LMFDB - Embedded newform 21.5.f.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,5,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, 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:	$2.17076922476$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.5.f.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(4.50000 + 2.59808i) q^{3} +(6.00000 - 10.3923i) q^{4} +(9.00000 - 5.19615i) q^{5} -10.3923i q^{6} +(38.5000 - 30.3109i) q^{7} -56.0000 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(4.50000 + 2.59808i) q^{3} +(6.00000 - 10.3923i) q^{4} +(9.00000 - 5.19615i) q^{5} -10.3923i q^{6} +(38.5000 - 30.3109i) q^{7} -56.0000 q^{8} +(13.5000 + 23.3827i) q^{9} +(-18.0000 - 10.3923i) q^{10} +(-97.0000 + 168.009i) q^{11} +(54.0000 - 31.1769i) q^{12} +164.545i q^{13} +(-91.0000 - 36.3731i) q^{14} +54.0000 q^{15} +(-40.0000 - 69.2820i) q^{16} +(-210.000 - 121.244i) q^{17} +(27.0000 - 46.7654i) q^{18} +(226.500 - 130.770i) q^{19} -124.708i q^{20} +(252.000 - 36.3731i) q^{21} +388.000 q^{22} +(56.0000 + 96.9948i) q^{23} +(-252.000 - 145.492i) q^{24} +(-258.500 + 447.735i) q^{25} +(285.000 - 164.545i) q^{26} +140.296i q^{27} +(-84.0000 - 581.969i) q^{28} +1040.00 q^{29} +(-54.0000 - 93.5307i) q^{30} +(-1009.50 - 582.835i) q^{31} +(-528.000 + 914.523i) q^{32} +(-873.000 + 504.027i) q^{33} +484.974i q^{34} +(189.000 - 472.850i) q^{35} +324.000 q^{36} +(537.500 + 930.977i) q^{37} +(-453.000 - 261.540i) q^{38} +(-427.500 + 740.452i) q^{39} +(-504.000 + 290.985i) q^{40} -1305.97i q^{41} +(-315.000 - 400.104i) q^{42} -1087.00 q^{43} +(1164.00 + 2016.11i) q^{44} +(243.000 + 140.296i) q^{45} +(112.000 - 193.990i) q^{46} +(1875.00 - 1082.53i) q^{47} -415.692i q^{48} +(563.500 - 2333.94i) q^{49} +1034.00 q^{50} +(-630.000 - 1091.19i) q^{51} +(1710.00 + 987.269i) q^{52} +(1100.00 - 1905.26i) q^{53} +(243.000 - 140.296i) q^{54} +2016.11i q^{55} +(-2156.00 + 1697.41i) q^{56} +1359.00 q^{57} +(-1040.00 - 1801.33i) q^{58} +(-4632.00 - 2674.29i) q^{59} +(324.000 - 561.184i) q^{60} +(606.000 - 349.874i) q^{61} +2331.34i q^{62} +(1228.50 + 491.036i) q^{63} +832.000 q^{64} +(855.000 + 1480.90i) q^{65} +(1746.00 + 1008.05i) q^{66} +(-1187.50 + 2056.81i) q^{67} +(-2520.00 + 1454.92i) q^{68} +581.969i q^{69} +(-1008.00 + 145.492i) q^{70} -8938.00 q^{71} +(-756.000 - 1309.43i) q^{72} +(7903.50 + 4563.09i) q^{73} +(1075.00 - 1861.95i) q^{74} +(-2326.50 + 1343.21i) q^{75} -3138.48i q^{76} +(1358.00 + 9408.50i) q^{77} +1710.00 q^{78} +(-4073.50 - 7055.51i) q^{79} +(-720.000 - 415.692i) q^{80} +(-364.500 + 631.333i) q^{81} +(-2262.00 + 1305.97i) q^{82} -6675.32i q^{83} +(1134.00 - 2837.10i) q^{84} -2520.00 q^{85} +(1087.00 + 1882.74i) q^{86} +(4680.00 + 2702.00i) q^{87} +(5432.00 - 9408.50i) q^{88} +(11814.0 - 6820.82i) q^{89} -561.184i q^{90} +(4987.50 + 6334.98i) q^{91} +1344.00 q^{92} +(-3028.50 - 5245.52i) q^{93} +(-3750.00 - 2165.06i) q^{94} +(1359.00 - 2353.86i) q^{95} +(-4752.00 + 2743.57i) q^{96} +3498.74i q^{97} +(-4606.00 + 1357.93i) q^{98} -5238.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 9 q^{3} + 12 q^{4} + 18 q^{5} + 77 q^{7} - 112 q^{8} + 27 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 9 * q^3 + 12 * q^4 + 18 * q^5 + 77 * q^7 - 112 * q^8 + 27 * q^9	\( 2 q - 2 q^{2} + 9 q^{3} + 12 q^{4} + 18 q^{5} + 77 q^{7} - 112 q^{8} + 27 q^{9} - 36 q^{10} - 194 q^{11} + 108 q^{12} - 182 q^{14} + 108 q^{15} - 80 q^{16} - 420 q^{17} + 54 q^{18} + 453 q^{19} + 504 q^{21} + 776 q^{22} + 112 q^{23} - 504 q^{24} - 517 q^{25} + 570 q^{26} - 168 q^{28} + 2080 q^{29} - 108 q^{30} - 2019 q^{31} - 1056 q^{32} - 1746 q^{33} + 378 q^{35} + 648 q^{36} + 1075 q^{37} - 906 q^{38} - 855 q^{39} - 1008 q^{40} - 630 q^{42} - 2174 q^{43} + 2328 q^{44} + 486 q^{45} + 224 q^{46} + 3750 q^{47} + 1127 q^{49} + 2068 q^{50} - 1260 q^{51} + 3420 q^{52} + 2200 q^{53} + 486 q^{54} - 4312 q^{56} + 2718 q^{57} - 2080 q^{58} - 9264 q^{59} + 648 q^{60} + 1212 q^{61} + 2457 q^{63} + 1664 q^{64} + 1710 q^{65} + 3492 q^{66} - 2375 q^{67} - 5040 q^{68} - 2016 q^{70} - 17876 q^{71} - 1512 q^{72} + 15807 q^{73} + 2150 q^{74} - 4653 q^{75} + 2716 q^{77} + 3420 q^{78} - 8147 q^{79} - 1440 q^{80} - 729 q^{81} - 4524 q^{82} + 2268 q^{84} - 5040 q^{85} + 2174 q^{86} + 9360 q^{87} + 10864 q^{88} + 23628 q^{89} + 9975 q^{91} + 2688 q^{92} - 6057 q^{93} - 7500 q^{94} + 2718 q^{95} - 9504 q^{96} - 9212 q^{98} - 10476 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 9 * q^3 + 12 * q^4 + 18 * q^5 + 77 * q^7 - 112 * q^8 + 27 * q^9 - 36 * q^10 - 194 * q^11 + 108 * q^12 - 182 * q^14 + 108 * q^15 - 80 * q^16 - 420 * q^17 + 54 * q^18 + 453 * q^19 + 504 * q^21 + 776 * q^22 + 112 * q^23 - 504 * q^24 - 517 * q^25 + 570 * q^26 - 168 * q^28 + 2080 * q^29 - 108 * q^30 - 2019 * q^31 - 1056 * q^32 - 1746 * q^33 + 378 * q^35 + 648 * q^36 + 1075 * q^37 - 906 * q^38 - 855 * q^39 - 1008 * q^40 - 630 * q^42 - 2174 * q^43 + 2328 * q^44 + 486 * q^45 + 224 * q^46 + 3750 * q^47 + 1127 * q^49 + 2068 * q^50 - 1260 * q^51 + 3420 * q^52 + 2200 * q^53 + 486 * q^54 - 4312 * q^56 + 2718 * q^57 - 2080 * q^58 - 9264 * q^59 + 648 * q^60 + 1212 * q^61 + 2457 * q^63 + 1664 * q^64 + 1710 * q^65 + 3492 * q^66 - 2375 * q^67 - 5040 * q^68 - 2016 * q^70 - 17876 * q^71 - 1512 * q^72 + 15807 * q^73 + 2150 * q^74 - 4653 * q^75 + 2716 * q^77 + 3420 * q^78 - 8147 * q^79 - 1440 * q^80 - 729 * q^81 - 4524 * q^82 + 2268 * q^84 - 5040 * q^85 + 2174 * q^86 + 9360 * q^87 + 10864 * q^88 + 23628 * q^89 + 9975 * q^91 + 2688 * q^92 - 6057 * q^93 - 7500 * q^94 + 2718 * q^95 - 9504 * q^96 - 9212 * q^98 - 10476 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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	−	1.73205i	−0.250000	−	0.433013i	0.713525	−	0.700629i	$-0.247097\pi$
$2$	−1.00000	−	1.73205i	−0.250000	−	0.433013i	−0.963525	+	0.267617i	$0.913764\pi$
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$4$	6.00000	−	10.3923i	0.375000	−	0.649519i
$5$	9.00000	−	5.19615i	0.360000	−	0.207846i	−0.309081	−	0.951036i	$-0.600021\pi$
$5$	9.00000	−	5.19615i	0.360000	−	0.207846i	0.669081	+	0.743190i	$0.266688\pi$
$6$		−	10.3923i		−	0.288675i
$7$	38.5000	−	30.3109i	0.785714	−	0.618590i
$7$	38.5000	−	30.3109i	0.785714	−	0.618590i
$8$	−56.0000			−0.875000
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$	−18.0000	−	10.3923i	−0.180000	−	0.103923i
$11$	−97.0000	+	168.009i	−0.801653	+	1.38850i	0.116875	+	0.993147i	$0.462712\pi$
$11$	−97.0000	+	168.009i	−0.801653	+	1.38850i	−0.918528	+	0.395357i	$0.870621\pi$
$12$	54.0000	−	31.1769i	0.375000	−	0.216506i
$13$			164.545i			0.973638i	0.873503	+	0.486819i	$0.161843\pi$
$13$			164.545i			0.973638i	−0.873503	+	0.486819i	$0.838157\pi$
$14$	−91.0000	−	36.3731i	−0.464286	−	0.185577i
$15$	54.0000			0.240000
$16$	−40.0000	−	69.2820i	−0.156250	−	0.270633i
$17$	−210.000	−	121.244i	−0.726644	−	0.419528i	0.0905494	−	0.995892i	$-0.471138\pi$
$17$	−210.000	−	121.244i	−0.726644	−	0.419528i	−0.817193	+	0.576364i	$0.804471\pi$
$18$	27.0000	−	46.7654i	0.0833333	−	0.144338i
$19$	226.500	−	130.770i	0.627424	−	0.362243i	−0.152330	−	0.988330i	$-0.548678\pi$
$19$	226.500	−	130.770i	0.627424	−	0.362243i	0.779754	+	0.626086i	$0.215344\pi$
$20$		−	124.708i		−	0.311769i
$21$	252.000	−	36.3731i	0.571429	−	0.0824786i
$22$	388.000			0.801653
$23$	56.0000	+	96.9948i	0.105860	+	0.183355i	0.914089	−	0.405513i	$-0.132907\pi$
$23$	56.0000	+	96.9948i	0.105860	+	0.183355i	−0.808229	+	0.588868i	$0.799574\pi$
$24$	−252.000	−	145.492i	−0.437500	−	0.252591i
$25$	−258.500	+	447.735i	−0.413600	+	0.716376i
$26$	285.000	−	164.545i	0.421598	−	0.243410i
$27$			140.296i			0.192450i
$28$	−84.0000	−	581.969i	−0.107143	−	0.742307i
$29$	1040.00			1.23662			0.618312	−	0.785933i	$-0.287817\pi$
$29$	1040.00			1.23662			0.618312	+	0.785933i	$0.287817\pi$
$30$	−54.0000	−	93.5307i	−0.0600000	−	0.103923i
$31$	−1009.50	−	582.835i	−1.05047	−	0.606488i	−0.127688	−	0.991814i	$-0.540756\pi$
$31$	−1009.50	−	582.835i	−1.05047	−	0.606488i	−0.922780	+	0.385326i	$0.874089\pi$
$32$	−528.000	+	914.523i	−0.515625	+	0.893089i
$33$	−873.000	+	504.027i	−0.801653	+	0.462835i
$34$			484.974i			0.419528i
$35$	189.000	−	472.850i	0.154286	−	0.386000i
$36$	324.000			0.250000
$37$	537.500	+	930.977i	0.392622	+	0.680042i	0.992795	−	0.119829i	$-0.0382346\pi$
$37$	537.500	+	930.977i	0.392622	+	0.680042i	−0.600172	+	0.799871i	$0.704901\pi$
$38$	−453.000	−	261.540i	−0.313712	−	0.181122i
$39$	−427.500	+	740.452i	−0.281065	+	0.486819i
$40$	−504.000	+	290.985i	−0.315000	+	0.181865i
$41$		−	1305.97i		−	0.776898i	−0.921470	−	0.388449i	$-0.873011\pi$
$41$		−	1305.97i		−	0.776898i	0.921470	−	0.388449i	$-0.126989\pi$
$42$	−315.000	−	400.104i	−0.178571	−	0.226816i
$43$	−1087.00			−0.587885			−0.293943	−	0.955823i	$-0.594967\pi$
$43$	−1087.00			−0.587885			−0.293943	+	0.955823i	$0.594967\pi$
$44$	1164.00	+	2016.11i	0.601240	+	1.04138i
$45$	243.000	+	140.296i	0.120000	+	0.0692820i
$46$	112.000	−	193.990i	0.0529301	−	0.0916775i
$47$	1875.00	−	1082.53i	0.848800	−	0.490055i	−0.0114455	−	0.999934i	$-0.503643\pi$
$47$	1875.00	−	1082.53i	0.848800	−	0.490055i	0.860246	+	0.509879i	$0.170310\pi$
$48$		−	415.692i		−	0.180422i
