LMFDB - Embedded newform 242.4.c.l.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not 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:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	242.81
Dual form			242.4.c.l.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 1.17557i) q^{2} +(-2.16312 + 6.65740i) q^{3} +(1.23607 + 3.80423i) q^{4} +(15.3713 - 11.1679i) q^{5} +(-11.3262 + 8.22899i) q^{6} +(4.32624 + 13.3148i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-17.7984 - 12.9313i) q^{9} +O(q^{10})$	\(q+(1.61803 + 1.17557i) q^{2} +(-2.16312 + 6.65740i) q^{3} +(1.23607 + 3.80423i) q^{4} +(15.3713 - 11.1679i) q^{5} +(-11.3262 + 8.22899i) q^{6} +(4.32624 + 13.3148i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-17.7984 - 12.9313i) q^{9} +38.0000 q^{10} -28.0000 q^{12} +(58.2492 + 42.3205i) q^{13} +(-8.65248 + 26.6296i) q^{14} +(41.0993 + 126.491i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(37.2148 - 27.0381i) q^{17} +(-13.5967 - 41.8465i) q^{18} +(-6.18034 + 19.0211i) q^{19} +(61.4853 + 44.6717i) q^{20} -98.0000 q^{21} -107.000 q^{23} +(-45.3050 - 32.9160i) q^{24} +(72.9280 - 224.449i) q^{25} +(44.4984 + 136.952i) q^{26} +(-28.3156 + 20.5725i) q^{27} +(-45.3050 + 32.9160i) q^{28} +(37.0820 + 114.127i) q^{29} +(-82.1985 + 252.981i) q^{30} +(-94.6550 - 68.7709i) q^{31} -32.0000 q^{32} +92.0000 q^{34} +(215.199 + 156.351i) q^{35} +(27.1935 - 83.6930i) q^{36} +(-62.1124 - 191.162i) q^{37} +(-32.3607 + 23.5114i) q^{38} +(-407.745 + 296.244i) q^{39} +(46.9706 + 144.561i) q^{40} +(-70.4559 + 216.841i) q^{41} +(-158.567 - 115.206i) q^{42} -242.000 q^{43} -418.000 q^{45} +(-173.130 - 125.786i) q^{46} +(-29.6656 + 91.3014i) q^{47} +(-34.6099 - 106.518i) q^{48} +(118.925 - 86.4044i) q^{49} +(381.856 - 277.435i) q^{50} +(99.5035 + 306.240i) q^{51} +(-88.9969 + 273.904i) q^{52} +(-370.530 - 269.206i) q^{53} -70.0000 q^{54} -112.000 q^{56} +(-113.262 - 82.2899i) q^{57} +(-74.1641 + 228.254i) q^{58} +(134.422 + 413.710i) q^{59} +(-430.397 + 312.702i) q^{60} +(540.423 - 392.641i) q^{61} +(-72.3100 - 222.547i) q^{62} +(95.1772 - 292.925i) q^{63} +(-51.7771 - 37.6183i) q^{64} +1368.00 q^{65} +439.000 q^{67} +(148.859 + 108.152i) q^{68} +(231.454 - 712.341i) q^{69} +(164.397 + 505.962i) q^{70} +(900.436 - 654.205i) q^{71} +(142.387 - 103.450i) q^{72} +(-22.2492 - 68.4761i) q^{73} +(124.225 - 382.325i) q^{74} +(1336.50 + 971.021i) q^{75} -80.0000 q^{76} -1008.00 q^{78} +(56.6312 + 41.1450i) q^{79} +(-93.9412 + 289.121i) q^{80} +(-259.265 - 797.936i) q^{81} +(-368.912 + 268.030i) q^{82} +(-289.628 + 210.427i) q^{83} +(-121.135 - 372.814i) q^{84} +(270.081 - 831.223i) q^{85} +(-391.564 - 284.488i) q^{86} -840.000 q^{87} +895.000 q^{89} +(-676.338 - 491.388i) q^{90} +(-311.489 + 958.665i) q^{91} +(-132.259 - 407.052i) q^{92} +(662.585 - 481.396i) q^{93} +(-155.331 + 112.855i) q^{94} +(117.426 + 361.401i) q^{95} +(69.2198 - 213.037i) q^{96} +(-330.888 - 240.404i) q^{97} +294.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 7 q^{3} - 4 q^{4} + 19 q^{5} - 14 q^{6} - 14 q^{7} + 8 q^{8} - 22 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 7 * q^3 - 4 * q^4 + 19 * q^5 - 14 * q^6 - 14 * q^7 + 8 * q^8 - 22 * q^9	\( 4 q + 2 q^{2} + 7 q^{3} - 4 q^{4} + 19 q^{5} - 14 q^{6} - 14 q^{7} + 8 q^{8} - 22 q^{9} + 152 q^{10} - 112 q^{12} + 72 q^{13} + 28 q^{14} - 133 q^{15} - 16 q^{16} + 46 q^{17} + 44 q^{18} + 20 q^{19} + 76 q^{20} - 392 q^{21} - 428 q^{23} - 56 q^{24} - 236 q^{25} - 144 q^{26} - 35 q^{27} - 56 q^{28} - 120 q^{29} + 266 q^{30} - 117 q^{31} - 128 q^{32} + 368 q^{34} + 266 q^{35} - 88 q^{36} + 201 q^{37} - 40 q^{38} - 504 q^{39} - 152 q^{40} + 228 q^{41} - 196 q^{42} - 968 q^{43} - 1672 q^{45} - 214 q^{46} + 96 q^{47} + 112 q^{48} + 147 q^{49} + 472 q^{50} - 322 q^{51} + 288 q^{52} - 458 q^{53} - 280 q^{54} - 448 q^{56} - 140 q^{57} + 240 q^{58} - 435 q^{59} - 532 q^{60} + 668 q^{61} + 234 q^{62} - 308 q^{63} - 64 q^{64} + 5472 q^{65} + 1756 q^{67} + 184 q^{68} - 749 q^{69} - 532 q^{70} + 1113 q^{71} + 176 q^{72} + 72 q^{73} - 402 q^{74} + 1652 q^{75} - 320 q^{76} - 4032 q^{78} + 70 q^{79} + 304 q^{80} + 839 q^{81} - 456 q^{82} - 358 q^{83} + 392 q^{84} - 874 q^{85} - 484 q^{86} - 3360 q^{87} + 3580 q^{89} - 836 q^{90} + 1008 q^{91} + 428 q^{92} + 819 q^{93} - 192 q^{94} - 380 q^{95} - 224 q^{96} - 409 q^{97} + 1176 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 7 * q^3 - 4 * q^4 + 19 * q^5 - 14 * q^6 - 14 * q^7 + 8 * q^8 - 22 * q^9 + 152 * q^10 - 112 * q^12 + 72 * q^13 + 28 * q^14 - 133 * q^15 - 16 * q^16 + 46 * q^17 + 44 * q^18 + 20 * q^19 + 76 * q^20 - 392 * q^21 - 428 * q^23 - 56 * q^24 - 236 * q^25 - 144 * q^26 - 35 * q^27 - 56 * q^28 - 120 * q^29 + 266 * q^30 - 117 * q^31 - 128 * q^32 + 368 * q^34 + 266 * q^35 - 88 * q^36 + 201 * q^37 - 40 * q^38 - 504 * q^39 - 152 * q^40 + 228 * q^41 - 196 * q^42 - 968 * q^43 - 1672 * q^45 - 214 * q^46 + 96 * q^47 + 112 * q^48 + 147 * q^49 + 472 * q^50 - 322 * q^51 + 288 * q^52 - 458 * q^53 - 280 * q^54 - 448 * q^56 - 140 * q^57 + 240 * q^58 - 435 * q^59 - 532 * q^60 + 668 * q^61 + 234 * q^62 - 308 * q^63 - 64 * q^64 + 5472 * q^65 + 1756 * q^67 + 184 * q^68 - 749 * q^69 - 532 * q^70 + 1113 * q^71 + 176 * q^72 + 72 * q^73 - 402 * q^74 + 1652 * q^75 - 320 * q^76 - 4032 * q^78 + 70 * q^79 + 304 * q^80 + 839 * q^81 - 456 * q^82 - 358 * q^83 + 392 * q^84 - 874 * q^85 - 484 * q^86 - 3360 * q^87 + 3580 * q^89 - 836 * q^90 + 1008 * q^91 + 428 * q^92 + 819 * q^93 - 192 * q^94 - 380 * q^95 - 224 * q^96 - 409 * q^97 + 1176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.61803	+	1.17557i	0.572061	+	0.415627i
$2$	1.61803	+	1.17557i	0.572061	+	0.415627i
$3$	−2.16312	+	6.65740i	−0.416292	+	1.28122i	0.494797	+	0.869008i	$0.335242\pi$
$3$	−2.16312	+	6.65740i	−0.416292	+	1.28122i	−0.911090	+	0.412208i	$0.864758\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	15.3713	−	11.1679i	1.37485	−	0.998889i	0.377513	−	0.926004i	$-0.376780\pi$
$5$	15.3713	−	11.1679i	1.37485	−	0.998889i	0.997340	−	0.0728846i	$-0.0232205\pi$
$6$	−11.3262	+	8.22899i	−0.770653	+	0.559912i
$7$	4.32624	+	13.3148i	0.233595	+	0.718931i	0.997305	+	0.0733714i	$0.0233759\pi$
$7$	4.32624	+	13.3148i	0.233595	+	0.718931i	−0.763710	+	0.645560i	$0.776624\pi$
$8$	−2.47214	+	7.60845i	−0.109254	+	0.336249i
$9$	−17.7984	−	12.9313i	−0.659199	−	0.478936i
$10$	38.0000			1.20167
$11$		0			0
$11$		0			0
$12$	−28.0000			−0.673575
$13$	58.2492	+	42.3205i	1.24273	+	0.902893i	0.997777	−	0.0666434i	$-0.0212290\pi$
$13$	58.2492	+	42.3205i	1.24273	+	0.902893i	0.244948	+	0.969536i	$0.421229\pi$
$14$	−8.65248	+	26.6296i	−0.165177	+	0.508361i
$15$	41.0993	+	126.491i	0.707452	+	2.17731i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	37.2148	−	27.0381i	0.530936	−	0.385748i	−0.289772	−	0.957096i	$-0.593579\pi$
$17$	37.2148	−	27.0381i	0.530936	−	0.385748i	0.820708	+	0.571348i	$0.193579\pi$
$18$	−13.5967	−	41.8465i	−0.178044	−	0.547962i
$19$	−6.18034	+	19.0211i	−0.0746246	+	0.229671i	−0.981410	−	0.191921i	$-0.938528\pi$
$19$	−6.18034	+	19.0211i	−0.0746246	+	0.229671i	0.906786	+	0.421592i	$0.138528\pi$
$20$	61.4853	+	44.6717i	0.687426	+	0.499445i
$21$	−98.0000			−1.01835
$22$		0			0
$23$	−107.000			−0.970045			−0.485023	−	0.874502i	$-0.661189\pi$
$23$	−107.000			−0.970045			−0.485023	+	0.874502i	$0.661189\pi$
$24$	−45.3050	−	32.9160i	−0.385326	−	0.279956i
$25$	72.9280	−	224.449i	0.583424	−	1.79559i
$26$	44.4984	+	136.952i	0.335649	+	1.03302i
$27$	−28.3156	+	20.5725i	−0.201827	+	0.146636i
$28$	−45.3050	+	32.9160i	−0.305780	+	0.222162i
$29$	37.0820	+	114.127i	0.237447	+	0.730787i	0.996787	+	0.0800930i	$0.0255217\pi$
$29$	37.0820	+	114.127i	0.237447	+	0.730787i	−0.759340	+	0.650694i	$0.774478\pi$
$30$	−82.1985	+	252.981i	−0.500244	+	1.53959i
$31$	−94.6550	−	68.7709i	−0.548404	−	0.398439i	0.278792	−	0.960351i	$-0.410066\pi$
$31$	−94.6550	−	68.7709i	−0.548404	−	0.398439i	−0.827197	+	0.561912i	$0.810066\pi$
$32$	−32.0000			−0.176777
$33$		0			0
$34$	92.0000			0.464055
$35$	215.199	+	156.351i	1.03929	+	0.755089i
$36$	27.1935	−	83.6930i	0.125896	−	0.387467i
