LMFDB - Embedded newform 430.2.e.g.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, 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("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 12x^{8} + x^{7} + 106x^{6} - 27x^{5} + 233x^{4} - 164x^{3} + 460x^{2} - 240x + 144 $ x^10 - x^9 + 12x^8 + x^7 + 106x^6 - 27x^5 + 233x^4 - 164x^3 + 460x^2 - 240*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			251.2
Root			$-0.850932 - 1.47386i$ of defining polynomial
Character	$\chi$	$=$	430.251
Dual form			430.2.e.g.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.850932 - 1.47386i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.850932 + 1.47386i) q^{6} +(-1.11274 + 1.92732i) q^{7} -1.00000 q^{8} +(0.0518303 - 0.0897728i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.850932 - 1.47386i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.850932 + 1.47386i) q^{6} +(-1.11274 + 1.92732i) q^{7} -1.00000 q^{8} +(0.0518303 - 0.0897728i) q^{9} +(-0.500000 - 0.866025i) q^{10} -2.26385 q^{11} +(-0.850932 - 1.47386i) q^{12} +(-2.41184 + 4.17743i) q^{13} +(1.11274 - 1.92732i) q^{14} +(0.850932 - 1.47386i) q^{15} +1.00000 q^{16} +(-2.16457 + 3.74915i) q^{17} +(-0.0518303 + 0.0897728i) q^{18} +(-2.83379 - 4.90826i) q^{19} +(0.500000 + 0.866025i) q^{20} +3.78746 q^{21} +2.26385 q^{22} +(1.37011 + 2.37311i) q^{23} +(0.850932 + 1.47386i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.41184 - 4.17743i) q^{26} -5.28201 q^{27} +(-1.11274 + 1.92732i) q^{28} +(-0.480817 + 0.832799i) q^{29} +(-0.850932 + 1.47386i) q^{30} +(5.00744 + 8.67314i) q^{31} -1.00000 q^{32} +(1.92638 + 3.33659i) q^{33} +(2.16457 - 3.74915i) q^{34} -2.22548 q^{35} +(0.0518303 - 0.0897728i) q^{36} +(5.29649 + 9.17380i) q^{37} +(2.83379 + 4.90826i) q^{38} +8.20925 q^{39} +(-0.500000 - 0.866025i) q^{40} -4.40373 q^{41} -3.78746 q^{42} +(6.54820 + 0.347967i) q^{43} -2.26385 q^{44} +0.103661 q^{45} +(-1.37011 - 2.37311i) q^{46} -10.0108 q^{47} +(-0.850932 - 1.47386i) q^{48} +(1.02362 + 1.77296i) q^{49} +(0.500000 - 0.866025i) q^{50} +7.36761 q^{51} +(-2.41184 + 4.17743i) q^{52} +(-1.56198 - 2.70544i) q^{53} +5.28201 q^{54} +(-1.13192 - 1.96055i) q^{55} +(1.11274 - 1.92732i) q^{56} +(-4.82272 + 8.35319i) q^{57} +(0.480817 - 0.832799i) q^{58} -4.32914 q^{59} +(0.850932 - 1.47386i) q^{60} +(-5.97479 + 10.3486i) q^{61} +(-5.00744 - 8.67314i) q^{62} +(0.115347 + 0.199788i) q^{63} +1.00000 q^{64} -4.82368 q^{65} +(-1.92638 - 3.33659i) q^{66} +(-5.62018 - 9.73443i) q^{67} +(-2.16457 + 3.74915i) q^{68} +(2.33175 - 4.03871i) q^{69} +2.22548 q^{70} +(6.74359 - 11.6802i) q^{71} +(-0.0518303 + 0.0897728i) q^{72} +(5.46367 - 9.46336i) q^{73} +(-5.29649 - 9.17380i) q^{74} +1.70186 q^{75} +(-2.83379 - 4.90826i) q^{76} +(2.51907 - 4.36316i) q^{77} -8.20925 q^{78} +(-3.66110 + 6.34121i) q^{79} +(0.500000 + 0.866025i) q^{80} +(4.33914 + 7.51560i) q^{81} +4.40373 q^{82} +(-4.58448 - 7.94055i) q^{83} +3.78746 q^{84} -4.32914 q^{85} +(-6.54820 - 0.347967i) q^{86} +1.63657 q^{87} +2.26385 q^{88} +(4.94209 + 8.55996i) q^{89} -0.103661 q^{90} +(-5.36751 - 9.29680i) q^{91} +(1.37011 + 2.37311i) q^{92} +(8.52198 - 14.7605i) q^{93} +10.0108 q^{94} +(2.83379 - 4.90826i) q^{95} +(0.850932 + 1.47386i) q^{96} +2.19855 q^{97} +(-1.02362 - 1.77296i) q^{98} +(-0.117336 + 0.203232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9} - 5 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 10 q^{16} + 4 q^{17} + 8 q^{18} + 4 q^{19} + 5 q^{20} - 4 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} - 5 q^{25} + 6 q^{26} - 26 q^{27} + 6 q^{28} - q^{29} + q^{30} - 8 q^{31} - 10 q^{32} - 14 q^{33} - 4 q^{34} + 12 q^{35} - 8 q^{36} + 14 q^{37} - 4 q^{38} + 8 q^{39} - 5 q^{40} - 6 q^{41} + 4 q^{42} + 15 q^{43} + 4 q^{44} - 16 q^{45} - 8 q^{46} - 22 q^{47} + q^{48} - 5 q^{49} + 5 q^{50} + 24 q^{51} - 6 q^{52} - 8 q^{53} + 26 q^{54} + 2 q^{55} - 6 q^{56} - 32 q^{57} + q^{58} + 8 q^{59} - q^{60} - 14 q^{61} + 8 q^{62} + 22 q^{63} + 10 q^{64} - 12 q^{65} + 14 q^{66} + 19 q^{67} + 4 q^{68} + 10 q^{69} - 12 q^{70} + 36 q^{71} + 8 q^{72} + 28 q^{73} - 14 q^{74} - 2 q^{75} + 4 q^{76} + 8 q^{77} - 8 q^{78} - 10 q^{79} + 5 q^{80} - 25 q^{81} + 6 q^{82} - 25 q^{83} - 4 q^{84} + 8 q^{85} - 15 q^{86} + 22 q^{87} - 4 q^{88} + 19 q^{89} + 16 q^{90} - 10 q^{91} + 8 q^{92} + 12 q^{93} + 22 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 5 q^{98} - 6 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9 - 5 * q^10 + 4 * q^11 + q^12 - 6 * q^13 - 6 * q^14 - q^15 + 10 * q^16 + 4 * q^17 + 8 * q^18 + 4 * q^19 + 5 * q^20 - 4 * q^21 - 4 * q^22 + 8 * q^23 - q^24 - 5 * q^25 + 6 * q^26 - 26 * q^27 + 6 * q^28 - q^29 + q^30 - 8 * q^31 - 10 * q^32 - 14 * q^33 - 4 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 - 4 * q^38 + 8 * q^39 - 5 * q^40 - 6 * q^41 + 4 * q^42 + 15 * q^43 + 4 * q^44 - 16 * q^45 - 8 * q^46 - 22 * q^47 + q^48 - 5 * q^49 + 5 * q^50 + 24 * q^51 - 6 * q^52 - 8 * q^53 + 26 * q^54 + 2 * q^55 - 6 * q^56 - 32 * q^57 + q^58 + 8 * q^59 - q^60 - 14 * q^61 + 8 * q^62 + 22 * q^63 + 10 * q^64 - 12 * q^65 + 14 * q^66 + 19 * q^67 + 4 * q^68 + 10 * q^69 - 12 * q^70 + 36 * q^71 + 8 * q^72 + 28 * q^73 - 14 * q^74 - 2 * q^75 + 4 * q^76 + 8 * q^77 - 8 * q^78 - 10 * q^79 + 5 * q^80 - 25 * q^81 + 6 * q^82 - 25 * q^83 - 4 * q^84 + 8 * q^85 - 15 * q^86 + 22 * q^87 - 4 * q^88 + 19 * q^89 + 16 * q^90 - 10 * q^91 + 8 * q^92 + 12 * q^93 + 22 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 5 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.850932	−	1.47386i	−0.491286	−	0.850932i	0.508664	−	0.860965i	$-0.330140\pi$
$3$	−0.850932	−	1.47386i	−0.491286	−	0.850932i	−0.999950	+	0.0100334i	$0.996806\pi$
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.850932	+	1.47386i	0.347391	+	0.601700i
$7$	−1.11274	+	1.92732i	−0.420576	+	0.728460i	−0.995996	−	0.0893988i	$-0.971505\pi$
$7$	−1.11274	+	1.92732i	−0.420576	+	0.728460i	0.575420	+	0.817858i	$0.304839\pi$
$8$	−1.00000			−0.353553
$9$	0.0518303	−	0.0897728i	0.0172768	−	0.0299243i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.26385			−0.682576			−0.341288	−	0.939959i	$-0.610863\pi$
$11$	−2.26385			−0.682576			−0.341288	+	0.939959i	$0.610863\pi$
$12$	−0.850932	−	1.47386i	−0.245643	−	0.425466i
$13$	−2.41184	+	4.17743i	−0.668925	+	1.15861i	0.309281	+	0.950971i	$0.399912\pi$
$13$	−2.41184	+	4.17743i	−0.668925	+	1.15861i	−0.978205	+	0.207641i	$0.933422\pi$
$14$	1.11274	−	1.92732i	0.297392	−	0.515099i
$15$	0.850932	−	1.47386i	0.219710	−	0.380548i
$16$	1.00000			0.250000
$17$	−2.16457	+	3.74915i	−0.524986	+	0.909302i	0.474591	+	0.880206i	$0.342596\pi$
$17$	−2.16457	+	3.74915i	−0.524986	+	0.909302i	−0.999577	+	0.0290952i	$0.990737\pi$
$18$	−0.0518303	+	0.0897728i	−0.0122165	+	0.0211596i
$19$	−2.83379	−	4.90826i	−0.650115	−	1.12603i	−0.983095	−	0.183099i	$-0.941387\pi$
$19$	−2.83379	−	4.90826i	−0.650115	−	1.12603i	0.332979	−	0.942934i	$-0.391946\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	3.78746			0.826493
$22$	2.26385			0.482654
$23$	1.37011	+	2.37311i	0.285689	+	0.494827i	0.972776	−	0.231748i	$-0.0744443\pi$
$23$	1.37011	+	2.37311i	0.285689	+	0.494827i	−0.687087	+	0.726575i	$0.741111\pi$
$24$	0.850932	+	1.47386i	0.173696	+	0.300850i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.41184	−	4.17743i	0.473001	−	0.819262i
$27$	−5.28201			−1.01652
$28$	−1.11274	+	1.92732i	−0.210288	+	0.364230i
$29$	−0.480817	+	0.832799i	−0.0892854	+	0.154647i	−0.907209	−	0.420680i	$-0.861792\pi$
$29$	−0.480817	+	0.832799i	−0.0892854	+	0.154647i	0.817924	+	0.575327i	$0.195125\pi$
$30$	−0.850932	+	1.47386i	−0.155358	+	0.269088i
$31$	5.00744	+	8.67314i	0.899362	+	1.55774i	0.828311	+	0.560269i	$0.189302\pi$
$31$	5.00744	+	8.67314i	0.899362	+	1.55774i	0.0710514	+	0.997473i	$0.477365\pi$
$32$	−1.00000			−0.176777
$33$	1.92638	+	3.33659i	0.335340	+	0.580825i
$34$	2.16457	−	3.74915i	0.371221	−	0.642973i
$35$	−2.22548			−0.376175
$36$	0.0518303	−	0.0897728i	0.00863839	−	0.0149621i
$37$	5.29649	+	9.17380i	0.870738	+	1.50816i	0.861234	+	0.508208i	$0.169692\pi$
$37$	5.29649	+	9.17380i	0.870738	+	1.50816i	0.00950406	+	0.999955i	$0.496975\pi$
$38$	2.83379	+	4.90826i	0.459701	+	0.796225i
$39$	8.20925			1.31453
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−4.40373			−0.687747			−0.343873	−	0.939016i	$-0.611739\pi$
$41$	−4.40373			−0.687747			−0.343873	+	0.939016i	$0.611739\pi$
$42$	−3.78746			−0.584418
$43$	6.54820	+	0.347967i	0.998591	+	0.0530644i
$43$	6.54820	+	0.347967i	0.998591	+	0.0530644i
$44$	−2.26385			−0.341288
$45$	0.103661			0.0154528
$46$	−1.37011	−	2.37311i	−0.202012	−	0.349896i
$47$	−10.0108			−1.46022			−0.730112	−	0.683327i	$-0.760532\pi$
$47$	−10.0108			−1.46022			−0.730112	+	0.683327i	$0.760532\pi$
$48$	−0.850932	−	1.47386i	−0.122821	−	0.212733i