$49$	563.500	−	2333.94i	0.234694	−	0.972069i
$50$	1034.00			0.413600
$51$	−630.000	−	1091.19i	−0.242215	−	0.419528i
$52$	1710.00	+	987.269i	0.632396	+	0.365114i
$53$	1100.00	−	1905.26i	0.391598	−	0.678268i	−0.601062	−	0.799202i	$-0.705256\pi$
$53$	1100.00	−	1905.26i	0.391598	−	0.678268i	0.992661	+	0.120934i	$0.0385889\pi$
$54$	243.000	−	140.296i	0.0833333	−	0.0481125i
$55$			2016.11i			0.666482i
$56$	−2156.00	+	1697.41i	−0.687500	+	0.541266i
$57$	1359.00			0.418283
$58$	−1040.00	−	1801.33i	−0.309156	−	0.535473i
$59$	−4632.00	−	2674.29i	−1.33065	−	0.768252i	−0.345253	−	0.938510i	$-0.612207\pi$
$59$	−4632.00	−	2674.29i	−1.33065	−	0.768252i	−0.985400	+	0.170257i	$0.945540\pi$
$60$	324.000	−	561.184i	0.0900000	−	0.155885i
$61$	606.000	−	349.874i	0.162859	−	0.0940269i	−0.416355	−	0.909202i	$-0.636693\pi$
$61$	606.000	−	349.874i	0.162859	−	0.0940269i	0.579215	+	0.815175i	$0.303359\pi$
$62$			2331.34i			0.606488i
$63$	1228.50	+	491.036i	0.309524	+	0.123718i
$64$	832.000			0.203125
$65$	855.000	+	1480.90i	0.202367	+	0.350510i
$66$	1746.00	+	1008.05i	0.400826	+	0.231417i
$67$	−1187.50	+	2056.81i	−0.264536	+	0.458189i	−0.967442	−	0.253093i	$-0.918552\pi$
$67$	−1187.50	+	2056.81i	−0.264536	+	0.458189i	0.702906	+	0.711282i	$0.251885\pi$
$68$	−2520.00	+	1454.92i	−0.544983	+	0.314646i
$69$			581.969i			0.122237i
$70$	−1008.00	+	145.492i	−0.205714	+	0.0296923i
$71$	−8938.00			−1.77306			−0.886530	−	0.462670i	$-0.846891\pi$
$71$	−8938.00			−1.77306			−0.886530	+	0.462670i	$0.846891\pi$
$72$	−756.000	−	1309.43i	−0.145833	−	0.252591i
$73$	7903.50	+	4563.09i	1.48311	+	0.856275i	0.999816	−	0.0191827i	$-0.00610642\pi$
$73$	7903.50	+	4563.09i	1.48311	+	0.856275i	0.483295	+	0.875457i	$0.339440\pi$
$74$	1075.00	−	1861.95i	0.196311	−	0.340021i
$75$	−2326.50	+	1343.21i	−0.413600	+	0.238792i
$76$		−	3138.48i		−	0.543365i
$77$	1358.00	+	9408.50i	0.229044	+	1.58686i
$78$	1710.00			0.281065
$79$	−4073.50	−	7055.51i	−0.652700	−	1.13051i	−0.982465	−	0.186446i	$-0.940303\pi$
$79$	−4073.50	−	7055.51i	−0.652700	−	1.13051i	0.329765	−	0.944063i	$-0.393030\pi$
$80$	−720.000	−	415.692i	−0.112500	−	0.0649519i
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$	−2262.00	+	1305.97i	−0.336407	+	0.194225i
$83$		−	6675.32i		−	0.968983i	−0.874796	−	0.484491i	$-0.839005\pi$
$83$		−	6675.32i		−	0.968983i	0.874796	−	0.484491i	$-0.160995\pi$
$84$	1134.00	−	2837.10i	0.160714	−	0.402083i
$85$	−2520.00			−0.348789
$86$	1087.00	+	1882.74i	0.146971	+	0.254562i
$87$	4680.00	+	2702.00i	0.618312	+	0.356982i
$88$	5432.00	−	9408.50i	0.701446	−	1.21494i
$89$	11814.0	−	6820.82i	1.49148	−	0.861105i	0.491526	−	0.870863i	$-0.336439\pi$
$89$	11814.0	−	6820.82i	1.49148	−	0.861105i	0.999952	+	0.00975750i	$0.00310596\pi$
$90$		−	561.184i		−	0.0692820i
$91$	4987.50	+	6334.98i	0.602282	+	0.765001i
$92$	1344.00			0.158790
$93$	−3028.50	−	5245.52i	−0.350156	−	0.606488i
$94$	−3750.00	−	2165.06i	−0.424400	−	0.245028i
$95$	1359.00	−	2353.86i	0.150582	−	0.260815i
$96$	−4752.00	+	2743.57i	−0.515625	+	0.297696i
$97$			3498.74i			0.371851i	0.982564	+	0.185925i	$0.0595283\pi$
$97$			3498.74i			0.371851i	−0.982564	+	0.185925i	$0.940472\pi$
$98$	−4606.00	+	1357.93i	−0.479592	+	0.141392i
$99$	−5238.00			−0.534435
$100$	3102.00	+	5372.82i	0.310200	+	0.537282i
$101$	6057.00	+	3497.01i	0.593765	+	0.342811i	0.766585	−	0.642143i	$-0.221954\pi$
$101$	6057.00	+	3497.01i	0.593765	+	0.342811i	−0.172820	+	0.984953i	$0.555288\pi$
$102$	−1260.00	+	2182.38i	−0.121107	+	0.209764i
$103$	−7906.50	+	4564.82i	−0.745263	+	0.430278i	−0.823980	−	0.566619i	$-0.808251\pi$
$103$	−7906.50	+	4564.82i	−0.745263	+	0.430278i	0.0787165	+	0.996897i	$0.474918\pi$
$104$		−	9214.51i		−	0.851933i
$105$	2079.00	−	1636.79i	0.188571	−	0.148461i
$106$	−4400.00			−0.391598
$107$	5366.00	+	9294.18i	0.468687	+	0.811790i	0.999359	−	0.0357871i	$-0.0113938\pi$
$107$	5366.00	+	9294.18i	0.468687	+	0.811790i	−0.530672	+	0.847577i	$0.678060\pi$
$108$	1458.00	+	841.777i	0.125000	+	0.0721688i
$109$	−3644.50	+	6312.46i	−0.306750	+	0.531307i	−0.977649	−	0.210241i	$-0.932575\pi$
$109$	−3644.50	+	6312.46i	−0.306750	+	0.531307i	0.670899	+	0.741549i	$0.265908\pi$
$110$	3492.00	−	2016.11i	0.288595	−	0.166620i
$111$			5585.86i			0.453361i
$112$	−3640.00	−	1454.92i	−0.290179	−	0.115986i
$113$	−4330.00			−0.339103			−0.169551	−	0.985521i	$-0.554232\pi$
$113$	−4330.00			−0.339103			−0.169551	+	0.985521i	$0.554232\pi$
$114$	−1359.00	−	2353.86i	−0.104571	−	0.181122i
$115$	1008.00	+	581.969i	0.0762193	+	0.0440052i
$116$	6240.00	−	10808.0i	0.463734	−	0.803210i
$117$	−3847.50	+	2221.36i	−0.281065	+	0.162273i
$118$			10697.1i			0.768252i
$119$	−11760.0	+	1697.41i	−0.830450	+	0.119865i
$120$	−3024.00			−0.210000
$121$	−11497.5	−	19914.3i	−0.785295	−	1.36017i
$122$	−1212.00	−	699.749i	−0.0814297	−	0.0470135i
$123$	3393.00	−	5876.85i	0.224271	−	0.388449i
$124$	−12114.0	+	6994.02i	−0.787851	+	0.454866i
$125$			11868.0i			0.759553i
$126$	−378.000	−	2618.86i	−0.0238095	−	0.164957i
$127$	18899.0			1.17174			0.585870	−	0.810405i	$-0.300753\pi$
$127$	18899.0			1.17174			0.585870	+	0.810405i	$0.300753\pi$
$128$	7616.00	+	13191.3i	0.464844	+	0.805133i
$129$	−4891.50	−	2824.11i	−0.293943	−	0.169708i
$130$	1710.00	−	2961.81i	0.101183	−	0.175255i
$131$	18963.0	−	10948.3i	1.10501	−	0.637975i	0.167474	−	0.985876i	$-0.446439\pi$
$131$	18963.0	−	10948.3i	1.10501	−	0.637975i	0.937531	+	0.347901i	$0.113106\pi$
$132$			12096.6i			0.694252i
$133$	4756.50	−	11900.1i	0.268896	−	0.672738i
$134$	4750.00			0.264536
$135$	729.000	+	1262.67i	0.0400000	+	0.0692820i
$136$	11760.0	+	6789.64i	0.635813	+	0.367087i
$137$	−10438.0	+	18079.1i	−0.556130	+	0.963245i	0.441685	+	0.897170i	$0.354381\pi$
$137$	−10438.0	+	18079.1i	−0.556130	+	0.963245i	−0.997815	+	0.0660748i	$0.978952\pi$
$138$	1008.00	−	581.969i	0.0529301	−	0.0305592i
$139$		−	29131.4i		−	1.50776i	−0.657014	−	0.753878i	$-0.728181\pi$
$139$		−	29131.4i		−	1.50776i	0.657014	−	0.753878i	$-0.271819\pi$
$140$	−3780.00	−	4801.24i	−0.192857	−	0.244961i
$141$	11250.0			0.565867
$142$	8938.00	+	15481.1i	0.443265	+	0.767758i
$143$	−27645.0	−	15960.8i	−1.35190	−	0.780520i
$144$	1080.00	−	1870.61i	0.0520833	−	0.0902110i
$145$	9360.00	−	5404.00i	0.445184	−	0.257027i
$146$		−	18252.4i		−	0.856275i
$147$	8599.50	−	9038.71i	0.397959	−	0.418284i
$148$	12900.0			0.588934
$149$	−2206.00	−	3820.90i	−0.0993649	−	0.172105i	0.812057	−	0.583578i	$-0.198348\pi$
$149$	−2206.00	−	3820.90i	−0.0993649	−	0.172105i	−0.911422	+	0.411473i	$0.865014\pi$
$150$	4653.00	+	2686.41i	0.206800	+	0.119396i
$151$	−10681.0	+	18500.0i	−0.468444	+	0.811369i	−0.999350	−	0.0360618i	$-0.988519\pi$
$151$	−10681.0	+	18500.0i	−0.468444	+	0.811369i	0.530905	+	0.847431i	$0.321852\pi$
$152$	−12684.0	+	7323.11i	−0.548996	+	0.316963i
$153$		−	6547.15i		−	0.279685i
$154$	14938.0	−	11760.6i	0.629870	−	0.495894i
$155$	−12114.0			−0.504225
$156$	5130.00	+	8885.42i	0.210799	+	0.365114i
$157$	−25242.0	−	14573.5i	−1.02406	−	0.591240i	−0.108781	−	0.994066i	$-0.534695\pi$
$157$	−25242.0	−	14573.5i	−1.02406	−	0.591240i	−0.915277	+	0.402826i	$0.868028\pi$
$158$	−8147.00	+	14111.0i	−0.326350	+	0.565255i
$159$	9900.00	−	5715.77i	0.391598	−	0.226089i
$160$			10974.3i			0.428683i
$161$	5096.00	+	2036.89i	0.196597	+	0.0785808i
$162$	1458.00			0.0555556
$163$	6473.00	+	11211.6i	0.243630	+	0.421979i	0.961745	−	0.273945i	$-0.0883285\pi$
$163$	6473.00	+	11211.6i	0.243630	+	0.421979i	−0.718116	+	0.695924i	$0.754995\pi$
$164$	−13572.0	−	7835.80i	−0.504610	−	0.291337i
$165$	−5238.00	+	9072.48i	−0.192397	+	0.333241i
$166$	−11562.0	+	6675.32i	−0.419582	+	0.242246i
$167$			35233.4i			1.26334i	0.775236	+	0.631672i	$0.217631\pi$
$167$			35233.4i			1.26334i	−0.775236	+	0.631672i	$0.782369\pi$
$168$	−14112.0	+	2036.89i	−0.500000	+	0.0721688i
$169$	1486.00			0.0520290
$170$	2520.00	+	4364.77i	0.0871972	+	0.151030i
$171$	6115.50	+	3530.79i	0.209141	+	0.120748i
$172$	−6522.00	+	11296.4i	−0.220457	+	0.381843i
$173$	−4992.00	+	2882.13i	−0.166795	+	0.0962990i	−0.581074	−	0.813851i	$-0.697367\pi$
$173$	−4992.00	+	2882.13i	−0.166795	+	0.0962990i	0.414279	+	0.910150i	$0.364034\pi$
$174$		−	10808.0i		−	0.356982i
$175$	3619.00	+	25073.2i	0.118171	+	0.818716i
$176$	15520.0			0.501033
$177$	−13896.0	−	24068.6i	−0.443551	−	0.768252i
$178$	−23628.0	−	13641.6i	−0.745739	−	0.430553i
$179$	−2605.00	+	4511.99i	−0.0813021	+	0.140819i	−0.903809	−	0.427935i	$-0.859241\pi$
$179$	−2605.00	+	4511.99i	−0.0813021	+	0.140819i	0.822507	+	0.568754i	$0.192575\pi$
$180$	2916.00	−	1683.55i	0.0900000	−	0.0519615i
$181$			11426.3i			0.348779i	0.984677	+	0.174389i	$0.0557951\pi$
$181$			11426.3i			0.348779i	−0.984677	+	0.174389i	$0.944205\pi$
$182$	5985.00	−	14973.6i	0.180685	−	0.452046i
$183$	3636.00			0.108573
$184$	−3136.00	−	5431.71i	−0.0926276	−	0.160436i
$185$	9675.00	+	5585.86i	0.282688	+	0.163210i
$186$	−6057.00	+	10491.0i	−0.175078	+	0.303244i
$187$	40740.0	−	23521.2i	1.16503	−	0.672631i
$188$		−	25980.8i		−	0.735083i
$189$	4252.50	+	5401.40i	0.119048	+	0.151211i
$190$	−5436.00			−0.150582
$191$	−6823.00	−	11817.8i	−0.187029	−	0.323943i	0.757229	−	0.653149i	$-0.226552\pi$