$37$	−62.1124	−	191.162i	−0.275979	−	0.849376i	−0.988959	−	0.148191i	$-0.952655\pi$
$37$	−62.1124	−	191.162i	−0.275979	−	0.849376i	0.712980	−	0.701185i	$-0.247345\pi$
$38$	−32.3607	+	23.5114i	−0.138147	+	0.100370i
$39$	−407.745	+	296.244i	−1.67414	+	1.21633i
$40$	46.9706	+	144.561i	0.185668	+	0.571426i
$41$	−70.4559	+	216.841i	−0.268375	+	0.825972i	0.722522	+	0.691348i	$0.242983\pi$
$41$	−70.4559	+	216.841i	−0.268375	+	0.825972i	−0.990897	+	0.134624i	$0.957017\pi$
$42$	−158.567	−	115.206i	−0.582559	−	0.423254i
$43$	−242.000			−0.858248			−0.429124	−	0.903246i	$-0.641178\pi$
$43$	−242.000			−0.858248			−0.429124	+	0.903246i	$0.641178\pi$
$44$		0			0
$45$	−418.000			−1.38471
$46$	−173.130	−	125.786i	−0.554925	−	0.403177i
$47$	−29.6656	+	91.3014i	−0.0920676	+	0.283355i	−0.986478	−	0.163892i	$-0.947595\pi$
$47$	−29.6656	+	91.3014i	−0.0920676	+	0.283355i	0.894411	+	0.447246i	$0.147595\pi$
$48$	−34.6099	−	106.518i	−0.104073	−	0.320304i
$49$	118.925	−	86.4044i	0.346722	−	0.251908i
$50$	381.856	−	277.435i	1.08005	−	0.784704i
$51$	99.5035	+	306.240i	0.273201	+	0.840828i
$52$	−88.9969	+	273.904i	−0.237339	+	0.730456i
$53$	−370.530	−	269.206i	−0.960305	−	0.697703i	−0.00708366	−	0.999975i	$-0.502255\pi$
$53$	−370.530	−	269.206i	−0.960305	−	0.697703i	−0.953222	+	0.302272i	$0.902255\pi$
$54$	−70.0000			−0.176404
$55$		0			0
$56$	−112.000			−0.267261
$57$	−113.262	−	82.2899i	−0.263192	−	0.191220i
$58$	−74.1641	+	228.254i	−0.167900	+	0.516744i
$59$	134.422	+	413.710i	0.296615	+	0.912888i	0.982674	+	0.185342i	$0.0593393\pi$
$59$	134.422	+	413.710i	0.296615	+	0.912888i	−0.686059	+	0.727546i	$0.740661\pi$
$60$	−430.397	+	312.702i	−0.926067	+	0.672827i
$61$	540.423	−	392.641i	1.13433	−	0.824139i	0.148011	−	0.988986i	$-0.452713\pi$
$61$	540.423	−	392.641i	1.13433	−	0.824139i	0.986319	+	0.164847i	$0.0527130\pi$
$62$	−72.3100	−	222.547i	−0.148119	−	0.455863i
$63$	95.1772	−	292.925i	0.190337	−	0.585796i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	1368.00			2.61045
$66$		0			0
$67$	439.000			0.800483			0.400242	−	0.916410i	$-0.368926\pi$
$67$	439.000			0.800483			0.400242	+	0.916410i	$0.368926\pi$
$68$	148.859	+	108.152i	0.265468	+	0.192874i
$69$	231.454	−	712.341i	0.403823	−	1.24284i
$70$	164.397	+	505.962i	0.280703	+	0.863915i
$71$	900.436	−	654.205i	1.50510	−	1.09352i	0.536806	−	0.843706i	$-0.319631\pi$
$71$	900.436	−	654.205i	1.50510	−	1.09352i	0.968294	−	0.249813i	$-0.0803692\pi$
$72$	142.387	−	103.450i	0.233062	−	0.169329i
$73$	−22.2492	−	68.4761i	−0.0356723	−	0.109788i	0.931635	−	0.363396i	$-0.118383\pi$
$73$	−22.2492	−	68.4761i	−0.0356723	−	0.109788i	−0.967307	+	0.253608i	$0.918383\pi$
$74$	124.225	−	382.325i	0.195147	−	0.600599i
$75$	1336.50	+	971.021i	2.05767	+	1.49498i
$76$	−80.0000			−0.120745
$77$		0			0
$78$	−1008.00			−1.46325
$79$	56.6312	+	41.1450i	0.0806520	+	0.0585971i	0.627381	−	0.778713i	$-0.284127\pi$
$79$	56.6312	+	41.1450i	0.0806520	+	0.0585971i	−0.546729	+	0.837310i	$0.684127\pi$
$80$	−93.9412	+	289.121i	−0.131287	+	0.404059i
$81$	−259.265	−	797.936i	−0.355645	−	1.09456i
$82$	−368.912	+	268.030i	−0.496823	+	0.360963i
$83$	−289.628	+	210.427i	−0.383022	+	0.278282i	−0.762590	−	0.646882i	$-0.776073\pi$
$83$	−289.628	+	210.427i	−0.383022	+	0.278282i	0.379568	+	0.925164i	$0.376073\pi$
$84$	−121.135	−	372.814i	−0.157344	−	0.484254i
$85$	270.081	−	831.223i	0.344640	−	1.06069i
$86$	−391.564	−	284.488i	−0.490970	−	0.356711i
$87$	−840.000			−1.03514
$88$		0			0
$89$	895.000			1.06595			0.532976	−	0.846130i	$-0.321073\pi$
$89$	895.000			1.06595			0.532976	+	0.846130i	$0.321073\pi$
$90$	−676.338	−	491.388i	−0.792137	−	0.575521i
$91$	−311.489	+	958.665i	−0.358823	+	1.10434i
$92$	−132.259	−	407.052i	−0.149880	−	0.461284i
$93$	662.585	−	481.396i	0.738783	−	0.536758i
$94$	−155.331	+	112.855i	−0.170438	+	0.123831i
$95$	117.426	+	361.401i	0.126818	+	0.390305i
$96$	69.2198	−	213.037i	0.0735908	−	0.226489i
$97$	−330.888	−	240.404i	−0.346357	−	0.251643i	0.400982	−	0.916086i	$-0.368669\pi$
$97$	−330.888	−	240.404i	−0.346357	−	0.251643i	−0.747339	+	0.664443i	$0.768669\pi$
$98$	294.000			0.303046
$99$		0			0
$100$	944.000			0.944000
$101$	726.497	+	527.831i	0.715734	+	0.520012i	0.885019	−	0.465556i	$-0.154146\pi$
$101$	726.497	+	527.831i	0.715734	+	0.520012i	−0.169284	+	0.985567i	$0.554146\pi$
$102$	−199.007	+	612.480i	−0.193183	+	0.594555i
$103$	−96.4133	−	296.730i	−0.0922319	−	0.283861i	0.894291	−	0.447487i	$-0.147681\pi$
$103$	−96.4133	−	296.730i	−0.0922319	−	0.283861i	−0.986522	+	0.163626i	$0.947681\pi$
$104$	−465.994	+	338.564i	−0.439370	+	0.319221i
$105$	−1506.39	+	1094.46i	−1.40008	+	1.01722i
$106$	−283.060	−	871.168i	−0.259370	−	0.798257i
$107$	84.6707	−	260.589i	0.0764993	−	0.235441i	−0.905493	−	0.424361i	$-0.860499\pi$
$107$	84.6707	−	260.589i	0.0764993	−	0.235441i	0.981992	+	0.188920i	$0.0604988\pi$
$108$	−113.262	−	82.2899i	−0.100914	−	0.0733181i
$109$	−1470.00			−1.29175			−0.645874	−	0.763444i	$-0.723507\pi$
$109$	−1470.00			−1.29175			−0.645874	+	0.763444i	$0.723507\pi$
$110$		0			0
$111$	1407.00			1.20312
$112$	−181.220	−	131.664i	−0.152890	−	0.111081i
$113$	34.9189	−	107.469i	0.0290699	−	0.0894679i	−0.935469	−	0.353409i	$-0.885022\pi$
$113$	34.9189	−	107.469i	0.0290699	−	0.0894679i	0.964539	+	0.263941i	$0.0850224\pi$
$114$	−86.5248	−	266.296i	−0.0710858	−	0.218780i
$115$	−1644.73	+	1194.97i	−1.33367	+	0.968968i
$116$	−388.328	+	282.137i	−0.310822	+	0.225825i
$117$	−489.483	−	1506.47i	−0.386775	−	1.19037i
$118$	−268.845	+	827.419i	−0.209739	+	0.645509i
$119$	521.007	+	378.534i	0.401350	+	0.291598i
$120$	−1064.00			−0.809412
$121$		0			0
$122$	1336.00			0.991441
$123$	−1291.19	−	938.105i	−0.946527	−	0.687692i
$124$	144.620	−	445.094i	0.104736	−	0.322344i
$125$	−651.717	−	2005.78i	−0.466331	−	1.43522i
$126$	498.354	−	362.076i	0.352357	−	0.256002i
$127$	1194.11	−	867.571i	0.834331	−	0.606177i	−0.0864502	−	0.996256i	$-0.527552\pi$
$127$	1194.11	−	867.571i	0.834331	−	0.606177i	0.920781	+	0.390079i	$0.127552\pi$
$128$	−39.5542	−	121.735i	−0.0273135	−	0.0840623i
$129$	523.475	−	1611.09i	0.357282	−	1.09960i
$130$	2213.47	+	1608.18i	1.49334	+	1.08498i
$131$	1342.00			0.895046			0.447523	−	0.894272i	$-0.352306\pi$
$131$	1342.00			0.895046			0.447523	+	0.894272i	$0.352306\pi$
$132$		0			0
$133$	−280.000			−0.182549
$134$	710.317	+	516.075i	0.457926	+	0.332702i
$135$	−205.496	+	632.453i	−0.131010	+	0.403206i
$136$	113.718	+	349.989i	0.0717004	+	0.220671i
$137$	−1431.15	+	1039.79i	−0.892493	+	0.648434i	−0.936527	−	0.350596i	$-0.885979\pi$
$137$	−1431.15	+	1039.79i	−0.892493	+	0.648434i	0.0440341	+	0.999030i	$0.485979\pi$
$138$	1211.91	−	880.502i	0.747568	−	0.543140i
$139$	−169.959	−	523.081i	−0.103711	−	0.319188i	0.885715	−	0.464229i	$-0.153669\pi$
$139$	−169.959	−	523.081i	−0.103711	−	0.319188i	−0.989426	+	0.145041i	$0.953669\pi$
$140$	−328.794	+	1011.92i	−0.198487	+	0.610880i
$141$	−543.659	−	394.992i	−0.324712	−	0.235917i
$142$	2226.00			1.31551
$143$		0			0
$144$	352.000			0.203704
$145$	1844.56	+	1340.15i	1.05643	+	0.767541i
$146$	44.4984	−	136.952i	0.0252241	−	0.0776318i
$147$	317.978	+	978.637i	0.178411	+	0.549093i
$148$	650.450	−	472.579i	0.361261	−	0.262472i
$149$	639.123	−	464.350i	0.351403	−	0.255309i	−0.398054	−	0.917362i	$-0.630314\pi$
$149$	639.123	−	464.350i	0.351403	−	0.255309i	0.749457	+	0.662053i	$0.230314\pi$
$150$	1020.99	+	3142.29i	0.555758	+	1.71045i
$151$	896.767	−	2759.97i	0.483297	−	1.48744i	−0.351135	−	0.936325i	$-0.614204\pi$
$151$	896.767	−	2759.97i	0.483297	−	1.48744i	0.834432	−	0.551111i	$-0.185796\pi$
$152$	−129.443	−	94.0456i	−0.0690736	−	0.0501849i
$153$	−1012.00			−0.534741
$154$		0			0
$155$	−2223.00			−1.15197
$156$	−1630.98	−	1184.98i	−0.837069	−	0.608166i
$157$	231.454	−	712.341i	0.117656	−	0.362108i	−0.874836	−	0.484420i	$-0.839031\pi$
$157$	231.454	−	712.341i	0.117656	−	0.362108i	0.992492	+	0.122311i	$0.0390307\pi$
$158$	43.2624	+	133.148i	0.0217834	+	0.0670423i
$159$	2593.71	−	1884.44i	1.29368	−	0.939911i
$160$	−491.882	+	357.373i	−0.243042	+	0.176580i
$161$	−462.907	−	1424.68i	−0.226598	−	0.697396i