$49$	1.02362	+	1.77296i	0.146231	+	0.253280i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	7.36761			1.03167
$52$	−2.41184	+	4.17743i	−0.334462	+	0.579306i
$53$	−1.56198	−	2.70544i	−0.214555	−	0.371620i	0.738580	−	0.674166i	$-0.235497\pi$
$53$	−1.56198	−	2.70544i	−0.214555	−	0.371620i	−0.953135	+	0.302546i	$0.902163\pi$
$54$	5.28201			0.718790
$55$	−1.13192	−	1.96055i	−0.152629	−	0.264360i
$56$	1.11274	−	1.92732i	0.148696	−	0.257549i
$57$	−4.82272	+	8.35319i	−0.638785	+	1.10641i
$58$	0.480817	−	0.832799i	0.0631343	−	0.109352i
$59$	−4.32914			−0.563606			−0.281803	−	0.959472i	$-0.590932\pi$
$59$	−4.32914			−0.563606			−0.281803	+	0.959472i	$0.590932\pi$
$60$	0.850932	−	1.47386i	0.109855	−	0.190274i
$61$	−5.97479	+	10.3486i	−0.764994	+	1.32501i	0.175256	+	0.984523i	$0.443925\pi$
$61$	−5.97479	+	10.3486i	−0.764994	+	1.32501i	−0.940250	+	0.340485i	$0.889409\pi$
$62$	−5.00744	−	8.67314i	−0.635945	−	1.10149i
$63$	0.115347	+	0.199788i	0.0145324	+	0.0251709i
$64$	1.00000			0.125000
$65$	−4.82368			−0.598304
$66$	−1.92638	−	3.33659i	−0.237121	−	0.410705i
$67$	−5.62018	−	9.73443i	−0.686614	−	1.18925i	−0.972927	−	0.231114i	$-0.925763\pi$
$67$	−5.62018	−	9.73443i	−0.686614	−	1.18925i	0.286313	−	0.958136i	$-0.407570\pi$
$68$	−2.16457	+	3.74915i	−0.262493	+	0.454651i
$69$	2.33175	−	4.03871i	0.280710	−	0.486203i
$70$	2.22548			0.265996
$71$	6.74359	−	11.6802i	0.800317	−	1.38619i	−0.119091	−	0.992883i	$-0.537998\pi$
$71$	6.74359	−	11.6802i	0.800317	−	1.38619i	0.919408	−	0.393306i	$-0.128669\pi$
$72$	−0.0518303	+	0.0897728i	−0.00610826	+	0.0105798i
$73$	5.46367	−	9.46336i	0.639474	−	1.10760i	−0.346074	−	0.938207i	$-0.612485\pi$
$73$	5.46367	−	9.46336i	0.639474	−	1.10760i	0.985548	−	0.169395i	$-0.0541813\pi$
$74$	−5.29649	−	9.17380i	−0.615705	−	1.06643i
$75$	1.70186			0.196514
$76$	−2.83379	−	4.90826i	−0.325058	−	0.563016i
$77$	2.51907	−	4.36316i	0.287075	−	0.497229i
$78$	−8.20925			−0.929515
$79$	−3.66110	+	6.34121i	−0.411906	+	0.713442i	−0.995098	−	0.0988920i	$-0.968470\pi$
$79$	−3.66110	+	6.34121i	−0.411906	+	0.713442i	0.583192	+	0.812334i	$0.301803\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	4.33914	+	7.51560i	0.482126	+	0.835067i
$82$	4.40373			0.486310
$83$	−4.58448	−	7.94055i	−0.503212	−	0.871588i	−0.999993	−	0.00371262i	$-0.998818\pi$
$83$	−4.58448	−	7.94055i	−0.503212	−	0.871588i	0.496781	−	0.867876i	$-0.334515\pi$
$84$	3.78746			0.413246
$85$	−4.32914			−0.469561
$86$	−6.54820	−	0.347967i	−0.706111	−	0.0375222i
$87$	1.63657			0.175459
$88$	2.26385			0.241327
$89$	4.94209	+	8.55996i	0.523861	+	0.907354i	0.999614	+	0.0277749i	$0.00884215\pi$
$89$	4.94209	+	8.55996i	0.523861	+	0.907354i	−0.475753	+	0.879579i	$0.657825\pi$
$90$	−0.103661			−0.0109268
$91$	−5.36751	−	9.29680i	−0.562668	−	0.974569i
$92$	1.37011	+	2.37311i	0.142844	+	0.247414i
$93$	8.52198	−	14.7605i	0.883688	−	1.53059i
$94$	10.0108			1.03253
$95$	2.83379	−	4.90826i	0.290740	−	0.503577i
$96$	0.850932	+	1.47386i	0.0868479	+	0.150425i
$97$	2.19855			0.223229			0.111615	−	0.993752i	$-0.464398\pi$
$97$	2.19855			0.223229			0.111615	+	0.993752i	$0.464398\pi$
$98$	−1.02362	−	1.77296i	−0.103401	−	0.179096i
$99$	−0.117336	+	0.203232i	−0.0117927	+	0.0204256i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.15747	−	10.6651i	0.612691	−	1.06121i	−0.378094	−	0.925767i	$-0.623420\pi$
$101$	6.15747	−	10.6651i	0.612691	−	1.06121i	0.990785	−	0.135445i	$-0.0432464\pi$
$102$	−7.36761			−0.729502
$103$	−0.511068	+	0.885196i	−0.0503571	+	0.0872210i	−0.890105	−	0.455755i	$-0.849369\pi$
$103$	−0.511068	+	0.885196i	−0.0503571	+	0.0872210i	0.839748	+	0.542976i	$0.182703\pi$
$104$	2.41184	−	4.17743i	0.236501	−	0.409631i
$105$	1.89373	+	3.28004i	0.184809	+	0.320099i
$106$	1.56198	+	2.70544i	0.151713	+	0.262775i
$107$	−3.52576			−0.340849			−0.170424	−	0.985371i	$-0.554514\pi$
$107$	−3.52576			−0.340849			−0.170424	+	0.985371i	$0.554514\pi$
$108$	−5.28201			−0.508261
$109$	0.261809	+	0.453466i	0.0250767	+	0.0434342i	0.878291	−	0.478126i	$-0.158684\pi$
$109$	0.261809	+	0.453466i	0.0250767	+	0.0434342i	−0.853215	+	0.521560i	$0.825350\pi$
$110$	1.13192	+	1.96055i	0.107925	+	0.186931i
$111$	9.01391	−	15.6126i	0.855563	−	1.48188i
$112$	−1.11274	+	1.92732i	−0.105144	+	0.182115i
$113$	7.37831			0.694093			0.347046	−	0.937848i	$-0.387185\pi$
$113$	7.37831			0.694093			0.347046	+	0.937848i	$0.387185\pi$
$114$	4.82272	−	8.35319i	0.451689	−	0.782348i
$115$	−1.37011	+	2.37311i	−0.127764	+	0.221294i
$116$	−0.480817	+	0.832799i	−0.0446427	+	0.0773235i
$117$	0.250013	+	0.433036i	0.0231137	+	0.0400341i
$118$	4.32914			0.398530
$119$	−4.81721	−	8.34365i	−0.441593	−	0.764862i
$120$	−0.850932	+	1.47386i	−0.0776791	+	0.134544i
$121$	−5.87500			−0.534091
$122$	5.97479	−	10.3486i	0.540932	−	0.936922i
$123$	3.74727	+	6.49046i	0.337880	+	0.585225i
$124$	5.00744	+	8.67314i	0.449681	+	0.778871i
$125$	−1.00000			−0.0894427
$126$	−0.115347	−	0.199788i	−0.0102760	−	0.0177985i
$127$	−9.24762			−0.820593			−0.410297	−	0.911952i	$-0.634575\pi$
$127$	−9.24762			−0.820593			−0.410297	+	0.911952i	$0.634575\pi$
$128$	−1.00000			−0.0883883
$129$	−5.05922	−	9.94721i	−0.445439	−	0.875803i
$130$	4.82368			0.423065
$131$	−12.5365			−1.09532			−0.547658	−	0.836702i	$-0.684480\pi$
$131$	−12.5365			−1.09532			−0.547658	+	0.836702i	$0.684480\pi$
$132$	1.92638	+	3.33659i	0.167670	+	0.290413i
$133$	12.6131			1.09369
$134$	5.62018	+	9.73443i	0.485509	+	0.840927i
$135$	−2.64100	−	4.57435i	−0.227301	−	0.393698i
$136$	2.16457	−	3.74915i	0.185610	−	0.321487i
$137$	−14.6965			−1.25561			−0.627805	−	0.778371i	$-0.716046\pi$
$137$	−14.6965			−1.25561			−0.627805	+	0.778371i	$0.716046\pi$
$138$	−2.33175	+	4.03871i	−0.198492	+	0.343798i
$139$	9.55217	+	16.5448i	0.810204	+	1.40332i	0.912721	+	0.408584i	$0.133977\pi$
$139$	9.55217	+	16.5448i	0.810204	+	1.40332i	−0.102517	+	0.994731i	$0.532689\pi$
$140$	−2.22548			−0.188087
$141$	8.51851	+	14.7545i	0.717388	+	1.24255i
$142$	−6.74359	+	11.6802i	−0.565910	+	0.980184i
$143$	5.46004	−	9.45707i	0.456592	−	0.790840i
$144$	0.0518303	−	0.0897728i	0.00431920	−	0.00748107i
$145$	−0.961634			−0.0798593
$146$	−5.46367	+	9.46336i	−0.452177	+	0.783193i
$147$	1.74206	−	3.01733i	0.143682	−	0.248865i
$148$	5.29649	+	9.17380i	0.435369	+	0.754082i
$149$	−1.96367	−	3.40118i	−0.160870	−	0.278636i	0.774311	−	0.632806i	$-0.218097\pi$
$149$	−1.96367	−	3.40118i	−0.160870	−	0.278636i	−0.935181	+	0.354170i	$0.884763\pi$
$150$	−1.70186			−0.138957
$151$	−2.00193			−0.162915			−0.0814574	−	0.996677i	$-0.525957\pi$
$151$	−2.00193			−0.162915			−0.0814574	+	0.996677i	$0.525957\pi$
$152$	2.83379	+	4.90826i	0.229850	+	0.398113i
$153$	0.224381	+	0.388639i	0.0181401	+	0.0314196i
$154$	−2.51907	+	4.36316i	−0.202993	+	0.351594i
$155$	−5.00744	+	8.67314i	−0.402207	+	0.696643i
$156$	8.20925			0.657266
$157$	3.11178	−	5.38975i	0.248347	−	0.430149i	−0.714721	−	0.699410i	$-0.753446\pi$
$157$	3.11178	−	5.38975i	0.248347	−	0.430149i	0.963067	+	0.269261i	$0.0867794\pi$
$158$	3.66110	−	6.34121i	0.291262	−	0.504480i
$159$	−2.65828	+	4.60428i	−0.210816	+	0.365143i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−6.09833			−0.480616
$162$	−4.33914	−	7.51560i	−0.340915	−	0.590482i
$163$	7.09656	−	12.2916i	0.555846	−	0.962753i	−0.441992	−	0.897019i	$-0.645728\pi$
$163$	7.09656	−	12.2916i	0.555846	−	0.962753i	0.997837	−	0.0657336i	$-0.0209387\pi$
$164$	−4.40373			−0.343873
$165$	−1.92638	+	3.33659i	−0.149968	+	0.259753i
$166$	4.58448	+	7.94055i	0.355824	+	0.616306i
$167$	−1.77992	−	3.08291i	−0.137734	−	0.238563i	0.788904	−	0.614516i	$-0.210649\pi$
$167$	−1.77992	−	3.08291i	−0.137734	−	0.238563i	−0.926639	+	0.375953i	$0.877315\pi$
$168$	−3.78746			−0.292209
$169$	−5.13396	−	8.89228i	−0.394920	−	0.684022i
$170$	4.32914			0.332030
$171$	−0.587505			−0.0449276
$172$	6.54820	+	0.347967i	0.499296	+	0.0265322i
$173$	−18.9825			−1.44321			−0.721607	−	0.692303i	$-0.756596\pi$
$173$	−18.9825			−1.44321			−0.721607	+	0.692303i	$0.756596\pi$
$174$	−1.63657			−0.124068
$175$	−1.11274	−	1.92732i	−0.0841153	−	0.145692i
$176$	−2.26385			−0.170644
$177$	3.68380	+	6.38054i	0.276892	+	0.479590i
$178$	−4.94209	−	8.55996i	−0.370426	−	0.641596i
$179$	3.20079	−	5.54393i	0.239238	−	0.414373i	−0.721258	−	0.692667i	$-0.756436\pi$
$179$	3.20079	−	5.54393i	0.239238	−	0.414373i	0.960496	+	0.278294i	$0.0897690\pi$
$180$	0.103661			0.00772641
$181$	0.178246	−	0.308731i	0.0132489	−	0.0229478i	−0.859325	−	0.511430i	$-0.829116\pi$
$181$	0.178246	−	0.308731i	0.0132489	−	0.0229478i	0.872574	+	0.488482i	$0.162449\pi$
$182$	5.36751	+	9.29680i	0.397866	+	0.689124i
$183$	20.3366			1.50332
$184$	−1.37011	−	2.37311i	−0.101006	−	0.174948i
$185$	−5.29649	+	9.17380i	−0.389406	+	0.674471i
$186$	−8.52198	+	14.7605i	−0.624862	+	1.08229i
$187$	4.90026	−	8.48750i	0.358342	−	0.620667i
$188$	−10.0108			−0.730112
$189$	5.87750	−	10.1801i	0.427525	−	0.740496i
$190$	−2.83379	+	4.90826i	−0.205585	+	0.356083i