$191$	−6823.00	−	11817.8i	−0.187029	−	0.323943i	−0.944258	+	0.329205i	$0.893219\pi$
$192$	3744.00	+	2161.60i	0.101562	+	0.0586371i
$193$	−698.500	+	1209.84i	−0.0187522	+	0.0324797i	−0.875249	−	0.483672i	$-0.839303\pi$
$193$	−698.500	+	1209.84i	−0.0187522	+	0.0324797i	0.856497	+	0.516152i	$0.172636\pi$
$194$	6060.00	−	3498.74i	0.161016	−	0.0929627i
$195$			8885.42i			0.233673i
$196$	−20874.0	−	19859.7i	−0.543367	−	0.516964i
$197$	25244.0			0.650468			0.325234	−	0.945634i	$-0.394557\pi$
$197$	25244.0			0.650468			0.325234	+	0.945634i	$0.394557\pi$
$198$	5238.00	+	9072.48i	0.133609	+	0.231417i
$199$	20958.0	+	12100.1i	0.529229	+	0.305551i	0.740702	−	0.671833i	$-0.234493\pi$
$199$	20958.0	+	12100.1i	0.529229	+	0.305551i	−0.211473	+	0.977384i	$0.567826\pi$
$200$	14476.0	−	25073.2i	0.361900	−	0.626829i
$201$	−10687.5	+	6170.43i	−0.264536	+	0.152730i
$202$		−	13988.0i		−	0.342811i
$203$	40040.0	−	31523.3i	0.971632	−	0.764962i
$204$	−15120.0			−0.363322
$205$	−6786.00	−	11753.7i	−0.161475	−	0.279683i
$206$	15813.0	+	9129.64i	0.372632	+	0.215139i
$207$	−1512.00	+	2618.86i	−0.0352867	+	0.0611184i
$208$	11400.0	−	6581.79i	0.263499	−	0.152131i
$209$			50738.7i			1.16157i
$210$	−4914.00	−	1964.15i	−0.111429	−	0.0445384i
$211$	−13366.0			−0.300218			−0.150109	−	0.988669i	$-0.547962\pi$
$211$	−13366.0			−0.300218			−0.150109	+	0.988669i	$0.547962\pi$
$212$	−13200.0	−	22863.1i	−0.293699	−	0.508701i
$213$	−40221.0	−	23221.6i	−0.886530	−	0.511839i
$214$	10732.0	−	18588.4i	0.234344	−	0.405895i
$215$	−9783.00	+	5648.22i	−0.211639	+	0.122190i
$216$		−	7856.58i		−	0.168394i
$217$	−56532.0	+	8159.69i	−1.20054	+	0.173282i
$218$	14578.0			0.306750
$219$	23710.5	+	41067.8i	0.494370	+	0.856275i
$220$	20952.0	+	12096.6i	0.432893	+	0.249931i
$221$	19950.0	−	34554.4i	0.408468	−	0.707488i
$222$	9675.00	−	5585.86i	0.196311	−	0.113340i
$223$			25281.0i			0.508376i	0.967155	+	0.254188i	$0.0818081\pi$
$223$			25281.0i			0.508376i	−0.967155	+	0.254188i	$0.918192\pi$
$224$	7392.00	+	51213.3i	0.147321	+	1.02067i
$225$	−13959.0			−0.275733
$226$	4330.00	+	7499.78i	0.0847756	+	0.146836i
$227$	37881.0	+	21870.6i	0.735139	+	0.424433i	0.820299	−	0.571934i	$-0.193807\pi$
$227$	37881.0	+	21870.6i	0.735139	+	0.424433i	−0.0851600	+	0.996367i	$0.527140\pi$
$228$	8154.00	−	14123.1i	0.156856	−	0.271682i
$229$	−32044.5	+	18500.9i	−0.611058	+	0.352795i	−0.773379	−	0.633943i	$-0.781435\pi$
$229$	−32044.5	+	18500.9i	−0.611058	+	0.352795i	0.162321	+	0.986738i	$0.448102\pi$
$230$		−	2327.88i		−	0.0440052i
$231$	−18333.0	+	45866.4i	−0.343566	+	0.859550i
$232$	−58240.0			−1.08205
$233$	−8599.00	−	14893.9i	−0.158393	−	0.274345i	0.775896	−	0.630860i	$-0.217298\pi$
$233$	−8599.00	−	14893.9i	−0.158393	−	0.274345i	−0.934289	+	0.356516i	$0.883965\pi$
$234$	7695.00	+	4442.71i	0.140533	+	0.0811365i
$235$	11250.0	−	19485.6i	0.203712	−	0.352840i
$236$	−55584.0	+	32091.4i	−0.997989	+	0.576189i
$237$		−	42333.1i		−	0.753673i
$238$	14700.0	+	18671.5i	0.259516	+	0.329629i
$239$	−66970.0			−1.17242			−0.586212	−	0.810158i	$-0.699381\pi$
$239$	−66970.0			−1.17242			−0.586212	+	0.810158i	$0.699381\pi$
$240$	−2160.00	−	3741.23i	−0.0375000	−	0.0649519i
$241$	24444.0	+	14112.7i	0.420861	+	0.242984i	0.695445	−	0.718579i	$-0.255207\pi$
$241$	24444.0	+	14112.7i	0.420861	+	0.242984i	−0.274585	+	0.961563i	$0.588540\pi$
$242$	−22995.0	+	39828.5i	−0.392647	+	0.680085i
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		−	8396.98i		−	0.141040i
$245$	−7056.00	−	23933.5i	−0.117551	−	0.398725i
$246$	−13572.0			−0.224271
$247$	21517.5	+	37269.4i	0.352694	+	0.610884i
$248$	56532.0	+	32638.8i	0.919160	+	0.530677i
$249$	17343.0	−	30039.0i	0.279721	−	0.484491i
$250$	20556.0	−	11868.0i	0.328896	−	0.189888i
$251$		−	96856.3i		−	1.53738i	−0.639623	−	0.768688i	$-0.720910\pi$
$251$		−	96856.3i		−	1.53738i	0.639623	−	0.768688i	$-0.279090\pi$
$252$	12474.0	−	9820.73i	0.196429	−	0.154647i
$253$	−21728.0			−0.339452
$254$	−18899.0	−	32734.0i	−0.292935	−	0.507378i
$255$	−11340.0	−	6547.15i	−0.174394	−	0.100687i
$256$	21888.0	−	37911.1i	0.333984	−	0.578478i
$257$	−64377.0	+	37168.1i	−0.974685	+	0.562735i	−0.900661	−	0.434522i	$-0.856917\pi$
$257$	−64377.0	+	37168.1i	−0.974685	+	0.562735i	−0.0740240	+	0.997256i	$0.523584\pi$
$258$			11296.4i			0.169708i
$259$	48912.5	+	19550.5i	0.729156	+	0.291447i
$260$	20520.0			0.303550
$261$	14040.0	+	24318.0i	0.206104	+	0.356982i
$262$	−37926.0	−	21896.6i	−0.552503	−	0.318988i
$263$	20396.0	−	35326.9i	0.294872	−	0.510733i	−0.680083	−	0.733135i	$-0.738056\pi$
$263$	20396.0	−	35326.9i	0.294872	−	0.510733i	0.974955	+	0.222402i	$0.0713897\pi$
$264$	48888.0	−	28225.5i	0.701446	−	0.404980i
$265$		−	22863.1i		−	0.325569i
$266$	−25368.0	+	3661.56i	−0.358528	+	0.0517490i
$267$	70884.0			0.994319
$268$	14250.0	+	24681.7i	0.198402	+	0.343642i
$269$	62061.0	+	35830.9i	0.857658	+	0.495169i	0.863227	−	0.504815i	$-0.168439\pi$
$269$	62061.0	+	35830.9i	0.857658	+	0.495169i	−0.00556923	+	0.999984i	$0.501773\pi$
$270$	1458.00	−	2525.33i	0.0200000	−	0.0346410i
$271$	−3306.00	+	1908.72i	−0.0450157	+	0.0259898i	−0.522339	−	0.852738i	$-0.674940\pi$
$271$	−3306.00	+	1908.72i	−0.0450157	+	0.0259898i	0.477323	+	0.878728i	$0.341607\pi$
$272$			19399.0i			0.262205i
$273$	5985.00	+	41465.3i	0.0803043	+	0.556365i
$274$	41752.0			0.556130
$275$	−50149.0	−	86860.6i	−0.663127	−	1.14857i
$276$	6048.00	+	3491.81i	0.0793951	+	0.0458388i
$277$	50694.5	−	87805.4i	0.660695	−	1.14436i	−0.319738	−	0.947506i	$-0.603595\pi$
$277$	50694.5	−	87805.4i	0.660695	−	1.14436i	0.980433	−	0.196852i	$-0.0630718\pi$
$278$	−50457.0	+	29131.4i	−0.652878	+	0.376939i
$279$		−	31473.1i		−	0.404325i
$280$	−10584.0	+	26479.6i	−0.135000	+	0.337750i
$281$	31916.0			0.404200			0.202100	−	0.979365i	$-0.435223\pi$
$281$	31916.0			0.404200			0.202100	+	0.979365i	$0.435223\pi$
$282$	−11250.0	−	19485.6i	−0.141467	−	0.245028i
$283$	16099.5	+	9295.05i	0.201020	+	0.116059i	0.597131	−	0.802144i	$-0.296307\pi$
$283$	16099.5	+	9295.05i	0.201020	+	0.116059i	−0.396111	+	0.918203i	$0.629640\pi$
$284$	−53628.0	+	92886.4i	−0.664898	+	1.15164i
$285$	12231.0	−	7061.57i	0.150582	−	0.0869384i
$286$			63843.4i			0.780520i
$287$	−39585.0	−	50279.7i	−0.480581	−	0.610420i
$288$	−28512.0			−0.343750
$289$	−12360.5	−	21409.0i	−0.147993	−	0.256331i
$290$	−18720.0	−	10808.0i	−0.222592	−	0.128514i
$291$	−9090.00	+	15744.3i	−0.107344	+	0.185925i
$292$	94842.0	−	54757.1i	1.11233	−	0.642206i
$293$			95934.8i			1.11748i	0.829342	+	0.558742i	$0.188716\pi$
$293$			95934.8i			1.11748i	−0.829342	+	0.558742i	$0.811284\pi$
$294$	−24255.0	−	5856.06i	−0.280612	−	0.0677503i
$295$	−55584.0			−0.638713
$296$	−30100.0	−	52134.7i	−0.343545	−	0.595037i
$297$	−23571.0	−	13608.7i	−0.267218	−	0.154278i
$298$	−4412.00	+	7641.81i	−0.0496824	+	0.0860525i
$299$	−15960.0	+	9214.51i	−0.178521	+	0.103069i
$300$			32236.9i			0.358188i
$301$	−41849.5	+	32947.9i	−0.461910	+	0.363660i
$302$	42724.0			0.468444
$303$	18171.0	+	31473.1i	0.197922	+	0.342811i
$304$	−18120.0	−	10461.6i	−0.196070	−	0.113201i
$305$	3636.00	−	6297.74i	0.0390863	−	0.0676994i
$306$	−11340.0	+	6547.15i	−0.121107	+	0.0699213i
$307$		−	148241.i		−	1.57287i	−0.617676	−	0.786433i	$-0.711926\pi$
$307$		−	148241.i		−	1.57287i	0.617676	−	0.786433i	$-0.288074\pi$
$308$	105924.	+	42338.2i	1.11659	+	0.446305i
$309$	−47439.0			−0.496842
$310$	12114.0	+	20982.1i	0.126056	+	0.218336i
$311$	28785.0	+	16619.0i	0.297609	+	0.171824i	0.641368	−	0.767233i	$-0.278367\pi$
$311$	28785.0	+	16619.0i	0.297609	+	0.171824i	−0.343760	+	0.939058i	$0.611700\pi$
$312$	23940.0	−	41465.3i	0.245932	−	0.425967i
$313$	−23284.5	+	13443.3i	−0.237672	+	0.137220i	−0.614106	−	0.789223i	$-0.710483\pi$
$313$	−23284.5	+	13443.3i	−0.237672	+	0.137220i	0.376434	+	0.926443i	$0.377150\pi$
$314$			58293.9i			0.591240i
$315$	13608.0	−	1964.15i	0.137143	−	0.0197949i
$316$	−97764.0			−0.979050
$317$	5294.00	+	9169.48i	0.0526824	+	0.0912486i	0.891164	−	0.453681i	$-0.149890\pi$
$317$	5294.00	+	9169.48i	0.0526824	+	0.0912486i	−0.838482	+	0.544930i	$0.816556\pi$
$318$	−19800.0	−	11431.5i	−0.195799	−	0.113045i
$319$	−100880.	+	174729.i	−0.991342	+	1.71706i
$320$	7488.00	−	4323.20i	0.0731250	−	0.0422187i
$321$			55765.1i			0.541193i
$322$	−1568.00	−	10863.4i	−0.0151229	−	0.104774i
$323$	−63420.0			−0.607885
$324$	4374.00	+	7575.99i	0.0416667	+	0.0721688i
$325$	−73672.5	−	42534.8i	−0.697491	−	0.402697i
$326$	12946.0	−	22423.1i	0.121815	−	0.210990i
$327$	−32800.5	+	18937.4i	−0.306750	+	0.177102i
$328$			73134.1i			0.679786i
$329$	39375.0	−	98510.4i	0.363772	−	0.910102i
$330$	20952.0			0.192397
$331$	63663.5	+	110268.i	0.581078	+	1.00646i	0.995352	+	0.0963045i	$0.0307023\pi$
$331$	63663.5	+	110268.i	0.581078	+	1.00646i	−0.414274	+	0.910152i	$0.635964\pi$
$332$	−69372.0	−	40051.9i	−0.629373	−	0.363369i
$333$	−14512.5	+	25136.4i	−0.130874	+	0.226681i
$334$	61026.0	−	35233.4i	0.547044	−	0.315836i
$335$			24681.7i			0.219931i
$336$	−12600.0	−	16004.1i	−0.111607	−	0.141760i
$337$	211553.			1.86277			0.931385	−	0.364035i	$-0.118601\pi$
$337$	211553.			1.86277			0.931385	+	0.364035i	$0.118601\pi$
$338$	−1486.00	−	2573.83i	−0.0130072	−	0.0225292i
