3679	+	45.6705i	1.21240	+	2.09993i
$474$	−12.5973	+	11.5664i	−0.578611	+	0.531264i
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$	2.52866			0.115901
$477$	17.2083	−	8.06627i	0.787913	−	0.369329i
$478$	2.29205			0.104836
$479$	8.41307	−	14.5719i	0.384403	−	0.665805i	−0.607283	−	0.794485i	$-0.707741\pi$
$479$	8.41307	−	14.5719i	0.384403	−	0.665805i	0.991686	+	0.128680i	$0.0410740\pi$
$480$	4.04755	+	1.27174i	0.184745	+	0.0580468i
$481$	10.4266	+	18.0595i	0.475413	+	0.823440i
$482$	−6.39565	−	11.0776i	−0.291314	−	0.504570i
$483$	1.01388	+	4.55179i	0.0461332	+	0.207113i
$484$	−6.11431	+	10.5903i	−0.277923	+	0.481377i
$485$	11.3981			0.517560
$486$	13.1052	−	8.44127i	0.594462	−	0.382904i
$487$	23.8788			1.08205			0.541026	−	0.841006i	$-0.318036\pi$
$487$	23.8788			1.08205			0.541026	+	0.841006i	$0.318036\pi$
$488$	7.20512	−	12.4796i	0.326160	−	0.564927i
$489$	−5.98492	−	26.8691i	−0.270647	−	1.21506i
$490$	6.73096	+	11.6584i	0.304074	+	0.526671i
$491$	3.64057	+	6.30565i	0.164296	+	0.284570i	0.936405	−	0.350921i	$-0.114131\pi$
$491$	3.64057	+	6.30565i	0.164296	+	0.284570i	−0.772109	+	0.635490i	$0.780798\pi$
$492$	−12.5428	−	3.94095i	−0.565473	−	0.177672i
$493$	−0.575296	+	0.996441i	−0.0259100	+	0.0448775i
$494$	2.16863			0.0975714
$495$	32.0685	−	15.0319i	1.44137	−	0.675633i
$496$	−5.26910			−0.236589
$497$	7.44980	−	12.9034i	0.334169	−	0.578798i
$498$	8.96519	−	8.23158i	0.401740	−	0.368866i
$499$	−16.9210	−	29.3080i	−0.757488	−	1.31201i	−0.944128	−	0.329579i	$-0.893093\pi$
$499$	−16.9210	−	29.3080i	−0.757488	−	1.31201i	0.186640	−	0.982428i	$-0.440240\pi$
$500$	4.89898	+	8.48528i	0.219089	+	0.379473i
$501$	−27.6777	+	25.4129i	−1.23655	+	1.13536i
$502$	−11.7943	+	20.4284i	−0.526407	+	0.911764i
$503$	32.9538			1.46934			0.734668	−	0.678426i	$-0.237338\pi$
$503$	32.9538			1.46934			0.734668	+	0.678426i	$0.237338\pi$
$504$	0.903151	−	10.5663i	0.0402296	−	0.470660i
$505$	−12.9112			−0.574539
$506$	1.83542	−	3.17904i	0.0815944	−	0.141326i
$507$	13.7101	+	4.30771i	0.608885	+	0.191312i
$508$	−4.90599	−	8.49742i	−0.217668	−	0.377012i
$509$	−2.49969	−	4.32960i	−0.110797	−	0.191906i	0.805295	−	0.592875i	$-0.202007\pi$
$509$	−2.49969	−	4.32960i	−0.110797	−	0.191906i	−0.916092	+	0.400969i	$0.868674\pi$
$510$	0.659833	+	2.96230i	0.0292179	+	0.131173i
$511$	20.7001	−	35.8535i	0.915716	−	1.58607i
$512$	−1.00000			−0.0441942
$513$	−3.17556	−	4.11288i	−0.140205	−	0.181588i
$514$	8.46721			0.373472
$515$	2.46320	−	4.26639i	0.108542	−	0.187999i
$516$	4.12045	+	18.4986i	0.181393	+	0.814357i
$517$	23.2102	+	40.2013i	1.02078	+	1.76805i
$518$	−16.9957	−	29.4375i	−0.746750	−	1.29341i
$519$	−27.6625	−	8.69155i	−1.21425	−	0.381517i
$520$	−2.65602	+	4.60037i	−0.116474	+	0.201739i
$521$	−2.25102			−0.0986190			−0.0493095	−	0.998784i	$-0.515702\pi$
$521$	−2.25102			−0.0986190			−0.0493095	+	0.998784i	$0.515702\pi$
$522$	3.95827	+	2.75984i	0.173249	+	0.120795i
$523$	39.9020			1.74479			0.872396	−	0.488801i	$-0.162565\pi$
$523$	39.9020			1.74479			0.872396	+	0.488801i	$0.162565\pi$
$524$	−1.94671	+	3.37180i	−0.0850423	+	0.147298i
$525$	−4.50999	+	4.14094i	−0.196832	+	0.180726i
$526$	14.4087	+	24.9566i	0.628249	+	1.08816i
$527$	−1.88458	−	3.26419i	−0.0820935	−	0.142190i
$528$	−6.14901	+	5.64584i	−0.267601	+	0.245704i
$529$	11.2099	−	19.4162i	0.487389	−	0.844182i
$530$	15.5175			0.674038
$531$	−14.8993	−	10.3883i	−0.646574	−	0.450812i
$532$	−3.53494			−0.153259
$533$	8.23065	−	14.2559i	0.356509	−	0.617492i
$534$	20.9069	+	6.56896i	0.904730	+	0.284267i
$535$	2.31672	+	4.01268i	0.100161	+	0.173483i
$536$	5.58914	+	9.68068i	0.241414	+	0.418142i
$537$	−8.51668	−	38.2353i	−0.367522	−	1.64998i
$538$	6.25742	−	10.8382i	0.269776	−	0.467266i
$539$	−26.4876			−1.14090
$540$	12.6140	−	1.69916i	0.542820	−	0.0731201i
$541$	−29.0041			−1.24698			−0.623492	−	0.781830i	$-0.714286\pi$
$541$	−29.0041			−1.24698			−0.623492	+	0.781830i	$0.714286\pi$
$542$	−5.76614	+	9.98725i	−0.247677	+	0.428989i
$543$	−1.40727	−	6.31787i	−0.0603915	−	0.271126i
$544$	−0.357666	−	0.619496i	−0.0153348	−	0.0265607i
$545$	−17.2837	−	29.9363i	−0.740353	−	1.28233i
$546$	12.6673	+	3.98008i	0.542112	+	0.170332i
$547$	−4.33057	+	7.50076i	−0.185162	+	0.320709i	−0.943631	−	0.330999i	$-0.892614\pi$
$547$	−4.33057	+	7.50076i	−0.185162	+	0.320709i	0.758469	+	0.651709i	$0.225948\pi$
$548$	−10.6117			−0.453310
$549$	3.68171	−	43.0737i	0.157132	−	1.83834i
$550$	4.81961			0.205509
$551$	0.804235	−	1.39298i	0.0342616	−	0.0593428i
$552$	0.971734	−	0.892219i	0.0413598	−	0.0379753i
$553$	17.4516	+	30.2270i	0.742116	+	1.28538i