$162$	518.531	−	1595.87i	0.251479	−	0.773973i
$163$	−993.473	−	721.800i	−0.477391	−	0.346845i	0.322923	−	0.946425i	$-0.395334\pi$
$163$	−993.473	−	721.800i	−0.477391	−	0.346845i	−0.800315	+	0.599580i	$0.795334\pi$
$164$	−912.000			−0.434239
$165$		0			0
$166$	−716.000			−0.334773
$167$	−1961.06	−	1424.79i	−0.908690	−	0.660202i	0.0319935	−	0.999488i	$-0.489814\pi$
$167$	−1961.06	−	1424.79i	−0.908690	−	0.660202i	−0.940683	+	0.339286i	$0.889814\pi$
$168$	242.269	−	745.628i	0.111259	−	0.342419i
$169$	923.034	+	2840.81i	0.420134	+	1.29304i
$170$	1414.16	−	1027.45i	0.638007	−	0.463539i
$171$	355.967	−	258.626i	0.159190	−	0.115658i
$172$	−299.128	−	920.623i	−0.132607	−	0.408121i
$173$	−1156.34	+	3558.85i	−0.508179	+	1.56402i	0.287180	+	0.957877i	$0.407282\pi$
$173$	−1156.34	+	3558.85i	−0.508179	+	1.56402i	−0.795359	+	0.606138i	$0.792718\pi$
$174$	−1359.15	−	987.479i	−0.592165	−	0.430233i
$175$	3304.00			1.42719
$176$		0			0
$177$	−3045.00			−1.29309
$178$	1448.14	+	1052.14i	0.609791	+	0.443039i
$179$	−81.8895	+	252.030i	−0.0341939	+	0.105238i	−0.966697	−	0.255925i	$-0.917620\pi$
$179$	−81.8895	+	252.030i	−0.0341939	+	0.105238i	0.932503	+	0.361163i	$0.117620\pi$
$180$	−516.676	−	1590.17i	−0.213949	−	0.658467i
$181$	−54.2041	+	39.3816i	−0.0222595	+	0.0161724i	−0.598859	−	0.800854i	$-0.704379\pi$
$181$	−54.2041	+	39.3816i	−0.0222595	+	0.0161724i	0.576600	+	0.817027i	$0.304379\pi$
$182$	−1630.98	+	1184.98i	−0.664265	+	0.482616i
$183$	1444.96	+	4447.14i	0.583687	+	1.79640i
$184$	264.519	−	814.104i	0.105981	−	0.326177i
$185$	−3089.64	−	2244.75i	−1.22786	−	0.892094i
$186$	1638.00			0.645720
$187$		0			0
$188$	−384.000			−0.148969
$189$	−396.418	−	288.015i	−0.152567	−	0.110847i
$190$	−234.853	+	722.803i	−0.0896738	+	0.275988i
$191$	−1067.04	−	3284.00i	−0.404230	−	1.24409i	−0.921536	−	0.388292i	$-0.873065\pi$
$191$	−1067.04	−	3284.00i	−0.404230	−	1.24409i	0.517306	−	0.855801i	$-0.326935\pi$
$192$	362.440	−	263.328i	0.136233	−	0.0989794i
$193$	3375.22	−	2452.24i	1.25883	−	0.914591i	0.260127	−	0.965574i	$-0.416235\pi$
$193$	3375.22	−	2452.24i	1.25883	−	0.914591i	0.998700	+	0.0509831i	$0.0162355\pi$
$194$	−252.776	−	777.964i	−0.0935477	−	0.287910i
$195$	−2959.15	+	9107.32i	−1.08671	+	3.34456i
$196$	475.702	+	345.618i	0.173361	+	0.125954i
$197$	−2426.00			−0.877388			−0.438694	−	0.898637i	$-0.644559\pi$
$197$	−2426.00			−0.877388			−0.438694	+	0.898637i	$0.644559\pi$
$198$		0			0
$199$	−400.000			−0.142489			−0.0712443	−	0.997459i	$-0.522697\pi$
$199$	−400.000			−0.142489			−0.0712443	+	0.997459i	$0.522697\pi$
$200$	1527.42	+	1109.74i	0.540026	+	0.392352i
$201$	−949.609	+	2922.60i	−0.333235	+	1.02559i
$202$	554.995	+	1708.10i	0.193313	+	0.594957i
$203$	−1359.15	+	987.479i	−0.469919	+	0.341416i
$204$	−1042.01	+	757.067i	−0.357625	+	0.259830i
$205$	1338.66	+	4119.98i	0.456079	+	1.40367i
$206$	192.827	−	593.459i	0.0652178	−	0.200720i
$207$	1904.43	+	1383.65i	0.639453	+	0.464590i
$208$	−1152.00			−0.384023
$209$		0			0
$210$	−3724.00			−1.22372
$211$	−2695.64	−	1958.50i	−0.879506	−	0.638999i	0.0536145	−	0.998562i	$-0.482926\pi$
$211$	−2695.64	−	1958.50i	−0.879506	−	0.638999i	−0.933121	+	0.359563i	$0.882926\pi$
$212$	566.119	−	1742.34i	0.183402	−	0.564453i
$213$	2407.55	+	7409.68i	0.774473	+	2.38358i
$214$	443.341	−	322.106i	0.141618	−	0.102891i
$215$	−3719.86	+	2702.64i	−1.17996	+	0.857294i
$216$	−86.5248	−	266.296i	−0.0272559	−	0.0838849i
$217$	506.170	−	1557.83i	0.158346	−	0.487338i
$218$	−2378.51	−	1728.09i	−0.738959	−	0.536885i
$219$	504.000			0.155512
$220$		0			0
$221$	3312.00			1.00810
$222$	2276.57	+	1654.03i	0.688260	+	0.500050i
$223$	1864.30	−	5737.72i	0.559833	−	1.72299i	−0.122993	−	0.992408i	$-0.539249\pi$
$223$	1864.30	−	5737.72i	0.559833	−	1.72299i	0.682826	−	0.730581i	$-0.260751\pi$
$224$	−138.440	−	426.073i	−0.0412941	−	0.127090i
$225$	−4200.42	+	3051.78i	−1.24457	+	0.904231i
$226$	182.838	−	132.839i	0.0538150	−	0.0390989i
$227$	−1744.71	−	5369.67i	−0.510134	−	1.57003i	−0.791964	−	0.610567i	$-0.790941\pi$
$227$	−1744.71	−	5369.67i	−0.510134	−	1.57003i	0.281830	−	0.959464i	$-0.409059\pi$
$228$	173.050	−	532.592i	0.0502653	−	0.154701i
$229$	3757.88	+	2730.26i	1.08440	+	0.787864i	0.978445	−	0.206507i	$-0.0662096\pi$
$229$	3757.88	+	2730.26i	1.08440	+	0.787864i	0.105956	+	0.994371i	$0.466210\pi$
$230$	−4066.00			−1.16567
$231$		0			0
$232$	−960.000			−0.271668
$233$	1967.53	+	1429.49i	0.553207	+	0.401928i	0.828966	−	0.559298i	$-0.188929\pi$
$233$	1967.53	+	1429.49i	0.553207	+	0.401928i	−0.275760	+	0.961227i	$0.588929\pi$
$234$	978.966	−	3012.95i	0.273491	−	0.841720i
$235$	563.647	+	1734.73i	0.156461	+	0.481537i
$236$	−1407.69	+	1022.75i	−0.388275	+	0.282098i
$237$	−396.418	+	288.015i	−0.108650	+	0.0789391i
$238$	398.014	+	1224.96i	0.108401	+	0.333624i
$239$	−1857.19	+	5715.85i	−0.502643	+	1.54698i	0.302053	+	0.953291i	$0.402328\pi$
$239$	−1857.19	+	5715.85i	−0.502643	+	1.54698i	−0.804697	+	0.593686i	$0.797672\pi$
$240$	−1721.59	−	1250.81i	−0.463033	−	0.336414i
$241$	−3728.00			−0.996438			−0.498219	−	0.867051i	$-0.666012\pi$
$241$	−3728.00			−0.996438			−0.498219	+	0.867051i	$0.666012\pi$
$242$		0			0
$243$	4928.00			1.30095
$244$	2161.69	+	1570.56i	0.567165	+	0.412069i
$245$	863.084	−	2656.30i	0.225063	−	0.692673i
$246$	−986.382	−	3035.77i	−0.255648	−	0.786804i
$247$	−1164.98	+	846.411i	−0.300106	+	0.218040i
$248$	757.240	−	550.167i	0.193890	−	0.140870i
$249$	−774.397	−	2383.35i	−0.197090	−	0.606580i
$250$	1303.43	−	4011.56i	0.329746	−	1.01485i
$251$	−426.352	−	309.763i	−0.107216	−	0.0778966i	0.532886	−	0.846187i	$-0.321108\pi$
$251$	−426.352	−	309.763i	−0.107216	−	0.0778966i	−0.640101	+	0.768291i	$0.721108\pi$
$252$	1232.00			0.307971
$253$		0			0
$254$	2952.00			0.729232
$255$	4949.57	+	3596.07i	1.21551	+	0.883116i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−551.904	−	1698.59i	−0.133957	−	0.412276i	0.861470	−	0.507809i	$-0.169544\pi$
$257$	−551.904	−	1698.59i	−0.133957	−	0.412276i	−0.995426	+	0.0955330i	$0.969544\pi$
$258$	2740.95	−	1991.42i	0.661411	−	0.480543i
$259$	2276.57	−	1654.03i	0.546175	−	0.396820i
$260$	1690.94	+	5204.18i	0.403337	+	1.24134i
$261$	815.805	−	2510.79i	0.193475	−	0.595456i
$262$	2171.40	+	1577.62i	0.512022	+	0.372005i
$263$	3198.00			0.749799			0.374899	−	0.927065i	$-0.377677\pi$
$263$	3198.00			0.749799			0.374899	+	0.927065i	$0.377677\pi$
$264$		0			0
$265$	−8702.00			−2.01721
$266$	−453.050	−	329.160i	−0.104430	−	0.0758725i
$267$	−1935.99	+	5958.37i	−0.443748	+	1.36572i
$268$	542.634	+	1670.06i	0.123681	+	0.380652i
$269$	1318.70	−	958.090i	0.298894	−	0.217159i	−0.428223	−	0.903673i	$-0.640860\pi$
$269$	1318.70	−	958.090i	0.298894	−	0.217159i	0.727116	+	0.686514i	$0.240860\pi$
$270$	−1075.99	+	781.754i	−0.242529	+	0.176208i
$271$	−1139.65	−	3507.50i	−0.255458	−	0.786219i	−0.993739	−	0.111726i	$-0.964362\pi$
$271$	−1139.65	−	3507.50i	−0.255458	−	0.786219i	0.738281	−	0.674493i	$-0.235638\pi$
$272$	−227.437	+	699.978i	−0.0506999	+	0.156038i
$273$	−5708.42	−	4147.41i	−1.26553	−	0.919461i
$274$	−3538.00			−0.780067
$275$		0			0
$276$	2996.00			0.653399
$277$	−4282.94	−	3111.74i	−0.929013	−	0.674968i	0.0167377	−	0.999860i	$-0.494672\pi$
$277$	−4282.94	−	3111.74i	−0.929013	−	0.674968i	−0.945751	+	0.324892i	$0.894672\pi$
$278$	339.919	−	1046.16i	0.0733344	−	0.225700i
$279$	795.410	+	2448.02i	0.170681	+	0.525301i
$280$	−1721.59	+	1250.81i	−0.367445	+	0.266964i
$281$	−4807.18	+	3492.62i	−1.02054	+	0.741467i	−0.966394	−	0.257066i	$-0.917244\pi$
$281$	−4807.18	+	3492.62i	−1.02054	+	0.741467i	−0.0541480	+	0.998533i	$0.517244\pi$
$282$	−415.319	−	1278.22i	−0.0877017	−	0.269918i
$283$	−2030.86	+	6250.34i	−0.426580	+	1.31288i	0.474894	+	0.880043i	$0.342487\pi$
$283$	−2030.86	+	6250.34i	−0.426580	+	1.31288i	−0.901473	+	0.432834i	$0.857513\pi$
$284$	3601.74	+	2616.82i	0.752550	+	0.546759i
$285$	−2660.00			−0.552859
$286$		0			0
$287$	−3192.00			−0.656508
$288$	569.548	+	413.801i	0.116531	+	0.0846647i
$289$	−864.321	+	2660.11i	−0.175925	+	0.541442i
$290$	1409.12	+	4336.82i	0.285332	+	0.878161i