$191$	4.78292	+	8.28426i	0.346080	+	0.599428i	0.985549	−	0.169388i	$-0.0541792\pi$
$191$	4.78292	+	8.28426i	0.346080	+	0.599428i	−0.639469	+	0.768817i	$0.720846\pi$
$192$	−0.850932	−	1.47386i	−0.0614107	−	0.106366i
$193$	11.0915			0.798384			0.399192	−	0.916867i	$-0.369291\pi$
$193$	11.0915			0.798384			0.399192	+	0.916867i	$0.369291\pi$
$194$	−2.19855			−0.157847
$195$	4.10463	+	7.10942i	0.293938	+	0.509116i
$196$	1.02362	+	1.77296i	0.0731155	+	0.126640i
$197$	−10.6695	+	18.4801i	−0.760171	+	1.31665i	0.182592	+	0.983189i	$0.441551\pi$
$197$	−10.6695	+	18.4801i	−0.760171	+	1.31665i	−0.942762	+	0.333465i	$0.891782\pi$
$198$	0.117336	−	0.203232i	0.00833870	−	0.0144431i
$199$	10.6788			0.757000			0.378500	−	0.925601i	$-0.376440\pi$
$199$	10.6788			0.757000			0.378500	+	0.925601i	$0.376440\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−9.56478	+	16.5667i	−0.674647	+	1.16852i
$202$	−6.15747	+	10.6651i	−0.433238	+	0.750390i
$203$	−1.07005	−	1.85338i	−0.0751027	−	0.130082i
$204$	7.36761			0.515836
$205$	−2.20186	−	3.81374i	−0.153785	−	0.266363i
$206$	0.511068	−	0.885196i	0.0356078	−	0.0616745i
$207$	0.284054			0.0197431
$208$	−2.41184	+	4.17743i	−0.167231	+	0.289653i
$209$	6.41526	+	11.1116i	0.443753	+	0.768603i
$210$	−1.89373	−	3.28004i	−0.130680	−	0.226344i
$211$	12.7383			0.876941			0.438470	−	0.898746i	$-0.355520\pi$
$211$	12.7383			0.876941			0.438470	+	0.898746i	$0.355520\pi$
$212$	−1.56198	−	2.70544i	−0.107277	−	0.185810i
$213$	−22.9533			−1.57274
$214$	3.52576			0.241016
$215$	2.97275	+	5.84489i	0.202740	+	0.398618i
$216$	5.28201			0.359395
$217$	−22.2879			−1.51300
$218$	−0.261809	−	0.453466i	−0.0177319	−	0.0307126i
$219$	−18.5968			−1.25666
$220$	−1.13192	−	1.96055i	−0.0763143	−	0.132180i
$221$	−10.4412	−	18.0847i	−0.702351	−	1.21651i
$222$	−9.01391	+	15.6126i	−0.604974	+	1.04785i
$223$	7.99264			0.535227			0.267613	−	0.963526i	$-0.413765\pi$
$223$	7.99264			0.535227			0.267613	+	0.963526i	$0.413765\pi$
$224$	1.11274	−	1.92732i	0.0743481	−	0.128775i
$225$	0.0518303	+	0.0897728i	0.00345536	+	0.00598485i
$226$	−7.37831			−0.490798
$227$	−4.76221	−	8.24838i	−0.316079	−	0.547464i	0.663588	−	0.748099i	$-0.269033\pi$
$227$	−4.76221	−	8.24838i	−0.316079	−	0.547464i	−0.979666	+	0.200634i	$0.935700\pi$
$228$	−4.82272	+	8.35319i	−0.319392	+	0.553204i
$229$	−6.51918	+	11.2916i	−0.430800	+	0.746167i	−0.996942	−	0.0781402i	$-0.975102\pi$
$229$	−6.51918	+	11.2916i	−0.430800	+	0.746167i	0.566143	+	0.824307i	$0.308435\pi$
$230$	1.37011	−	2.37311i	0.0903427	−	0.156478i
$231$	−8.57424			−0.564144
$232$	0.480817	−	0.832799i	0.0315672	−	0.0546759i
$233$	−7.52993	+	13.0422i	−0.493302	+	0.854424i	−0.999970	−	0.00771675i	$-0.997544\pi$
$233$	−7.52993	+	13.0422i	−0.493302	+	0.854424i	0.506668	+	0.862141i	$0.330877\pi$
$234$	−0.250013	−	0.433036i	−0.0163439	−	0.0283084i
$235$	−5.00540	−	8.66961i	−0.326516	−	0.565543i
$236$	−4.32914			−0.281803
$237$	12.4614			0.809454
$238$	4.81721	+	8.34365i	0.312253	+	0.540839i
$239$	9.55559	+	16.5508i	0.618100	+	1.07058i	0.989832	+	0.142240i	$0.0454305\pi$
$239$	9.55559	+	16.5508i	0.618100	+	1.07058i	−0.371733	+	0.928340i	$0.621236\pi$
$240$	0.850932	−	1.47386i	0.0549274	−	0.0951371i
$241$	8.29138	−	14.3611i	0.534095	−	0.925080i	−0.465112	−	0.885252i	$-0.653986\pi$
$241$	8.29138	−	14.3611i	0.534095	−	0.925080i	0.999207	−	0.0398275i	$-0.0126808\pi$
$242$	5.87500			0.377659
$243$	−0.538393	+	0.932524i	−0.0345379	+	0.0598214i
$244$	−5.97479	+	10.3486i	−0.382497	+	0.662504i
$245$	−1.02362	+	1.77296i	−0.0653965	+	0.113270i
$246$	−3.74727	−	6.49046i	−0.238917	−	0.413817i
$247$	27.3386			1.73951
$248$	−5.00744	−	8.67314i	−0.317973	−	0.550745i
$249$	−7.80215	+	13.5137i	−0.494441	+	0.856398i
$250$	1.00000			0.0632456
$251$	10.8084	−	18.7206i	0.682218	−	1.18164i	−0.292084	−	0.956393i	$-0.594349\pi$
$251$	10.8084	−	18.7206i	0.682218	−	1.18164i	0.974302	−	0.225244i	$-0.0723178\pi$
$252$	0.115347	+	0.199788i	0.00726621	+	0.0125854i
$253$	−3.10173	−	5.37236i	−0.195004	−	0.337757i
$254$	9.24762			0.580247
$255$	3.68380	+	6.38054i	0.230689	+	0.399565i
$256$	1.00000			0.0625000
$257$	28.0811			1.75165			0.875824	−	0.482630i	$-0.160318\pi$
$257$	28.0811			1.75165			0.875824	+	0.482630i	$0.160318\pi$
$258$	5.05922	+	9.94721i	0.314973	+	0.619286i
$259$	−23.5745			−1.46485
$260$	−4.82368			−0.299152
$261$	0.0498418	+	0.0863285i	0.00308513	+	0.00534360i
$262$	12.5365			0.774505
$263$	6.13835	+	10.6319i	0.378507	+	0.655593i	0.990845	−	0.135003i	$-0.0431044\pi$
$263$	6.13835	+	10.6319i	0.378507	+	0.655593i	−0.612339	+	0.790596i	$0.709771\pi$
$264$	−1.92638	−	3.33659i	−0.118560	−	0.205353i
$265$	1.56198	−	2.70544i	0.0959519	−	0.166194i
$266$	−12.6131			−0.773357
$267$	8.41077	−	14.5679i	0.514731	−	0.891540i
$268$	−5.62018	−	9.73443i	−0.343307	−	0.594625i
$269$	15.4750			0.943529			0.471765	−	0.881725i	$-0.343617\pi$
$269$	15.4750			0.943529			0.471765	+	0.881725i	$0.343617\pi$
$270$	2.64100	+	4.57435i	0.160726	+	0.278386i
$271$	−12.4893	+	21.6322i	−0.758673	+	1.31406i	0.184855	+	0.982766i	$0.440818\pi$
$271$	−12.4893	+	21.6322i	−0.758673	+	1.31406i	−0.943528	+	0.331294i	$0.892515\pi$
$272$	−2.16457	+	3.74915i	−0.131246	+	0.227325i
$273$	−9.13477	+	15.8219i	−0.552861	+	0.957584i
$274$	14.6965			0.887850
$275$	1.13192	−	1.96055i	0.0682576	−	0.118226i
$276$	2.33175	−	4.03871i	0.140355	−	0.243102i
$277$	1.13988	+	1.97433i	0.0684887	+	0.118626i	0.898236	−	0.439513i	$-0.144849\pi$
$277$	1.13988	+	1.97433i	0.0684887	+	0.118626i	−0.829748	+	0.558139i	$0.811516\pi$
$278$	−9.55217	−	16.5448i	−0.572901	−	0.992294i
$279$	1.03815			0.0621523
$280$	2.22548			0.132998
$281$	−3.14412	−	5.44577i	−0.187562	−	0.324867i	0.756875	−	0.653560i	$-0.226725\pi$
$281$	−3.14412	−	5.44577i	−0.187562	−	0.324867i	−0.944437	+	0.328693i	$0.893392\pi$
$282$	−8.51851	−	14.7545i	−0.507270	−	0.878617i
$283$	−7.61314	+	13.1863i	−0.452554	+	0.783847i	−0.998544	−	0.0539452i	$-0.982820\pi$
$283$	−7.61314	+	13.1863i	−0.452554	+	0.783847i	0.545990	+	0.837792i	$0.316154\pi$
$284$	6.74359	−	11.6802i	0.400158	−	0.693095i
$285$	−9.64544			−0.571346
$286$	−5.46004	+	9.45707i	−0.322859	+	0.559208i
$287$	4.90021	−	8.48740i	0.289250	−	0.500996i
$288$	−0.0518303	+	0.0897728i	−0.00305413	+	0.00528991i
$289$	−0.870733	−	1.50815i	−0.0512196	−	0.0887150i
$290$	0.961634			0.0564691
$291$	−1.87082	−	3.24035i	−0.109669	−	0.189953i
$292$	5.46367	−	9.46336i	0.319737	−	0.553801i
$293$	15.5150			0.906396			0.453198	−	0.891410i	$-0.350283\pi$
$293$	15.5150			0.906396			0.453198	+	0.891410i	$0.350283\pi$
$294$	−1.74206	+	3.01733i	−0.101599	+	0.175974i
$295$	−2.16457	−	3.74915i	−0.126026	−	0.218284i
$296$	−5.29649	−	9.17380i	−0.307852	−	0.533216i
$297$	11.9577			0.693854
$298$	1.96367	+	3.40118i	0.113752	+	0.197025i
$299$	−13.2180			−0.764417
$300$	1.70186			0.0982571
$301$	−7.95709	+	12.2333i	−0.458639	+	0.705116i
$302$	2.00193			0.115198
$303$	−20.9583			−1.20403
$304$	−2.83379	−	4.90826i	−0.162529	−	0.281508i
$305$	−11.9496			−0.684231
$306$	−0.224381	−	0.388639i	−0.0128270	−	0.0222170i
$307$	6.74665	+	11.6855i	0.385052	+	0.666929i	0.991776	−	0.127983i	$-0.0408502\pi$
$307$	6.74665	+	11.6855i	0.385052	+	0.666929i	−0.606725	+	0.794912i	$0.707517\pi$
$308$	2.51907	−	4.36316i	0.143538	−	0.248614i
$309$	1.73954			0.0989588
$310$	5.00744	−	8.67314i	0.284403	−	0.492601i
$311$	8.07130	+	13.9799i	0.457682	+	0.792728i	0.998838	−	0.0481943i	$-0.0153467\pi$
$311$	8.07130	+	13.9799i	0.457682	+	0.792728i	−0.541156	+	0.840922i	$0.682013\pi$
$312$	−8.20925			−0.464757
$313$	1.47020	+	2.54647i	0.0831008	+	0.143935i	0.904580	−	0.426303i	$-0.140184\pi$
$313$	1.47020	+	2.54647i	0.0831008	+	0.143935i	−0.821480	+	0.570238i	$0.806851\pi$
$314$	−3.11178	+	5.38975i	−0.175608	+	0.304161i
$315$	−0.115347	+	0.199788i	−0.00649909	+	0.0112568i
$316$	−3.66110	+	6.34121i	−0.205953	+	0.356721i
$317$	23.8553			1.33985			0.669923	−	0.742431i	$-0.266327\pi$
$317$	23.8553			1.33985			0.669923	+	0.742431i	$0.266327\pi$
$318$	2.65828	−	4.60428i	0.149069	−	0.258195i
$319$	1.08850	−	1.88533i	0.0609441	−	0.105558i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	3.00019	+	5.19647i	0.167454	+	0.290039i
$322$	6.09833			0.339847
$323$	24.5357			1.36520
$324$	4.33914	+	7.51560i	0.241063	+	0.417534i
$325$	−2.41184	−	4.17743i	−0.133785	−	0.231722i
$326$	−7.09656	+	12.2916i	−0.393042	+	0.680769i
$327$	0.445563	−	0.771737i	0.0246397	−	0.0426772i
$328$	4.40373			0.243155
$329$	11.1394	−	19.2940i	0.614136	−	1.06371i
$330$	1.92638	−	3.33659i	0.106044	−	0.183673i
$331$	8.26823	−	14.3210i	0.454463	−	0.787153i	−0.544194	−	0.838959i	$-0.683164\pi$
$331$	8.26823	−	14.3210i	0.454463	−	0.787153i	0.998657	+	0.0518062i	$0.0164978\pi$
$332$	−4.58448	−	7.94055i	−0.251606	−	0.435794i
$333$	1.09808			0.0601742
$334$	1.77992	+	3.08291i	0.0973928	+	0.168689i