$554$	−9.61011	−	16.6452i	−0.408295	−	0.707187i
$555$	30.0509	−	27.5918i	1.27559	−	1.17121i
$556$	0.593871	−	1.02861i	0.0251857	−	0.0436230i
$557$	−31.5939			−1.33868			−0.669339	−	0.742958i	$-0.733422\pi$
$557$	−31.5939			−1.33868			−0.669339	+	0.742958i	$0.733422\pi$
$558$	−14.3129	+	6.70908i	−0.605913	+	0.284018i
$559$	−23.7290			−1.00363
$560$	4.32940	−	7.49874i	0.182951	−	0.316880i
$561$	−5.69687	−	1.78996i	−0.240522	−	0.0755721i
$562$	14.0494	+	24.3343i	0.592638	+	1.02648i
$563$	19.4876	+	33.7536i	0.821306	+	1.42254i	0.904710	+	0.426028i	$0.140088\pi$
$563$	19.4876	+	33.7536i	0.821306	+	1.42254i	−0.0834034	+	0.996516i	$0.526579\pi$
$564$	3.62701	+	16.2833i	0.152725	+	0.685652i
$565$	13.4472	−	23.2912i	0.565727	−	0.979868i
$566$	−4.62905			−0.194574
$567$	−11.0006	−	29.8521i	−0.461983	−	1.25367i
$568$	−4.21495			−0.176855
$569$	1.46962	−	2.54546i	0.0616098	−	0.106711i	−0.833575	−	0.552406i	$-0.813710\pi$
$569$	1.46962	−	2.54546i	0.0616098	−	0.106711i	0.895185	+	0.445694i	$0.147043\pi$
$570$	−0.922415	−	4.14115i	−0.0386357	−	0.173454i
$571$	−7.24886	−	12.5554i	−0.303355	−	0.525427i	0.673538	−	0.739152i	$-0.264774\pi$
$571$	−7.24886	−	12.5554i	−0.303355	−	0.525427i	−0.976894	+	0.213725i	$0.931440\pi$
$572$	−5.22598	−	9.05166i	−0.218509	−	0.378469i
$573$	−22.5568	−	7.08734i	−0.942322	−	0.296078i
$574$	−13.4162	+	23.2376i	−0.559982	+	0.969917i
$575$	−0.761648			−0.0317629
$576$	−2.71638	+	1.27329i	−0.113183	+	0.0530536i
$577$	16.3113			0.679046			0.339523	−	0.940598i	$-0.389734\pi$
$577$	16.3113			0.679046			0.339523	+	0.940598i	$0.389734\pi$
$578$	−8.24415	+	14.2793i	−0.342911	+	0.593940i
$579$	12.1605	−	11.1654i	0.505372	−	0.464018i
$580$	1.96997	+	3.41208i	0.0817984	+	0.141679i
$581$	−12.4199	−	21.5119i	−0.515264	−	0.892464i
$582$	−5.93676	+	5.45096i	−0.246086	+	0.225950i
$583$	−15.2661	+	26.4417i	−0.632257	+	1.09510i
$584$	−11.7117			−0.484633
$585$	−1.35719	+	15.8782i	−0.0561128	+	0.656484i
$586$	−27.3741			−1.13082
$587$	10.6588	−	18.4617i	0.439937	−	0.761994i	−0.557747	−	0.830011i	$-0.688334\pi$
$587$	10.6588	−	18.4617i	0.439937	−	0.761994i	0.997684	+	0.0680172i	$0.0216673\pi$
$588$	−9.08130	−	2.85335i	−0.374507	−	0.117670i
$589$	2.63455	+	4.56317i	0.108555	+	0.188022i
$590$	−7.41513	−	12.8434i	−0.305276	−	0.528753i
$591$	1.86036	+	8.35202i	0.0765249	+	0.343556i
$592$	−4.80793	+	8.32757i	−0.197605	+	0.342261i
$593$	−36.1522			−1.48459			−0.742296	−	0.670072i	$-0.766263\pi$
$593$	−36.1522			−1.48459			−0.742296	+	0.670072i	$0.766263\pi$
$594$	−9.51428	+	23.1657i	−0.390376	+	0.950502i
$595$	6.19392			0.253926
$596$	−1.75883	+	3.04638i	−0.0720444	+	0.124785i
$597$	−3.12867	−	14.0461i	−0.128048	−	0.574867i
$598$	0.825867	+	1.43044i	0.0337722	+	0.0584952i
$599$	−13.9313	−	24.1297i	−0.569217	−	0.985914i	−0.996644	−	0.0818633i	$-0.973913\pi$
$599$	−13.9313	−	24.1297i	−0.569217	−	0.985914i	0.427426	−	0.904050i	$-0.359420\pi$
$600$	1.65241	+	0.519186i	0.0674592	+	0.0211957i
$601$	3.34961	−	5.80169i	0.136633	−	0.236656i	−0.789587	−	0.613639i	$-0.789705\pi$
$601$	3.34961	−	5.80169i	0.136633	−	0.236656i	0.926220	+	0.376983i	$0.123038\pi$
$602$	38.6791			1.57644
$603$	27.5085	+	19.1799i	1.12023	+	0.781064i
$604$	−23.8968			−0.972345
$605$	−14.9769	+	25.9408i	−0.608899	+	1.05464i
$606$	6.72485	−	6.17457i	0.273179	−	0.250825i
$607$	−5.74295	−	9.94709i	−0.233099	−	0.403740i	0.725619	−	0.688096i	$-0.241553\pi$
$607$	−5.74295	−	9.94709i	−0.233099	−	0.403740i	−0.958719	+	0.284357i	$0.908220\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$	7.25419	−	6.66059i	0.293954	−	0.269901i
$610$	17.6489	−	30.5687i	0.714582	−	1.23769i
$611$	−20.8874			−0.845013
$612$	−1.76035	−	1.22738i	−0.0711581	−	0.0496138i
$613$	−23.9423			−0.967021			−0.483511	−	0.875339i	$-0.660639\pi$
$613$	−23.9423			−0.967021			−0.483511	+	0.875339i	$0.660639\pi$
$614$	7.54473	−	13.0679i	0.304481	−	0.527376i
$615$	−30.7235	−	9.65333i	−1.23889	−	0.389260i
$616$	8.51851	+	14.7545i	0.343221	+	0.594476i
$617$	−8.85840	−	15.3432i	−0.356626	−	0.617694i	0.630769	−	0.775971i	$-0.282740\pi$
$617$	−8.85840	−	15.3432i	−0.356626	−	0.617694i	−0.987395	+	0.158277i	$0.949406\pi$
$618$	0.757364	+	3.40016i	0.0304657	+	0.136775i
$619$	−10.7553	+	18.6287i	−0.432292	+	0.748752i	−0.997070	−	0.0764905i	$-0.975629\pi$
$619$	−10.7553	+	18.6287i	−0.432292	+	0.748752i	0.564778	+	0.825243i	$0.308962\pi$
$620$	−12.9066			−0.518342
$621$	1.50355	−	3.66090i	0.0603355	−	0.146907i
$622$	17.8910			0.717362
$623$	22.3627	−	38.7334i	0.895945	−	1.55182i
$624$	−0.816652	−	3.66633i	−0.0326922	−	0.146771i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	6.93392	+	12.0099i	0.277135	+	0.480012i