$339$	−19485.0	−	11249.7i	−0.169551	−	0.0978905i
$340$	−15120.0	+	26188.6i	−0.130796	+	0.226545i
$341$	195843.	−	113070.i	1.68422	−	0.972386i
$342$		−	14123.1i		−	0.120748i
$343$	−49049.0	−	106937.i	−0.416910	−	0.908948i
$344$	60872.0			0.514400
$345$	3024.00	+	5237.72i	0.0254064	+	0.0440052i
$346$	9984.00	+	5764.27i	0.0833974	+	0.0481495i
$347$	12542.0	−	21723.4i	0.104162	−	0.180413i	−0.809234	−	0.587487i	$-0.800117\pi$
$347$	12542.0	−	21723.4i	0.104162	−	0.180413i	0.913395	+	0.407074i	$0.133451\pi$
$348$	56160.0	−	32424.0i	0.463734	−	0.267737i
$349$			3831.30i			0.0314554i	0.999876	+	0.0157277i	$0.00500649\pi$
$349$			3831.30i			0.0314554i	−0.999876	+	0.0157277i	$0.994994\pi$
$350$	39809.0	−	31341.5i	0.324971	−	0.255849i
$351$	−23085.0			−0.187377
$352$	−102432.	−	177417.i	−0.826705	−	1.43189i
$353$	6327.00	+	3652.90i	0.0507748	+	0.0293149i	0.525173	−	0.850996i	$-0.324001\pi$
$353$	6327.00	+	3652.90i	0.0507748	+	0.0293149i	−0.474398	+	0.880311i	$0.657334\pi$
$354$	−27792.0	+	48137.2i	−0.221775	+	0.384126i
$355$	−80442.0	+	46443.2i	−0.638302	+	0.368524i
$356$		−	163700.i		−	1.29166i
$357$	−57330.0	−	22915.0i	−0.449827	−	0.179798i
$358$	10420.0			0.0813021
$359$	117254.	+	203090.i	0.909785	+	1.57579i	0.814362	+	0.580357i	$0.197087\pi$
$359$	117254.	+	203090.i	0.909785	+	1.57579i	0.0954228	+	0.995437i	$0.469580\pi$
$360$	−13608.0	−	7856.58i	−0.105000	−	0.0606218i
$361$	−30959.0	+	53622.6i	−0.237560	+	0.411465i
$362$	19791.0	−	11426.3i	0.151026	−	0.0871947i
$363$		−	119486.i		−	0.906780i
$364$	95760.0	−	13821.8i	0.722739	−	0.104318i
$365$	94842.0			0.711893
$366$	−3636.00	−	6297.74i	−0.0271432	−	0.0470135i
$367$	−88303.5	−	50982.0i	−0.655610	−	0.378517i	0.134992	−	0.990847i	$-0.456899\pi$
$367$	−88303.5	−	50982.0i	−0.655610	−	0.378517i	−0.790602	+	0.612330i	$0.790232\pi$
$368$	4480.00	−	7759.59i	0.0330813	−	0.0572985i
$369$	30537.0	−	17630.5i	0.224271	−	0.129483i
$370$		−	22343.5i		−	0.163210i
$371$	−15400.0	−	106694.i	−0.111885	−	0.775164i
$372$	−72684.0			−0.525234
$373$	48918.5	+	84729.3i	0.351605	+	0.608998i	0.986531	−	0.163575i	$-0.0523026\pi$
$373$	48918.5	+	84729.3i	0.351605	+	0.608998i	−0.634926	+	0.772573i	$0.718969\pi$
$374$	−81480.0	−	47042.5i	−0.582516	−	0.336316i
$375$	−30834.0	+	53406.1i	−0.219264	+	0.379776i
$376$	−105000.	+	60621.8i	−0.742700	+	0.428798i
$377$			171127.i			1.20402i
$378$	5103.00	−	12766.9i	0.0357143	−	0.0893518i
$379$	74105.0			0.515904			0.257952	−	0.966158i	$-0.416952\pi$
$379$	74105.0			0.515904			0.257952	+	0.966158i	$0.416952\pi$
$380$	−16308.0	−	28246.3i	−0.112936	−	0.195611i
$381$	85045.5	+	49101.0i	0.585870	+	0.338252i
$382$	−13646.0	+	23635.6i	−0.0935144	+	0.161972i
$383$	−223974.	+	129311.i	−1.52686	+	0.881535i	−0.527372	+	0.849635i	$0.676823\pi$
$383$	−223974.	+	129311.i	−1.52686	+	0.881535i	−0.999491	+	0.0319002i	$0.989844\pi$
$384$			79147.8i			0.536755i
$385$	61110.0	+	77620.1i	0.412279	+	0.523664i
$386$	2794.00			0.0187522
$387$	−14674.5	−	25417.0i	−0.0979809	−	0.169708i
$388$	36360.0	+	20992.5i	0.241524	+	0.139444i
$389$	−42655.0	+	73880.6i	−0.281884	+	0.488238i	−0.971849	−	0.235605i	$-0.924293\pi$
$389$	−42655.0	+	73880.6i	−0.281884	+	0.488238i	0.689965	+	0.723843i	$0.257626\pi$
$390$	15390.0	−	8885.42i	0.101183	−	0.0584183i
$391$		−	27158.6i		−	0.177645i
$392$	−31556.0	+	130701.i	−0.205357	+	0.850561i
$393$	113778.			0.736670
$394$	−25244.0	−	43723.9i	−0.162617	−	0.281661i
$395$	−73323.0	−	42333.1i	−0.469944	−	0.271322i
$396$	−31428.0	+	54434.9i	−0.200413	+	0.347126i
$397$	−60775.5	+	35088.8i	−0.385609	+	0.222632i	−0.680256	−	0.732975i	$-0.738131\pi$
$397$	−60775.5	+	35088.8i	−0.385609	+	0.222632i	0.294647	+	0.955606i	$0.404798\pi$
$398$		−	48400.4i		−	0.305551i
$399$	52321.5	−	41192.5i	0.328651	−	0.258745i
$400$	41360.0			0.258500
$401$	29852.0	+	51705.2i	0.185646	+	0.321548i	0.943794	−	0.330535i	$-0.107229\pi$
$401$	29852.0	+	51705.2i	0.185646	+	0.321548i	−0.758148	+	0.652082i	$0.773896\pi$
$402$	21375.0	+	12340.9i	0.132268	+	0.0763648i
$403$	95902.5	−	166108.i	0.590500	−	1.02278i
$404$	72684.0	−	41964.1i	0.445324	−	0.257108i
$405$			7575.99i			0.0461880i
$406$	−94640.0	−	37828.0i	−0.574146	−	0.229489i
$407$	−208550.			−1.25899
$408$	35280.0	+	61106.8i	0.211938	+	0.367087i
$409$	−30511.5	−	17615.8i	−0.182397	−	0.105307i	0.406022	−	0.913864i	$-0.366916\pi$
$409$	−30511.5	−	17615.8i	−0.182397	−	0.105307i	−0.588418	+	0.808557i	$0.700249\pi$
$410$	−13572.0	+	23507.4i	−0.0807377	+	0.139842i
$411$	−93942.0	+	54237.4i	−0.556130	+	0.321082i
$412$			109556.i			0.645417i
$413$	−259392.	+	37440.0i	−1.52075	+	0.219501i
$414$	6048.00			0.0352867
$415$	−34686.0	−	60077.9i	−0.201399	−	0.348834i
$416$	−150480.	−	86879.7i	−0.869545	−	0.502032i
$417$	75685.5	−	131091.i	0.435252	−	0.753878i
$418$	87882.0	−	50738.7i	0.502976	−	0.290393i
$419$			9689.09i			0.0551893i	0.999619	+	0.0275947i	$0.00878477\pi$
$419$			9689.09i			0.0551893i	−0.999619	+	0.0275947i	$0.991215\pi$
$420$	−4536.00	−	31426.3i	−0.0257143	−	0.178154i
$421$	258923.			1.46085			0.730426	−	0.682991i	$-0.239321\pi$
$421$	258923.			1.46085			0.730426	+	0.682991i	$0.239321\pi$
$422$	13366.0	+	23150.6i	0.0750545	+	0.129998i
$423$	50625.0	+	29228.4i	0.282933	+	0.163352i
$424$	−61600.0	+	106694.i	−0.342649	+	0.593485i
$425$	108570.	−	62682.9i	0.601080	−	0.347033i
$426$			92886.4i			0.511839i
$427$	12726.0	−	31838.6i	0.0697969	−	0.174621i
$428$	128784.			0.703031
$429$	−82935.0	−	143648.i	−0.450633	−	0.780520i
$430$	19566.0	+	11296.4i	0.105819	+	0.0610948i
$431$	47525.0	−	82315.7i	0.255839	−	0.443127i	−0.709284	−	0.704923i	$-0.750981\pi$
$431$	47525.0	−	82315.7i	0.255839	−	0.443127i	0.965123	+	0.261796i	$0.0843148\pi$
$432$	9720.00	−	5611.84i	0.0520833	−	0.0300703i
$433$		−	144489.i		−	0.770655i	−0.922780	−	0.385328i	$-0.874088\pi$
$433$		−	144489.i		−	0.770655i	0.922780	−	0.385328i	$-0.125912\pi$
$434$	70665.0	+	89756.6i	0.375167	+	0.476526i
$435$	56160.0			0.296790
$436$	43734.0	+	75749.5i	0.230063	+	0.398480i
$437$	25368.0	+	14646.2i	0.132838	+	0.0766942i
$438$	47421.0	−	82135.6i	0.247185	−	0.428137i
$439$	16842.0	−	9723.73i	0.0873906	−	0.0504550i	−0.455668	−	0.890150i	$-0.650600\pi$
$439$	16842.0	−	9723.73i	0.0873906	−	0.0504550i	0.543058	+	0.839695i	$0.317266\pi$
$440$		−	112902.i		−	0.583171i
$441$	62181.0	−	18332.0i	0.319728	−	0.0942613i
$442$	−79800.0			−0.408468
$443$	59438.0	+	102950.i	0.302870	+	0.524587i	0.976785	−	0.214222i	$-0.0687218\pi$
$443$	59438.0	+	102950.i	0.302870	+	0.524587i	−0.673915	+	0.738809i	$0.735388\pi$
$444$	58050.0	+	33515.2i	0.294467	+	0.170010i
$445$	70884.0	−	122775.i	0.357955	−	0.619996i
$446$	43788.0	−	25281.0i	0.220133	−	0.127094i
$447$		−	22925.4i		−	0.114737i
$448$	32032.0	−	25218.7i	0.159598	−	0.125651i
$449$	−323110.			−1.60272			−0.801360	−	0.598182i	$-0.795890\pi$
$449$	−323110.			−1.60272			−0.801360	+	0.598182i	$0.795890\pi$
$450$	13959.0	+	24177.7i	0.0689333	+	0.119396i
$451$	219414.	+	126679.i	1.07873	+	0.622803i
$452$	−25980.0	+	44998.7i	−0.127163	+	0.220254i
$453$	−96129.0	+	55500.1i	−0.468444	+	0.270456i
$454$		−	87482.4i		−	0.424433i
$455$	77805.0	+	31099.0i	0.375824	+	0.150218i
$456$	−76104.0			−0.365997
$457$	−66578.5	−	115317.i	−0.318788	−	0.552157i	0.661448	−	0.749991i	$-0.269942\pi$
$457$	−66578.5	−	115317.i	−0.318788	−	0.552157i	−0.980235	+	0.197835i	$0.936609\pi$
$458$	64089.0	+	37001.8i	0.305529	+	0.176397i
$459$	17010.0	−	29462.2i	0.0807382	−	0.139843i
$460$	12096.0	−	6983.63i	0.0571645	−	0.0330039i
$461$		−	42248.2i		−	0.198795i	−0.995048	−	0.0993977i	$-0.968308\pi$
$461$		−	42248.2i		−	0.198795i	0.995048	−	0.0993977i	$-0.0316916\pi$
$462$	97776.0	−	14112.7i	0.458087	−	0.0661192i
$463$	−412345.			−1.92353			−0.961765	−	0.273878i	$-0.911694\pi$
$463$	−412345.			−1.92353			−0.961765	+	0.273878i	$0.911694\pi$
$464$	−41600.0	−	72053.3i	−0.193222	−	0.334671i
$465$	−54513.0	−	31473.1i	−0.252112	−	0.145557i
$466$	−17198.0	+	29787.8i	−0.0791965	+	0.137172i
$467$	224799.	−	129788.i	1.03077	−	0.595114i	0.113563	−	0.993531i	$-0.463774\pi$
$467$	224799.	−	129788.i	1.03077	−	0.595114i	0.917204	+	0.398417i	$0.130440\pi$
$468$			53312.5i			0.243410i
$469$	16625.0	+	115181.i	0.0755816	+	0.523645i
$470$	−45000.0			−0.203712
$471$	−75726.0	−	131161.i	−0.341353	−	0.591240i
$472$	259392.	+	149760.i	1.16432	+	0.672221i
$473$	105439.	−	182626.i	0.471280	−	0.816281i
$474$	−73323.0	+	42333.1i	−0.326350	+	0.188418i
$475$			135216.i			0.599295i
$476$	−52920.0	+	132398.i	−0.233564	+	0.584342i
$477$	59400.0			0.261066
$478$	66970.0	+	115995.i	0.293106	+	0.507674i
$479$	193788.	+	111884.i	0.844609	+	0.487635i	0.858828	−	0.512264i	$-0.171193\pi$
$479$	193788.	+	111884.i	0.844609	+	0.487635i	−0.0142190	+	0.999899i	$0.504526\pi$
$480$	−28512.0	+	49384.2i	−0.123750	+	0.214341i
$481$	−153188.	+	88442.8i	−0.662115	+	0.382272i
$482$		−	56451.0i		−	0.242984i
$483$	17640.0	+	22405.8i	0.0756144	+	0.0960431i
$484$	−275940.			−1.17794
$485$	18180.0	+	31488.7i	0.0772877	+	0.133866i
$486$	6561.00	+	3788.00i	0.0277778	+	0.0160375i
$487$	−41168.5	+	71305.9i	−0.173583	+	0.300655i	−0.939670	−	0.342082i	$-0.888868\pi$