$335$	5.62018	−	9.73443i	0.307063	−	0.531849i
$336$	3.78746			0.206623
$337$	2.03964	−	3.53276i	0.111106	−	0.192442i	−0.805110	−	0.593125i	$-0.797894\pi$
$337$	2.03964	−	3.53276i	0.111106	−	0.192442i	0.916217	+	0.400683i	$0.131227\pi$
$338$	5.13396	+	8.89228i	0.279251	+	0.483676i
$339$	−6.27843	−	10.8746i	−0.340998	−	0.590625i
$340$	−4.32914			−0.234781
$341$	−11.3361	−	19.6347i	−0.613883	−	1.06328i
$342$	0.587505			0.0317686
$343$	−20.1344			−1.08716
$344$	−6.54820	−	0.347967i	−0.353055	−	0.0187611i
$345$	4.66350			0.251074
$346$	18.9825			1.02051
$347$	5.60723	+	9.71201i	0.301012	+	0.521368i	0.976365	−	0.216126i	$-0.0693422\pi$
$347$	5.60723	+	9.71201i	0.301012	+	0.521368i	−0.675353	+	0.737494i	$0.736009\pi$
$348$	1.63657			0.0877293
$349$	−16.5112	−	28.5983i	−0.883827	−	1.53083i	−0.847053	−	0.531509i	$-0.821625\pi$
$349$	−16.5112	−	28.5983i	−0.883827	−	1.53083i	−0.0367741	−	0.999324i	$-0.511708\pi$
$350$	1.11274	+	1.92732i	0.0594785	+	0.103020i
$351$	12.7394	−	22.0652i	0.679977	−	1.17775i
$352$	2.26385			0.120663
$353$	−3.83854	+	6.64855i	−0.204305	+	0.353867i	−0.949911	−	0.312520i	$-0.898827\pi$
$353$	−3.83854	+	6.64855i	−0.204305	+	0.353867i	0.745606	+	0.666387i	$0.232160\pi$
$354$	−3.68380	−	6.38054i	−0.195792	−	0.339122i
$355$	13.4872			0.715825
$356$	4.94209	+	8.55996i	0.261930	+	0.453677i
$357$	−8.19824	+	14.1998i	−0.433897	+	0.751531i
$358$	−3.20079	+	5.54393i	−0.169167	+	0.293006i
$359$	−6.12086	+	10.6016i	−0.323046	+	0.559533i	−0.981115	−	0.193425i	$-0.938040\pi$
$359$	−6.12086	+	10.6016i	−0.323046	+	0.559533i	0.658069	+	0.752958i	$0.271374\pi$
$360$	−0.103661			−0.00546340
$361$	−6.56070	+	11.3635i	−0.345300	+	0.598077i
$362$	−0.178246	+	0.308731i	−0.00936841	+	0.0162266i
$363$	4.99922	+	8.65890i	0.262391	+	0.454475i
$364$	−5.36751	−	9.29680i	−0.281334	−	0.487285i
$365$	10.9273			0.571963
$366$	−20.3366			−1.06301
$367$	7.45050	+	12.9046i	0.388913	+	0.673617i	0.992304	−	0.123829i	$-0.0395174\pi$
$367$	7.45050	+	12.9046i	0.388913	+	0.673617i	−0.603391	+	0.797446i	$0.706184\pi$
$368$	1.37011	+	2.37311i	0.0714222	+	0.123707i
$369$	−0.228247	+	0.395335i	−0.0118820	+	0.0205803i
$370$	5.29649	−	9.17380i	0.275352	−	0.476923i
$371$	6.95233			0.360947
$372$	8.52198	−	14.7605i	0.441844	−	0.765296i
$373$	15.5812	−	26.9874i	0.806763	−	1.39735i	−0.108331	−	0.994115i	$-0.534551\pi$
$373$	15.5812	−	26.9874i	0.806763	−	1.39735i	0.915094	−	0.403240i	$-0.132116\pi$
$374$	−4.90026	+	8.48750i	−0.253386	+	0.438878i
$375$	0.850932	+	1.47386i	0.0439419	+	0.0761096i
$376$	10.0108			0.516267
$377$	−2.31931	−	4.01716i	−0.119450	−	0.206894i
$378$	−5.87750	+	10.1801i	−0.302306	+	0.523610i
$379$	−6.26385			−0.321752			−0.160876	−	0.986975i	$-0.551432\pi$
$379$	−6.26385			−0.321752			−0.160876	+	0.986975i	$0.551432\pi$
$380$	2.83379	−	4.90826i	0.145370	−	0.251789i
$381$	7.86909	+	13.6297i	0.403146	+	0.698269i
$382$	−4.78292	−	8.28426i	−0.244716	−	0.423860i
$383$	3.49261			0.178464			0.0892321	−	0.996011i	$-0.471559\pi$
$383$	3.49261			0.178464			0.0892321	+	0.996011i	$0.471559\pi$
$384$	0.850932	+	1.47386i	0.0434239	+	0.0752125i
$385$	5.03815			0.256768
$386$	−11.0915			−0.564543
$387$	0.370633	−	0.569815i	0.0188404	−	0.0289653i
$388$	2.19855			0.111615
$389$	−26.6817			−1.35281			−0.676407	−	0.736528i	$-0.736464\pi$
$389$	−26.6817			−1.35281			−0.676407	+	0.736528i	$0.736464\pi$
$390$	−4.10463	−	7.10942i	−0.207846	−	0.359999i
$391$	−11.8628			−0.599930
$392$	−1.02362	−	1.77296i	−0.0517005	−	0.0895479i
$393$	10.6677	+	18.4770i	0.538113	+	0.932039i
$394$	10.6695	−	18.4801i	0.537522	−	0.931015i
$395$	−7.32220			−0.368420
$396$	−0.117336	+	0.203232i	−0.00589635	+	0.0102128i
$397$	−17.7232	−	30.6975i	−0.889502	−	1.54066i	−0.840465	−	0.541867i	$-0.817718\pi$
$397$	−17.7232	−	30.6975i	−0.889502	−	1.54066i	−0.0490380	−	0.998797i	$-0.515616\pi$
$398$	−10.6788			−0.535280
$399$	−10.7329	−	18.5899i	−0.537315	−	0.930658i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	2.33175	−	4.03871i	0.116442	−	0.201683i	−0.801913	−	0.597440i	$-0.796184\pi$
$401$	2.33175	−	4.03871i	0.116442	−	0.201683i	0.918355	+	0.395757i	$0.129518\pi$
$402$	9.56478	−	16.5667i	0.477048	−	0.826271i
$403$	−48.3086			−2.40642
$404$	6.15747	−	10.6651i	0.306346	−	0.530606i
$405$	−4.33914	+	7.51560i	−0.215613	+	0.373453i
$406$	1.07005	+	1.85338i	0.0531056	+	0.0919816i
$407$	−11.9905	−	20.7681i	−0.594345	−	1.02944i
$408$	−7.36761			−0.364751
$409$	4.75115			0.234929			0.117465	−	0.993077i	$-0.462523\pi$
$409$	4.75115			0.234929			0.117465	+	0.993077i	$0.462523\pi$
$410$	2.20186	+	3.81374i	0.108742	+	0.188347i
$411$	12.5057	+	21.6606i	0.616863	+	1.06844i
$412$	−0.511068	+	0.885196i	−0.0251785	+	0.0436105i
$413$	4.81721	−	8.34365i	0.237039	−	0.410564i
$414$	−0.284054			−0.0139605
$415$	4.58448	−	7.94055i	0.225043	−	0.389786i
$416$	2.41184	−	4.17743i	0.118250	−	0.204815i
$417$	16.2565	−	28.1571i	0.796084	−	1.37886i
$418$	−6.41526	−	11.1116i	−0.313781	−	0.543484i
$419$	−13.7861			−0.673496			−0.336748	−	0.941595i	$-0.609327\pi$
$419$	−13.7861			−0.673496			−0.336748	+	0.941595i	$0.609327\pi$
$420$	1.89373	+	3.28004i	0.0924047	+	0.160050i
$421$	8.26521	−	14.3158i	0.402822	−	0.697708i	−0.591244	−	0.806493i	$-0.701363\pi$
$421$	8.26521	−	14.3158i	0.402822	−	0.697708i	0.994065	+	0.108785i	$0.0346962\pi$
$422$	−12.7383			−0.620091
$423$	−0.518863	+	0.898697i	−0.0252280	+	0.0436962i
$424$	1.56198	+	2.70544i	0.0758566	+	0.131388i
$425$	−2.16457	−	3.74915i	−0.104997	−	0.181860i
$426$	22.9533			1.11209
$427$	−13.2968	−	23.0307i	−0.643476	−	1.11453i
$428$	−3.52576			−0.170424
$429$	−18.5845			−0.897268
$430$	−2.97275	−	5.84489i	−0.143359	−	0.281866i
$431$	−5.04437			−0.242979			−0.121489	−	0.992593i	$-0.538767\pi$
$431$	−5.04437			−0.242979			−0.121489	+	0.992593i	$0.538767\pi$
$432$	−5.28201			−0.254131
$433$	5.58101	+	9.66659i	0.268206	+	0.464547i	0.968399	−	0.249407i	$-0.0802358\pi$
$433$	5.58101	+	9.66659i	0.268206	+	0.464547i	−0.700193	+	0.713954i	$0.746903\pi$
$434$	22.2879			1.06985
$435$	0.818285	+	1.41731i	0.0392337	+	0.0679548i
$436$	0.261809	+	0.453466i	0.0125384	+	0.0217171i
$437$	7.76523	−	13.4498i	0.371461	−	0.643390i
$438$	18.5968			0.888592
$439$	−11.8430	+	20.5127i	−0.565236	+	0.979017i	0.431792	+	0.901973i	$0.357881\pi$
$439$	−11.8430	+	20.5127i	−0.565236	+	0.979017i	−0.997028	+	0.0770437i	$0.975452\pi$
$440$	1.13192	+	1.96055i	0.0539623	+	0.0934655i
$441$	0.212218			0.0101056
$442$	10.4412	+	18.0847i	0.496637	+	0.860201i
$443$	−15.9654	+	27.6529i	−0.758539	+	1.31383i	0.185057	+	0.982728i	$0.440753\pi$
$443$	−15.9654	+	27.6529i	−0.758539	+	1.31383i	−0.943596	+	0.331100i	$0.892580\pi$
$444$	9.01391	−	15.6126i	0.427781	−	0.740939i
$445$	−4.94209	+	8.55996i	−0.234278	+	0.405781i
$446$	−7.99264			−0.378462
$447$	−3.34190	+	5.78834i	−0.158067	+	0.273779i
$448$	−1.11274	+	1.92732i	−0.0525720	+	0.0910575i
$449$	16.1474	+	27.9681i	0.762041	+	1.31989i	0.941797	+	0.336183i	$0.109136\pi$
$449$	16.1474	+	27.9681i	0.762041	+	1.31989i	−0.179755	+	0.983711i	$0.557531\pi$
$450$	−0.0518303	−	0.0897728i	−0.00244331	−	0.00423193i
$451$	9.96937			0.469439
$452$	7.37831			0.347046
$453$	1.70351	+	2.95056i	0.0800377	+	0.138629i
$454$	4.76221	+	8.24838i	0.223501	+	0.387116i
$455$	5.36751	−	9.29680i	0.251633	−	0.435841i
$456$	4.82272	−	8.35319i	0.225845	−	0.391174i
$457$	−4.25241			−0.198919			−0.0994596	−	0.995042i	$-0.531711\pi$
$457$	−4.25241			−0.198919			−0.0994596	+	0.995042i	$0.531711\pi$
$458$	6.51918	−	11.2916i	0.304621	−	0.527620i
$459$	11.4333	−	19.8030i	0.533660	−	0.924326i
$460$	−1.37011	+	2.37311i	−0.0638819	+	0.110647i
$461$	0.551077	+	0.954493i	0.0256662	+	0.0444552i	0.878573	−	0.477608i	$-0.158496\pi$
$461$	0.551077	+	0.954493i	0.0256662	+	0.0444552i	−0.852907	+	0.522063i	$0.825163\pi$
$462$	8.57424			0.398910
$463$	−12.9666	−	22.4588i	−0.602608	−	1.04375i	−0.992425	−	0.122855i	$-0.960795\pi$
$463$	−12.9666	−	22.4588i	−0.602608	−	1.04375i	0.389817	−	0.920892i	$-0.372538\pi$
$464$	−0.480817	+	0.832799i	−0.0223214	+	0.0386617i
$465$	17.0440			0.790394
$466$	7.52993	−	13.0422i	0.348817	−	0.604169i
$467$	17.9859	+	31.1524i	0.832286	+	1.44156i	0.896221	+	0.443608i	$0.146302\pi$
$467$	17.9859	+	31.1524i	0.832286	+	1.44156i	−0.0639346	+	0.997954i	$0.520365\pi$
$468$	0.250013	+	0.433036i	0.0115569	+	0.0200171i
$469$	25.0152			1.15509
$470$	5.00540	+	8.66961i	0.230882	+	0.399899i
$471$	−10.5916			−0.488037
$472$	4.32914			0.199265
$473$	−14.8241	−	0.787743i	−0.681614	−	0.0362205i
$474$	−12.4614			−0.572371
$475$	5.66757			0.260046
$476$	−4.81721	−	8.34365i	−0.220797	−	0.382431i
$477$	−0.323833			−0.0148273
$478$	−9.55559	−	16.5508i	−0.437062	−	0.757014i
$479$	−2.81914	−	4.88289i	−0.128810	−	0.223105i	0.794406	−	0.607387i	$-0.207782\pi$
$479$	−2.81914	−	4.88289i	−0.128810	−	0.223105i	−0.923216	+	0.384282i	$0.874449\pi$