$627$	7.96395	+	2.50228i	0.318050	+	0.0999312i
$628$	2.18403	−	3.78285i	0.0871522	−	0.150952i
$629$	−6.87853			−0.274265
$630$	2.21226	−	25.8820i	0.0881386	−	1.03116i
$631$	−27.5276			−1.09586			−0.547929	−	0.836525i	$-0.684583\pi$
$631$	−27.5276			−1.09586			−0.547929	+	0.836525i	$0.684583\pi$
$632$	4.93688	−	8.55093i	0.196378	−	0.340138i
$633$	19.9380	−	18.3065i	0.792466	−	0.727620i
$634$	2.49313	+	4.31823i	0.0990148	+	0.171499i
$635$	−12.0172	−	20.8143i	−0.476887	−	0.825992i
$636$	−8.08239	+	7.42102i	−0.320488	+	0.294263i
$637$	5.95919	−	10.3216i	0.236112	−	0.408958i
$638$	−7.75220			−0.306913
$639$	−11.4494	+	5.36684i	−0.452932	+	0.212309i
$640$	−2.44949			−0.0968246
$641$	−4.07142	+	7.05191i	−0.160812	+	0.278534i	−0.935160	−	0.354226i	$-0.884744\pi$
$641$	−4.07142	+	7.05191i	−0.160812	+	0.278534i	0.774348	+	0.632759i	$0.218078\pi$
$642$	−3.12568	−	0.982091i	−0.123361	−	0.0387600i
$643$	−4.65485	−	8.06243i	−0.183569	−	0.317951i	0.759524	−	0.650479i	$-0.225432\pi$
$643$	−4.65485	−	8.06243i	−0.183569	−	0.317951i	−0.943093	+	0.332528i	$0.892098\pi$
$644$	−1.34619	−	2.33167i	−0.0530473	−	0.0918806i
$645$	10.0930	+	45.3122i	0.397411	+	1.78417i
$646$	−0.357666	+	0.619496i	−0.0140722	+	0.0243737i
$647$	−12.9290			−0.508290			−0.254145	−	0.967166i	$-0.581794\pi$
$647$	−12.9290			−0.508290			−0.254145	+	0.967166i	$0.581794\pi$
$648$	−5.75748	+	6.91747i	−0.226175	+	0.271744i
$649$	29.1800			1.14541
$650$	−1.08432	+	1.87809i	−0.0425304	+	0.0736648i
$651$	7.01405	+	31.4894i	0.274902	+	1.23417i
$652$	7.94653	+	13.7638i	0.311210	+	0.539032i
$653$	18.2030	+	31.5286i	0.712339	+	1.23381i	0.963977	+	0.265986i	$0.0856976\pi$
$653$	18.2030	+	31.5286i	0.712339	+	1.23381i	−0.251637	+	0.967822i	$0.580969\pi$
$654$	23.3189	+	7.32681i	0.911842	+	0.286501i
$655$	−4.76844	+	8.25918i	−0.186318	+	0.322713i
$656$	7.59063			0.296364
$657$	−31.8134	+	14.9123i	−1.24116	+	0.581786i
$658$	34.0471			1.32729
$659$	−19.2072	+	33.2679i	−0.748207	+	1.29593i	0.200475	+	0.979699i	$0.435752\pi$
$659$	−19.2072	+	33.2679i	−0.748207	+	1.29593i	−0.948682	+	0.316233i	$0.897582\pi$
$660$	−15.0619	+	13.8294i	−0.586285	+	0.538310i
$661$	−11.3964	−	19.7392i	−0.443269	−	0.767764i	0.554661	−	0.832077i	$-0.312848\pi$
$661$	−11.3964	−	19.7392i	−0.443269	−	0.767764i	−0.997930	+	0.0643121i	$0.979515\pi$
$662$	1.65709	+	2.87017i	0.0644048	+	0.111552i
$663$	1.97919	−	1.81724i	0.0768653	−	0.0705756i
$664$	−3.51347	+	6.08550i	−0.136349	+	0.236163i
$665$	−8.65880			−0.335774
$666$	−2.45678	+	28.7428i	−0.0951983	+	1.11376i
$667$	1.22509			0.0474356
$668$	10.8469	−	18.7874i	0.419680	−	0.726907i
$669$	5.72597	+	1.79910i	0.221379	+	0.0695572i
$670$	13.6905	+	23.7127i	0.528912	+	0.916102i
$671$	34.7259	+	60.1469i	1.34058	+	2.32195i
$672$	1.33117	+	5.97624i	0.0513509	+	0.230538i
$673$	1.96911	−	3.41060i	0.0759036	−	0.131469i	−0.825575	−	0.564292i	$-0.809149\pi$
$673$	1.96911	−	3.41060i	0.0759036	−	0.131469i	0.901479	+	0.432823i	$0.142483\pi$
$674$	−1.64006			−0.0631726
$675$	5.14964	−	0.693678i	0.198210	−	0.0266997i
$676$	−8.29703			−0.319117
$677$	−10.7623	+	18.6409i	−0.413629	+	0.716427i	−0.995283	−	0.0970094i	$-0.969072\pi$
$677$	−10.7623	+	18.6409i	−0.413629	+	0.716427i	0.581654	+	0.813436i	$0.302406\pi$
$678$	4.13463	+	18.5623i	0.158789	+	0.712880i
$679$	8.22447	+	14.2452i	0.315626	+	0.546681i
$680$	−0.876100	−	1.51745i	−0.0335969	−	0.0581915i
$681$	−24.3426	−	7.64845i	−0.932811	−	0.293089i
$682$	12.6975	−	21.9927i	0.486212	−	0.842144i
$683$	16.6317			0.636396			0.318198	−	0.948024i	$-0.396922\pi$
$683$	16.6317			0.636396			0.318198	+	0.948024i	$0.396922\pi$
$684$	2.46089	+	1.71581i	0.0940945	+	0.0656058i
$685$	−25.9933			−0.993153
$686$	2.65862	−	4.60486i	0.101507	−	0.175815i
$687$	14.0613	−	12.9107i	0.536473	−	0.492574i
$688$	−5.47096	−	9.47599i	−0.208579	−	0.361269i
$689$	−6.86914	−	11.8977i	−0.261693	−	0.453266i
$690$	2.38025	−	2.18548i	0.0906147	−	0.0831998i
$691$	11.2178	−	19.4297i	0.426744	−	0.739142i	−0.569838	−	0.821757i	$-0.692994\pi$
$691$	11.2178	−	19.4297i	0.426744	−	0.739142i	0.996581	+	0.0826155i	$0.0263273\pi$
$692$	16.7407			0.636387
$693$	41.9263	+	29.2324i	1.59265	+	1.11045i
$694$	−15.1852			−0.576422
$695$	1.45468	−	2.51958i	0.0551792	−	0.0955732i
$696$	−2.65785	−	0.835096i	−0.100745	−	0.0316542i
$697$	2.71491	+	4.70237i	0.102835	+	0.178115i
$698$	−4.84775	−	8.39655i	−0.183490	−	0.317814i
$699$	11.2648	+	50.5730i	0.426074	+	1.91285i
$700$	1.76747	−	3.06135i	0.0668041	−	0.115708i
$701$	13.0706			0.493671			0.246835	−	0.969057i	$-0.420609\pi$