$487$	−41168.5	+	71305.9i	−0.173583	+	0.300655i	0.766087	+	0.642737i	$0.222201\pi$
$488$	−33936.0	+	19593.0i	−0.142502	+	0.0822736i
$489$			67269.4i			0.281319i
$490$	−34398.0	+	36154.8i	−0.143265	+	0.150582i
$491$	812.000			0.00336816			0.00168408	−	0.999999i	$-0.499464\pi$
$491$	812.000			0.00336816			0.00168408	+	0.999999i	$0.499464\pi$
$492$	−40716.0	−	70522.2i	−0.168203	−	0.291337i
$493$	−218400.	−	126093.i	−0.898584	−	0.518798i
$494$	43035.0	−	74538.8i	0.176347	−	0.305442i
$495$	−47142.0	+	27217.4i	−0.192397	+	0.111080i
$496$			93253.6i			0.379055i
$497$	−344113.	+	270919.i	−1.39312	+	1.09680i
$498$	−69372.0			−0.279721
$499$	−204824.	−	354766.i	−0.822585	−	1.42476i	−0.903751	−	0.428059i	$-0.859198\pi$
$499$	−204824.	−	354766.i	−0.822585	−	1.42476i	0.0811660	−	0.996701i	$-0.474136\pi$
$500$	123336.	+	71208.1i	0.493344	+	0.284832i
$501$	−91539.0	+	158550.i	−0.364696	+	0.631672i
$502$	−167760.	+	96856.3i	−0.665704	+	0.384344i
$503$		−	151530.i		−	0.598912i	−0.954110	−	0.299456i	$-0.903195\pi$
$503$		−	151530.i		−	0.598912i	0.954110	−	0.299456i	$-0.0968052\pi$
$504$	−68796.0	−	27498.0i	−0.270833	−	0.108253i
$505$	72684.0			0.285007
$506$	21728.0	+	37634.0i	0.0848631	+	0.146987i
$507$	6687.00	+	3860.74i	0.0260145	+	0.0150195i
$508$	113394.	−	196404.i	0.439403	−	0.761068i
$509$	262197.	−	151380.i	1.01203	−	0.584294i	0.100243	−	0.994963i	$-0.468038\pi$
$509$	262197.	−	151380.i	1.01203	−	0.584294i	0.911785	+	0.410669i	$0.134705\pi$
$510$			26188.6i			0.100687i
$511$	442596.	−	63883.2i	1.69498	−	0.244650i
$512$	156160.			0.595703
$513$	18346.5	+	31777.1i	0.0697138	+	0.120748i
$514$	128754.	+	74336.2i	0.487343	+	0.281367i
$515$	−47439.0	+	82166.8i	−0.178863	+	0.309800i
$516$	−58698.0	+	33889.3i	−0.220457	+	0.127281i
$517$			420022.i			1.57142i
$518$	−15050.0	−	104269.i	−0.0560889	−	0.388595i
$519$	−29952.0			−0.111196
$520$	−47880.0	−	82930.6i	−0.177071	−	0.306696i
$521$	−263244.	−	151984.i	−0.969802	−	0.559915i	−0.0706261	−	0.997503i	$-0.522500\pi$
$521$	−263244.	−	151984.i	−0.969802	−	0.559915i	−0.899176	+	0.437587i	$0.855833\pi$
$522$	28080.0	−	48636.0i	0.103052	−	0.178491i
$523$	−113876.	+	65746.1i	−0.416320	+	0.240362i	−0.693501	−	0.720455i	$-0.743933\pi$
$523$	−113876.	+	65746.1i	−0.416320	+	0.240362i	0.277182	+	0.960817i	$0.410600\pi$
$524$		−	262759.i		−	0.956963i
$525$	−48856.5	+	122232.i	−0.177257	+	0.443471i
$526$	−81584.0			−0.294872
$527$	141330.	+	244791.i	0.508877	+	0.881401i
$528$	69840.0	+	40322.1i	0.250517	+	0.144636i
$529$	133648.	−	231486.i	0.477587	−	0.827205i
$530$	−39600.0	+	22863.1i	−0.140975	+	0.0813922i
$531$		−	144411.i		−	0.512168i
$532$	−95130.0	−	120831.i	−0.336120	−	0.426930i
$533$	214890.			0.756418
$534$	−70884.0	−	122775.i	−0.248580	−	0.430553i
$535$	96588.0	+	55765.1i	0.337455	+	0.194830i
$536$	66500.0	−	115181.i	0.231469	−	0.400915i
$537$	−23445.0	+	13536.0i	−0.0813021	+	0.0469398i
$538$		−	143324.i		−	0.495169i
$539$	337463.	+	321065.i	1.16158	+	1.10514i
$540$	17496.0			0.0600000
$541$	−17651.5	−	30573.3i	−0.0603097	−	0.104459i	0.834294	−	0.551320i	$-0.185875\pi$
$541$	−17651.5	−	30573.3i	−0.0603097	−	0.104459i	−0.894604	+	0.446860i	$0.852542\pi$
$542$	6612.00	+	3817.44i	0.0225079	+	0.0129949i
$543$	−29686.5	+	51418.5i	−0.100684	+	0.174389i
$544$	221760.	−	128033.i	0.749351	−	0.432638i
$545$			75749.5i			0.255027i
$546$	65835.0	−	51831.6i	0.220837	−	0.173864i
$547$	153398.			0.512678			0.256339	−	0.966587i	$-0.417484\pi$
$547$	153398.			0.512678			0.256339	+	0.966587i	$0.417484\pi$
$548$	125256.	+	216950.i	0.417097	+	0.722434i
$549$	16362.0	+	9446.61i	0.0542865	+	0.0313423i
$550$	−100298.	+	173721.i	−0.331564	+	0.574285i
$551$	235560.	−	136001.i	0.775887	−	0.447958i
$552$		−	32590.3i		−	0.106957i
$553$	−370688.	−	148166.i	−1.21216	−	0.484504i
$554$	−202778.			−0.660695
$555$	29025.0	+	50272.8i	0.0942294	+	0.163210i
$556$	−302742.	−	174788.i	−0.979317	−	0.565409i
$557$	48035.0	−	83199.1i	0.154827	−	0.268169i	−0.778169	−	0.628055i	$-0.783851\pi$
$557$	48035.0	−	83199.1i	0.154827	−	0.268169i	0.932996	+	0.359886i	$0.117185\pi$
$558$	−54513.0	+	31473.1i	−0.175078	+	0.101081i
$559$		−	178860.i		−	0.572388i
$560$	−40320.0	+	5819.69i	−0.128571	+	0.0185577i
$561$	244440.			0.776688
$562$	−31916.0	−	55280.1i	−0.101050	−	0.175024i
$563$	−70215.0	−	40538.6i	−0.221520	−	0.127895i	0.385134	−	0.922861i	$-0.374155\pi$
$563$	−70215.0	−	40538.6i	−0.221520	−	0.127895i	−0.606654	+	0.794966i	$0.707489\pi$
$564$	67500.0	−	116913.i	0.212200	−	0.367541i
$565$	−38970.0	+	22499.3i	−0.122077	+	0.0704811i
$566$		−	37180.2i		−	0.116059i
$567$	5103.00	+	35354.6i	0.0158730	+	0.109971i
$568$	500528.			1.55143
$569$	−268885.	−	465722.i	−0.830505	−	1.43848i	−0.897639	−	0.440732i	$-0.854719\pi$
$569$	−268885.	−	465722.i	−0.830505	−	1.43848i	0.0671340	−	0.997744i	$-0.478614\pi$
$570$	−24462.0	−	14123.1i	−0.0752909	−	0.0434692i
$571$	−90185.5	+	156206.i	−0.276608	+	0.479099i	−0.970540	−	0.240942i	$-0.922544\pi$
$571$	−90185.5	+	156206.i	−0.276608	+	0.479099i	0.693932	+	0.720041i	$0.255877\pi$
$572$	−331740.	+	191530.i	−1.01392	+	0.585390i
$573$		−	70906.7i		−	0.215962i
$574$	−47502.0	+	118843.i	−0.144174	+	0.360703i
$575$	−57904.0			−0.175135
$576$	11232.0	+	19454.4i	0.0338542	+	0.0586371i
$577$	479837.	+	277034.i	1.44126	+	0.832111i	0.997934	−	0.0642509i	$-0.0204658\pi$
$577$	479837.	+	277034.i	1.44126	+	0.832111i	0.443324	+	0.896361i	$0.353799\pi$
$578$	−24721.0	+	42818.0i	−0.0739964	+	0.128165i
$579$	−6286.50	+	3629.51i	−0.0187522	+	0.0108266i
$580$		−	129696.i		−	0.385541i
$581$	−202335.	−	257000.i	−0.599403	−	0.761344i
$582$	36360.0			0.107344
$583$	213400.	+	369620.i	0.627852	+	1.08747i
$584$	−442596.	−	255533.i	−1.29772	−	0.749240i
$585$	−23085.0	+	39984.4i	−0.0674556	+	0.116837i
$586$	166164.	−	95934.8i	0.483884	−	0.279371i
$587$			306954.i			0.890835i	0.895323	+	0.445417i	$0.146945\pi$
$587$			306954.i			0.890835i	−0.895323	+	0.445417i	$0.853055\pi$
$588$	−42336.0	−	143601.i	−0.122449	−	0.415339i
$589$	−304869.			−0.878785
$590$	55584.0	+	96274.3i	0.159678	+	0.276571i
$591$	113598.	+	65585.8i	0.325234	+	0.187774i
$592$	43000.0	−	74478.2i	0.122694	−	0.212513i
$593$	−277509.	+	160220.i	−0.789165	+	0.455624i	−0.839668	−	0.543099i	$-0.817251\pi$
$593$	−277509.	+	160220.i	−0.789165	+	0.455624i	0.0505037	+	0.998724i	$0.483917\pi$
$594$			54434.9i			0.154278i
$595$	−97020.0	+	76383.4i	−0.274048	+	0.215757i
$596$	−52944.0			−0.149047
$597$	62874.0	+	108901.i	0.176410	+	0.305551i
$598$	31920.0	+	18429.0i	0.0892607	+	0.0515347i
$599$	−161986.	+	280568.i	−0.451465	+	0.781960i	−0.998477	−	0.0551645i	$-0.982432\pi$
$599$	−161986.	+	280568.i	−0.451465	+	0.781960i	0.547013	+	0.837124i	$0.315765\pi$
$600$	130284.	−	75219.5i	0.361900	−	0.208943i
$601$			376993.i			1.04372i	0.853031	+	0.521860i	$0.174762\pi$
$601$			376993.i			1.04372i	−0.853031	+	0.521860i	$0.825238\pi$
$602$	98917.0	+	39537.5i	0.272947	+	0.109098i
$603$	−64125.0			−0.176357
$604$	128172.	+	222000.i	0.351333	+	0.608527i
$605$	−206955.	−	119486.i	−0.565412	−	0.326441i
$606$	36342.0	−	62946.2i	0.0989609	−	0.171405i
$607$	91309.5	−	52717.6i	0.247821	−	0.143080i	−0.370945	−	0.928655i	$-0.620966\pi$
$607$	91309.5	−	52717.6i	0.247821	−	0.143080i	0.618766	+	0.785575i	$0.287633\pi$
$608$			276186.i			0.747127i
$609$	262080.	−	37828.0i	0.706642	−	0.101995i
$610$	−14544.0			−0.0390863
$611$	178125.	+	308522.i	0.477136	+	0.826424i
$612$	−68040.0	−	39282.9i	−0.181661	−	0.104882i
$613$	−254635.	+	441041.i	−0.677637	+	1.17370i	0.298054	+	0.954549i	$0.403663\pi$
$613$	−254635.	+	441041.i	−0.677637	+	1.17370i	−0.975691	+	0.219153i	$0.929671\pi$
$614$	−256761.	+	148241.i	−0.681071	+	0.393216i
$615$		−	70522.2i		−	0.186456i
$616$	−76048.0	−	526876.i	−0.200413	−	1.38850i
$617$	−141154.			−0.370786			−0.185393	−	0.982664i	$-0.559356\pi$
$617$	−141154.			−0.370786			−0.185393	+	0.982664i	$0.559356\pi$
$618$	47439.0	+	82166.8i	0.124211	+	0.215139i
$619$	−441005.	−	254614.i	−1.15096	−	0.664509i	−0.201842	−	0.979418i	$-0.564693\pi$
$619$	−441005.	−	254614.i	−1.15096	−	0.664509i	−0.949122	+	0.314909i	$0.898026\pi$
$620$	−72684.0	+	125892.i	−0.189084	+	0.327504i
$621$	−13608.0	+	7856.58i	−0.0352867	+	0.0203728i
$622$		−	66476.1i		−	0.171824i
$623$	248094.	−	620694.i	0.639205	−	1.59920i
$624$	68400.0			0.175666
$625$	−99894.5	−	173022.i	−0.255730	−	0.442937i
$626$	46569.0	+	26886.6i	0.118836	+	0.0686100i
$627$	−131823.	+	228324.i	−0.335317	+	0.580787i
$628$	−302904.	+	174882.i	−0.768043	+	0.443430i
$629$		−	260674.i		−	0.658864i
$630$	−17010.0	−	21605.6i	−0.0428571	−	0.0544359i
$631$	135542.			0.340420			0.170210	−	0.985408i	$-0.445555\pi$
$631$	135542.			0.340420			0.170210	+	0.985408i	$0.445555\pi$
$632$	228116.	+	395109.i	0.571112	+	0.989196i
$633$	−60147.0	−	34725.9i	−0.150109	−	0.0866654i
$634$	10588.0	−	18339.0i	0.0263412	−	0.0456243i
$635$	170091.	−	98202.1i	0.421827	−	0.243542i
$636$		−	137178.i		−	0.339134i
$637$	384038.	+	92721.0i	0.946444	+	0.228507i
$638$	403520.			0.991342
$639$	−120663.	−	208994.i	−0.295510	−	0.511839i
$640$	137088.	+	79147.8i	0.334688	+	0.193232i
$641$	−29554.0	+	51189.0i	−0.0719284	+	0.124584i	−0.899746	−	0.436413i	$-0.856249\pi$