$480$	−0.850932	+	1.47386i	−0.0388395	+	0.0672721i
$481$	−51.0972			−2.32983
$482$	−8.29138	+	14.3611i	−0.377662	+	0.654130i
$483$	5.18926	+	8.98807i	0.236120	+	0.408971i
$484$	−5.87500			−0.267045
$485$	1.09928	+	1.90400i	0.0499156	+	0.0864563i
$486$	0.538393	−	0.932524i	0.0244220	−	0.0423001i
$487$	−0.775841	+	1.34380i	−0.0351567	+	0.0608932i	−0.883068	−	0.469244i	$-0.844526\pi$
$487$	−0.775841	+	1.34380i	−0.0351567	+	0.0608932i	0.847912	+	0.530138i	$0.177860\pi$
$488$	5.97479	−	10.3486i	0.270466	−	0.468461i
$489$	−24.1548			−1.09232
$490$	1.02362	−	1.77296i	0.0462423	−	0.0800940i
$491$	10.1408	−	17.5644i	0.457648	−	0.792669i	−0.541189	−	0.840901i	$-0.682025\pi$
$491$	10.1408	−	17.5644i	0.457648	−	0.792669i	0.998836	+	0.0482325i	$0.0153588\pi$
$492$	3.74727	+	6.49046i	0.168940	+	0.292613i
$493$	−2.08152	−	3.60531i	−0.0937471	−	0.162375i
$494$	−27.3386			−1.23002
$495$	−0.234672			−0.0105477
$496$	5.00744	+	8.67314i	0.224841	+	0.389435i
$497$	15.0077	+	25.9942i	0.673189	+	1.16600i
$498$	7.80215	−	13.5137i	0.349623	−	0.605565i
$499$	9.57402	−	16.5827i	0.428592	−	0.742343i	−0.568156	−	0.822921i	$-0.692343\pi$
$499$	9.57402	−	16.5827i	0.428592	−	0.742343i	0.996748	+	0.0805777i	$0.0256765\pi$
$500$	−1.00000			−0.0447214
$501$	−3.02918	+	5.24669i	−0.135334	+	0.234405i
$502$	−10.8084	+	18.7206i	−0.482401	+	0.835543i
$503$	9.34827	−	16.1917i	0.416819	−	0.721952i	−0.578799	−	0.815471i	$-0.696478\pi$
$503$	9.34827	−	16.1917i	0.416819	−	0.721952i	0.995618	+	0.0935189i	$0.0298116\pi$
$504$	−0.115347	−	0.199788i	−0.00513798	−	0.00889925i
$505$	12.3149			0.548008
$506$	3.10173	+	5.37236i	0.137889	+	0.238830i
$507$	−8.73730	+	15.1335i	−0.388037	+	0.672100i
$508$	−9.24762			−0.410297
$509$	−17.8162	+	30.8586i	−0.789690	+	1.36778i	0.136467	+	0.990645i	$0.456425\pi$
$509$	−17.8162	+	30.8586i	−0.789690	+	1.36778i	−0.926157	+	0.377138i	$0.876908\pi$
$510$	−3.68380	−	6.38054i	−0.163122	−	0.282535i
$511$	12.1593	+	21.0605i	0.537896	+	0.931663i
$512$	−1.00000			−0.0441942
$513$	14.9681	+	25.9255i	0.660857	+	1.14464i
$514$	−28.0811			−1.23860
$515$	−1.02214			−0.0450407
$516$	−5.05922	−	9.94721i	−0.222720	−	0.437901i
$517$	22.6629			0.996714
$518$	23.5745			1.03580
$519$	16.1528	+	27.9775i	0.709030	+	1.22808i
$520$	4.82368			0.211533
$521$	7.26311	+	12.5801i	0.318203	+	0.551143i	0.980113	−	0.198440i	$-0.0635874\pi$
$521$	7.26311	+	12.5801i	0.318203	+	0.551143i	−0.661910	+	0.749583i	$0.730254\pi$
$522$	−0.0498418	−	0.0863285i	−0.00218152	−	0.00377850i
$523$	−13.1977	+	22.8591i	−0.577096	+	0.999559i	0.418715	+	0.908118i	$0.362481\pi$
$523$	−13.1977	+	22.8591i	−0.577096	+	0.999559i	−0.995810	+	0.0914413i	$0.970853\pi$
$524$	−12.5365			−0.547658
$525$	−1.89373	+	3.28004i	−0.0826493	+	0.143153i
$526$	−6.13835	−	10.6319i	−0.267645	−	0.463574i
$527$	−43.3558			−1.88861
$528$	1.92638	+	3.33659i	0.0838349	+	0.145206i
$529$	7.74557	−	13.4157i	0.336764	−	0.583292i
$530$	−1.56198	+	2.70544i	−0.0678482	+	0.117517i
$531$	−0.224381	+	0.388639i	−0.00973730	+	0.0168655i
$532$	12.6131			0.546846
$533$	10.6211	−	18.3963i	0.460051	−	0.796831i
$534$	−8.41077	+	14.5679i	−0.363970	+	0.630414i
$535$	−1.76288	−	3.05340i	−0.0762161	−	0.132010i
$536$	5.62018	+	9.73443i	0.242755	+	0.420464i
$537$	−10.8946			−0.470137
$538$	−15.4750			−0.667176
$539$	−2.31731	−	4.01370i	−0.0998138	−	0.172882i
$540$	−2.64100	−	4.57435i	−0.113651	−	0.196849i
$541$	−5.20915	+	9.02251i	−0.223959	+	0.387908i	−0.956007	−	0.293345i	$-0.905231\pi$
$541$	−5.20915	+	9.02251i	−0.223959	+	0.387908i	0.732048	+	0.681253i	$0.238565\pi$
$542$	12.4893	−	21.6322i	0.536463	−	0.929180i
$543$	−0.606701			−0.0260360
$544$	2.16457	−	3.74915i	0.0928052	−	0.160743i
$545$	−0.261809	+	0.453466i	−0.0112147	+	0.0194243i
$546$	9.13477	−	15.8219i	0.390932	−	0.677114i
$547$	1.25920	+	2.18099i	0.0538393	+	0.0932524i	0.891689	−	0.452649i	$-0.149521\pi$
$547$	1.25920	+	2.18099i	0.0538393	+	0.0932524i	−0.837850	+	0.545901i	$0.816187\pi$
$548$	−14.6965			−0.627805
$549$	0.619351	+	1.07275i	0.0264333	+	0.0457837i
$550$	−1.13192	+	1.96055i	−0.0482654	+	0.0835981i
$551$	5.45013			0.232183
$552$	−2.33175	+	4.03871i	−0.0992458	+	0.171899i
$553$	−8.14771	−	14.1122i	−0.346476	−	0.600114i
$554$	−1.13988	−	1.97433i	−0.0484288	−	0.0838812i
$555$	18.0278			0.765238
$556$	9.55217	+	16.5448i	0.405102	+	0.701658i
$557$	45.7666			1.93919			0.969596	−	0.244709i	$-0.0786926\pi$
$557$	45.7666			1.93919			0.969596	+	0.244709i	$0.0786926\pi$
$558$	−1.03815			−0.0439483
$559$	−17.2468	+	26.5154i	−0.729463	+	1.12148i
$560$	−2.22548			−0.0940437
$561$	−16.6791			−0.704194
$562$	3.14412	+	5.44577i	0.132627	+	0.229716i
$563$	12.2782			0.517464			0.258732	−	0.965949i	$-0.416695\pi$
$563$	12.2782			0.517464			0.258732	+	0.965949i	$0.416695\pi$
$564$	8.51851	+	14.7545i	0.358694	+	0.621276i
$565$	3.68915	+	6.38980i	0.155204	+	0.268821i
$566$	7.61314	−	13.1863i	0.320004	−	0.554263i
$567$	−19.3133			−0.811084
$568$	−6.74359	+	11.6802i	−0.282955	+	0.490092i
$569$	17.0747	+	29.5743i	0.715809	+	1.23982i	0.962647	+	0.270761i	$0.0872753\pi$
$569$	17.0747	+	29.5743i	0.715809	+	1.23982i	−0.246837	+	0.969057i	$0.579391\pi$
$570$	9.64544			0.404003
$571$	6.90164	+	11.9540i	0.288824	+	0.500259i	0.973529	−	0.228562i	$-0.0734023\pi$
$571$	6.90164	+	11.9540i	0.288824	+	0.500259i	−0.684705	+	0.728820i	$0.740069\pi$
$572$	5.46004	−	9.45707i	0.228296	−	0.395420i
$573$	8.13988	−	14.0987i	0.340048	−	0.588981i
$574$	−4.90021	+	8.48740i	−0.204531	+	0.354257i
$575$	−2.74023			−0.114275
$576$	0.0518303	−	0.0897728i	0.00215960	−	0.00374053i
$577$	−20.0811	+	34.7815i	−0.835989	+	1.44797i	0.0572344	+	0.998361i	$0.481772\pi$
$577$	−20.0811	+	34.7815i	−0.835989	+	1.44797i	−0.893223	+	0.449614i	$0.851562\pi$
$578$	0.870733	+	1.50815i	0.0362177	+	0.0627310i
$579$	−9.43812	−	16.3473i	−0.392235	−	0.679370i
$580$	−0.961634			−0.0399297
$581$	20.4053			0.846556
$582$	1.87082	+	3.24035i	0.0775479	+	0.134317i
$583$	3.53609	+	6.12469i	0.146450	+	0.253659i
$584$	−5.46367	+	9.46336i	−0.226088	+	0.391597i
$585$	−0.250013	+	0.433036i	−0.0103368	+	0.0179038i
$586$	−15.5150			−0.640919
$587$	−0.877341	+	1.51960i	−0.0362117	+	0.0627206i	−0.883563	−	0.468312i	$-0.844862\pi$
$587$	−0.877341	+	1.51960i	−0.0362117	+	0.0627206i	0.847352	+	0.531032i	$0.178196\pi$
$588$	1.74206	−	3.01733i	0.0718412	−	0.124433i
$589$	28.3800	−	49.1556i	1.16938	−	2.02542i
$590$	2.16457	+	3.74915i	0.0891140	+	0.154350i
$591$	36.3161			1.49384
$592$	5.29649	+	9.17380i	0.217685	+	0.377041i
$593$	−15.4937	+	26.8359i	−0.636251	+	1.10202i	0.349998	+	0.936750i	$0.386182\pi$
$593$	−15.4937	+	26.8359i	−0.636251	+	1.10202i	−0.986249	+	0.165268i	$0.947151\pi$
$594$	−11.9577			−0.490629
$595$	4.81721	−	8.34365i	0.197486	−	0.342056i
$596$	−1.96367	−	3.40118i	−0.0804351	−	0.139318i
$597$	−9.08693	−	15.7390i	−0.371903	−	0.644155i
$598$	13.2180			0.540524
$599$	10.1111	+	17.5129i	0.413128	+	0.715559i	0.995230	−	0.0975568i	$-0.0311028\pi$
$599$	10.1111	+	17.5129i	0.413128	+	0.715559i	−0.582102	+	0.813116i	$0.697769\pi$
$600$	−1.70186			−0.0694783
$601$	−35.8291			−1.46150			−0.730749	−	0.682647i	$-0.760829\pi$
$601$	−35.8291			−1.46150			−0.730749	+	0.682647i	$0.760829\pi$
$602$	7.95709	−	12.2333i	0.324307	−	0.498592i
$603$	−1.16518			−0.0474499
$604$	−2.00193			−0.0814574
$605$	−2.93750	−	5.08790i	−0.119426	−	0.206852i
$606$	20.9583			0.851375
$607$	16.6365	+	28.8153i	0.675256	+	1.16958i	0.976394	+	0.215998i	$0.0693004\pi$
$607$	16.6365	+	28.8153i	0.675256	+	1.16958i	−0.301137	+	0.953581i	$0.597366\pi$
$608$	2.83379	+	4.90826i	0.114925	+	0.199056i
$609$	−1.82108	+	3.15420i	−0.0737938	+	0.127815i
$610$	11.9496			0.483824
$611$	24.1445	−	41.8194i	0.976780	−	1.69183i
$612$	0.224381	+	0.388639i	0.00907006	+	0.0157098i
$613$	31.0140			1.25265			0.626323	−	0.779564i	$-0.284559\pi$
$613$	31.0140			1.25265			0.626323	+	0.779564i	$0.284559\pi$
$614$	−6.74665	−	11.6855i	−0.272273	−	0.471590i
$615$	−3.74727	+	6.49046i	−0.151105	+	0.261721i
$616$	−2.51907	+	4.36316i	−0.101496	+	0.175797i
$617$	18.4062	−	31.8805i	0.741006	−	1.28346i	−0.211032	−	0.977479i	$-0.567682\pi$
$617$	18.4062	−	31.8805i	0.741006	−	1.28346i	0.952038	−	0.305980i	$-0.0989842\pi$
$618$	−1.73954			−0.0699744
$619$	−21.8188	+	37.7912i	−0.876970	+	1.51896i	−0.0223205	+	0.999751i	$0.507105\pi$
$619$	−21.8188	+	37.7912i	−0.876970	+	1.51896i	−0.854649	+	0.519206i	$0.826228\pi$
$620$	−5.00744	+	8.67314i	−0.201104	+	0.348322i
$621$	−7.23696	−	12.5348i	−0.290409	−	0.503003i
$622$	−8.07130	−	13.9799i	−0.323630	−	0.560543i
$623$	−21.9971			−0.881294
$624$	8.20925			0.328633
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.47020	−	2.54647i	−0.0587612	−	0.101777i
$627$	10.9179	−	18.9104i	0.436019	−	0.755207i
$628$	3.11178	−	5.38975i	0.124173	−	0.215075i
$629$	−45.8585			−1.82850
$630$	0.115347	−	0.199788i	0.00459555	−	0.00795973i