$701$	13.0706			0.493671			0.246835	+	0.969057i	$0.420609\pi$
$702$	−6.88663	−	8.91933i	−0.259919	−	0.336638i
$703$	9.61585			0.362669
$704$	2.40980	−	4.17390i	0.0908229	−	0.157310i
$705$	8.88432	+	39.8859i	0.334603	+	1.50219i
$706$	−9.07862	−	15.7246i	−0.341679	−	0.591805i
$707$	−9.31626	−	16.1362i	−0.350374	−	0.606866i
$708$	10.0044	+	3.14338i	0.375987	+	0.118135i
$709$	12.0449	−	20.8624i	0.452357	−	0.783505i	−0.546175	−	0.837671i	$-0.683917\pi$
$709$	12.0449	−	20.8624i	0.452357	−	0.783505i	0.998532	+	0.0541662i	$0.0172501\pi$
$710$	−10.3245			−0.387471
$711$	2.52267	−	29.5137i	0.0946076	−	1.10685i
$712$	−12.6524			−0.474169
$713$	−2.00660	+	3.47553i	−0.0751477	+	0.130160i
$714$	−3.22614	+	2.96215i	−0.120735	+	0.110856i
$715$	−12.8010	−	22.1720i	−0.478730	−	0.829184i
$716$	11.3081	+	19.5862i	0.422603	+	0.731970i
$717$	−2.92427	+	2.68498i	−0.109209	+	0.100273i
$718$	−4.94174	+	8.55935i	−0.184424	+	0.319432i
$719$	45.1495			1.68379			0.841896	−	0.539640i	$-0.181440\pi$
$719$	45.1495			1.68379			0.841896	+	0.539640i	$0.181440\pi$
$720$	−6.65375	+	3.11890i	−0.247971	+	0.116235i
$721$	7.10945			0.264770
$722$	0.500000	−	0.866025i	0.0186081	−	0.0322301i
$723$	21.1364	+	6.64107i	0.786072	+	0.246984i
$724$	1.86851	+	3.23635i	0.0694426	+	0.120278i
$725$	0.804235	+	1.39298i	0.0298686	+	0.0517339i
$726$	−4.60499	−	20.6739i	−0.170907	−	0.767282i
$727$	−9.21182	+	15.9553i	−0.341648	+	0.591751i	−0.984739	−	0.174039i	$-0.944318\pi$
$727$	−9.21182	+	15.9553i	−0.341648	+	0.591751i	0.643091	+	0.765790i	$0.277652\pi$
$728$	−7.66599			−0.284120
$729$	−6.83159	+	26.1214i	−0.253022	+	0.967461i
$730$	−28.6876			−1.06178
$731$	3.91356	−	6.77848i	0.144748	−	0.250711i
$732$	5.42653	+	24.3622i	0.200570	+	0.900454i
$733$	15.0147	+	26.0062i	0.554581	+	0.960562i	0.997936	+	0.0642158i	$0.0204546\pi$
$733$	15.0147	+	26.0062i	0.554581	+	0.960562i	−0.443355	+	0.896346i	$0.646212\pi$
$734$	17.9144	+	31.0287i	0.661234	+	1.14529i
$735$	−22.2446	−	6.98925i	−0.820503	−	0.257802i
$736$	−0.380824	+	0.659606i	−0.0140374	+	0.0243134i
$737$	−53.8750			−1.98451
$738$	20.6191	−	9.66506i	0.758998	−	0.355776i
$739$	−29.9443			−1.10152			−0.550760	−	0.834663i	$-0.685662\pi$
$739$	−29.9443			−1.10152			−0.550760	+	0.834663i	$0.685662\pi$
$740$	−11.7770	+	20.3983i	−0.432930	+	0.749857i
$741$	−2.76681	+	2.54041i	−0.101641	+	0.0933242i
$742$	11.1969	+	19.3936i	0.411052	+	0.711963i
$743$	−21.8596	−	37.8619i	−0.801949	−	1.38902i	−0.918331	−	0.395812i	$-0.870463\pi$
$743$	−21.8596	−	37.8619i	−0.801949	−	1.38902i	0.116382	−	0.993205i	$-0.462870\pi$
$744$	6.72248	−	6.17239i	0.246458	−	0.226291i
$745$	−4.30823	+	7.46208i	−0.157841	+	0.273389i
$746$	−8.21924			−0.300928
$747$	−1.79533	+	21.0042i	−0.0656877	+	0.768504i
$748$	3.44762			0.126058
$749$	−3.34334	+	5.79083i	−0.122163	+	0.211592i
$750$	−16.1902	−	5.08697i	−0.591183	−	0.185750i
$751$	−6.09761	−	10.5614i	−0.222505	−	0.385390i	0.733063	−	0.680161i	$-0.238090\pi$
$751$	−6.09761	−	10.5614i	−0.222505	−	0.385390i	−0.955568	+	0.294771i	$0.904757\pi$
$752$	−4.81579	−	8.34120i	−0.175614	−	0.304172i
$753$	−8.88290	−	39.8795i	−0.323711	−	1.45329i
$754$	1.74409	−	3.02086i	0.0635161	−	0.110013i
$755$	−58.5349			−2.13030
$756$	11.2254	+	14.5388i	0.408265	+	0.528771i
$757$	−20.4127			−0.741910			−0.370955	−	0.928651i	$-0.620970\pi$
$757$	−20.4127			−0.741910			−0.370955	+	0.928651i	$0.620970\pi$
$758$	−18.1452	+	31.4283i	−0.659062	+	1.14153i
$759$	1.38235	+	6.20600i	0.0501760	+	0.225263i
$760$	1.22474	+	2.12132i	0.0444262	+	0.0769484i
$761$	−0.517634	−	0.896568i	−0.0187642	−	0.0325006i	0.856491	−	0.516162i	$-0.172640\pi$
$761$	−0.517634	−	0.896568i	−0.0187642	−	0.0325006i	−0.875255	+	0.483662i	$0.839307\pi$
$762$	16.2134	+	5.09425i	0.587348	+	0.184545i
$763$	24.9427	−	43.2021i	0.902987	−	1.56402i
$764$	13.6509			0.493871
$765$	−4.31197	−	3.00645i	−0.155900	−	0.108698i
$766$	8.60417			0.310881
$767$	−6.56491	+	11.3708i	−0.237045	+	0.410574i
$768$	1.27583	−	1.17143i	0.0460376	−	0.0422704i
$769$	7.90752	+	13.6962i	0.285152	+	0.493898i	0.972646	−	0.232292i	$-0.0746224\pi$
$769$	7.90752	+	13.6962i	0.285152	+	0.493898i	−0.687494	+	0.726190i	$0.741289\pi$
$770$	20.8660	+	36.1410i	0.751959	+	1.30243i
$771$	−10.8027	+	9.91876i	−0.389051	+	0.357215i
$772$	−4.76570	+	8.25444i	−0.171521	+	0.297084i
$773$	38.7080			1.39223			0.696114	−	0.717931i	$-0.254911\pi$
$773$	38.7080			1.39223			0.696114	+	0.717931i	$0.254911\pi$
$774$	−26.9269	−	18.7743i	−0.967867	−	0.674828i
$775$	−5.26910			−0.189272
$776$	2.32662	−	4.02983i	0.0835209	−	0.144662i
$777$	56.1677	+	17.6479i	2.01501	+	0.633115i