$291$	2316.22	−	1682.83i	0.466594	−	0.339001i
$292$	232.997	−	169.282i	0.0466956	−	0.0339263i
$293$	1751.51	+	5390.59i	0.349229	+	1.07482i	0.959280	+	0.282455i	$0.0911489\pi$
$293$	1751.51	+	5390.59i	0.349229	+	1.07482i	−0.610051	+	0.792362i	$0.708851\pi$
$294$	−635.957	+	1957.27i	−0.126156	+	0.388267i
$295$	6686.53	+	4858.05i	1.31968	+	0.958801i
$296$	1608.00			0.315754
$297$		0			0
$298$	1580.00			0.307137
$299$	−6232.67	−	4528.30i	−1.20550	−	0.875847i
$300$	−2041.98	+	6284.58i	−0.392980	+	1.20947i
$301$	−1046.95	−	3222.18i	−0.200482	−	0.617021i
$302$	4695.53	−	3411.51i	0.894694	−	0.650033i
$303$	−5085.48	+	3694.82i	−0.964202	+	0.700534i
$304$	−98.8854	−	304.338i	−0.0186561	−	0.0574177i
$305$	3922.04	−	12070.8i	0.736313	−	2.26614i
$306$	−1637.45	−	1189.68i	−0.305905	−	0.222253i
$307$	9844.00			1.83005			0.915027	−	0.403392i	$-0.132169\pi$
$307$	9844.00			1.83005			0.915027	+	0.403392i	$0.132169\pi$
$308$		0			0
$309$	2184.00			0.402082
$310$	−3596.89	−	2613.29i	−0.658999	−	0.478791i
$311$	−1875.12	+	5771.01i	−0.341891	+	1.05223i	0.621337	+	0.783544i	$0.286590\pi$
$311$	−1875.12	+	5771.01i	−0.341891	+	1.05223i	−0.963227	+	0.268688i	$0.913410\pi$
$312$	−1245.96	−	3834.66i	−0.226085	−	0.695817i
$313$	−3028.15	+	2200.08i	−0.546841	+	0.397303i	−0.826619	−	0.562761i	$-0.809739\pi$
$313$	−3028.15	+	2200.08i	−0.546841	+	0.397303i	0.279778	+	0.960065i	$0.409739\pi$
$314$	1211.91	−	880.502i	0.217809	−	0.158247i
$315$	−1808.37	−	5565.58i	−0.323460	−	0.995508i
$316$	−86.5248	+	266.296i	−0.0154032	+	0.0474060i
$317$	−5540.96	−	4025.74i	−0.981739	−	0.713275i	−0.0236422	−	0.999720i	$-0.507526\pi$
$317$	−5540.96	−	4025.74i	−0.981739	−	0.713275i	−0.958097	+	0.286446i	$0.907526\pi$
$318$	6412.00			1.13071
$319$		0			0
$320$	−1216.00			−0.212426
$321$	1551.69	+	1127.37i	0.269804	+	0.196024i
$322$	925.815	−	2849.37i	0.160229	−	0.493133i
$323$	284.296	+	874.972i	0.0489741	+	0.150727i
$324$	2715.06	−	1972.61i	0.465545	−	0.338239i
$325$	13746.8	−	9987.65i	2.34627	−	1.70466i
$326$	−758.946	−	2335.79i	−0.128939	−	0.396833i
$327$	3179.78	−	9786.37i	0.537745	−	1.65501i
$328$	−1475.65	−	1072.12i	−0.248412	−	0.180482i
$329$	−1344.00			−0.225219
$330$		0			0
$331$	9617.00			1.59697			0.798487	−	0.602013i	$-0.205634\pi$
$331$	9617.00			1.59697			0.798487	+	0.602013i	$0.205634\pi$
$332$	−1158.51	−	841.708i	−0.191511	−	0.139141i
$333$	−1366.47	+	4205.57i	−0.224872	+	0.692084i
$334$	−1498.11	−	4610.72i	−0.245429	−	0.755352i
$335$	6748.01	−	4902.72i	1.10055	−	0.799594i
$336$	1268.54	−	921.647i	0.205966	−	0.149643i
$337$	−317.051	−	975.784i	−0.0512489	−	0.157728i	0.922157	−	0.386817i	$-0.126425\pi$
$337$	−317.051	−	975.784i	−0.0512489	−	0.157728i	−0.973406	+	0.229089i	$0.926425\pi$
$338$	−1846.07	+	5681.61i	−0.297079	+	0.914316i
$339$	639.932	+	464.938i	0.102526	+	0.0744896i
$340$	3496.00			0.557639
$341$		0			0
$342$	880.000			0.139137
$343$	5549.86	+	4032.21i	0.873656	+	0.634748i
$344$	598.257	−	1841.25i	0.0937670	−	0.288585i
$345$	−4397.62	−	13534.5i	−0.686261	−	2.11209i
$346$	−6054.68	+	4398.98i	−0.940757	+	0.683500i
$347$	2051.67	−	1490.62i	0.317404	−	0.230608i	−0.417663	−	0.908602i	$-0.637151\pi$
$347$	2051.67	−	1490.62i	0.317404	−	0.230608i	0.735067	+	0.677994i	$0.237151\pi$
$348$	−1038.30	−	3195.55i	−0.159938	−	0.492240i
$349$	2401.06	−	7389.71i	0.368269	−	1.13342i	−0.579639	−	0.814873i	$-0.696807\pi$
$349$	2401.06	−	7389.71i	0.368269	−	1.13342i	0.947909	−	0.318543i	$-0.103193\pi$
$350$	5345.98	+	3884.08i	0.816443	+	0.593180i
$351$	−2520.00			−0.383213
$352$		0			0
$353$	−9597.00			−1.44702			−0.723508	−	0.690316i	$-0.757472\pi$
$353$	−9597.00			−1.44702			−0.723508	+	0.690316i	$0.757472\pi$
$354$	−4926.91	−	3579.61i	−0.739725	−	0.537441i
$355$	6534.78	−	20112.0i	0.976987	−	3.00686i
$356$	1106.28	+	3404.78i	0.164699	+	0.506891i
$357$	−3647.05	+	2649.74i	−0.540679	+	0.392826i
$358$	−428.779	+	311.526i	−0.0633008	+	0.0459907i
$359$	1779.94	+	5478.09i	0.261676	+	0.805355i	0.992441	+	0.122726i	$0.0391635\pi$
$359$	1779.94	+	5478.09i	0.261676	+	0.805355i	−0.730765	+	0.682629i	$0.760837\pi$
$360$	1033.35	−	3180.33i	0.151285	−	0.465606i
$361$	5225.44	+	3796.50i	0.761837	+	0.553507i
$362$	−134.000			−0.0194555
$363$		0			0
$364$	−4032.00			−0.580589
$365$	−1106.74	−	804.090i	−0.158710	−	0.115310i
$366$	−2889.93	+	8894.28i	−0.412729	+	1.27025i
$367$	−584.351	−	1798.45i	−0.0831141	−	0.255799i	0.900860	−	0.434109i	$-0.142937\pi$
$367$	−584.351	−	1798.45i	−0.0831141	−	0.255799i	−0.983974	+	0.178310i	$0.942937\pi$
$368$	1385.04	−	1006.29i	0.196196	−	0.142545i
$369$	4058.03	−	2948.33i	0.572500	−	0.415946i
$370$	−2360.27	−	7264.17i	−0.331634	−	1.02067i
$371$	1981.42	−	6098.17i	0.277278	−	0.853373i
$372$	2650.34	+	1925.58i	0.369392	+	0.268379i
$373$	−11582.0			−1.60776			−0.803878	−	0.594794i	$-0.797234\pi$
$373$	−11582.0			−1.60776			−0.803878	+	0.594794i	$0.797234\pi$
$374$		0			0
$375$	14763.0			2.03295
$376$	−621.325	−	451.419i	−0.0852191	−	0.0619153i
$377$	−2669.91	+	8217.13i	−0.364741	+	1.12256i
$378$	−302.837	−	932.035i	−0.0412070	−	0.126822i
$379$	−1557.36	+	1131.49i	−0.211071	+	0.153352i	−0.688298	−	0.725428i	$-0.741642\pi$
$379$	−1557.36	+	1131.49i	−0.211071	+	0.153352i	0.477227	+	0.878780i	$0.341642\pi$
$380$	−1229.71	+	893.434i	−0.166007	+	0.120611i
$381$	3192.76	+	9826.32i	0.429318	+	1.32131i
$382$	2134.07	−	6568.00i	0.285834	−	0.879707i
$383$	2675.42	+	1943.81i	0.356939	+	0.259331i	0.751774	−	0.659421i	$-0.229198\pi$
$383$	2675.42	+	1943.81i	0.356939	+	0.259331i	−0.394835	+	0.918752i	$0.629198\pi$
$384$	896.000			0.119072
$385$		0			0
$386$	8344.00			1.10025
$387$	4307.21	+	3129.37i	0.565756	+	0.411046i
$388$	505.552	−	1555.93i	0.0661482	−	0.203583i
$389$	−2248.10	−	6918.94i	−0.293016	−	0.901810i	−0.983881	−	0.178826i	$-0.942770\pi$
$389$	−2248.10	−	6918.94i	−0.293016	−	0.901810i	0.690865	−	0.722984i	$-0.257230\pi$
$390$	−15494.3	+	11257.3i	−2.01175	+	1.46162i
$391$	−3981.98	+	2893.08i	−0.515032	+	0.374193i
$392$	363.404	+	1118.44i	0.0468231	+	0.144107i
$393$	−2902.91	+	8934.22i	−0.372601	+	1.14675i
$394$	−3925.35	−	2851.93i	−0.501920	−	0.364666i
$395$	1330.00			0.169417
$396$		0			0
$397$	11374.0			1.43790			0.718948	−	0.695064i	$-0.244624\pi$
$397$	11374.0			1.43790			0.718948	+	0.695064i	$0.244624\pi$
$398$	−647.214	−	470.228i	−0.0815123	−	0.0592221i
$399$	605.673	−	1864.07i	0.0759940	−	0.233885i
$400$	1166.85	+	3591.19i	0.145856	+	0.448899i
$401$	3719.86	−	2702.64i	0.463244	−	0.336567i	−0.331558	−	0.943435i	$-0.607574\pi$
$401$	3719.86	−	2702.64i	0.463244	−	0.336567i	0.794803	+	0.606868i	$0.207574\pi$
$402$	−4972.22	+	3612.53i	−0.616895	+	0.448200i
$403$	−2603.16	−	8011.70i	−0.321768	−	0.990301i
$404$	−1109.99	+	3416.20i	−0.136693	+	0.420698i
$405$	−12896.5	−	9369.88i	−1.58231	−	1.14961i
$406$	−3360.00			−0.410724
$407$		0			0
$408$	−2576.00			−0.312576
$409$	−8065.90	−	5860.22i	−0.975142	−	0.708482i	−0.0185243	−	0.999828i	$-0.505897\pi$
$409$	−8065.90	−	5860.22i	−0.975142	−	0.708482i	−0.956618	+	0.291346i	$0.905897\pi$
$410$	−2677.32	+	8239.95i	−0.322497	+	0.992542i
$411$	−3826.56	−	11776.9i	−0.459246	−	1.41341i
$412$	1009.65	−	733.556i	0.120733	−	0.0877177i
$413$	−4926.91	+	3579.61i	−0.587016	+	0.426492i
$414$	1454.85	+	4477.57i	0.172710	+	0.531548i
$415$	−2101.93	+	6469.09i	−0.248626	+	0.765193i
$416$	−1863.98	−	1354.26i	−0.219685	−	0.159610i
$417$	3850.00			0.452123
$418$		0			0
$419$	−8940.00			−1.04236			−0.521178	−	0.853448i	$-0.674507\pi$
$419$	−8940.00			−1.04236			−0.521178	+	0.853448i	$0.674507\pi$
$420$	−6025.56	−	4377.82i	−0.700041	−	0.508609i
$421$	1687.85	−	5194.67i	0.195394	−	0.601360i	−0.804578	−	0.593847i	$-0.797608\pi$
$421$	1687.85	−	5194.67i	0.195394	−	0.601360i	0.999972	−	0.00751337i	$-0.00239160\pi$
$422$	−2059.29	−	6337.84i	−0.237547	−	0.731093i
$423$	1708.64	−	1241.40i	0.196400	−	0.142693i
$424$	2964.24	−	2153.65i	0.339519	−	0.246675i
$425$	−3354.69	−	10324.7i	−0.382885	−	1.17840i
$426$	−4815.10	+	14819.4i	−0.547635	+	1.68545i
$427$	7565.93	+	5496.97i	0.857473	+	0.622990i
$428$	1096.00			0.123778
$429$		0			0
$430$	−9196.00			−1.03133