$631$	−18.8685	+	32.6812i	−0.751144	+	1.30102i	0.196125	+	0.980579i	$0.437164\pi$
$631$	−18.8685	+	32.6812i	−0.751144	+	1.30102i	−0.947269	+	0.320441i	$0.896169\pi$
$632$	3.66110	−	6.34121i	0.145631	−	0.252240i
$633$	−10.8394	−	18.7744i	−0.430828	−	0.746217i
$634$	−23.8553			−0.947414
$635$	−4.62381	−	8.00867i	−0.183490	−	0.317814i
$636$	−2.65828	+	4.60428i	−0.105408	+	0.182572i
$637$	−9.87521			−0.391270
$638$	−1.08850	+	1.88533i	−0.0430940	+	0.0746409i
$639$	−0.699045	−	1.21078i	−0.0276538	−	0.0478978i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.4471			0.531129			0.265564	−	0.964093i	$-0.414442\pi$
$641$	13.4471			0.531129			0.265564	+	0.964093i	$0.414442\pi$
$642$	−3.00019	−	5.19647i	−0.118408	−	0.205088i
$643$	28.9188			1.14045			0.570224	−	0.821490i	$-0.306857\pi$
$643$	28.9188			1.14045			0.570224	+	0.821490i	$0.306857\pi$
$644$	−6.09833			−0.240308
$645$	6.08492	−	9.35501i	0.239594	−	0.368353i
$646$	−24.5357			−0.965345
$647$	−42.5991			−1.67475			−0.837373	−	0.546632i	$-0.815910\pi$
$647$	−42.5991			−1.67475			−0.837373	+	0.546632i	$0.815910\pi$
$648$	−4.33914	−	7.51560i	−0.170457	−	0.295241i
$649$	9.80052			0.384704
$650$	2.41184	+	4.17743i	0.0946002	+	0.163852i
$651$	18.9655	+	32.8492i	0.743316	+	1.28746i
$652$	7.09656	−	12.2916i	0.277923	−	0.481376i
$653$	16.3186			0.638596			0.319298	−	0.947654i	$-0.396553\pi$
$653$	16.3186			0.638596			0.319298	+	0.947654i	$0.396553\pi$
$654$	−0.445563	+	0.771737i	−0.0174229	+	0.0301773i
$655$	−6.26823	−	10.8569i	−0.244920	−	0.424214i
$656$	−4.40373			−0.171937
$657$	−0.566368	−	0.980978i	−0.0220961	−	0.0382716i
$658$	−11.1394	+	19.2940i	−0.434260	+	0.752160i
$659$	−22.6932	+	39.3059i	−0.884003	+	1.53114i	−0.0371518	+	0.999310i	$0.511829\pi$
$659$	−22.6932	+	39.3059i	−0.884003	+	1.53114i	−0.846852	+	0.531829i	$0.821505\pi$
$660$	−1.92638	+	3.33659i	−0.0749842	+	0.129876i
$661$	1.13220			0.0440373			0.0220187	−	0.999758i	$-0.492991\pi$
$661$	1.13220			0.0440373			0.0220187	+	0.999758i	$0.492991\pi$
$662$	−8.26823	+	14.3210i	−0.321354	+	0.556601i
$663$	−17.7695	+	30.7777i	−0.690110	+	1.19531i
$664$	4.58448	+	7.94055i	0.177912	+	0.308153i
$665$	6.30654	+	10.9232i	0.244557	+	0.423585i
$666$	−1.09808			−0.0425496
$667$	−2.63510			−0.102031
$668$	−1.77992	−	3.08291i	−0.0688671	−	0.119281i
$669$	−6.80119	−	11.7800i	−0.262949	−	0.455441i
$670$	−5.62018	+	9.73443i	−0.217126	+	0.376074i
$671$	13.5260	−	23.4277i	0.522166	−	0.904418i
$672$	−3.78746			−0.146105
$673$	9.91367	−	17.1710i	0.382144	−	0.661893i	−0.609225	−	0.792998i	$-0.708519\pi$
$673$	9.91367	−	17.1710i	0.382144	−	0.661893i	0.991368	+	0.131105i	$0.0418525\pi$
$674$	−2.03964	+	3.53276i	−0.0785639	+	0.136077i
$675$	2.64100	−	4.57435i	0.101652	−	0.176067i
$676$	−5.13396	−	8.89228i	−0.197460	−	0.342011i
$677$	20.7374			0.797002			0.398501	−	0.917168i	$-0.369531\pi$
$677$	20.7374			0.797002			0.398501	+	0.917168i	$0.369531\pi$
$678$	6.27843	+	10.8746i	0.241122	+	0.417635i
$679$	−2.44642	+	4.23732i	−0.0938849	+	0.162613i
$680$	4.32914			0.166015
$681$	−8.10462	+	14.0376i	−0.310570	+	0.537923i
$682$	11.3361	+	19.6347i	0.434081	+	0.751850i
$683$	−22.3440	−	38.7010i	−0.854970	−	1.48085i	−0.876673	−	0.481087i	$-0.840242\pi$
$683$	−22.3440	−	38.7010i	−0.854970	−	1.48085i	0.0217028	−	0.999764i	$-0.493091\pi$
$684$	−0.587505			−0.0224638
$685$	−7.34827	−	12.7276i	−0.280763	−	0.486295i
$686$	20.1344			0.768737
$687$	22.1895			0.846583
$688$	6.54820	+	0.347967i	0.249648	+	0.0132661i
$689$	15.0690			0.574084
$690$	−4.66350			−0.177536
$691$	−18.3996	−	31.8691i	−0.699955	−	1.21236i	−0.968482	−	0.249085i	$-0.919870\pi$
$691$	−18.3996	−	31.8691i	−0.699955	−	1.21236i	0.268527	−	0.963272i	$-0.413463\pi$
$692$	−18.9825			−0.721607
$693$	−0.261129	−	0.452289i	−0.00991947	−	0.0171810i
$694$	−5.60723	−	9.71201i	−0.212848	−	0.368663i
$695$	−9.55217	+	16.5448i	−0.362334	+	0.627582i
$696$	−1.63657			−0.0620340
$697$	9.53218	−	16.5102i	0.361057	−	0.625369i
$698$	16.5112	+	28.5983i	0.624960	+	1.08246i
$699$	25.6298			0.969409
$700$	−1.11274	−	1.92732i	−0.0420576	−	0.0728460i
$701$	16.5513	−	28.6677i	0.625135	−	1.08277i	−0.363380	−	0.931641i	$-0.618377\pi$
$701$	16.5513	−	28.6677i	0.625135	−	1.08277i	0.988515	−	0.151125i	$-0.0482895\pi$
$702$	−12.7394	+	22.0652i	−0.480816	+	0.832798i
$703$	30.0183	−	51.9932i	1.13216	−	1.96096i
$704$	−2.26385			−0.0853220
$705$	−8.51851	+	14.7545i	−0.320825	+	0.555686i
$706$	3.83854	−	6.64855i	0.144465	−	0.250221i
$707$	13.7033	+	23.7349i	0.515367	+	0.892642i
$708$	3.68380	+	6.38054i	0.138446	+	0.239795i
$709$	−1.18368			−0.0444539			−0.0222270	−	0.999753i	$-0.507076\pi$
$709$	−1.18368			−0.0444539			−0.0222270	+	0.999753i	$0.507076\pi$
$710$	−13.4872			−0.506165
$711$	0.379512	+	0.657335i	0.0142328	+	0.0246520i
$712$	−4.94209	−	8.55996i	−0.185213	−	0.320798i
$713$	−13.7215	+	23.7664i	−0.513875	+	0.890058i
$714$	8.19824	−	14.1998i	0.306811	−	0.531413i
$715$	10.9201			0.408388
$716$	3.20079	−	5.54393i	0.119619	−	0.207186i
$717$	16.2623	−	28.1671i	0.607327	−	1.05192i
$718$	6.12086	−	10.6016i	0.228428	−	0.395649i
$719$	5.36536	+	9.29308i	0.200094	+	0.346573i	0.948559	−	0.316602i	$-0.102542\pi$
$719$	5.36536	+	9.29308i	0.200094	+	0.346573i	−0.748464	+	0.663175i	$0.769209\pi$
$720$	0.103661			0.00386321
$721$	−1.13737	−	1.96999i	−0.0423580	−	0.0733662i
$722$	6.56070	−	11.3635i	0.244164	−	0.422904i
$723$	−28.2216			−1.04957
$724$	0.178246	−	0.308731i	0.00662446	−	0.0114739i
$725$	−0.480817	−	0.832799i	−0.0178571	−	0.0309294i
$726$	−4.99922	−	8.65890i	−0.185538	−	0.321362i
$727$	−37.2868			−1.38289			−0.691446	−	0.722428i	$-0.743026\pi$
$727$	−37.2868			−1.38289			−0.691446	+	0.722428i	$0.743026\pi$
$728$	5.36751	+	9.29680i	0.198933	+	0.344562i
$729$	27.8674			1.03212
$730$	−10.9273			−0.404439
$731$	−15.4786	+	23.7970i	−0.572497	+	0.880162i
$732$	20.3366			0.751661
$733$	−49.6607			−1.83426			−0.917130	−	0.398589i	$-0.869500\pi$
$733$	−49.6607			−1.83426			−0.917130	+	0.398589i	$0.869500\pi$
$734$	−7.45050	−	12.9046i	−0.275003	−	0.476319i
$735$	3.48411			0.128513
$736$	−1.37011	−	2.37311i	−0.0505031	−	0.0874739i
$737$	12.7232	+	22.0373i	0.468666	+	0.811753i
$738$	0.228247	−	0.395335i	0.00840188	−	0.0145525i
$739$	13.2013			0.485617			0.242808	−	0.970074i	$-0.421931\pi$
$739$	13.2013			0.485617			0.242808	+	0.970074i	$0.421931\pi$
$740$	−5.29649	+	9.17380i	−0.194703	+	0.337236i
$741$	−23.2633	−	40.2932i	−0.854598	−	1.48021i
$742$	−6.95233			−0.255228
$743$	0.786672	+	1.36256i	0.0288602	+	0.0499873i	0.880095	−	0.474798i	$-0.157479\pi$
$743$	0.786672	+	1.36256i	0.0288602	+	0.0499873i	−0.851235	+	0.524785i	$0.824146\pi$
$744$	−8.52198	+	14.7605i	−0.312431	+	0.541146i
$745$	1.96367	−	3.40118i	0.0719434	−	0.124610i
$746$	−15.5812	+	26.9874i	−0.570468	+	0.988079i
$747$	−0.950460			−0.0347755
$748$	4.90026	−	8.48750i	0.179171	−	0.310334i
$749$	3.92326	−	6.79529i	0.143353	−	0.248294i
$750$	−0.850932	−	1.47386i	−0.0310716	−	0.0538176i
$751$	16.8415	+	29.1703i	0.614553	+	1.06444i	0.990463	+	0.137781i	$0.0439971\pi$
$751$	16.8415	+	29.1703i	0.614553	+	1.06444i	−0.375909	+	0.926656i	$0.622670\pi$
$752$	−10.0108			−0.365056
$753$	−36.7887			−1.34066
$754$	2.31931	+	4.01716i	0.0844642	+	0.146296i
$755$	−1.00096	−	1.73372i	−0.0364288	−	0.0630966i
$756$	5.87750	−	10.1801i	0.213763	−	0.370248i
$757$	−24.3812	+	42.2294i	−0.886148	+	1.53485i	−0.0417568	+	0.999128i	$0.513295\pi$
$757$	−24.3812	+	42.2294i	−0.886148	+	1.53485i	−0.844392	+	0.535726i	$0.820038\pi$
$758$	6.26385			0.227513
$759$	−5.27872	+	9.14302i	−0.191605	+	0.331870i
$760$	−2.83379	+	4.90826i	−0.102792	+	0.178041i
$761$	−2.63335	+	4.56110i	−0.0954590	+	0.165340i	−0.909800	−	0.415047i	$-0.863765\pi$
$761$	−2.63335	+	4.56110i	−0.0954590	+	0.165340i	0.814341	+	0.580387i	$0.197099\pi$
$762$	−7.86909	−	13.6297i	−0.285067	−	0.493751i
$763$	−1.16530			−0.0421867
$764$	4.78292	+	8.28426i	0.173040	+	0.299714i
$765$	−0.224381	+	0.388639i	−0.00811251	+	0.0140513i
$766$	−3.49261			−0.126193
$767$	10.4412	−	18.0847i	0.377010	−	0.653001i
$768$	−0.850932	−	1.47386i	−0.0307054	−	0.0531832i
$769$	−2.80411	−	4.85687i	−0.101119	−	0.175143i	0.811027	−	0.585009i	$-0.198909\pi$
$769$	−2.80411	−	4.85687i	−0.101119	−	0.175143i	−0.912146	+	0.409866i	$0.865576\pi$
$770$	−5.03815			−0.181562
$771$	−23.8951	−	41.3875i	−0.860560	−	1.49053i
$772$	11.0915			0.399192
$773$	−5.84295			−0.210156			−0.105078	−	0.994464i	$-0.533509\pi$
$773$	−5.84295			−0.210156			−0.105078	+	0.994464i	$0.533509\pi$
$774$	−0.370633	+	0.569815i	−0.0133221	+	0.0204816i
$775$	−10.0149			−0.359745
$776$	−2.19855			−0.0789235
$777$	20.0603	+	34.7454i	0.719659	+	1.24649i
$778$	26.6817			0.956584
$779$	12.4792	+	21.6147i	0.447115	+	0.774425i
$780$	4.10463	+	7.10942i	0.146969	+	0.254558i
$781$	−15.2665	+	26.4423i	−0.546277	+	0.946179i
$782$	11.8628			0.424214
$783$	2.53968	−	4.39885i	0.0907607	−	0.157202i