$778$	−14.3782	−	24.9039i	−0.515485	−	0.892846i
$779$	−3.79532	−	6.57368i	−0.135981	−	0.235527i
$780$	−2.00038	−	8.98064i	−0.0716251	−	0.321559i
$781$	10.1572	−	17.5928i	0.363453	−	0.629519i
$782$	−0.544831			−0.0194831
$783$	−8.28305	+	1.11576i	−0.296012	+	0.0398740i
$784$	5.49581			0.196279
$785$	5.34975	−	9.26604i	0.190941	−	0.330719i
$786$	−1.46616	−	6.58228i	−0.0522962	−	0.234782i
$787$	16.5768	+	28.7118i	0.590899	+	1.02347i	0.994112	+	0.108361i	$0.0345601\pi$
$787$	16.5768	+	28.7118i	0.590899	+	1.02347i	−0.403213	+	0.915106i	$0.632107\pi$
$788$	−2.47011	−	4.27835i	−0.0879939	−	0.152410i
$789$	−47.6180	−	14.9616i	−1.69525	−	0.532647i
$790$	12.0928	−	20.9454i	0.430244	−	0.745204i
$791$	38.8121			1.38000
$792$	1.23137	−	14.4063i	0.0437550	−	0.511905i
$793$	−31.2505			−1.10974
$794$	−2.19307	+	3.79851i	−0.0778291	+	0.134804i
$795$	−19.7977	+	18.1777i	−0.702153	+	0.644697i
$796$	4.15412	+	7.19514i	0.147239	+	0.255025i
$797$	11.5670	+	20.0347i	0.409725	+	0.709665i	0.994859	−	0.101272i	$-0.0322913\pi$
$797$	11.5670	+	20.0347i	0.409725	+	0.709665i	−0.585134	+	0.810937i	$0.698958\pi$
$798$	4.50999	−	4.14094i	0.159652	−	0.146588i
$799$	3.44489	−	5.96673i	0.121872	−	0.211088i
$800$	−1.00000			−0.0353553
$801$	−34.3688	+	16.1101i	−1.21436	+	0.569224i
$802$	−18.1260			−0.640052
$803$	28.2229	−	48.8834i	0.995963	−	1.72506i
$804$	−18.4711	−	5.80361i	−0.651424	−	0.204678i
$805$	−3.29748	−	5.71140i	−0.116221	−	0.201300i
$806$	5.71337	+	9.89585i	0.201245	+	0.348566i
$807$	4.71277	+	21.1578i	0.165897	+	0.744790i
$808$	−2.63548	+	4.56478i	−0.0927158	+	0.160589i
$809$	−9.58467			−0.336979			−0.168489	−	0.985703i	$-0.553889\pi$
$809$	−9.58467			−0.336979			−0.168489	+	0.985703i	$0.553889\pi$
$810$	−14.1029	+	16.9443i	−0.495525	+	0.595361i
$811$	−1.79092			−0.0628877			−0.0314438	−	0.999506i	$-0.510011\pi$
$811$	−1.79092			−0.0628877			−0.0314438	+	0.999506i	$0.510011\pi$
$812$	−2.84292	+	4.92409i	−0.0997671	+	0.172802i
$813$	−4.34276	−	19.4967i	−0.152307	−	0.683779i
$814$	−23.1723	−	40.1356i	−0.812190	−	1.40675i
$815$	19.4649	+	33.7143i	0.681827	+	1.18096i
$816$	1.18202	+	0.371391i	0.0413790	+	0.0130013i
$817$	−5.47096	+	9.47599i	−0.191405	+	0.331523i
$818$	−21.3796			−0.747520
$819$	−20.8238	+	9.76101i	−0.727641	+	0.341077i
$820$	18.5932			0.649302
$821$	−0.444105	+	0.769213i	−0.0154994	+	0.0268457i	−0.873671	−	0.486517i	$-0.838267\pi$
$821$	−0.444105	+	0.769213i	−0.0154994	+	0.0268457i	0.858172	+	0.513363i	$0.171600\pi$
$822$	13.5388	−	12.4309i	0.472219	−	0.433578i
$823$	−4.32332	−	7.48822i	−0.150702	−	0.261023i	0.780784	−	0.624801i	$-0.214820\pi$
$823$	−4.32332	−	7.48822i	−0.150702	−	0.261023i	−0.931486	+	0.363778i	$0.881487\pi$
$824$	−1.00560	−	1.74175i	−0.0350316	−	0.0606766i
$825$	−6.14901	+	5.64584i	−0.214081	+	0.196563i
$826$	10.7010	−	18.5347i	0.372336	−	0.644905i
$827$	−11.1280			−0.386957			−0.193478	−	0.981105i	$-0.561977\pi$
$827$	−11.1280			−0.386957			−0.193478	+	0.981105i	$0.561977\pi$
$828$	−0.194595	+	2.27664i	−0.00676266	+	0.0791188i
$829$	6.64049			0.230634			0.115317	−	0.993329i	$-0.463212\pi$
$829$	6.64049			0.230634			0.115317	+	0.993329i	$0.463212\pi$
$830$	−8.60620	+	14.9064i	−0.298726	+	0.517408i
$831$	31.7596	+	9.97888i	1.10173	+	0.346164i
$832$	1.08432	+	1.87809i	0.0375919	+	0.0651111i
$833$	1.96566	+	3.40463i	0.0681062	+	0.117963i
$834$	0.447273	+	2.00802i	0.0154878	+	0.0695320i
$835$	26.5694	−	46.0196i	0.919473	−	1.59257i
$836$	−4.81961			−0.166690
$837$	10.4016	−	25.3262i	0.359532	−	0.875403i
$838$	3.20168			0.110600
$839$	−11.3139	+	19.5962i	−0.390599	+	0.676537i	−0.992529	−	0.122012i	$-0.961065\pi$
$839$	−11.3139	+	19.5962i	−0.390599	+	0.676537i	0.601930	+	0.798549i	$0.294399\pi$
$840$	3.26068	+	14.6387i	0.112504	+	0.505084i
$841$	13.2064	+	22.8742i	0.455393	+	0.788765i
$842$	13.5458	+	23.4620i	0.466819	+	0.808555i
$843$	−46.4306	−	14.5885i	−1.59916	−	0.502455i
$844$	−7.81375	+	13.5338i	−0.268960	+	0.465853i
$845$	−20.3235			−0.699149
$846$	−23.7023	−	16.5260i	−0.814901	−	0.568176i
$847$	−43.2275			−1.48531
$848$	3.16750	−	5.48627i	0.108772	−	0.188399i
$849$	5.90589	−	5.42262i	0.202690	−	0.186104i
$850$	−0.357666	−	0.619496i	−0.0122678	−	0.0212485i
$851$	3.66195	+	6.34268i	0.125530	+	0.217424i
$852$	5.37756	−	4.93753i	0.184232	−	0.169157i
$853$	−4.92079	+	8.52306i	−0.168485	+	0.291824i	−0.937887	−	0.346940i	$-0.887221\pi$
$853$	−4.92079	+	8.52306i	−0.168485	+	0.291824i	0.769403	+	0.638764i	$0.220554\pi$
$854$	50.9393			1.74311
$855$	6.02793	+	4.20287i	0.206151	+	0.143735i
$856$	1.89160			0.0646534
$857$	4.69502	−	8.13202i	0.160379	−	0.277784i	−0.774626	−	0.632420i	$-0.782062\pi$