$431$	−3189.14	−	2317.05i	−0.356417	−	0.258952i	0.395139	−	0.918621i	$-0.370696\pi$
$431$	−3189.14	−	2317.05i	−0.356417	−	0.258952i	−0.751556	+	0.659669i	$0.770696\pi$
$432$	173.050	−	532.592i	0.0192728	−	0.0593156i
$433$	3947.07	+	12147.8i	0.438070	+	1.34824i	0.889908	+	0.456140i	$0.150769\pi$
$433$	3947.07	+	12147.8i	0.438070	+	1.34824i	−0.451838	+	0.892100i	$0.649231\pi$
$434$	2650.34	−	1925.58i	0.293135	−	0.212975i
$435$	−12911.9	+	9381.05i	−1.42317	+	1.03399i
$436$	−1817.02	−	5592.21i	−0.199586	−	0.614262i
$437$	661.296	−	2035.26i	0.0723892	−	0.222791i
$438$	815.489	+	592.488i	0.0889625	+	0.0646350i
$439$	−4880.00			−0.530546			−0.265273	−	0.964173i	$-0.585462\pi$
$439$	−4880.00			−0.530546			−0.265273	+	0.964173i	$0.585462\pi$
$440$		0			0
$441$	−3234.00			−0.349206
$442$	5358.93	+	3893.49i	0.576693	+	0.418992i
$443$	−4102.82	+	12627.2i	−0.440024	+	1.35426i	0.447825	+	0.894121i	$0.352199\pi$
$443$	−4102.82	+	12627.2i	−0.440024	+	1.35426i	−0.887849	+	0.460134i	$0.847801\pi$
$444$	1739.15	+	5352.55i	0.185893	+	0.572118i
$445$	13757.3	−	9995.29i	1.46553	−	1.06477i
$446$	9761.60	−	7092.22i	1.03638	−	0.752974i
$447$	1708.86	+	5259.34i	0.180820	+	0.556506i
$448$	276.879	−	852.147i	0.0291994	−	0.0898664i
$449$	3952.05	+	2871.33i	0.415387	+	0.301796i	0.775779	−	0.631005i	$-0.217357\pi$
$449$	3952.05	+	2871.33i	0.415387	+	0.301796i	−0.360392	+	0.932801i	$0.617357\pi$
$450$	−10384.0			−1.08779
$451$		0			0
$452$	452.000			0.0470360
$453$	16434.4	+	11940.3i	1.70453	+	1.23842i
$454$	3489.42	−	10739.3i	0.360719	−	1.11018i
$455$	5918.29	+	18214.6i	0.609789	+	1.87674i
$456$	906.099	−	658.319i	0.0930526	−	0.0676067i
$457$	−14468.5	+	10512.0i	−1.48098	+	1.07599i	−0.503735	+	0.863858i	$0.668041\pi$
$457$	−14468.5	+	10512.0i	−1.48098	+	1.07599i	−0.977241	+	0.212134i	$0.931959\pi$
$458$	2870.77	+	8835.32i	0.292887	+	0.901413i
$459$	−497.517	+	1531.20i	−0.0505929	+	0.155709i
$460$	−6578.93	−	4779.87i	−0.666835	−	0.484484i
$461$	4532.00			0.457866			0.228933	−	0.973442i	$-0.426476\pi$
$461$	4532.00			0.457866			0.228933	+	0.973442i	$0.426476\pi$
$462$		0			0
$463$	−1977.00			−0.198443			−0.0992214	−	0.995065i	$-0.531635\pi$
$463$	−1977.00			−0.198443			−0.0992214	+	0.995065i	$0.531635\pi$
$464$	−1553.31	−	1128.55i	−0.155411	−	0.112913i
$465$	4808.61	−	14799.4i	0.479557	−	1.47593i
$466$	1503.06	+	4625.94i	0.149416	+	0.459855i
$467$	−5807.93	+	4219.71i	−0.575501	+	0.418126i	−0.837099	−	0.547051i	$-0.815750\pi$
$467$	−5807.93	+	4219.71i	−0.575501	+	0.418126i	0.261598	+	0.965177i	$0.415750\pi$
$468$	5125.93	−	3724.21i	0.506295	−	0.367845i
$469$	1899.22	+	5845.19i	0.186989	+	0.575492i
$470$	−1127.29	+	3469.45i	−0.110634	+	0.340498i
$471$	4241.68	+	3081.76i	0.414960	+	0.301486i
$472$	−3480.00			−0.339364
$473$		0			0
$474$	−980.000			−0.0949639
$475$	3818.56	+	2774.35i	0.368858	+	0.267991i
$476$	−796.028	+	2449.92i	−0.0766510	+	0.235908i
$477$	3113.66	+	9582.85i	0.298877	+	0.919850i
$478$	−9724.38	+	7065.18i	−0.930508	+	0.676054i
$479$	2912.46	−	2116.03i	0.277816	−	0.201845i	−0.440148	−	0.897925i	$-0.645074\pi$
$479$	2912.46	−	2116.03i	0.277816	−	0.201845i	0.717964	+	0.696080i	$0.245074\pi$
$480$	−1315.18	−	4047.70i	−0.125061	−	0.384898i
$481$	4472.09	−	13763.7i	0.423929	−	1.30472i
$482$	−6032.03	−	4382.53i	−0.570024	−	0.414147i
$483$	10486.0			0.987846
$484$		0			0
$485$	−7771.00			−0.727552
$486$	7973.67	+	5793.21i	0.744224	+	0.540711i
$487$	−2994.68	+	9216.69i	−0.278649	+	0.857593i	0.709582	+	0.704623i	$0.248884\pi$
$487$	−2994.68	+	9216.69i	−0.278649	+	0.857593i	−0.988231	+	0.152970i	$0.951116\pi$
$488$	1651.39	+	5082.45i	0.153186	+	0.471458i
$489$	6954.31	−	5052.60i	0.643118	−	0.467253i
$490$	4519.17	−	3283.37i	0.416643	−	0.302709i
$491$	4348.49	+	13383.3i	0.399683	+	1.23010i	0.925254	+	0.379349i	$0.123852\pi$
$491$	4348.49	+	13383.3i	0.399683	+	1.23010i	−0.525571	+	0.850750i	$0.676148\pi$
$492$	1972.76	−	6071.54i	0.180771	−	0.556354i
$493$	4465.77	+	3244.57i	0.407968	+	0.296406i
$494$	−2880.00			−0.262302
$495$		0			0
$496$	1872.00			0.169466
$497$	12606.1	+	9158.87i	1.13775	+	0.826623i
$498$	1548.79	−	4766.70i	0.139364	−	0.428917i
$499$	1229.89	+	3785.20i	0.110335	+	0.339577i	0.990946	−	0.134264i	$-0.0428670\pi$
$499$	1229.89	+	3785.20i	0.110335	+	0.339577i	−0.880610	+	0.473841i	$0.842867\pi$
$500$	6824.87	−	4958.56i	0.610435	−	0.443507i
$501$	13727.4	−	9973.54i	1.22414	−	0.889391i
$502$	−325.704	−	1002.41i	−0.0289579	−	0.0891233i
$503$	−674.275	+	2075.21i	−0.0597703	+	0.183954i	−0.976484	−	0.215592i	$-0.930832\pi$
$503$	−674.275	+	2075.21i	−0.0597703	+	0.183954i	0.916713	+	0.399545i	$0.130832\pi$
$504$	1993.42	+	1448.30i	0.176178	+	0.128001i
$505$	17062.0			1.50346
$506$		0			0
$507$	−20909.0			−1.83156
$508$	4776.44	+	3470.28i	0.417166	+	0.303089i
$509$	4905.64	−	15098.0i	0.427188	−	1.31475i	−0.473695	−	0.880689i	$-0.657080\pi$
$509$	4905.64	−	15098.0i	0.427188	−	1.31475i	0.900883	−	0.434062i	$-0.142920\pi$
$510$	3781.13	+	11637.1i	0.328297	+	1.01039i
$511$	815.489	−	592.488i	0.0705971	−	0.0512918i
$512$	414.217	−	300.946i	0.0357538	−	0.0259767i
$513$	−216.312	−	665.740i	−0.0186168	−	0.0572965i
$514$	1103.81	−	3397.17i	0.0947216	−	0.291523i
$515$	−4795.85	−	3484.39i	−0.410351	−	0.298137i
$516$	6776.00			0.578095
$517$		0			0
$518$	5628.00			0.477375
$519$	−21191.4	−	15396.4i	−1.79229	−	1.30218i
$520$	−3381.88	+	10408.4i	−0.285203	+	0.877763i
$521$	2112.75	+	6502.37i	0.177661	+	0.546783i	0.999745	−	0.0225824i	$-0.00718881\pi$
$521$	2112.75	+	6502.37i	0.177661	+	0.546783i	−0.822084	+	0.569366i	$0.807189\pi$
$522$	4271.61	−	3103.51i	0.358167	−	0.260224i
$523$	13924.8	−	10117.0i	1.16422	−	0.845858i	0.173918	−	0.984760i	$-0.444357\pi$
$523$	13924.8	−	10117.0i	1.16422	−	0.845858i	0.990306	+	0.138902i	$0.0443574\pi$
$524$	1658.80	+	5105.27i	0.138292	+	0.425620i
$525$	−7146.95	+	21996.0i	−0.594130	+	1.82854i
$526$	5174.47	+	3759.47i	0.428931	+	0.311637i
$527$	−5382.00			−0.444865
$528$		0			0
$529$	−718.000			−0.0590121
$530$	−14080.1	−	10229.8i	−1.15397	−	0.838405i
$531$	2957.29	−	9101.61i	0.241687	−	0.743835i
$532$	−346.099	−	1065.18i	−0.0282054	−	0.0868074i
$533$	−13280.8	+	9649.08i	−1.07928	+	0.784143i
$534$	−10137.0	+	7364.95i	−0.821480	+	0.596840i
$535$	−1608.74	−	4951.20i	−0.130004	−	0.400110i
$536$	−1085.27	+	3340.11i	−0.0874560	+	0.269162i
$537$	−1500.73	−	1090.34i	−0.120598	−	0.0876196i
$538$	3260.00			0.261243
$539$		0			0
$540$	−2660.00			−0.211978
$541$	17821.0	+	12947.7i	1.41624	+	1.02896i	0.992378	+	0.123232i	$0.0393258\pi$
$541$	17821.0	+	12947.7i	1.41624	+	1.02896i	0.423862	+	0.905727i	$0.360674\pi$
$542$	2279.31	−	7014.99i	0.180636	−	0.555940i
$543$	−144.929	−	446.046i	−0.0114540	−	0.0352516i
$544$	−1190.87	+	865.220i	−0.0938571	+	0.0681912i
$545$	−22595.8	+	16416.8i	−1.77596	+	1.29031i
$546$	−4360.85	−	13421.3i	−0.341808	−	1.05198i
$547$	−6086.40	+	18732.0i	−0.475751	+	1.46421i	0.369192	+	0.929353i	$0.379634\pi$
$547$	−6086.40	+	18732.0i	−0.475751	+	1.46421i	−0.844943	+	0.534857i	$0.820366\pi$
$548$	−5724.60	−	4159.17i	−0.446246	−	0.324217i
$549$	−14696.0			−1.14246
$550$		0			0
$551$	−2400.00			−0.185560
$552$	4847.63	+	3522.01i	0.373784	+	0.271570i
$553$	−302.837	+	932.035i	−0.0232874	+	0.0716712i
$554$	−3271.87	−	10069.8i	−0.250918	−	0.772246i
$555$	21627.5	−	15713.3i	1.65412	−	1.20179i
$556$	1779.84	−	1293.13i	0.135759	−	0.0986346i
$557$	−3672.98	−	11304.3i	−0.279406	−	0.859922i	−0.988020	−	0.154326i	$-0.950679\pi$
$557$	−3672.98	−	11304.3i	−0.279406	−	0.859922i	0.708614	−	0.705596i	$-0.249321\pi$
$558$	−1590.82	+	4896.04i	−0.120690	+	0.371444i
$559$	−14096.3	−	10241.6i	−1.06657	−	0.774906i
$560$	−4256.00			−0.321159
$561$		0			0
$562$	−11884.0			−0.891986
$563$	10171.0	+	7389.64i	0.761376	+	0.553172i	0.899332	−	0.437266i	$-0.144053\pi$
$563$	10171.0	+	7389.64i	0.761376	+	0.553172i	−0.137956	+	0.990438i	$0.544053\pi$
$564$	830.638	−	2556.44i	0.0620145	−	0.190861i
$565$	−663.459	−	2041.92i	−0.0494017	−	0.152043i
$566$	−10633.7	+	7725.85i	−0.789697	+	0.573749i
$567$	9502.71	−	6904.13i	0.703839	−	0.511369i