$784$	1.02362	+	1.77296i	0.0365578	+	0.0633199i
$785$	6.22355			0.222128
$786$	−10.6677	−	18.4770i	−0.380503	−	0.659051i
$787$	−10.8861	+	18.8553i	−0.388048	+	0.672119i	−0.992187	−	0.124760i	$-0.960184\pi$
$787$	−10.8861	+	18.8553i	−0.388048	+	0.672119i	0.604139	+	0.796879i	$0.293517\pi$
$788$	−10.6695	+	18.4801i	−0.380085	+	0.658327i
$789$	10.4466	−	18.0941i	0.371910	−	0.644167i
$790$	7.32220			0.260512
$791$	−8.21014	+	14.2204i	−0.291919	+	0.505618i
$792$	0.117336	−	0.203232i	0.00416935	−	0.00722153i
$793$	−28.8205	−	49.9186i	−1.02345	−	1.77266i
$794$	17.7232	+	30.6975i	0.628973	+	1.08941i
$795$	−5.31657			−0.188559
$796$	10.6788			0.378500
$797$	−9.48336	−	16.4257i	−0.335918	−	0.581827i	0.647743	−	0.761859i	$-0.275713\pi$
$797$	−9.48336	−	16.4257i	−0.335918	−	0.581827i	−0.983661	+	0.180032i	$0.942380\pi$
$798$	10.7329	+	18.5899i	0.379939	+	0.658074i
$799$	21.6691	−	37.5319i	0.766597	−	1.32778i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	1.02460			0.0362025
$802$	−2.33175	+	4.03871i	−0.0823369	+	0.142612i
$803$	−12.3689	+	21.4236i	−0.436490	+	0.756022i
$804$	−9.56478	+	16.5667i	−0.337324	+	0.584262i
$805$	−3.04916	−	5.28131i	−0.107469	−	0.186142i
$806$	48.3086			1.70160
$807$	−13.1682	−	22.8080i	−0.463542	−	0.802879i
$808$	−6.15747	+	10.6651i	−0.216619	+	0.375195i
$809$	−9.32435			−0.327827			−0.163913	−	0.986475i	$-0.552412\pi$
$809$	−9.32435			−0.327827			−0.163913	+	0.986475i	$0.552412\pi$
$810$	4.33914	−	7.51560i	0.152462	−	0.264071i
$811$	22.9919	+	39.8232i	0.807355	+	1.39838i	0.914690	+	0.404157i	$0.132435\pi$
$811$	22.9919	+	39.8232i	0.807355	+	1.39838i	−0.107334	+	0.994223i	$0.534232\pi$
$812$	−1.07005	−	1.85338i	−0.0375513	−	0.0650408i
$813$	42.5103			1.49090
$814$	11.9905	+	20.7681i	0.420265	+	0.727921i
$815$	14.1931			0.497163
$816$	7.36761			0.257918
$817$	−16.8483	−	33.1264i	−0.589447	−	1.15894i
$818$	−4.75115			−0.166120
$819$	−1.11280			−0.0388843
$820$	−2.20186	−	3.81374i	−0.0768924	−	0.133182i
$821$	−23.6778			−0.826363			−0.413181	−	0.910649i	$-0.635582\pi$
$821$	−23.6778			−0.826363			−0.413181	+	0.910649i	$0.635582\pi$
$822$	−12.5057	−	21.6606i	−0.436188	−	0.755500i
$823$	−13.1444	−	22.7667i	−0.458183	−	0.793597i	0.540682	−	0.841227i	$-0.318166\pi$
$823$	−13.1444	−	22.7667i	−0.458183	−	0.793597i	−0.998865	+	0.0476304i	$0.984833\pi$
$824$	0.511068	−	0.885196i	0.0178039	−	0.0308373i
$825$	−3.85276			−0.134136
$826$	−4.81721	+	8.34365i	−0.167612	+	0.290313i
$827$	11.4444	+	19.8223i	0.397962	+	0.689290i	0.993474	−	0.114056i	$-0.0363842\pi$
$827$	11.4444	+	19.8223i	0.397962	+	0.689290i	−0.595512	+	0.803346i	$0.703051\pi$
$828$	0.284054			0.00987156
$829$	−1.58255	−	2.74105i	−0.0549642	−	0.0952007i	0.837234	−	0.546845i	$-0.184171\pi$
$829$	−1.58255	−	2.74105i	−0.0549642	−	0.0952007i	−0.892198	+	0.451644i	$0.850838\pi$
$830$	−4.58448	+	7.94055i	−0.159130	+	0.275620i
$831$	1.93992	−	3.36004i	0.0672951	−	0.116558i
$832$	−2.41184	+	4.17743i	−0.0836156	+	0.144826i
$833$	−8.86277			−0.307077
$834$	−16.2565	+	28.1571i	−0.562916	+	0.974999i
$835$	1.77992	−	3.08291i	0.0615966	−	0.106688i
$836$	6.41526	+	11.1116i	0.221876	+	0.384301i
$837$	−26.4493	−	45.8116i	−0.914222	−	1.58348i
$838$	13.7861			0.476233
$839$	10.0147			0.345745			0.172872	−	0.984944i	$-0.444695\pi$
$839$	10.0147			0.345745			0.172872	+	0.984944i	$0.444695\pi$
$840$	−1.89373	−	3.28004i	−0.0653400	−	0.113172i
$841$	14.0376	+	24.3139i	0.484056	+	0.838410i
$842$	−8.26521	+	14.3158i	−0.284838	+	0.493354i
$843$	−5.35086	+	9.26795i	−0.184293	+	0.319205i
$844$	12.7383			0.438470
$845$	5.13396	−	8.89228i	0.176614	−	0.305904i
$846$	0.518863	−	0.898697i	0.0178389	−	0.0308978i
$847$	6.53735	−	11.3230i	0.224626	−	0.389063i
$848$	−1.56198	−	2.70544i	−0.0536387	−	0.0929050i
$849$	25.9130			0.889333
$850$	2.16457	+	3.74915i	0.0742442	+	0.128595i
$851$	−14.5136	+	25.1383i	−0.497520	+	0.861730i
$852$	−22.9533			−0.786368
$853$	13.5018	−	23.3857i	0.462292	−	0.800713i	−0.536783	−	0.843720i	$-0.680361\pi$
$853$	13.5018	−	23.3857i	0.462292	−	0.800713i	0.999075	+	0.0430075i	$0.0136940\pi$
$854$	13.2968	+	23.0307i	0.455007	+	0.788094i
$855$	−0.293752	−	0.508794i	−0.0100461	−	0.0174004i
$856$	3.52576			0.120508
$857$	20.0922	+	34.8006i	0.686335	+	1.18877i	0.973015	+	0.230740i	$0.0741148\pi$
$857$	20.0922	+	34.8006i	0.686335	+	1.18877i	−0.286681	+	0.958026i	$0.592552\pi$
$858$	18.5845			0.634464
$859$	33.0496			1.12764			0.563819	−	0.825898i	$-0.309331\pi$
$859$	33.0496			1.12764			0.563819	+	0.825898i	$0.309331\pi$
$860$	2.97275	+	5.84489i	0.101370	+	0.199309i
$861$	−16.6790			−0.568417
$862$	5.04437			0.171812
$863$	−4.75364	−	8.23354i	−0.161816	−	0.280273i	0.773704	−	0.633547i	$-0.218402\pi$
$863$	−4.75364	−	8.23354i	−0.161816	−	0.280273i	−0.935520	+	0.353274i	$0.885068\pi$
$864$	5.28201			0.179698
$865$	−9.49126	−	16.4393i	−0.322712	−	0.558954i
$866$	−5.58101	−	9.66659i	−0.189650	−	0.328484i
$867$	−1.48187	+	2.56667i	−0.0503269	+	0.0871688i
$868$	−22.2879			−0.756501
$869$	8.28817	−	14.3555i	0.281157	−	0.486978i
$870$	−0.818285	−	1.41731i	−0.0277424	−	0.0480513i
$871$	54.2199			1.83717
$872$	−0.261809	−	0.453466i	−0.00886596	−	0.0153563i
$873$	0.113952	−	0.197370i	0.00385668	−	0.00667997i
$874$	−7.76523	+	13.4498i	−0.262663	+	0.454945i
$875$	1.11274	−	1.92732i	0.0376175	−	0.0651554i
$876$	−18.5968			−0.628329
$877$	20.4722	−	35.4589i	0.691297	−	1.19736i	−0.280116	−	0.959966i	$-0.590373\pi$
$877$	20.4722	−	35.4589i	0.691297	−	1.19736i	0.971413	−	0.237396i	$-0.0762939\pi$
$878$	11.8430	−	20.5127i	0.399682	−	0.692269i
$879$	−13.2022	−	22.8669i	−0.445299	−	0.771281i
$880$	−1.13192	−	1.96055i	−0.0381571	−	0.0660901i
$881$	4.85604			0.163604			0.0818021	−	0.996649i	$-0.473932\pi$
$881$	4.85604			0.163604			0.0818021	+	0.996649i	$0.473932\pi$
$882$	−0.212218			−0.00714574
$883$	−10.2359	−	17.7291i	−0.344466	−	0.596633i	0.640790	−	0.767716i	$-0.278607\pi$
$883$	−10.2359	−	17.7291i	−0.344466	−	0.596633i	−0.985257	+	0.171083i	$0.945273\pi$
$884$	−10.4412	−	18.0847i	−0.351176	−	0.608254i
$885$	−3.68380	+	6.38054i	−0.123830	+	0.214479i
$886$	15.9654	−	27.6529i	0.536368	−	0.929016i
$887$	−41.2700			−1.38571			−0.692856	−	0.721076i	$-0.743648\pi$
$887$	−41.2700			−1.38571			−0.692856	+	0.721076i	$0.743648\pi$
$888$	−9.01391	+	15.6126i	−0.302487	+	0.523923i
$889$	10.2902	−	17.8231i	0.345122	−	0.597769i
$890$	4.94209	−	8.55996i	0.165659	−	0.286930i
$891$	−9.82314	−	17.0142i	−0.329088	−	0.569996i
$892$	7.99264			0.267613
$893$	28.3685	+	49.1356i	0.949315	+	1.64426i
$894$	3.34190	−	5.78834i	0.111770	−	0.193591i
$895$	6.40158			0.213981
$896$	1.11274	−	1.92732i	0.0371740	−	0.0643873i
$897$	11.2476	+	19.4814i	0.375547	+	0.650467i
$898$	−16.1474	−	27.9681i	−0.538845	−	0.933306i
$899$	−9.63064			−0.321200
$900$	0.0518303	+	0.0897728i	0.00172768	+	0.00299243i
$901$	13.5241			0.450553
$902$	−9.96937			−0.331944
$903$	24.8011	+	1.31791i	0.825328	+	0.0438573i
$904$	−7.37831			−0.245399
$905$	0.356492			0.0118502
$906$	−1.70351	−	2.95056i	−0.0565952	−	0.0980257i
$907$	30.6018			1.01612			0.508059	−	0.861322i	$-0.330363\pi$
$907$	30.6018			1.01612			0.508059	+	0.861322i	$0.330363\pi$
$908$	−4.76221	−	8.24838i	−0.158039	−	0.273732i
$909$	−0.638288	−	1.10555i	−0.0211707	−	0.0366687i
$910$	−5.36751	+	9.29680i	−0.177931	+	0.308186i
$911$	0.632745			0.0209638			0.0104819	−	0.999945i	$-0.496663\pi$
$911$	0.632745			0.0209638			0.0104819	+	0.999945i	$0.496663\pi$
$912$	−4.82272	+	8.35319i	−0.159696	+	0.276602i
$913$	10.3786	+	17.9762i	0.343480	+	0.594925i
$914$	4.25241			0.140657
$915$	10.1683	+	17.6120i	0.336153	+	0.582234i
$916$	−6.51918	+	11.2916i	−0.215400	+	0.373084i
$917$	13.9498	−	24.1618i	0.460664	−	0.797893i
$918$	−11.4333	+	19.8030i	−0.377354	+	0.653597i
$919$	−13.8947			−0.458343			−0.229171	−	0.973386i	$-0.573602\pi$
$919$	−13.8947			−0.458343			−0.229171	+	0.973386i	$0.573602\pi$
$920$	1.37011	−	2.37311i	0.0451714	−	0.0782391i
$921$	11.4819	−	19.8872i	0.378341	−	0.655306i
$922$	−0.551077	−	0.954493i	−0.0181487	−	0.0314346i
$923$	32.5289	+	56.3418i	1.07070	+	1.85451i
$924$	−8.57424			−0.282072
$925$	−10.5930			−0.348295
$926$	12.9666	+	22.4588i	0.426108	+	0.738041i
$927$	0.0529777	+	0.0917600i	0.00174002	+	0.00301380i
$928$	0.480817	−	0.832799i	0.0157836	−	0.0273380i
$929$	27.3213	−	47.3218i	0.896382	−	1.55258i	0.0642961	−	0.997931i	$-0.479520\pi$
$929$	27.3213	−	47.3218i	0.896382	−	1.55258i	0.832085	−	0.554647i	$-0.187147\pi$
$930$	−17.0440			−0.558893
$931$	5.80143	−	10.0484i	0.190134	−	0.329322i
$932$	−7.52993	+	13.0422i	−0.246651	+	0.427212i
$933$	13.7363	−	23.7919i	0.449705	−	0.778911i
$934$	−17.9859	−	31.1524i	−0.588515	−	1.01934i
$935$	9.80052			0.320511
$936$	−0.250013	−	0.433036i	−0.00817194	−	0.0141542i
$937$	−1.81737	+	3.14778i	−0.0593709	+	0.102833i	−0.894183	−	0.447701i	$-0.852243\pi$