$641$	−29554.0	+	51189.0i	−0.0719284	+	0.124584i	0.827818	+	0.560997i	$0.189582\pi$
$642$	96588.0	−	55765.1i	0.234344	−	0.135298i
$643$		−	520594.i		−	1.25915i	−0.776940	−	0.629574i	$-0.783229\pi$
$643$		−	520594.i		−	1.25915i	0.776940	−	0.629574i	$-0.216771\pi$
$644$	51744.0	−	40737.8i	0.124764	−	0.0982259i
$645$	−58698.0			−0.141092
$646$	63420.0	+	109847.i	0.151971	+	0.263222i
$647$	51207.0	+	29564.4i	0.122327	+	0.0706253i	0.559915	−	0.828550i	$-0.310834\pi$
$647$	51207.0	+	29564.4i	0.122327	+	0.0706253i	−0.437588	+	0.899176i	$0.644167\pi$
$648$	20412.0	−	35354.6i	0.0486111	−	0.0841969i
$649$	898608.	−	518812.i	2.13344	−	1.23174i
$650$			170139.i			0.402697i
$651$	−275594.	−	110156.i	−0.650290	−	0.259923i
$652$	155352.			0.365445
$653$	−337591.	−	584725.i	−0.791707	−	1.37128i	−0.924909	−	0.380188i	$-0.875859\pi$
$653$	−337591.	−	584725.i	−0.791707	−	1.37128i	0.133202	−	0.991089i	$-0.457474\pi$
$654$	65601.0	+	37874.8i	0.153375	+	0.0885512i
$655$	113778.	−	197069.i	0.265201	−	0.459342i
$656$	−90480.0	+	52238.7i	−0.210254	+	0.121390i
$657$			246407.i			0.570850i
$658$	−210000.	+	30310.9i	−0.485029	+	0.0700079i
$659$	74684.0			0.171972			0.0859858	−	0.996296i	$-0.472596\pi$
$659$	74684.0			0.171972			0.0859858	+	0.996296i	$0.472596\pi$
$660$	62856.0	+	108870.i	0.144298	+	0.249931i
$661$	−692030.	−	399543.i	−1.58388	−	0.914452i	−0.994286	−	0.106751i	$-0.965955\pi$
$661$	−692030.	−	399543.i	−1.58388	−	0.914452i	−0.589592	−	0.807701i	$-0.700711\pi$
$662$	127327.	−	220537.i	0.290539	−	0.503228i
$663$	179550.	−	103663.i	0.408468	−	0.235829i
$664$			373818.i			0.847860i
$665$	−19026.0	−	131816.i	−0.0430233	−	0.298074i
$666$	58050.0			0.130874
$667$	58240.0	+	100875.i	0.130909	+	0.226741i
$668$	366156.	+	211400.i	0.820565	+	0.473754i
$669$	−65682.0	+	113765.i	−0.146755	+	0.254188i
$670$	42750.0	−	24681.7i	0.0952328	−	0.0549827i
$671$			135751.i			0.301508i
$672$	−99792.0	+	249665.i	−0.220982	+	0.552864i
$673$	155765.			0.343906			0.171953	−	0.985105i	$-0.444992\pi$
$673$	155765.			0.343906			0.171953	+	0.985105i	$0.444992\pi$
$674$	−211553.	−	366421.i	−0.465693	−	0.806603i
$675$	−62815.5	−	36266.5i	−0.137867	−	0.0795974i
$676$	8916.00	−	15443.0i	0.0195109	−	0.0337938i
$677$	324858.	−	187557.i	0.708788	−	0.409219i	−0.101824	−	0.994802i	$-0.532468\pi$
$677$	324858.	−	187557.i	0.708788	−	0.409219i	0.810612	+	0.585584i	$0.199135\pi$
$678$			44998.7i			0.0978905i
$679$	106050.	+	134702.i	0.230023	+	0.292168i
$680$	141120.			0.305190
$681$	113643.	+	196835.i	0.245046	+	0.424433i
$682$	−391686.	−	226140.i	−0.842111	−	0.486193i
$683$	−101788.	+	176302.i	−0.218200	+	0.377934i	−0.954258	−	0.298985i	$-0.903352\pi$
$683$	−101788.	+	176302.i	−0.218200	+	0.377934i	0.736058	+	0.676919i	$0.236685\pi$
$684$	73386.0	−	42369.4i	0.156856	−	0.0905608i
$685$			216950.i			0.462358i
$686$	−136171.	+	191892.i	−0.289359	+	0.407764i
$687$	−192267.			−0.407372
$688$	43480.0	+	75309.6i	0.0918571	+	0.159101i
$689$	313500.	+	180999.i	0.660388	+	0.381275i
$690$	6048.00	−	10475.4i	0.0127032	−	0.0220026i
$691$	−504128.	+	291058.i	−1.05581	+	0.609570i	−0.924269	−	0.381741i	$-0.875325\pi$
$691$	−504128.	+	291058.i	−1.05581	+	0.609570i	−0.131537	+	0.991311i	$0.541991\pi$
$692$			69171.2i			0.144448i
$693$	−201663.	+	158768.i	−0.419913	+	0.330596i
$694$	−50168.0			−0.104162
$695$	−151371.	−	262182.i	−0.313381	−	0.542792i
$696$	−262080.	−	151312.i	−0.541023	−	0.312360i
$697$	−158340.	+	274253.i	−0.325931	+	0.564528i
$698$	6636.00	−	3831.30i	0.0136206	−	0.00786384i
$699$		−	89363.4i		−	0.182897i
$700$	282282.	+	112829.i	0.576086	+	0.230264i
$701$	372680.			0.758403			0.379202	−	0.925314i	$-0.376199\pi$
$701$	372680.			0.758403			0.379202	+	0.925314i	$0.376199\pi$
$702$	23085.0	+	39984.4i	0.0468442	+	0.0811365i
$703$	243488.	+	140578.i	0.492681	+	0.284450i
$704$	−80704.0	+	139783.i	−0.162836	+	0.282040i
$705$	101250.	−	58456.7i	0.203712	−	0.117613i
$706$		−	14611.6i		−	0.0293149i
$707$	339192.	−	48958.1i	0.678589	−	0.0979459i
$708$	−333504.			−0.665326
$709$	−56197.0	−	97336.1i	−0.111795	−	0.193634i	0.804699	−	0.593683i	$-0.202327\pi$
$709$	−56197.0	−	97336.1i	−0.111795	−	0.193634i	−0.916494	+	0.400049i	$0.868993\pi$
$710$	160884.	+	92886.4i	0.319151	+	0.184262i
$711$	109984.	−	190499.i	0.217567	−	0.376836i
$712$	−661584.	+	381966.i	−1.30504	+	0.753467i
$713$		−	130555.i		−	0.256812i
$714$	17640.0	+	122214.i	0.0346021	+	0.239730i
$715$	−331740.			−0.648912
$716$	31260.0	+	54143.9i	0.0609766	+	0.105615i
$717$	−301365.	−	173993.i	−0.586212	−	0.338449i
$718$	234508.	−	406180.i	0.454892	−	0.787897i
$719$	91977.0	−	53102.9i	0.177919	−	0.102721i	−0.408396	−	0.912805i	$-0.633912\pi$
$719$	91977.0	−	53102.9i	0.177919	−	0.102721i	0.586314	+	0.810084i	$0.300578\pi$
$720$		−	22447.4i		−	0.0433013i
$721$	−166036.	+	415399.i	−0.319399	+	0.799088i
$722$	123836.			0.237560
$723$	73332.0	+	127015.i	0.140287	+	0.242984i
$724$	118746.	+	68558.0i	0.226538	+	0.130792i
$725$	−268840.	+	465645.i	−0.511467	+	0.885887i
$726$	−206955.	+	119486.i	−0.392647	+	0.226695i
$727$		−	662165.i		−	1.25284i	−0.779484	−	0.626422i	$-0.784519\pi$
$727$		−	662165.i		−	1.25284i	0.779484	−	0.626422i	$-0.215481\pi$
$728$	−279300.	−	354759.i	−0.526997	−	0.669376i
$729$	−19683.0			−0.0370370
$730$	−94842.0	−	164271.i	−0.177973	−	0.308259i
$731$	228270.	+	131792.i	0.427183	+	0.246634i
$732$	21816.0	−	37786.4i	0.0407149	−	0.0705202i
$733$	20290.5	−	11714.7i	0.0377646	−	0.0218034i	−0.480999	−	0.876721i	$-0.659726\pi$
$733$	20290.5	−	11714.7i	0.0377646	−	0.0218034i	0.518763	+	0.854918i	$0.326393\pi$
$734$			203928.i			0.378517i
$735$	30429.0	−	126033.i	0.0563265	−	0.233297i
$736$	−118272.			−0.218336
$737$	−230375.	−	399021.i	−0.424131	−	0.734617i
$738$	−61074.0	−	35261.1i	−0.112136	−	0.0647415i
$739$	−440706.	+	763324.i	−0.806974	+	1.39772i	0.107976	+	0.994153i	$0.465563\pi$
$739$	−440706.	+	763324.i	−0.806974	+	1.39772i	−0.914950	+	0.403567i	$0.867770\pi$
$740$	116100.	−	67030.4i	0.212016	−	0.122408i
$741$			223616.i			0.407256i
$742$	−169400.	+	133368.i	−0.307684	+	0.242239i
$743$	−224686.			−0.407004			−0.203502	−	0.979075i	$-0.565232\pi$
$743$	−224686.			−0.407004			−0.203502	+	0.979075i	$0.565232\pi$
$744$	169596.	+	293749.i	0.306387	+	0.530677i
$745$	−39708.0	−	22925.4i	−0.0715427	−	0.0413052i
$746$	97837.0	−	169459.i	0.175803	−	0.304499i
$747$	156087.	−	90116.9i	0.279721	−	0.161497i
$748$		−	564510.i		−	1.00895i
$749$	488306.	+	195178.i	0.870419	+	0.347910i
$750$	123336.			0.219264
$751$	114430.	+	198198.i	0.202889	+	0.351414i	0.949458	−	0.313894i	$-0.101634\pi$
$751$	114430.	+	198198.i	0.202889	+	0.351414i	−0.746569	+	0.665308i	$0.768300\pi$
$752$	−150000.	−	86602.5i	−0.265250	−	0.153142i
$753$	251640.	−	435853.i	0.443802	−	0.768688i
$754$	296400.	−	171127.i	0.521357	−	0.301006i
$755$			222000.i			0.389457i
$756$	81648.0	−	11784.9i	0.142857	−	0.0206197i
$757$	95150.0			0.166042			0.0830208	−	0.996548i	$-0.473543\pi$
$757$	95150.0			0.166042			0.0830208	+	0.996548i	$0.473543\pi$
$758$	−74105.0	−	128354.i	−0.128976	−	0.223393i
$759$	−97776.0	−	56451.0i	−0.169726	−	0.0979914i
$760$	−76104.0	+	131816.i	−0.131759	+	0.228213i
$761$	−929034.	+	536378.i	−1.60421	+	0.926193i	−0.613583	+	0.789631i	$0.710272\pi$
$761$	−929034.	+	536378.i	−1.60421	+	0.926193i	−0.990631	+	0.136563i	$0.956394\pi$
$762$		−	196404.i		−	0.338252i
$763$	51023.0	+	353498.i	0.0876429	+	0.607208i
$764$	−163752.			−0.280543
$765$	−34020.0	−	58924.4i	−0.0581315	−	0.100687i
$766$	447948.	+	258623.i	0.763431	+	0.440767i
$767$	440040.	−	762172.i	0.748000	−	1.29557i
$768$	196992.	−	113733.i	0.333984	−	0.192826i
$769$			279842.i			0.473217i	0.971605	+	0.236609i	$0.0760359\pi$
$769$			279842.i			0.473217i	−0.971605	+	0.236609i	$0.923964\pi$
$770$	73332.0	−	183466.i	0.123684	−	0.309438i
$771$	−386262.			−0.649790
$772$	8382.00	+	14518.0i	0.0140641	+	0.0243598i
$773$	1.01217e6	+	584378.i	1.69393	+	0.977992i	0.951288	+	0.308305i	$0.0997616\pi$
$773$	1.01217e6	+	584378.i	1.69393	+	0.977992i	0.742643	+	0.669687i	$0.233572\pi$
$774$	−29349.0	+	50834.0i	−0.0489904	+	0.0848539i
$775$	521911.	−	301326.i	0.868947	−	0.501687i
$776$		−	195930.i		−	0.325369i
$777$	169312.	+	215056.i	0.280445	+	0.356212i
$778$	170620.			0.281884
$779$	−170781.	−	295801.i	−0.281426	−	0.487445i
$780$	92340.0	+	53312.5i	0.151775	+	0.0876274i
$781$	866986.	−	1.50166e6i	1.42138	−	2.46190i
$782$	−47040.0	+	27158.6i	−0.0769226	+	0.0444113i
$783$			145908.i			0.237988i
$784$	−184240.	+	54317.1i	−0.299745	+	0.0883699i
$785$	−302904.			−0.491548
$786$	−113778.	−	197069.i	−0.184168	−	0.318988i
$787$	224040.	+	129350.i	0.361723	+	0.208841i	0.669836	−	0.742509i	$-0.266364\pi$
$787$	224040.	+	129350.i	0.361723	+	0.208841i	−0.308113	+	0.951350i	$0.599698\pi$
$788$	151464.	−	262343.i	0.243925	−	0.422491i
$789$	183564.	−	105981.i	0.294872	−	0.170244i
$790$			169332.i			0.271322i
$791$	−166705.	+	131246.i	−0.266438	+	0.209765i
$792$	293328.			0.467631
$793$	57570.0	+	99714.2i	0.0915482	+	0.158566i
$794$	121551.	+	70177.5i	0.192805	+	0.111316i
$795$	59400.0	−	102884.i	0.0939836	−	0.162784i
$796$	251496.	−	145201.i	0.396922	−	0.229163i