$568$	2751.49	+	8468.21i	0.203257	+	0.625560i
$569$	−3992.50	+	12287.7i	−0.294155	+	0.905317i	0.689349	+	0.724430i	$0.257897\pi$
$569$	−3992.50	+	12287.7i	−0.294155	+	0.905317i	−0.983504	+	0.180887i	$0.942103\pi$
$570$	−4303.97	−	3127.02i	−0.316269	−	0.229783i
$571$	412.000			0.0301956			0.0150978	−	0.999886i	$-0.495194\pi$
$571$	412.000			0.0301956			0.0150978	+	0.999886i	$0.495194\pi$
$572$		0			0
$573$	24171.0			1.76223
$574$	−5164.76	−	3752.42i	−0.375563	−	0.272862i
$575$	−7803.30	+	24016.1i	−0.565948	+	1.74181i
$576$	435.096	+	1339.09i	0.0314740	+	0.0968669i
$577$	−18323.4	+	13312.7i	−1.32204	+	0.960515i	−0.322131	+	0.946695i	$0.604399\pi$
$577$	−18323.4	+	13312.7i	−1.32204	+	0.960515i	−0.999905	+	0.0138194i	$0.995601\pi$
$578$	−4525.64	+	3288.07i	−0.325678	+	0.236619i
$579$	9024.53	+	27774.7i	0.647749	+	1.99357i
$580$	−2818.23	+	8673.64i	−0.201760	+	0.620954i
$581$	−4054.79	−	2945.98i	−0.289537	−	0.210361i
$582$	5726.00			0.407818
$583$		0			0
$584$	576.000			0.0408134
$585$	−24348.2	−	17690.0i	−1.72081	−	1.25024i
$586$	−3503.02	+	10781.2i	−0.246942	+	0.760011i
$587$	−7501.70	−	23087.8i	−0.527476	−	1.62340i	−0.759368	−	0.650661i	$-0.774492\pi$
$587$	−7501.70	−	23087.8i	−0.527476	−	1.62340i	0.231892	−	0.972741i	$-0.425508\pi$
$588$	−3329.91	+	2419.32i	−0.233543	+	0.169679i
$589$	1893.10	−	1375.42i	0.132434	−	0.0962192i
$590$	5108.05	+	15721.0i	0.356432	+	1.09699i
$591$	5247.73	−	16150.8i	0.365250	−	1.12412i
$592$	2601.80	+	1890.32i	0.180631	+	0.131236i
$593$	−14292.0			−0.989717			−0.494858	−	0.868974i	$-0.664780\pi$
$593$	−14292.0			−0.989717			−0.494858	+	0.868974i	$0.664780\pi$
$594$		0			0
$595$	12236.0			0.843071
$596$	2556.49	+	1857.40i	0.175701	+	0.127655i
$597$	865.248	−	2662.96i	0.0593170	−	0.182559i
$598$	−4761.33	−	14653.9i	−0.325594	−	1.00208i
$599$	−14853.6	+	10791.7i	−1.01319	+	0.736124i	−0.964875	−	0.262708i	$-0.915384\pi$
$599$	−14853.6	+	10791.7i	−1.01319	+	0.736124i	−0.0483127	+	0.998832i	$0.515384\pi$
$600$	−10692.0	+	7768.17i	−0.727496	+	0.528557i
$601$	−30.2837	−	93.2035i	−0.00205540	−	0.00632588i	0.950024	−	0.312178i	$-0.101059\pi$
$601$	−30.2837	−	93.2035i	−0.00205540	−	0.00632588i	−0.952079	+	0.305852i	$0.901059\pi$
$602$	2093.90	−	6444.36i	0.141762	−	0.436300i
$603$	−7813.49	−	5676.83i	−0.527678	−	0.383380i
$604$	11608.0			0.781991
$605$		0			0
$606$	−12572.0			−0.842744
$607$	−17842.1	−	12963.0i	−1.19306	−	0.866808i	−0.199475	−	0.979903i	$-0.563924\pi$
$607$	−17842.1	−	12963.0i	−1.19306	−	0.866808i	−0.993584	+	0.113095i	$0.963924\pi$
$608$	197.771	−	608.676i	0.0131919	−	0.0406005i
$609$	−3634.04	−	11184.4i	−0.241804	−	0.744197i
$610$	20536.1	−	14920.3i	1.36309	−	0.990339i
$611$	−5591.93	+	4062.77i	−0.370254	+	0.269005i
$612$	−1250.90	−	3849.88i	−0.0826220	−	0.254284i
$613$	88.9969	−	273.904i	0.00586387	−	0.0180471i	−0.948082	−	0.318027i	$-0.896980\pi$
$613$	88.9969	−	273.904i	0.00586387	−	0.0180471i	0.953946	+	0.299980i	$0.0969799\pi$
$614$	15927.9	+	11572.3i	1.04690	+	0.760620i
$615$	−30324.0			−1.98826
$616$		0			0
$617$	−5086.00			−0.331855			−0.165928	−	0.986138i	$-0.553062\pi$
$617$	−5086.00			−0.331855			−0.165928	+	0.986138i	$0.553062\pi$
$618$	3533.79	+	2567.45i	0.230016	+	0.167116i
$619$	8437.71	−	25968.6i	0.547884	−	1.68621i	−0.166148	−	0.986101i	$-0.553133\pi$
$619$	8437.71	−	25968.6i	0.547884	−	1.68621i	0.714032	−	0.700113i	$-0.246867\pi$
$620$	−2747.78	−	8456.79i	−0.177989	−	0.547795i
$621$	3029.77	−	2201.26i	0.195782	−	0.142244i
$622$	−9818.23	+	7133.36i	−0.632918	+	0.459842i
$623$	3871.98	+	11916.7i	0.249001	+	0.766347i
$624$	2491.91	−	7669.32i	0.159866	−	0.492017i
$625$	−8552.12	−	6213.48i	−0.547336	−	0.397663i
$626$	−7486.00			−0.477956
$627$		0			0
$628$	2996.00			0.190372
$629$	−7480.17	−	5434.66i	−0.474172	−	0.344506i
$630$	3616.73	−	11131.2i	0.228721	−	0.703931i
$631$	345.172	+	1062.33i	0.0217767	+	0.0670217i	0.961354	−	0.275314i	$-0.0887819\pi$
$631$	345.172	+	1062.33i	0.0217767	+	0.0670217i	−0.939578	+	0.342336i	$0.888782\pi$
$632$	−453.050	+	329.160i	−0.0285148	+	0.0207172i
$633$	18869.5	−	13709.5i	1.18483	−	0.860828i
$634$	−4232.91	−	13027.6i	−0.265159	−	0.816074i
$635$	8666.07	−	26671.4i	0.541579	−	1.66681i
$636$	10374.8	+	7537.76i	0.646838	+	0.469955i
$637$	10584.0			0.658326
$638$		0			0
$639$	−24486.0			−1.51589
$640$	−1967.53	−	1429.49i	−0.121521	−	0.0882902i
$641$	3104.69	−	9555.26i	0.191307	−	0.588784i	−0.808692	−	0.588232i	$-0.799824\pi$
$641$	3104.69	−	9555.26i	0.191307	−	0.588784i	1.00000		0.000551907i	$-0.000175677\pi$
$642$	1185.39	+	3648.25i	0.0728716	+	0.224276i
$643$	3719.05	−	2702.05i	0.228095	−	0.165721i	−0.467868	−	0.883798i	$-0.654978\pi$
$643$	3719.05	−	2702.05i	0.228095	−	0.165721i	0.695963	+	0.718078i	$0.254978\pi$
$644$	4847.63	−	3522.01i	0.296620	−	0.215507i
$645$	−9946.02	−	30610.7i	−0.607169	−	1.86867i
$646$	−568.591	+	1749.94i	−0.0346299	+	0.106580i
$647$	−1503.96	−	1092.69i	−0.0913862	−	0.0663960i	0.541154	−	0.840924i	$-0.317988\pi$
$647$	−1503.96	−	1092.69i	−0.0913862	−	0.0663960i	−0.632540	+	0.774528i	$0.717988\pi$
$648$	6712.00			0.406902
$649$		0			0
$650$	33984.0			2.05071
$651$	9276.19	+	6739.55i	0.558468	+	0.405751i
$652$	1517.89	−	4671.59i	0.0911736	−	0.280604i
$653$	−258.647	−	796.034i	−0.0155002	−	0.0477048i	0.943007	−	0.332772i	$-0.107984\pi$
$653$	−258.647	−	796.034i	−0.0155002	−	0.0477048i	−0.958507	+	0.285067i	$0.907984\pi$
$654$	16649.6	−	12096.6i	0.995489	−	0.723265i
$655$	20628.3	−	14987.3i	1.23056	−	0.894052i
$656$	−1127.29	−	3469.45i	−0.0670937	−	0.206493i
$657$	−489.483	+	1506.47i	−0.0290663	+	0.0894568i
$658$	−2174.64	−	1579.97i	−0.128839	−	0.0936072i
$659$	−4770.00			−0.281962			−0.140981	−	0.990012i	$-0.545026\pi$
$659$	−4770.00			−0.281962			−0.140981	+	0.990012i	$0.545026\pi$
$660$		0			0
$661$	−2343.00			−0.137870			−0.0689351	−	0.997621i	$-0.521960\pi$
$661$	−2343.00			−0.137870			−0.0689351	+	0.997621i	$0.521960\pi$
$662$	15560.6	+	11305.5i	0.913567	+	0.663745i
$663$	−7164.25	+	22049.3i	−0.419663	+	1.29159i
$664$	−885.025	−	2723.83i	−0.0517253	−	0.159194i
$665$	−4303.97	+	3127.02i	−0.250979	+	0.182347i
$666$	−7154.95	+	5198.37i	−0.416289	+	0.302452i
$667$	−3967.78	−	12211.6i	−0.230334	−	0.708896i
$668$	2996.23	−	9221.44i	0.173544	−	0.534114i
$669$	34165.6	+	24822.8i	1.97447	+	1.43453i
$670$	16682.0			0.961913
$671$		0			0
$672$	3136.00			0.180021
$673$	15211.1	+	11051.5i	0.871243	+	0.632995i	0.930920	−	0.365223i	$-0.119007\pi$
$673$	15211.1	+	11051.5i	0.871243	+	0.632995i	−0.0596775	+	0.998218i	$0.519007\pi$
$674$	634.103	−	1951.57i	0.0362385	−	0.111531i
$675$	2552.48	+	7855.73i	0.145548	+	0.447951i
$676$	−9666.14	+	7022.86i	−0.549962	+	0.399571i
$677$	−707.081	+	513.724i	−0.0401408	+	0.0291640i	−0.607675	−	0.794186i	$-0.707898\pi$
$677$	−707.081	+	513.724i	−0.0401408	+	0.0291640i	0.567534	+	0.823350i	$0.307898\pi$
$678$	488.865	+	1504.57i	0.0276914	+	0.0852252i
$679$	1769.43	−	5445.75i	0.100007	−	0.307789i
$680$	5656.65	+	4109.79i	0.319004	+	0.231770i
$681$	39522.0			2.22392
$682$		0			0
$683$	30888.0			1.73045			0.865224	−	0.501385i	$-0.167176\pi$
$683$	30888.0			1.73045			0.865224	+	0.501385i	$0.167176\pi$
$684$	1423.87	+	1034.50i	0.0795951	+	0.0578292i
$685$	−10386.4	+	31966.0i	−0.579333	+	1.78300i
$686$	4239.71	+	13048.5i	0.235966	+	0.726230i
$687$	−26305.2	+	19111.8i	−1.46085	+	1.06137i
$688$	3132.51	−	2275.90i	0.173584	−	0.126116i
$689$	−10190.1	−	31362.0i	−0.563445	−	1.73411i
$690$	8795.24	−	27069.0i	0.485260	−	1.49348i
$691$	−3759.50	−	2731.44i	−0.206973	−	0.150375i	0.479470	−	0.877558i	$-0.340829\pi$
$691$	−3759.50	−	2731.44i	−0.206973	−	0.150375i	−0.686443	+	0.727184i	$0.740829\pi$
$692$	−14968.0			−0.822251
$693$		0			0
$694$	5072.00			0.277421
$695$	−8454.23	−	6142.36i	−0.461420	−	0.335241i
$696$	2076.59	−	6391.10i	0.113094	−	0.348066i
$697$	3240.97	+	9974.68i	0.176127	+	0.542063i
$698$	12572.1	−	9134.18i	0.681751	−	0.495321i
$699$	−13772.7	+	10006.5i	−0.745253	+	0.541458i
$700$	4083.97	+	12569.2i	0.220514	+	0.678671i
$701$	−2378.81	+	7321.23i	−0.128169	+	0.394464i	−0.994465	−	0.105067i	$-0.966494\pi$