$937$	−1.81737	+	3.14778i	−0.0593709	+	0.102833i	0.834812	+	0.550535i	$0.185576\pi$
$938$	−25.0152			−0.816775
$939$	2.50209	−	4.33374i	0.0816525	−	0.141426i
$940$	−5.00540	−	8.66961i	−0.163258	−	0.282771i
$941$	−22.9450	−	39.7420i	−0.747987	−	1.29555i	−0.948786	−	0.315919i	$-0.897687\pi$
$941$	−22.9450	−	39.7420i	−0.747987	−	1.29555i	0.200799	−	0.979632i	$-0.435646\pi$
$942$	10.5916			0.345094
$943$	−6.03361	−	10.4505i	−0.196481	−	0.340316i
$944$	−4.32914			−0.140902
$945$	11.7550			0.382390
$946$	14.8241	+	0.787743i	0.481974	+	0.0256117i
$947$	−36.1089			−1.17338			−0.586690	−	0.809811i	$-0.699569\pi$
$947$	−36.1089			−1.17338			−0.586690	+	0.809811i	$0.699569\pi$
$948$	12.4614			0.404727
$949$	26.3550	+	45.6482i	0.855520	+	1.48180i
$950$	−5.66757			−0.183880
$951$	−20.2992	−	35.1592i	−0.658247	−	1.14012i
$952$	4.81721	+	8.34365i	0.156127	+	0.270419i
$953$	25.6653	−	44.4535i	0.831379	−	1.43999i	−0.0655656	−	0.997848i	$-0.520885\pi$
$953$	25.6653	−	44.4535i	0.831379	−	1.43999i	0.896945	−	0.442143i	$-0.145782\pi$
$954$	0.323833			0.0104845
$955$	−4.78292	+	8.28426i	−0.154772	+	0.268072i
$956$	9.55559	+	16.5508i	0.309050	+	0.535290i
$957$	−3.70494			−0.119764
$958$	2.81914	+	4.88289i	0.0910823	+	0.157759i
$959$	16.3534	−	28.3250i	0.528080	−	0.914661i
$960$	0.850932	−	1.47386i	0.0274637	−	0.0475685i
$961$	−34.6489	+	60.0136i	−1.11771	+	1.93592i
$962$	51.0972			1.64744
$963$	−0.182742	+	0.316518i	−0.00588877	+	0.0101996i
$964$	8.29138	−	14.3611i	0.267047	−	0.462540i
$965$	5.54575	+	9.60553i	0.178524	+	0.309213i
$966$	−5.18926	−	8.98807i	−0.166962	−	0.289186i
$967$	1.96816			0.0632919			0.0316459	−	0.999499i	$-0.489925\pi$
$967$	1.96816			0.0632919			0.0316459	+	0.999499i	$0.489925\pi$
$968$	5.87500			0.188830
$969$	−20.8782	−	36.1622i	−0.670705	−	1.16170i
$970$	−1.09928	−	1.90400i	−0.0352956	−	0.0611338i
$971$	21.7401	−	37.6549i	0.697673	−	1.20840i	−0.271598	−	0.962411i	$-0.587552\pi$
$971$	21.7401	−	37.6549i	0.697673	−	1.20840i	0.969271	−	0.245994i	$-0.0791144\pi$
$972$	−0.538393	+	0.932524i	−0.0172690	+	0.0299107i
$973$	−42.5163			−1.36301
$974$	0.775841	−	1.34380i	0.0248596	−	0.0430580i
$975$	−4.10463	+	7.10942i	−0.131453	+	0.227684i
$976$	−5.97479	+	10.3486i	−0.191248	+	0.331252i
$977$	−6.30563	−	10.9217i	−0.201735	−	0.349415i	0.747352	−	0.664428i	$-0.231325\pi$
$977$	−6.30563	−	10.9217i	−0.201735	−	0.349415i	−0.949088	+	0.315012i	$0.897991\pi$
$978$	24.1548			0.772384
$979$	−11.1881	−	19.3784i	−0.357575	−	0.619337i
$980$	−1.02362	+	1.77296i	−0.0326983	+	0.0566350i
$981$	0.0542785			0.00173298
$982$	−10.1408	+	17.5644i	−0.323606	+	0.560501i
$983$	−4.53116	−	7.84820i	−0.144521	−	0.250319i	0.784673	−	0.619910i	$-0.212831\pi$
$983$	−4.53116	−	7.84820i	−0.144521	−	0.250319i	−0.929194	+	0.369592i	$0.879498\pi$
$984$	−3.74727	−	6.49046i	−0.119459	−	0.206908i
$985$	−21.3390			−0.679917
$986$	2.08152	+	3.60531i	0.0662892	+	0.114816i
$987$	−37.9155			−1.20687
$988$	27.3386			0.869756
$989$	8.14602	+	16.0163i	0.259028	+	0.509290i
$990$	0.234672			0.00745836
$991$	−17.1110			−0.543550			−0.271775	−	0.962361i	$-0.587611\pi$
$991$	−17.1110			−0.543550			−0.271775	+	0.962361i	$0.587611\pi$
$992$	−5.00744	−	8.67314i	−0.158986	−	0.275372i
$993$	−28.1428			−0.893085
$994$	−15.0077	−	25.9942i	−0.476016	−	0.824484i
$995$	5.33940	+	9.24811i	0.169270	+	0.293185i
$996$	−7.80215	+	13.5137i	−0.247221	+	0.428199i
$997$	15.0236			0.475803			0.237902	−	0.971289i	$-0.423540\pi$
$997$	15.0236			0.475803			0.237902	+	0.971289i	$0.423540\pi$
$998$	−9.57402	+	16.5827i	−0.303060	+	0.524916i
$999$	−27.9761	−	48.4561i	−0.885125	−	1.53308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.g.251.2	yes	10
43.6	even	3	inner	430.2.e.g.221.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.g.221.2	✓	10	43.6	even	3	inner
430.2.e.g.251.2	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.850932 - 1.47386i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.850932 + 1.47386i) q^{6} +(-1.11274 + 1.92732i) q^{7} -1.00000 q^{8} +(0.0518303 - 0.0897728i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.850932 - 1.47386i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.850932 + 1.47386i) q^{6} +(-1.11274 + 1.92732i) q^{7} -1.00000 q^{8} +(0.0518303 - 0.0897728i) q^{9} +(-0.500000 - 0.866025i) q^{10} -2.26385 q^{11} +(-0.850932 - 1.47386i) q^{12} +(-2.41184 + 4.17743i) q^{13} +(1.11274 - 1.92732i) q^{14} +(0.850932 - 1.47386i) q^{15} +1.00000 q^{16} +(-2.16457 + 3.74915i) q^{17} +(-0.0518303 + 0.0897728i) q^{18} +(-2.83379 - 4.90826i) q^{19} +(0.500000 + 0.866025i) q^{20} +3.78746 q^{21} +2.26385 q^{22} +(1.37011 + 2.37311i) q^{23} +(0.850932 + 1.47386i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.41184 - 4.17743i) q^{26} -5.28201 q^{27} +(-1.11274 + 1.92732i) q^{28} +(-0.480817 + 0.832799i) q^{29} +(-0.850932 + 1.47386i) q^{30} +(5.00744 + 8.67314i) q^{31} -1.00000 q^{32} +(1.92638 + 3.33659i) q^{33} +(2.16457 - 3.74915i) q^{34} -2.22548 q^{35} +(0.0518303 - 0.0897728i) q^{36} +(5.29649 + 9.17380i) q^{37} +(2.83379 + 4.90826i) q^{38} +8.20925 q^{39} +(-0.500000 - 0.866025i) q^{40} -4.40373 q^{41} -3.78746 q^{42} +(6.54820 + 0.347967i) q^{43} -2.26385 q^{44} +0.103661 q^{45} +(-1.37011 - 2.37311i) q^{46} -10.0108 q^{47} +(-0.850932 - 1.47386i) q^{48} +(1.02362 + 1.77296i) q^{49} +(0.500000 - 0.866025i) q^{50} +7.36761 q^{51} +(-2.41184 + 4.17743i) q^{52} +(-1.56198 - 2.70544i) q^{53} +5.28201 q^{54} +(-1.13192 - 1.96055i) q^{55} +(1.11274 - 1.92732i) q^{56} +(-4.82272 + 8.35319i) q^{57} +(0.480817 - 0.832799i) q^{58} -4.32914 q^{59} +(0.850932 - 1.47386i) q^{60} +(-5.97479 + 10.3486i) q^{61} +(-5.00744 - 8.67314i) q^{62} +(0.115347 + 0.199788i) q^{63} +1.00000 q^{64} -4.82368 q^{65} +(-1.92638 - 3.33659i) q^{66} +(-5.62018 - 9.73443i) q^{67} +(-2.16457 + 3.74915i) q^{68} +(2.33175 - 4.03871i) q^{69} +2.22548 q^{70} +(6.74359 - 11.6802i) q^{71} +(-0.0518303 + 0.0897728i) q^{72} +(5.46367 - 9.46336i) q^{73} +(-5.29649 - 9.17380i) q^{74} +1.70186 q^{75} +(-2.83379 - 4.90826i) q^{76} +(2.51907 - 4.36316i) q^{77} -8.20925 q^{78} +(-3.66110 + 6.34121i) q^{79} +(0.500000 + 0.866025i) q^{80} +(4.33914 + 7.51560i) q^{81} +4.40373 q^{82} +(-4.58448 - 7.94055i) q^{83} +3.78746 q^{84} -4.32914 q^{85} +(-6.54820 - 0.347967i) q^{86} +1.63657 q^{87} +2.26385 q^{88} +(4.94209 + 8.55996i) q^{89} -0.103661 q^{90} +(-5.36751 - 9.29680i) q^{91} +(1.37011 + 2.37311i) q^{92} +(8.52198 - 14.7605i) q^{93} +10.0108 q^{94} +(2.83379 - 4.90826i) q^{95} +(0.850932 + 1.47386i) q^{96} +2.19855 q^{97} +(-1.02362 - 1.77296i) q^{98} +(-0.117336 + 0.203232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9} - 5 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 10 q^{16} + 4 q^{17} + 8 q^{18} + 4 q^{19} + 5 q^{20} - 4 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} - 5 q^{25} + 6 q^{26} - 26 q^{27} + 6 q^{28} - q^{29} + q^{30} - 8 q^{31} - 10 q^{32} - 14 q^{33} - 4 q^{34} + 12 q^{35} - 8 q^{36} + 14 q^{37} - 4 q^{38} + 8 q^{39} - 5 q^{40} - 6 q^{41} + 4 q^{42} + 15 q^{43} + 4 q^{44} - 16 q^{45} - 8 q^{46} - 22 q^{47} + q^{48} - 5 q^{49} + 5 q^{50} + 24 q^{51} - 6 q^{52} - 8 q^{53} + 26 q^{54} + 2 q^{55} - 6 q^{56} - 32 q^{57} + q^{58} + 8 q^{59} - q^{60} - 14 q^{61} + 8 q^{62} + 22 q^{63} + 10 q^{64} - 12 q^{65} + 14 q^{66} + 19 q^{67} + 4 q^{68} + 10 q^{69} - 12 q^{70} + 36 q^{71} + 8 q^{72} + 28 q^{73} - 14 q^{74} - 2 q^{75} + 4 q^{76} + 8 q^{77} - 8 q^{78} - 10 q^{79} + 5 q^{80} - 25 q^{81} + 6 q^{82} - 25 q^{83} - 4 q^{84} + 8 q^{85} - 15 q^{86} + 22 q^{87} - 4 q^{88} + 19 q^{89} + 16 q^{90} - 10 q^{91} + 8 q^{92} + 12 q^{93} + 22 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 5 q^{98} - 6 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9 - 5 * q^10 + 4 * q^11 + q^12 - 6 * q^13 - 6 * q^14 - q^15 + 10 * q^16 + 4 * q^17 + 8 * q^18 + 4 * q^19 + 5 * q^20 - 4 * q^21 - 4 * q^22 + 8 * q^23 - q^24 - 5 * q^25 + 6 * q^26 - 26 * q^27 + 6 * q^28 - q^29 + q^30 - 8 * q^31 - 10 * q^32 - 14 * q^33 - 4 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 - 4 * q^38 + 8 * q^39 - 5 * q^40 - 6 * q^41 + 4 * q^42 + 15 * q^43 + 4 * q^44 - 16 * q^45 - 8 * q^46 - 22 * q^47 + q^48 - 5 * q^49 + 5 * q^50 + 24 * q^51 - 6 * q^52 - 8 * q^53 + 26 * q^54 + 2 * q^55 - 6 * q^56 - 32 * q^57 + q^58 + 8 * q^59 - q^60 - 14 * q^61 + 8 * q^62 + 22 * q^63 + 10 * q^64 - 12 * q^65 + 14 * q^66 + 19 * q^67 + 4 * q^68 + 10 * q^69 - 12 * q^70 + 36 * q^71 + 8 * q^72 + 28 * q^73 - 14 * q^74 - 2 * q^75 + 4 * q^76 + 8 * q^77 - 8 * q^78 - 10 * q^79 + 5 * q^80 - 25 * q^81 + 6 * q^82 - 25 * q^83 - 4 * q^84 + 8 * q^85 - 15 * q^86 + 22 * q^87 - 4 * q^88 + 19 * q^89 + 16 * q^90 - 10 * q^91 + 8 * q^92 + 12 * q^93 + 22 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 5 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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