$857$	4.69502	−	8.13202i	0.160379	−	0.277784i	0.935005	+	0.354636i	$0.115395\pi$
$858$	17.2709	+	5.42652i	0.589618	+	0.185258i
$859$	−27.6550	−	47.8999i	−0.943577	−	1.63432i	−0.758576	−	0.651585i	$-0.774104\pi$
$859$	−27.6550	−	47.8999i	−0.943577	−	1.63432i	−0.185001	−	0.982738i	$-0.559229\pi$
$860$	−13.4011	−	23.2113i	−0.456973	−	0.791500i
$861$	−10.1044	−	45.3634i	−0.344357	−	1.54598i
$862$	−8.43969	+	14.6180i	−0.287457	+	0.497890i
$863$	40.8518			1.39061			0.695306	−	0.718714i	$-0.255269\pi$
$863$	40.8518			1.39061			0.695306	+	0.718714i	$0.255269\pi$
$864$	1.97408	−	4.80656i	0.0671595	−	0.163522i
$865$	41.0062			1.39425
$866$	13.7684	−	23.8476i	0.467870	−	0.810374i
$867$	−6.20907	−	27.8754i	−0.210871	−	0.946699i
$868$	−9.31297	−	16.1305i	−0.316103	−	0.547506i
$869$	23.7938	+	41.2121i	0.807150	+	1.39803i
$870$	−6.51037	−	2.04556i	−0.220722	−	0.0693510i
$871$	12.1208	−	20.9938i	0.410698	−	0.711349i
$872$	−14.1121			−0.477896
$873$	1.18887	−	13.9090i	0.0402371	−	0.470749i
$874$	0.761648			0.0257631
$875$	−17.3176	+	29.9950i	−0.585442	+	1.01401i
$876$	14.9421	−	13.7194i	0.504848	−	0.463537i
$877$	8.39803	+	14.5458i	0.283581	+	0.491177i	0.972264	−	0.233885i	$-0.0751441\pi$
$877$	8.39803	+	14.5458i	0.283581	+	0.491177i	−0.688683	+	0.725063i	$0.741811\pi$
$878$	−0.716365	−	1.24078i	−0.0241761	−	0.0418743i
$879$	34.9248	−	32.0669i	1.17798	−	1.08159i
$880$	5.90279	−	10.2239i	0.198983	−	0.344649i
$881$	−14.4415			−0.486547			−0.243273	−	0.969958i	$-0.578221\pi$
$881$	−14.4415			−0.486547			−0.243273	+	0.969958i	$0.578221\pi$
$882$	14.9287	−	6.99774i	0.502676	−	0.235626i
$883$	55.1581			1.85622			0.928108	−	0.372310i	$-0.121434\pi$
$883$	55.1581			1.85622			0.928108	+	0.372310i	$0.121434\pi$
$884$	−0.775647	+	1.34346i	−0.0260878	+	0.0451854i
$885$	24.5056	+	7.69967i	0.823747	+	0.258821i
$886$	1.48941	+	2.57974i	0.0500378	+	0.0866681i
$887$	−8.33341	−	14.4339i	−0.279809	−	0.484643i	0.691528	−	0.722349i	$-0.256938\pi$
$887$	−8.33341	−	14.4339i	−0.279809	−	0.484643i	−0.971337	+	0.237706i	$0.923604\pi$
$888$	−3.62108	−	16.2567i	−0.121516	−	0.545541i
$889$	17.3424	−	30.0379i	0.581645	−	1.00744i
$890$	−30.9919			−1.03885
$891$	−14.9985	−	40.7009i	−0.502468	−	1.36353i
$892$	−3.46523			−0.116024
$893$	−4.81579	+	8.34120i	−0.161154	+	0.279128i
$894$	−1.32466	−	5.94702i	−0.0443032	−	0.198898i
$895$	27.6991	+	47.9762i	0.925877	+	1.60367i
$896$	−1.76747	−	3.06135i	−0.0590470	−	0.102272i
$897$	−2.72934	−	0.857558i	−0.0911299	−	0.0286330i
$898$	−3.65564	+	6.33176i	−0.121990	+	0.211294i
$899$	8.47519			0.282663
$900$	−2.71638	+	1.27329i	−0.0905461	+	0.0424429i
$901$	4.53163			0.150970
$902$	−18.2919	+	31.6826i	−0.609055	+	1.05491i
$903$	−49.3480	+	45.3099i	−1.64220	+	1.50782i
$904$	−5.48979	−	9.50859i	−0.182588	−	0.316251i
$905$	4.57689	+	7.92741i	0.152141	+	0.263516i
$906$	30.4882	−	27.9934i	1.01290	−	0.930020i
$907$	−28.3598	+	49.1207i	−0.941673	+	1.63103i	−0.179394	+	0.983777i	$0.557414\pi$
$907$	−28.3598	+	49.1207i	−0.941673	+	1.63103i	−0.762279	+	0.647249i	$0.775920\pi$
$908$	14.7316			0.488886
$909$	−1.34669	+	15.7554i	−0.0446669	+	0.522574i
$910$	−18.7778			−0.622477
$911$	8.07535	−	13.9869i	0.267548	−	0.463407i	−0.700680	−	0.713476i	$-0.747120\pi$
$911$	8.07535	−	13.9869i	0.267548	−	0.463407i	0.968228	+	0.250069i	$0.0804532\pi$
$912$	−1.65241	−	0.519186i	−0.0547166	−	0.0171920i
$913$	−16.9335	−	29.3297i	−0.560418	−	0.970673i
$914$	14.0894	+	24.4036i	0.466037	+	0.807200i
$915$	13.2922	+	59.6750i	0.439427	+	1.97280i
$916$	−5.51065	+	9.54472i	−0.182077	+	0.315367i
$917$	−13.7630			−0.454494
$918$	3.68371	−	0.496210i	0.121580	−	0.0163774i
$919$	29.6054			0.976593			0.488296	−	0.872678i	$-0.337619\pi$
$919$	29.6054			0.976593			0.488296	+	0.872678i	$0.337619\pi$
$920$	−0.932824	+	1.61570i	−0.0307543	+	0.0532680i
$921$	5.68231	+	25.5105i	0.187238	+	0.840601i
$922$	14.4021	+	24.9452i	0.474308	+	0.821525i
$923$	4.57034	+	7.91606i	0.150435	+	0.260560i
$924$	−28.1521	−	8.84539i	−0.926136	−	0.290992i
$925$	−4.80793	+	8.32757i	−0.158084	+	0.273809i
$926$	−21.5500			−0.708177
$927$	−4.94933	−	3.45083i	−0.162557	−	0.113340i
$928$	1.60847			0.0528006
$929$	10.2121	−	17.6880i	0.335050	−	0.580323i	−0.648445	−	0.761262i	$-0.724580\pi$
$929$	10.2121	−	17.6880i	0.335050	−	0.580323i	0.983494	+	0.180939i	$0.0579136\pi$
$930$	16.4667	−	15.1192i	0.539963	−	0.495778i
$931$	−2.74790	−	4.75951i	−0.0900589	−	0.155987i
$932$	−14.9569	−	25.9062i	−0.489931	−	0.848585i
$933$	−22.8259	+	20.9580i	−0.747285	+	0.686136i
$934$	−4.81703	+	8.34335i	−0.157618	+	0.273003i