$701$	−2378.81	+	7321.23i	−0.128169	+	0.394464i	0.866296	+	0.499531i	$0.166494\pi$
$702$	−4077.45	−	2962.44i	−0.219221	−	0.159274i
$703$	4020.00			0.215672
$704$		0			0
$705$	−12768.0			−0.682086
$706$	−15528.3	−	11282.0i	−0.827782	−	0.601419i
$707$	−3884.96	+	11956.7i	−0.206661	+	0.636036i
$708$	−3763.83	−	11583.9i	−0.199793	−	0.614899i
$709$	14792.9	−	10747.7i	0.783580	−	0.569304i	−0.122471	−	0.992472i	$-0.539082\pi$
$709$	14792.9	−	10747.7i	0.783580	−	0.569304i	0.906051	+	0.423168i	$0.139082\pi$
$710$	34216.6	−	24859.8i	1.80863	−	1.31404i
$711$	−475.886	−	1464.63i	−0.0251014	−	0.0772543i
$712$	−2212.56	+	6809.56i	−0.116460	+	0.358426i
$713$	10128.1	+	7358.48i	0.531977	+	0.386504i
$714$	−9016.00			−0.472570
$715$		0			0
$716$	−1060.00			−0.0553269
$717$	−34035.3	−	24728.1i	−1.77277	−	1.28799i
$718$	−3559.88	+	10956.2i	−0.185033	+	0.569472i
$719$	5984.11	+	18417.2i	0.310389	+	0.955280i	0.977611	+	0.210421i	$0.0674833\pi$
$719$	5984.11	+	18417.2i	0.310389	+	0.955280i	−0.667222	+	0.744859i	$0.732517\pi$
$720$	5410.71	−	3931.11i	0.280063	−	0.203477i
$721$	3533.79	−	2567.45i	0.182531	−	0.132617i
$722$	3991.88	+	12285.7i	0.205765	+	0.633280i
$723$	8064.11	−	24818.8i	0.414810	−	1.27665i
$724$	−216.817	−	157.526i	−0.0111297	−	0.00808622i
$725$	28320.0			1.45073
$726$		0			0
$727$	9.00000			0.000459136			0.000229568	−	1.00000i	$-0.499927\pi$
$727$	9.00000			0.000459136			0.000229568		1.00000i	$0.499927\pi$
$728$	−6523.91	−	4739.90i	−0.332132	−	0.241308i
$729$	−3659.69	+	11263.4i	−0.185931	+	0.572238i
$730$	−845.470	−	2602.09i	−0.0428661	−	0.131928i
$731$	−9005.98	+	6543.23i	−0.455675	+	0.331067i
$732$	−15131.9	+	10993.9i	−0.764057	+	0.555120i
$733$	7956.57	+	24487.8i	0.400931	+	1.23394i	0.924245	+	0.381800i	$0.124696\pi$
$733$	7956.57	+	24487.8i	0.400931	+	1.23394i	−0.523314	+	0.852140i	$0.675304\pi$
$734$	1168.70	−	3596.90i	0.0587706	−	0.180877i
$735$	15817.1	+	11491.8i	0.793772	+	0.576709i
$736$	3424.00			0.171481
$737$		0			0
$738$	10032.0			0.500384
$739$	18356.6	+	13336.8i	0.913746	+	0.663875i	0.941959	−	0.335727i	$-0.108982\pi$
$739$	18356.6	+	13336.8i	0.913746	+	0.663875i	−0.0282135	+	0.999602i	$0.508982\pi$
$740$	4720.54	−	14528.3i	0.234501	−	0.721719i
$741$	−3114.89	−	9586.65i	−0.154424	−	0.475269i
$742$	10374.8	−	7537.76i	0.513305	−	0.372938i
$743$	−2935.11	+	2132.48i	−0.144924	+	0.105294i	−0.657885	−	0.753118i	$-0.728549\pi$
$743$	−2935.11	+	2132.48i	−0.144924	+	0.105294i	0.512961	+	0.858412i	$0.328549\pi$
$744$	2024.68	+	6231.32i	0.0997693	+	0.307058i
$745$	4638.35	−	14275.4i	0.228102	−	0.702025i
$746$	−18740.1	−	13615.5i	−0.919736	−	0.668227i
$747$	7876.00			0.385767
$748$		0			0
$749$	3836.00			0.187135
$750$	23887.0	+	17354.9i	1.16297	+	0.844951i
$751$	−10312.8	+	31739.6i	−0.501092	+	1.54220i	0.306150	+	0.951983i	$0.400959\pi$
$751$	−10312.8	+	31739.6i	−0.501092	+	1.54220i	−0.807242	+	0.590220i	$0.799041\pi$
$752$	−474.650	−	1460.82i	−0.0230169	−	0.0708387i
$753$	2984.46	−	2168.34i	0.144435	−	0.104939i
$754$	−13979.8	+	10156.9i	−0.675219	+	0.490575i
$755$	−17038.6	−	52439.4i	−0.821321	−	2.52777i
$756$	605.673	−	1864.07i	0.0291377	−	0.0896767i
$757$	−9670.99	−	7026.38i	−0.464330	−	0.337356i	0.330897	−	0.943667i	$-0.392649\pi$
$757$	−9670.99	−	7026.38i	−0.464330	−	0.337356i	−0.795228	+	0.606311i	$0.792649\pi$
$758$	−3850.00			−0.184483
$759$		0			0
$760$	−3040.00			−0.145095
$761$	10814.9	+	7857.51i	0.515166	+	0.374290i	0.814780	−	0.579771i	$-0.196858\pi$
$761$	10814.9	+	7857.51i	0.515166	+	0.374290i	−0.299614	+	0.954061i	$0.596858\pi$
$762$	−6385.53	+	19652.6i	−0.303574	+	0.934304i
$763$	−6359.57	−	19572.7i	−0.301746	−	0.928677i
$764$	11174.1	−	8118.49i	0.529144	−	0.384446i
$765$	−15555.8	+	11301.9i	−0.735190	+	0.534147i
$766$	2043.84	+	6290.29i	0.0964059	+	0.296707i
$767$	−9678.41	+	29787.1i	−0.455629	+	1.40228i
$768$	1449.76	+	1053.31i	0.0681167	+	0.0494897i
$769$	−37640.0			−1.76506			−0.882531	−	0.470254i	$-0.844162\pi$
$769$	−37640.0			−1.76506			−0.882531	+	0.470254i	$0.844162\pi$
$770$		0			0
$771$	12502.0			0.583980
$772$	13500.9	+	9808.96i	0.629413	+	0.457296i
$773$	−5482.58	+	16873.6i	−0.255103	+	0.785127i	0.738706	+	0.674027i	$0.235437\pi$
$773$	−5482.58	+	16873.6i	−0.255103	+	0.785127i	−0.993809	+	0.111099i	$0.964563\pi$
$774$	3290.41	+	10126.8i	0.152805	+	0.470287i
$775$	−22338.6	+	16229.9i	−1.03539	+	0.752253i
$776$	2647.10	−	1923.23i	0.122456	−	0.0889691i
$777$	6087.02	+	18733.9i	0.281043	+	0.864962i
$778$	4496.20	−	13837.9i	0.207193	−	0.637676i
$779$	−3689.12	−	2680.30i	−0.169674	−	0.123276i
$780$	−38304.0			−1.75834
$781$		0			0
$782$	−9844.00			−0.450154
$783$	−3397.87	−	2468.70i	−0.155083	−	0.112674i
$784$	−726.808	+	2236.88i	−0.0331090	+	0.101899i
$785$	−4397.62	−	13534.5i	−0.199946	−	0.615371i
$786$	−15199.8	+	11043.3i	−0.689770	+	0.501147i
$787$	−18400.3	+	13368.6i	−0.833417	+	0.605513i	−0.920524	−	0.390686i	$-0.872238\pi$
$787$	−18400.3	+	13368.6i	−0.833417	+	0.605513i	0.0871069	+	0.996199i	$0.472238\pi$
$788$	−2998.70	−	9229.05i	−0.135564	−	0.417223i
$789$	−6917.65	+	21290.4i	−0.312136	+	0.960655i
$790$	2151.99	+	1563.51i	0.0969167	+	0.0704141i
$791$	1582.00			0.0711118
$792$		0			0
$793$	48096.0			2.15377
$794$	18403.5	+	13370.9i	0.822565	+	0.597628i
$795$	18823.5	−	57932.7i	0.839748	−	2.58448i
$796$	−494.427	−	1521.69i	−0.0220157	−	0.0677574i
$797$	25331.1	−	18404.1i	1.12582	−	0.817953i	0.140735	−	0.990047i	$-0.455054\pi$
$797$	25331.1	−	18404.1i	1.12582	−	0.817953i	0.985080	+	0.172095i	$0.0550535\pi$
$798$	3171.35	−	2304.12i	0.140682	−	0.102212i
$799$	1364.62	+	4199.87i	0.0604215	+	0.185958i
$800$	−2333.70	+	7182.38i	−0.103136	+	0.317419i
$801$	−15929.5	−	11573.5i	−0.702675	−	0.510523i
$802$	9196.00			0.404890
$803$		0			0
$804$	−12292.0			−0.539186
$805$	−23026.2	−	16729.5i	−1.00816	−	0.732471i
$806$	5206.32	−	16023.4i	0.227524	−	0.700248i
$807$	3525.88	+	10851.6i	0.153800	+	0.473349i
$808$	−5811.98	+	4222.65i	−0.253050	+	0.183852i
$809$	−3187.53	+	2315.87i	−0.138526	+	0.100645i	−0.654890	−	0.755724i	$-0.727285\pi$
$809$	−3187.53	+	2315.87i	−0.138526	+	0.100645i	0.516364	+	0.856369i	$0.327285\pi$
$810$	−9852.08	−	30321.6i	−0.427366	−	1.31530i
$811$	−6062.30	+	18657.8i	−0.262486	+	0.807848i	0.729776	+	0.683686i	$0.239624\pi$
$811$	−6062.30	+	18657.8i	−0.262486	+	0.807848i	−0.992262	+	0.124162i	$0.960376\pi$
$812$	−5436.59	−	3949.92i	−0.234959	−	0.170708i
$813$	25816.0			1.11366
$814$		0			0
$815$	−23332.0			−1.00280
$816$	−4168.06	−	3028.27i	−0.178813	−	0.129915i
$817$	1495.64	−	4603.11i	0.0640464	−	0.197115i
$818$	−6161.80	−	18964.1i	−0.263377	−	0.810591i
$819$	17940.8	−	13034.7i	0.765447	−	0.556130i
$820$	−14018.6	+	10185.1i	−0.597015	+	0.433757i
$821$	9907.70	+	30492.8i	0.421171	+	1.29623i	0.906614	+	0.421962i	$0.138658\pi$
$821$	9907.70	+	30492.8i	0.421171	+	1.29623i	−0.485443	+	0.874268i	$0.661342\pi$
$822$	7653.11	−	23553.9i	0.324736	−	0.999435i
$823$	345.450	+	250.984i	0.0146314	+	0.0106303i	0.595077	−	0.803669i	$-0.297122\pi$
$823$	345.450	+	250.984i	0.0146314	+	0.0106303i	−0.580446	+	0.814299i	$0.697122\pi$
$824$	2496.00			0.105525
$825$		0			0
$826$	−12180.0			−0.513071
$827$	2634.16	+	1913.83i	0.110760	+	0.0804720i	0.641787	−	0.766883i	$-0.278193\pi$
$827$	2634.16	+	1913.83i	0.110760	+	0.0804720i	−0.531026	+	0.847355i	$0.678193\pi$
$828$	−2909.70	+	8955.15i	−0.122125	+	0.375861i
$829$	−2829.05	−	8706.92i	−0.118525	−	0.364782i	0.874141	−	0.485672i	$-0.161425\pi$
$829$	−2829.05	−	8706.92i	−0.118525	−	0.364782i	−0.992666	+	0.120890i	$0.961425\pi$
$830$	−11005.9	+	7996.23i	−0.460264	+	0.334401i
$831$	29980.6	−	21782.1i	1.25152	−	0.909283i
$832$	−1423.95	−	4382.47i	−0.0593348	−	0.182614i
$833$	2089.57	−	6431.04i	0.0869141	−	0.267494i
$834$	6229.43	+	4525.95i	0.258642	+	0.187915i
$835$	−46056.0			−1.90878
$836$		0			0
$837$	4095.00			0.169109
$838$	−14465.2	−	10509.6i	−0.596292	−	0.433232i
$839$	9043.38	−	27832.7i	0.372124	−	1.14528i	−0.573274	−	0.819364i	$-0.694327\pi$
$839$	9043.38	−	27832.7i	0.372124	−	1.14528i	0.945398	−	0.325917i	$-0.105673\pi$
$840$	−4603.12	−	14166.9i	−0.189075	−	0.581912i