$797$		−	243415.i		−	0.383205i	−0.981473	−	0.191603i	$-0.938632\pi$
$797$		−	243415.i		−	0.383205i	0.981473	−	0.191603i	$-0.0613685\pi$
$798$	−123669.	−	49431.0i	−0.194203	−	0.0776236i
$799$	−525000.			−0.822367
$800$	−272976.	−	472808.i	−0.426525	−	0.738763i
$801$	318978.	+	184162.i	0.497159	+	0.287035i
$802$	59704.0	−	103410.i	0.0928228	−	0.160774i
$803$	−1.53328e6	+	885239.i	−2.37788	+	1.37287i
$804$			148090.i			0.229094i
$805$	56448.0	−	8147.57i	0.0871078	−	0.0125729i
$806$	−383610.			−0.590500
$807$	186183.	+	322478.i	0.285886	+	0.495169i
$808$	−339192.	−	195833.i	−0.519545	−	0.299959i
$809$	−229615.	+	397705.i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$809$	−229615.	+	397705.i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$810$	13122.0	−	7575.99i	0.0200000	−	0.0115470i
$811$		−	831509.i		−	1.26423i	−0.774876	−	0.632114i	$-0.782187\pi$
$811$		−	831509.i		−	1.26423i	0.774876	−	0.632114i	$-0.217813\pi$
$812$	−87360.0	−	605248.i	−0.132495	−	0.917955i
$813$	−19836.0			−0.0300105
$814$	208550.	+	361219.i	0.314747	+	0.545158i
$815$	116514.	+	67269.4i	0.175413	+	0.101275i
$816$	−50400.0	+	87295.4i	−0.0756920	+	0.131102i
$817$	−246206.	+	142147.i	−0.368853	+	0.212958i
$818$			70463.3i			0.105307i
$819$	−80797.5	+	202143.i	−0.120456	+	0.301364i
$820$	−162864.			−0.242213
$821$	352799.	+	611066.i	0.523409	+	0.906571i	0.999629	+	0.0272445i	$0.00867326\pi$
$821$	352799.	+	611066.i	0.523409	+	0.906571i	−0.476220	+	0.879326i	$0.657993\pi$
$822$	187884.	+	108475.i	0.278065	+	0.160541i
$823$	193193.	−	334620.i	0.285228	−	0.494029i	−0.687437	−	0.726244i	$-0.741264\pi$
$823$	193193.	−	334620.i	0.285228	−	0.494029i	0.972664	+	0.232215i	$0.0745974\pi$
$824$	442764.	−	255630.i	0.652106	−	0.376493i
$825$		−	521164.i		−	0.765713i
$826$	324240.	+	411840.i	0.475233	+	0.603627i
$827$	−842158.			−1.23135			−0.615676	−	0.787999i	$-0.711117\pi$
$827$	−842158.			−1.23135			−0.615676	+	0.787999i	$0.711117\pi$
$828$	18144.0	+	31426.3i	0.0264650	+	0.0458388i
$829$	122446.	+	70694.5i	0.178171	+	0.102867i	0.586433	−	0.809998i	$-0.300532\pi$
$829$	122446.	+	70694.5i	0.178171	+	0.102867i	−0.408262	+	0.912865i	$0.633865\pi$
$830$	−69372.0	+	120156.i	−0.100700	+	0.174417i
$831$	456250.	−	263416.i	0.660695	−	0.381453i
$832$			136901.i			0.197770i
$833$	−401310.	+	421806.i	−0.578349	+	0.607887i
$834$	−302742.			−0.435252
$835$	183078.	+	317100.i	0.262581	+	0.454804i
$836$	527292.	+	304432.i	0.754464	+	0.435590i
$837$	81769.5	−	141629.i	0.116719	−	0.202163i
$838$	16782.0	−	9689.09i	0.0238977	−	0.0137973i
$839$			634914.i			0.901968i	0.892532	+	0.450984i	$0.148927\pi$
$839$			634914.i			0.901968i	−0.892532	+	0.450984i	$0.851073\pi$
$840$	−116424.	+	91660.1i	−0.165000	+	0.129904i
$841$	374319.			0.529237
$842$	−258923.	−	448468.i	−0.365213	−	0.632568i
$843$	143622.	+	82920.2i	0.202100	+	0.116682i
$844$	−80196.0	+	138904.i	−0.112582	+	0.194997i
$845$	13374.0	−	7721.48i	0.0187304	−	0.0108140i
$846$		−	116913.i		−	0.163352i
$847$	−1.04627e6	−	418199.i	−1.45840	−	0.582930i
$848$	−176000.			−0.244749
$849$	48298.5	+	83655.5i	0.0670067	+	0.116059i
$850$	−217140.	−	125366.i	−0.300540	−	0.173517i
$851$	−60200.0	+	104269.i	−0.0831261	+	0.143979i
$852$	−482652.	+	278659.i	−0.664898	+	0.383879i
$853$			1.17683e6i			1.61739i	0.588229	+	0.808694i	$0.299825\pi$
$853$			1.17683e6i			1.61739i	−0.588229	+	0.808694i	$0.700175\pi$
$854$	−67872.0	+	9796.48i	−0.0930625	+	0.0134324i
$855$	73386.0			0.100388
$856$	−300496.	−	520474.i	−0.410101	−	0.710316i
$857$	−587808.	−	339371.i	−0.800339	−	0.462076i	0.0432508	−	0.999064i	$-0.486229\pi$
$857$	−587808.	−	339371.i	−0.800339	−	0.462076i	−0.843590	+	0.536988i	$0.819562\pi$
$858$	−165870.	+	287295.i	−0.225317	+	0.390260i
$859$	118368.	−	68339.8i	0.160416	−	0.0926163i	−0.417643	−	0.908611i	$-0.637144\pi$
$859$	118368.	−	68339.8i	0.160416	−	0.0926163i	0.578059	+	0.815995i	$0.303810\pi$
$860$			135557.i			0.183285i
$861$	−47502.0	−	329104.i	−0.0640775	−	0.443942i
$862$	−190100.			−0.255839
$863$	80597.0	+	139598.i	0.108217	+	0.187438i	0.915048	−	0.403345i	$-0.132152\pi$
$863$	80597.0	+	139598.i	0.108217	+	0.187438i	−0.806831	+	0.590783i	$0.798819\pi$
$864$	−128304.	−	74076.3i	−0.171875	−	0.0992321i
$865$	−29952.0	+	51878.4i	−0.0400307	+	0.0693353i
$866$	−250263.	+	144489.i	−0.333704	+	0.192664i
$867$		−	128454.i		−	0.170887i
$868$	−254394.	+	636456.i	−0.337651	+	0.844751i
$869$	1.58052e6			2.09296
$870$	−56160.0	−	97272.0i	−0.0741974	−	0.128514i
$871$	−338438.	−	195397.i	−0.446110	−	0.257562i
$872$	204092.	−	353498.i	0.268406	−	0.464894i
$873$	−81810.0	+	47233.0i	−0.107344	+	0.0619751i
$874$		−	58584.9i		−	0.0766942i
$875$	359730.	+	456918.i	0.469851	+	0.596791i
$876$	569052.			0.741556
$877$	−63415.0	−	109838.i	−0.0824504	−	0.142808i	0.821852	−	0.569702i	$-0.192941\pi$
$877$	−63415.0	−	109838.i	−0.0824504	−	0.142808i	−0.904302	+	0.426893i	$0.859608\pi$
$878$	−33684.0	−	19447.5i	−0.0436953	−	0.0252275i
$879$	−249246.	+	431707.i	−0.322590	+	0.558742i
$880$	139680.	−	80644.3i	0.180372	−	0.104138i
$881$			546926.i			0.704656i	0.935877	+	0.352328i	$0.114610\pi$
$881$			546926.i			0.704656i	−0.935877	+	0.352328i	$0.885390\pi$
$882$	−93933.0	−	89368.6i	−0.120748	−	0.114881i
$883$	155933.			0.199994			0.0999969	−	0.994988i	$-0.468117\pi$
$883$	155933.			0.199994			0.0999969	+	0.994988i	$0.468117\pi$
$884$	−239400.	−	414653.i	−0.306351	−	0.530616i
$885$	−250128.	−	144411.i	−0.319357	−	0.184381i
$886$	118876.	−	205899.i	0.151435	−	0.262293i
$887$	589707.	−	340467.i	0.749530	−	0.432741i	−0.0759940	−	0.997108i	$-0.524213\pi$
$887$	589707.	−	340467.i	0.749530	−	0.432741i	0.825524	+	0.564367i	$0.190880\pi$
$888$		−	312808.i		−	0.396691i
$889$	727612.	−	572845.i	0.920653	−	0.724826i
$890$	−283536.			−0.357955
$891$	−70713.0	−	122479.i	−0.0890725	−	0.154278i
$892$	262728.	+	151686.i	0.330200	+	0.190641i
$893$	283125.	−	490387.i	0.355038	−	0.614945i
$894$	−39708.0	+	22925.4i	−0.0496824	+	0.0286842i
$895$			54143.9i			0.0675933i
$896$	693056.	+	277017.i	0.863281	+	0.345057i
$897$	−95760.0			−0.119014
$898$	323110.	+	559643.i	0.400680	+	0.693998i
$899$	−1.04988e6	−	606149.i	−1.29903	−	0.749997i
$900$	−83754.0	+	145066.i	−0.103400	+	0.179094i
$901$	−462000.	+	266736.i	−0.569105	+	0.328573i
$902$		−	506715.i		−	0.622803i
$903$	−273924.	+	39537.5i	−0.335934	+	0.0484880i
$904$	242480.			0.296715
$905$	59373.0	+	102837.i	0.0724923	+	0.125560i
$906$	192258.	+	111000.i	0.234222	+	0.135228i
$907$	−169220.	+	293099.i	−0.205702	+	0.356286i	−0.950356	−	0.311164i	$-0.899281\pi$
$907$	−169220.	+	293099.i	−0.205702	+	0.356286i	0.744654	+	0.667450i	$0.232614\pi$
$908$	454572.	−	262447.i	0.551355	−	0.318325i
$909$			188839.i			0.228540i
$910$	−23940.0	−	165861.i	−0.0289096	−	0.200291i
$911$	658004.			0.792851			0.396426	−	0.918067i	$-0.370250\pi$
$911$	658004.			0.792851			0.396426	+	0.918067i	$0.370250\pi$
$912$	−54360.0	−	94154.3i	−0.0653566	−	0.113201i
$913$	1.12151e6	+	647506.i	1.34544	+	0.776788i
$914$	−133157.	+	230635.i	−0.159394	+	0.276078i
$915$	32724.0	−	18893.2i	0.0390863	−	0.0225665i
$916$			444022.i			0.529192i
$917$	398223.	−	996295.i	0.473574	−	1.18481i
$918$	−68040.0			−0.0807382
$919$	−655904.	−	1.13606e6i	−0.776622	−	1.34515i	−0.933878	−	0.357591i	$-0.883598\pi$
$919$	−655904.	−	1.13606e6i	−0.776622	−	1.34515i	0.157257	−	0.987558i	$-0.449735\pi$
$920$	−56448.0	−	32590.3i	−0.0666919	−	0.0385046i
$921$	385142.	−	667085.i	0.454047	−	0.786433i
$922$	−73176.0	+	42248.2i	−0.0860809	+	0.0496988i
$923$		−	1.47070e6i		−	1.72632i
$924$	366660.	+	465721.i	0.429457	+	0.545484i
$925$	−555775.			−0.649554
$926$	412345.	+	714202.i	0.480882	+	0.832913i
$927$	−213476.	−	123250.i	−0.248421	−	0.143426i
$928$	−549120.	+	951104.i	−0.637634	+	1.10441i
$929$	464583.	−	268227.i	0.538309	−	0.310793i	−0.206084	−	0.978534i	$-0.566072\pi$
$929$	464583.	−	268227.i	0.538309	−	0.310793i	0.744393	+	0.667741i	$0.232739\pi$
$930$			125892.i			0.145557i
$931$	−177576.	−	602326.i	−0.204873	−	0.694916i
$932$	−206376.			−0.237590
$933$	86355.0	+	149571.i	0.0992029	+	0.171824i
$934$	−449598.	−	259576.i	−0.515384	−	0.297557i
$935$	244440.	−	423382.i	0.279608	−	0.484295i
$936$	215460.	−	124396.i	0.245932	−	0.141989i
$937$		−	1.41972e6i		−	1.61705i	−0.588463	−	0.808524i	$-0.700267\pi$
$937$		−	1.41972e6i		−	1.61705i	0.588463	−	0.808524i	$-0.299733\pi$
$938$	182875.	−	143977.i	0.207849	−	0.163639i
$939$	−139707.			−0.158448
$940$	−135000.	−	233827.i	−0.152784	−	0.264630i
$941$	−34458.0	−	19894.3i	−0.0389144	−	0.0224673i	0.480417	−	0.877040i	$-0.340485\pi$
$941$	−34458.0	−	19894.3i	−0.0389144	−	0.0224673i	−0.519331	+	0.854573i	$0.673819\pi$
$942$	−151452.	+	262323.i	−0.170676	+	0.295620i
$943$	126672.	−	73134.1i	0.142448	−	0.0822426i
$944$			427886.i			0.480158i
$945$	66339.0	+	26516.0i	0.0742857	+	0.0296923i
$946$	−421756.			−0.471280
$947$	173045.	+	299723.i	0.192956	+	0.334210i	0.946229	−	0.323499i	$-0.104859\pi$
$947$	173045.	+	299723.i	0.192956	+	0.334210i	−0.753272	+	0.657709i	$0.771526\pi$
$948$	−439938.	−	253998.i	−0.489525	−	0.282627i
$949$	−750832.	+	1.30048e6i	−0.833702	+	1.44401i