$935$	8.44491			0.276178
$936$	5.33677	+	3.72097i	0.174438	+	0.121624i
$937$	44.4709			1.45280			0.726400	−	0.687272i	$-0.241192\pi$
$937$	44.4709			1.45280			0.726400	+	0.687272i	$0.241192\pi$
$938$	−19.7573	+	34.2206i	−0.645098	+	1.11734i
$939$	−22.9153	−	7.19999i	−0.747812	−	0.234963i
$940$	−11.7962	−	20.4317i	−0.384751	−	0.666408i
$941$	1.49284	+	2.58568i	0.0486653	+	0.0842908i	0.889332	−	0.457262i	$-0.151170\pi$
$941$	1.49284	+	2.58568i	0.0486653	+	0.0842908i	−0.840667	+	0.541553i	$0.817837\pi$
$942$	1.64490	+	7.38471i	0.0535936	+	0.240607i
$943$	2.89069	−	5.00683i	0.0941339	−	0.163045i
$944$	−6.05442			−0.197055
$945$	27.4966	+	35.6126i	0.894464	+	1.15848i
$946$	52.7358			1.71459
$947$	6.57072	−	11.3808i	0.213520	−	0.369827i	−0.739294	−	0.673383i	$-0.764841\pi$
$947$	6.57072	−	11.3808i	0.213520	−	0.369827i	0.952814	+	0.303556i	$0.0981740\pi$
$948$	3.71820	+	16.6928i	0.120762	+	0.542156i
$949$	12.6992	+	21.9956i	0.412233	+	0.714008i
$950$	0.500000	+	0.866025i	0.0162221	+	0.0280976i
$951$	−8.23932	−	2.58880i	−0.267178	−	0.0839475i
$952$	1.26433	−	2.18988i	0.0409771	−	0.0709745i
$953$	26.1201			0.846113			0.423057	−	0.906103i	$-0.360957\pi$
$953$	26.1201			0.846113			0.423057	+	0.906103i	$0.360957\pi$
$954$	1.61855	−	18.9359i	0.0524023	−	0.613074i
$955$	33.4376			1.08202
$956$	1.14603	−	1.98497i	0.0370651	−	0.0641987i
$957$	9.89050	−	9.08118i	0.319714	−	0.293553i
$958$	−8.41307	−	14.5719i	−0.271814	−	0.470796i
$959$	−18.7559	−	32.4862i	−0.605660	−	1.04903i
$960$	3.12514	−	2.86941i	0.100863	−	0.0926099i
$961$	1.61830	−	2.80298i	0.0522033	−	0.0904188i
$962$	20.8533			0.672336
$963$	5.13830	−	2.40855i	0.165579	−	0.0776143i
$964$	−12.7913			−0.411980
$965$	−11.6735	+	20.2192i	−0.375785	+	0.650878i
$966$	4.44890	+	1.39785i	0.143141	+	0.0449750i
$967$	2.33711	+	4.04799i	0.0751563	+	0.130175i	0.901154	−	0.433499i	$-0.142721\pi$
$967$	2.33711	+	4.04799i	0.0751563	+	0.130175i	−0.825998	+	0.563673i	$0.809388\pi$
$968$	6.11431	+	10.5903i	0.196521	+	0.340385i
$969$	−0.269376	−	1.20935i	−0.00865360	−	0.0388501i
$970$	5.69904	−	9.87102i	0.182985	−	0.316939i
$971$	−6.04764			−0.194078			−0.0970390	−	0.995281i	$-0.530937\pi$
$971$	−6.04764			−0.194078			−0.0970390	+	0.995281i	$0.530937\pi$
$972$	−0.757777	−	15.5700i	−0.0243057	−	0.499409i
$973$	4.19860			0.134601
$974$	11.9394	−	20.6797i	0.382563	−	0.662619i
$975$	−0.816652	−	3.66633i	−0.0261538	−	0.117417i
$976$	−7.20512	−	12.4796i	−0.230630	−	0.399463i
$977$	0.755293	+	1.30821i	0.0241640	+	0.0418532i	0.877855	−	0.478927i	$-0.158974\pi$
$977$	0.755293	+	1.30821i	0.0241640	+	0.0418532i	−0.853691	+	0.520781i	$0.825641\pi$
$978$	−26.2618	−	8.25146i	−0.839759	−	0.263853i
$979$	30.4898	−	52.8099i	0.974459	−	1.68781i
$980$	13.4619			0.430025
$981$	−38.3339	+	17.9688i	−1.22391	+	0.573698i
$982$	7.28113			0.232350
$983$	6.56473	−	11.3704i	0.209382	−	0.362661i	−0.742138	−	0.670247i	$-0.766188\pi$
$983$	6.56473	−	11.3704i	0.209382	−	0.362661i	0.951520	+	0.307587i	$0.0995214\pi$
$984$	−9.68437	+	8.89191i	−0.308726	+	0.283464i
$985$	−6.05050	−	10.4798i	−0.192785	−	0.333913i
$986$	0.575296	+	0.996441i	0.0183211	+	0.0317332i
$987$	−43.4383	+	39.8839i	−1.38266	+	1.26952i
$988$	1.08432	−	1.87809i	0.0344967	−	0.0597500i
$989$	−8.33389			−0.265002
$990$	3.01624	−	35.2881i	0.0958624	−	1.12153i
$991$	−13.8165			−0.438896			−0.219448	−	0.975624i	$-0.570426\pi$
$991$	−13.8165			−0.438896			−0.219448	+	0.975624i	$0.570426\pi$
$992$	−2.63455	+	4.56317i	−0.0836470	+	0.144881i
$993$	−5.47638	−	1.72068i	−0.173788	−	0.0546042i
$994$	−7.44980	−	12.9034i	−0.236293	−	0.409272i
$995$	10.1755	+	17.6244i	0.322584	+	0.558732i
$996$	−2.64616	−	11.8799i	−0.0838469	−	0.376428i
$997$	−1.63400	+	2.83017i	−0.0517493	+	0.0896324i	−0.890740	−	0.454514i	$-0.849813\pi$
$997$	−1.63400	+	2.83017i	−0.0517493	+	0.0896324i	0.838990	+	0.544146i	$0.183146\pi$
$998$	−33.8420			−1.07125
$999$	−30.5358	−	39.5489i	−0.966109	−	1.25127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.e.d.115.4	✓	12
3.2	odd	2		1026.2.e.c.343.6		12
9.2	odd	6		3078.2.a.w.1.1		6
9.4	even	3	inner	342.2.e.d.229.4	yes	12
9.5	odd	6		1026.2.e.c.685.6		12
9.7	even	3		3078.2.a.u.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.e.d.115.4	✓	12	1.1	even	1	trivial
342.2.e.d.229.4	yes	12	9.4	even	3	inner
1026.2.e.c.343.6		12	3.2	odd	2
1026.2.e.c.685.6		12	9.5	odd	6
3078.2.a.u.1.4		6	9.7	even	3
3078.2.a.w.1.1		6	9.2	odd	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.376574 + 1.69062i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(1.65241 + 0.519186i) q^{6} +(1.76747 - 3.06135i) q^{7} -1.00000 q^{8} +(-2.71638 + 1.27329i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.376574 + 1.69062i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(1.65241 + 0.519186i) q^{6} +(1.76747 - 3.06135i) q^{7} -1.00000 q^{8} +(-2.71638 + 1.27329i) q^{9} -2.44949 q^{10} +(2.40980 - 4.17390i) q^{11} +(1.27583 - 1.17143i) q^{12} +(1.08432 + 1.87809i) q^{13} +(-1.76747 - 3.06135i) q^{14} +(3.12514 - 2.86941i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.715332 q^{17} +(-0.255493 + 2.98910i) q^{18} +1.00000 q^{19} +(-1.22474 + 2.12132i) q^{20} +(5.84116 + 1.83529i) q^{21} +(-2.40980 - 4.17390i) q^{22} +(0.380824 + 0.659606i) q^{23} +(-0.376574 - 1.69062i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.16863 q^{26} +(-3.17556 - 4.11288i) q^{27} -3.53494 q^{28} +(0.804235 - 1.39298i) q^{29} +(-0.922415 - 4.14115i) q^{30} +(2.63455 + 4.56317i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.96395 + 2.50228i) q^{33} +(-0.357666 + 0.619496i) q^{34} -8.65880 q^{35} +(2.46089 + 1.71581i) q^{36} +9.61585 q^{37} +(0.500000 - 0.866025i) q^{38} +(-2.76681 + 2.54041i) q^{39} +(1.22474 + 2.12132i) q^{40} +(-3.79532 - 6.57368i) q^{41} +(4.50999 - 4.14094i) q^{42} +(-5.47096 + 9.47599i) q^{43} -4.81961 q^{44} +(6.02793 + 4.20287i) q^{45} +0.761648 q^{46} +(-4.81579 + 8.34120i) q^{47} +(-1.65241 - 0.519186i) q^{48} +(-2.74790 - 4.75951i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.269376 - 1.20935i) q^{51} +(1.08432 - 1.87809i) q^{52} -6.33500 q^{53} +(-5.14964 + 0.693678i) q^{54} -11.8056 q^{55} +(-1.76747 + 3.06135i) q^{56} +(0.376574 + 1.69062i) q^{57} +(-0.804235 - 1.39298i) q^{58} +(3.02721 + 5.24329i) q^{59} +(-4.04755 - 1.27174i) q^{60} +(-7.20512 + 12.4796i) q^{61} +5.26910 q^{62} +(-0.903151 + 10.5663i) q^{63} +1.00000 q^{64} +(2.65602 - 4.60037i) q^{65} +(6.14901 - 5.64584i) q^{66} +(-5.58914 - 9.68068i) q^{67} +(0.357666 + 0.619496i) q^{68} +(-0.971734 + 0.892219i) q^{69} +(-4.32940 + 7.49874i) q^{70} +4.21495 q^{71} +(2.71638 - 1.27329i) q^{72} +11.7117 q^{73} +(4.80793 - 8.32757i) q^{74} +(-1.65241 - 0.519186i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(-8.51851 - 14.7545i) q^{77} +(0.816652 + 3.66633i) q^{78} +(-4.93688 + 8.55093i) q^{79} +2.44949 q^{80} +(5.75748 - 6.91747i) q^{81} -7.59063 q^{82} +(3.51347 - 6.08550i) q^{83} +(-1.33117 - 5.97624i) q^{84} +(0.876100 + 1.51745i) q^{85} +(5.47096 + 9.47599i) q^{86} +(2.65785 + 0.835096i) q^{87} +(-2.40980 + 4.17390i) q^{88} +12.6524 q^{89} +(6.65375 - 3.11890i) q^{90} +7.66599 q^{91} +(0.380824 - 0.659606i) q^{92} +(-6.72248 + 6.17239i) q^{93} +(4.81579 + 8.34120i) q^{94} +(-1.22474 - 2.12132i) q^{95} +(-1.27583 + 1.17143i) q^{96} +(-2.32662 + 4.02983i) q^{97} -5.49581 q^{98} +(-1.23137 + 14.4063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} - 8 q^{9} + 4 q^{11} - 8 q^{13} + 4 q^{14} + 12 q^{15} - 6 q^{16} - 8 q^{17} - 4 q^{18} + 12 q^{19} + 14 q^{21} - 4 q^{22} + 4 q^{23} - 6 q^{25} - 16 q^{26} - 18 q^{27} + 8 q^{28} - 8 q^{31} + 6 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 44 q^{37} + 6 q^{38} - 14 q^{39} + 4 q^{41} + 10 q^{42} - 20 q^{43} - 8 q^{44} - 24 q^{45} + 8 q^{46} + 10 q^{47} - 18 q^{49} + 6 q^{50} + 28 q^{51} - 8 q^{52} + 8 q^{53} + 4 q^{56} + 16 q^{59} - 12 q^{60} - 12 q^{61} - 16 q^{62} - 12 q^{63} + 12 q^{64} - 24 q^{65} - 28 q^{66} - 20 q^{67} + 4 q^{68} + 40 q^{69} + 8 q^{71} + 8 q^{72} + 8 q^{73} + 22 q^{74} - 6 q^{76} - 20 q^{77} - 10 q^{78} - 16 q^{79} - 8 q^{81} + 8 q^{82} + 8 q^{83} - 4 q^{84} + 20 q^{86} + 42 q^{87} - 4 q^{88} - 8 q^{89} + 24 q^{90} + 68 q^{91} + 4 q^{92} + 16 q^{93} - 10 q^{94} - 24 q^{97} - 36 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 - 8 * q^9 + 4 * q^11 - 8 * q^13 + 4 * q^14 + 12 * q^15 - 6 * q^16 - 8 * q^17 - 4 * q^18 + 12 * q^19 + 14 * q^21 - 4 * q^22 + 4 * q^23 - 6 * q^25 - 16 * q^26 - 18 * q^27 + 8 * q^28 - 8 * q^31 + 6 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 44 * q^37 + 6 * q^38 - 14 * q^39 + 4 * q^41 + 10 * q^42 - 20 * q^43 - 8 * q^44 - 24 * q^45 + 8 * q^46 + 10 * q^47 - 18 * q^49 + 6 * q^50 + 28 * q^51 - 8 * q^52 + 8 * q^53 + 4 * q^56 + 16 * q^59 - 12 * q^60 - 12 * q^61 - 16 * q^62 - 12 * q^63 + 12 * q^64 - 24 * q^65 - 28 * q^66 - 20 * q^67 + 4 * q^68 + 40 * q^69 + 8 * q^71 + 8 * q^72 + 8 * q^73 + 22 * q^74 - 6 * q^76 - 20 * q^77 - 10 * q^78 - 16 * q^79 - 8 * q^81 + 8 * q^82 + 8 * q^83 - 4 * q^84 + 20 * q^86 + 42 * q^87 - 4 * q^88 - 8 * q^89 + 24 * q^90 + 68 * q^91 + 4 * q^92 + 16 * q^93 - 10 * q^94 - 24 * q^97 - 36 * q^98 - 4 * q^99

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