$950$	234201.	−	135216.i	0.259502	−	0.149824i
$951$			55016.9i			0.0608324i
$952$	658560.	−	95054.9i	0.726644	−	0.104882i
$953$	806780.			0.888320			0.444160	−	0.895948i	$-0.353502\pi$
$953$	806780.			0.888320			0.444160	+	0.895948i	$0.353502\pi$
$954$	−59400.0	−	102884.i	−0.0652664	−	0.113045i
$955$	−122814.	−	70906.7i	−0.134661	−	0.0777464i
$956$	−401820.	+	695973.i	−0.439659	+	0.761511i
$957$	−907920.	+	524188.i	−0.991342	+	0.572352i
$958$		−	447534.i		−	0.487635i
$959$	146132.	+	1.01243e6i	0.158894	+	1.10085i
$960$	44928.0			0.0487500
$961$	217633.	+	376951.i	0.235656	+	0.408168i
$962$	306375.	+	176886.i	0.331057	+	0.191136i
$963$	−144882.	+	250943.i	−0.156229	+	0.270597i
$964$	293328.	−	169353.i	0.315645	−	0.182238i
$965$			14518.0i			0.0155903i
$966$	21168.0	−	52959.2i	0.0226843	−	0.0567528i
$967$	660791.			0.706661			0.353331	−	0.935499i	$-0.385049\pi$
$967$	660791.			0.706661			0.353331	+	0.935499i	$0.385049\pi$
$968$	643860.	+	1.11520e6i	0.687133	+	1.19015i
$969$	−285390.	−	164770.i	−0.303942	−	0.175481i
$970$	36360.0	−	62977.4i	0.0386439	−	0.0669331i
$971$	−694758.	+	401119.i	−0.736877	+	0.425436i	−0.820933	−	0.571025i	$-0.806546\pi$
$971$	−694758.	+	401119.i	−0.736877	+	0.425436i	0.0840556	+	0.996461i	$0.473213\pi$
$972$			45455.9i			0.0481125i
$973$	−882998.	−	1.12156e6i	−0.932682	−	1.18467i
$974$	164674.			0.173583
$975$	−221018.	−	382814.i	−0.232497	−	0.402697i
$976$	−48480.0	−	27989.9i	−0.0508936	−	0.0293834i
$977$	−340723.	+	590150.i	−0.356954	+	0.618263i	−0.987450	−	0.157930i	$-0.949518\pi$
$977$	−340723.	+	590150.i	−0.356954	+	0.618263i	0.630496	+	0.776192i	$0.282851\pi$
$978$	116514.	−	67269.4i	0.121815	−	0.0703299i
$979$			2.64648e6i			2.76123i
$980$	−291060.	−	70272.8i	−0.303061	−	0.0731703i
$981$	−196803.			−0.204500
$982$	−812.000	−	1406.43i	−0.000842041	−	0.00145846i
$983$	−1.34161e6	−	774580.i	−1.38842	−	0.801603i	−0.395280	−	0.918561i	$-0.629352\pi$
$983$	−1.34161e6	−	774580.i	−1.38842	−	0.801603i	−0.993137	+	0.116958i	$0.962686\pi$
$984$	−190008.	+	329104.i	−0.196237	+	0.339893i
$985$	227196.	−	131172.i	0.234168	−	0.135197i
$986$			504373.i			0.518798i
$987$	433125.	−	340998.i	0.444610	−	0.350039i
$988$	516420.			0.529041
$989$	−60872.0	−	105433.i	−0.0622336	−	0.107792i
$990$	94284.0	+	54434.9i	0.0961983	+	0.0555401i
$991$	−39152.5	+	67814.1i	−0.0398669	+	0.0690515i	−0.885270	−	0.465077i	$-0.846027\pi$
$991$	−39152.5	+	67814.1i	−0.0398669	+	0.0690515i	0.845403	+	0.534128i	$0.179360\pi$
$992$	1.06603e6	−	615474.i	1.08330	−	0.625441i
$993$			661610.i			0.670971i
$994$	813358.	+	325102.i	0.823207	+	0.329039i
$995$	251496.			0.254030
$996$	−208116.	−	360467.i	−0.209791	−	0.363369i
$997$	−1.36361e6	−	787282.i	−1.37183	−	0.792027i	−0.380673	−	0.924710i	$-0.624308\pi$
$997$	−1.36361e6	−	787282.i	−1.37183	−	0.792027i	−0.991159	+	0.132683i	$0.957641\pi$
$998$	−409649.	+	709533.i	−0.411293	+	0.712380i
$999$	−130612.	+	75409.2i	−0.130874	+	0.0755602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.5.f.a.10.1	✓	2
3.2	odd	2		63.5.m.c.10.1		2
4.3	odd	2		336.5.bh.b.241.1		2
7.2	even	3		147.5.f.a.19.1		2
7.3	odd	6		147.5.d.b.97.2		2
7.4	even	3		147.5.d.b.97.1		2
7.5	odd	6	inner	21.5.f.a.19.1	yes	2
7.6	odd	2		147.5.f.a.31.1		2
21.5	even	6		63.5.m.c.19.1		2
21.11	odd	6		441.5.d.a.244.1		2
21.17	even	6		441.5.d.a.244.2		2
28.19	even	6		336.5.bh.b.145.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.5.f.a.10.1	✓	2	1.1	even	1	trivial
21.5.f.a.19.1	yes	2	7.5	odd	6	inner
63.5.m.c.10.1		2	3.2	odd	2
63.5.m.c.19.1		2	21.5	even	6
147.5.d.b.97.1		2	7.4	even	3
147.5.d.b.97.2		2	7.3	odd	6
147.5.f.a.19.1		2	7.2	even	3
147.5.f.a.31.1		2	7.6	odd	2
336.5.bh.b.145.1		2	28.19	even	6
336.5.bh.b.241.1		2	4.3	odd	2
441.5.d.a.244.1		2	21.11	odd	6
441.5.d.a.244.2		2	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(4.50000 + 2.59808i) q^{3} +(6.00000 - 10.3923i) q^{4} +(9.00000 - 5.19615i) q^{5} -10.3923i q^{6} +(38.5000 - 30.3109i) q^{7} -56.0000 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(4.50000 + 2.59808i) q^{3} +(6.00000 - 10.3923i) q^{4} +(9.00000 - 5.19615i) q^{5} -10.3923i q^{6} +(38.5000 - 30.3109i) q^{7} -56.0000 q^{8} +(13.5000 + 23.3827i) q^{9} +(-18.0000 - 10.3923i) q^{10} +(-97.0000 + 168.009i) q^{11} +(54.0000 - 31.1769i) q^{12} +164.545i q^{13} +(-91.0000 - 36.3731i) q^{14} +54.0000 q^{15} +(-40.0000 - 69.2820i) q^{16} +(-210.000 - 121.244i) q^{17} +(27.0000 - 46.7654i) q^{18} +(226.500 - 130.770i) q^{19} -124.708i q^{20} +(252.000 - 36.3731i) q^{21} +388.000 q^{22} +(56.0000 + 96.9948i) q^{23} +(-252.000 - 145.492i) q^{24} +(-258.500 + 447.735i) q^{25} +(285.000 - 164.545i) q^{26} +140.296i q^{27} +(-84.0000 - 581.969i) q^{28} +1040.00 q^{29} +(-54.0000 - 93.5307i) q^{30} +(-1009.50 - 582.835i) q^{31} +(-528.000 + 914.523i) q^{32} +(-873.000 + 504.027i) q^{33} +484.974i q^{34} +(189.000 - 472.850i) q^{35} +324.000 q^{36} +(537.500 + 930.977i) q^{37} +(-453.000 - 261.540i) q^{38} +(-427.500 + 740.452i) q^{39} +(-504.000 + 290.985i) q^{40} -1305.97i q^{41} +(-315.000 - 400.104i) q^{42} -1087.00 q^{43} +(1164.00 + 2016.11i) q^{44} +(243.000 + 140.296i) q^{45} +(112.000 - 193.990i) q^{46} +(1875.00 - 1082.53i) q^{47} -415.692i q^{48} +(563.500 - 2333.94i) q^{49} +1034.00 q^{50} +(-630.000 - 1091.19i) q^{51} +(1710.00 + 987.269i) q^{52} +(1100.00 - 1905.26i) q^{53} +(243.000 - 140.296i) q^{54} +2016.11i q^{55} +(-2156.00 + 1697.41i) q^{56} +1359.00 q^{57} +(-1040.00 - 1801.33i) q^{58} +(-4632.00 - 2674.29i) q^{59} +(324.000 - 561.184i) q^{60} +(606.000 - 349.874i) q^{61} +2331.34i q^{62} +(1228.50 + 491.036i) q^{63} +832.000 q^{64} +(855.000 + 1480.90i) q^{65} +(1746.00 + 1008.05i) q^{66} +(-1187.50 + 2056.81i) q^{67} +(-2520.00 + 1454.92i) q^{68} +581.969i q^{69} +(-1008.00 + 145.492i) q^{70} -8938.00 q^{71} +(-756.000 - 1309.43i) q^{72} +(7903.50 + 4563.09i) q^{73} +(1075.00 - 1861.95i) q^{74} +(-2326.50 + 1343.21i) q^{75} -3138.48i q^{76} +(1358.00 + 9408.50i) q^{77} +1710.00 q^{78} +(-4073.50 - 7055.51i) q^{79} +(-720.000 - 415.692i) q^{80} +(-364.500 + 631.333i) q^{81} +(-2262.00 + 1305.97i) q^{82} -6675.32i q^{83} +(1134.00 - 2837.10i) q^{84} -2520.00 q^{85} +(1087.00 + 1882.74i) q^{86} +(4680.00 + 2702.00i) q^{87} +(5432.00 - 9408.50i) q^{88} +(11814.0 - 6820.82i) q^{89} -561.184i q^{90} +(4987.50 + 6334.98i) q^{91} +1344.00 q^{92} +(-3028.50 - 5245.52i) q^{93} +(-3750.00 - 2165.06i) q^{94} +(1359.00 - 2353.86i) q^{95} +(-4752.00 + 2743.57i) q^{96} +3498.74i q^{97} +(-4606.00 + 1357.93i) q^{98} -5238.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 9 q^{3} + 12 q^{4} + 18 q^{5} + 77 q^{7} - 112 q^{8} + 27 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 9 * q^3 + 12 * q^4 + 18 * q^5 + 77 * q^7 - 112 * q^8 + 27 * q^9	\( 2 q - 2 q^{2} + 9 q^{3} + 12 q^{4} + 18 q^{5} + 77 q^{7} - 112 q^{8} + 27 q^{9} - 36 q^{10} - 194 q^{11} + 108 q^{12} - 182 q^{14} + 108 q^{15} - 80 q^{16} - 420 q^{17} + 54 q^{18} + 453 q^{19} + 504 q^{21} + 776 q^{22} + 112 q^{23} - 504 q^{24} - 517 q^{25} + 570 q^{26} - 168 q^{28} + 2080 q^{29} - 108 q^{30} - 2019 q^{31} - 1056 q^{32} - 1746 q^{33} + 378 q^{35} + 648 q^{36} + 1075 q^{37} - 906 q^{38} - 855 q^{39} - 1008 q^{40} - 630 q^{42} - 2174 q^{43} + 2328 q^{44} + 486 q^{45} + 224 q^{46} + 3750 q^{47} + 1127 q^{49} + 2068 q^{50} - 1260 q^{51} + 3420 q^{52} + 2200 q^{53} + 486 q^{54} - 4312 q^{56} + 2718 q^{57} - 2080 q^{58} - 9264 q^{59} + 648 q^{60} + 1212 q^{61} + 2457 q^{63} + 1664 q^{64} + 1710 q^{65} + 3492 q^{66} - 2375 q^{67} - 5040 q^{68} - 2016 q^{70} - 17876 q^{71} - 1512 q^{72} + 15807 q^{73} + 2150 q^{74} - 4653 q^{75} + 2716 q^{77} + 3420 q^{78} - 8147 q^{79} - 1440 q^{80} - 729 q^{81} - 4524 q^{82} + 2268 q^{84} - 5040 q^{85} + 2174 q^{86} + 9360 q^{87} + 10864 q^{88} + 23628 q^{89} + 9975 q^{91} + 2688 q^{92} - 6057 q^{93} - 7500 q^{94} + 2718 q^{95} - 9504 q^{96} - 9212 q^{98} - 10476 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 9 * q^3 + 12 * q^4 + 18 * q^5 + 77 * q^7 - 112 * q^8 + 27 * q^9 - 36 * q^10 - 194 * q^11 + 108 * q^12 - 182 * q^14 + 108 * q^15 - 80 * q^16 - 420 * q^17 + 54 * q^18 + 453 * q^19 + 504 * q^21 + 776 * q^22 + 112 * q^23 - 504 * q^24 - 517 * q^25 + 570 * q^26 - 168 * q^28 + 2080 * q^29 - 108 * q^30 - 2019 * q^31 - 1056 * q^32 - 1746 * q^33 + 378 * q^35 + 648 * q^36 + 1075 * q^37 - 906 * q^38 - 855 * q^39 - 1008 * q^40 - 630 * q^42 - 2174 * q^43 + 2328 * q^44 + 486 * q^45 + 224 * q^46 + 3750 * q^47 + 1127 * q^49 + 2068 * q^50 - 1260 * q^51 + 3420 * q^52 + 2200 * q^53 + 486 * q^54 - 4312 * q^56 + 2718 * q^57 - 2080 * q^58 - 9264 * q^59 + 648 * q^60 + 1212 * q^61 + 2457 * q^63 + 1664 * q^64 + 1710 * q^65 + 3492 * q^66 - 2375 * q^67 - 5040 * q^68 - 2016 * q^70 - 17876 * q^71 - 1512 * q^72 + 15807 * q^73 + 2150 * q^74 - 4653 * q^75 + 2716 * q^77 + 3420 * q^78 - 8147 * q^79 - 1440 * q^80 - 729 * q^81 - 4524 * q^82 + 2268 * q^84 - 5040 * q^85 + 2174 * q^86 + 9360 * q^87 + 10864 * q^88 + 23628 * q^89 + 9975 * q^91 + 2688 * q^92 - 6057 * q^93 - 7500 * q^94 + 2718 * q^95 - 9504 * q^96 - 9212 * q^98 - 10476 * q^99

Introduction

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