$841$	8081.27	−	5871.39i	0.331349	−	0.240739i
$842$	8837.70	−	6420.97i	0.361719	−	0.262804i
$843$	−12853.3	−	39558.2i	−0.525136	−	1.61620i
$844$	4118.58	−	12675.7i	0.167971	−	0.516961i
$845$	45914.1	+	33358.6i	1.86922	+	1.35807i
$846$	4224.00			0.171660
$847$		0			0
$848$	7328.00			0.296751
$849$	−37218.0	−	27040.5i	−1.50450	−	1.09308i
$850$	6709.38	−	20649.3i	0.270741	−	0.833255i
$851$	6646.03	+	20454.4i	0.267712	+	0.823933i
$852$	−25212.2	+	18317.7i	−1.01380	+	0.736567i
$853$	−16664.1	+	12107.2i	−0.668897	+	0.485982i	−0.869656	−	0.493659i	$-0.835659\pi$
$853$	−16664.1	+	12107.2i	−0.668897	+	0.485982i	0.200759	+	0.979641i	$0.435659\pi$
$854$	5779.85	+	17788.6i	0.231595	+	0.712778i
$855$	2583.38	−	7950.83i	0.103333	−	0.318027i
$856$	1773.37	+	1288.43i	0.0708089	+	0.0514456i
$857$	9944.00			0.396360			0.198180	−	0.980166i	$-0.436497\pi$
$857$	9944.00			0.396360			0.198180	+	0.980166i	$0.436497\pi$
$858$		0			0
$859$	−31745.0			−1.26091			−0.630457	−	0.776224i	$-0.717133\pi$
$859$	−31745.0			−1.26091			−0.630457	+	0.776224i	$0.717133\pi$
$860$	−14879.4	−	10810.5i	−0.589982	−	0.428647i
$861$	6904.68	−	21250.4i	0.273299	−	0.841129i
$862$	−2436.29	−	7498.13i	−0.0962649	−	0.296273i
$863$	−23112.0	+	16791.8i	−0.911636	+	0.662342i	−0.941428	−	0.337214i	$-0.890515\pi$
$863$	−23112.0	+	16791.8i	−0.911636	+	0.662342i	0.0297924	+	0.999556i	$0.490515\pi$
$864$	906.099	−	658.319i	0.0356784	−	0.0259219i
$865$	21970.5	+	67618.2i	0.863606	+	2.65791i
$866$	−7894.15	+	24295.7i	−0.309762	+	0.953350i
$867$	−15839.7	−	11508.2i	−0.620468	−	0.450797i
$868$	6552.00			0.256209
$869$		0			0
$870$	−31920.0			−1.24390
$871$	25571.4	+	18578.7i	0.994781	+	0.722751i
$872$	3634.04	−	11184.4i	0.141129	−	0.434349i
$873$	2780.53	+	8557.61i	0.107797	+	0.331765i
$874$	3462.59	−	2515.72i	0.134009	−	0.0973633i
$875$	23887.0	−	17354.9i	0.922891	−	0.670519i
$876$	622.978	+	1917.33i	0.0240280	+	0.0739504i
$877$	−10486.8	+	32275.1i	−0.403779	+	1.24270i	0.518132	+	0.855301i	$0.326628\pi$
$877$	−10486.8	+	32275.1i	−0.403779	+	1.24270i	−0.921911	+	0.387403i	$0.873372\pi$
$878$	−7896.01	−	5736.78i	−0.303505	−	0.220509i
$879$	−39676.0			−1.52246
$880$		0			0
$881$	7117.00			0.272166			0.136083	−	0.990697i	$-0.456549\pi$
$881$	7117.00			0.272166			0.136083	+	0.990697i	$0.456549\pi$
$882$	−5232.72	−	3801.80i	−0.199767	−	0.145140i
$883$	−1289.22	+	3967.81i	−0.0491344	+	0.151220i	−0.972613	−	0.232429i	$-0.925333\pi$
$883$	−1289.22	+	3967.81i	−0.0491344	+	0.151220i	0.923479	+	0.383649i	$0.125333\pi$
$884$	4093.86	+	12599.6i	0.155759	+	0.479378i
$885$	−46805.7	+	34006.3i	−1.77780	+	1.29165i
$886$	−21482.6	+	15608.0i	−0.814586	+	0.591831i
$887$	2834.92	+	8724.99i	0.107314	+	0.330278i	0.990267	−	0.139184i	$-0.0444479\pi$
$887$	2834.92	+	8724.99i	0.107314	+	0.330278i	−0.882953	+	0.469462i	$0.844448\pi$
$888$	−3478.30	+	10705.1i	−0.131446	+	0.404549i
$889$	16717.5	+	12146.0i	0.630695	+	0.458227i
$890$	34010.0			1.28092
$891$		0			0
$892$	24132.0			0.905829
$893$	−1553.31	−	1128.55i	−0.0582079	−	0.0422905i
$894$	−3417.73	+	10518.7i	−0.127859	+	0.393509i
$895$	1555.90	+	4788.57i	0.0581095	+	0.178843i
$896$	1449.76	−	1053.31i	0.0540547	−	0.0392731i
$897$	43628.7	−	31698.1i	1.62399	−	1.17990i
$898$	3019.10	+	9291.82i	0.112192	+	0.345292i
$899$	4338.60	−	13352.8i	0.160957	−	0.495375i
$900$	−16801.7	−	12207.1i	−0.622284	−	0.452116i
$901$	−21068.0			−0.778998
$902$		0			0
$903$	23716.0			0.873997
$904$	731.351	+	531.358i	0.0269075	+	0.0195494i
$905$	−393.379	+	1210.69i	−0.0144490	+	0.0444695i
$906$	12554.7	+	38639.5i	0.460379	+	1.41690i
$907$	30189.3	−	21933.8i	1.10520	−	0.802977i	0.123301	−	0.992369i	$-0.460652\pi$
$907$	30189.3	−	21933.8i	1.10520	−	0.802977i	0.981901	+	0.189393i	$0.0606520\pi$
$908$	18270.8	−	13274.5i	0.667774	−	0.485166i
$909$	−6104.94	−	18789.1i	−0.222759	−	0.685582i
$910$	−11836.6	+	36429.3i	−0.431186	+	1.32705i
$911$	−27775.2	−	20179.8i	−1.01013	−	0.733906i	−0.0458972	−	0.998946i	$-0.514615\pi$
$911$	−27775.2	−	20179.8i	−1.01013	−	0.733906i	−0.964237	+	0.265041i	$0.914615\pi$
$912$	2240.00			0.0813309
$913$		0			0
$914$	−35768.0			−1.29442
$915$	71876.3	+	52221.2i	2.59689	+	1.88675i
$916$	−5741.54	+	17670.6i	−0.207102	+	0.637395i
$917$	5805.81	+	17868.4i	0.209078	+	0.643477i
$918$	−2605.03	+	1892.67i	−0.0936590	+	0.0680472i
$919$	−30475.7	+	22141.9i	−1.09391	+	0.794769i	−0.980055	−	0.198729i	$-0.936319\pi$
$919$	−30475.7	+	22141.9i	−1.09391	+	0.794769i	−0.113851	+	0.993498i	$0.536319\pi$
$920$	−5025.85	−	15468.0i	−0.180106	−	0.554309i
$921$	−21293.7	+	65535.4i	−0.761838	+	2.34470i
$922$	7332.93	+	5327.69i	0.261928	+	0.190301i
$923$	80136.0			2.85776
$924$		0			0
$925$	−47436.0			−1.68615
$926$	−3198.85	−	2324.10i	−0.113521	−	0.0824781i
$927$	−2121.09	+	6528.05i	−0.0751519	+	0.231294i
$928$	−1186.63	−	3652.06i	−0.0419751	−	0.129186i
$929$	28275.1	−	20543.1i	0.998576	−	0.725508i	0.0367938	−	0.999323i	$-0.488286\pi$
$929$	28275.1	−	20543.1i	0.998576	−	0.725508i	0.961782	+	0.273815i	$0.0882855\pi$
$930$	25178.2	−	18293.1i	0.887771	−	0.645003i
$931$	908.510	+	2796.11i	0.0319820	+	0.0984304i
$932$	−3006.12	+	9251.88i	−0.105653	+	0.325167i
$933$	−34363.8	−	24966.8i	−1.20581	−	0.876072i
$934$	−14358.0			−0.503007
$935$		0			0
$936$	12672.0			0.442518
$937$	−13886.0	−	10088.7i	−0.484135	−	0.351745i	0.318789	−	0.947826i	$-0.396724\pi$
$937$	−13886.0	−	10088.7i	−0.484135	−	0.351745i	−0.802924	+	0.596081i	$0.796724\pi$
$938$	−3798.44	+	11690.4i	−0.132221	+	0.406935i
$939$	−8096.55	−	24918.6i	−0.281386	−	0.866016i
$940$	−5902.59	+	4288.48i	−0.204810	+	0.148803i
$941$	−5276.41	+	3833.54i	−0.182791	+	0.132805i	−0.675418	−	0.737435i	$-0.736037\pi$
$941$	−5276.41	+	3833.54i	−0.182791	+	0.132805i	0.492627	+	0.870241i	$0.336037\pi$
$942$	3240.35	+	9972.78i	0.112077	+	0.344937i
$943$	7538.78	−	23202.0i	0.260336	−	0.801230i
$944$	−5630.76	−	4090.99i	−0.194137	−	0.141049i
$945$	−9310.00			−0.320481
$946$		0			0
$947$	−53901.0			−1.84957			−0.924787	−	0.380484i	$-0.875757\pi$
$947$	−53901.0			−1.84957			−0.924787	+	0.380484i	$0.875757\pi$
$948$	−1585.67	−	1152.06i	−0.0543252	−	0.0394696i
$949$	1601.94	−	4930.28i	0.0547959	−	0.168644i
$950$	2917.12	+	8977.97i	0.0996251	+	0.306615i
$951$	38786.7	−	28180.2i	1.32255	−	0.960889i
$952$	−4168.06	+	3028.27i	−0.141899	+	0.103095i
$953$	−4685.32	−	14419.9i	−0.159257	−	0.490144i	0.839310	−	0.543653i	$-0.182959\pi$
$953$	−4685.32	−	14419.9i	−0.159257	−	0.490144i	−0.998567	+	0.0535094i	$0.982959\pi$
$954$	−6227.31	+	19165.7i	−0.211338	+	0.650432i
$955$	−53077.2	−	38562.8i	−1.79847	−	1.30666i
$956$	−24040.0			−0.813294
$957$		0			0
$958$	7200.00			0.242820
$959$	−20036.1	−	14557.1i	−0.674661	−	0.490170i
$960$	2630.35	−	8095.39i	0.0884315	−	0.272164i
$961$	−4975.79	−	15313.9i	−0.167023	−	0.514045i
$962$	23416.2	−	17012.9i	0.784790	−	0.570183i
$963$	−4876.75	+	3543.17i	−0.163189	+	0.118564i
$964$	−4608.06	−	14182.2i	−0.153958	−	0.473834i
$965$	24495.2	−	75388.3i	0.817126	−	2.51486i
$966$	16966.7	+	12327.0i	0.565108	+	0.410575i
$967$	1864.00			0.0619878			0.0309939	−	0.999520i	$-0.490133\pi$
$967$	1864.00			0.0619878			0.0309939	+	0.999520i	$0.490133\pi$
$968$		0			0
$969$	−6440.00			−0.213501
$970$	−12573.7	−	9135.36i	−0.416205	−	0.302390i
$971$	17594.5	−	54150.3i	0.581498	−	1.78967i	−0.0314034	−	0.999507i	$-0.509998\pi$
$971$	17594.5	−	54150.3i	0.581498	−	1.78967i	0.612901	−	0.790160i	$-0.290002\pi$
$972$	6091.34	+	18747.2i	0.201008	+	0.618639i
$973$	6229.43	−	4525.95i	0.205248	−	0.149121i
$974$	−15680.4	+	11392.5i	−0.515843	+	0.374782i
$975$	36755.7	+	113122.i	1.20731	+	3.71571i
$976$	−3302.77	+	10164.9i	−0.108319	+	0.333371i
$977$	−9925.83	−	7211.54i	−0.325031	−	0.236149i	0.413288	−	0.910600i	$-0.364380\pi$
$977$	−9925.83	−	7211.54i	−0.325031	−	0.236149i	−0.738319	+	0.674451i	$0.764380\pi$
$978$	17192.0			0.562106
$979$		0			0
$980$	11172.0			0.364160
$981$	26163.6	+	19009.0i	0.851519	+	0.618664i
$982$	−8696.97	+	26766.5i	−0.282619	+	0.869811i
$983$	−2974.91	−	9155.82i	−0.0965257	−	0.297076i	0.891123	−	0.453763i	$-0.149919\pi$
$983$	−2974.91	−	9155.82i	−0.0965257	−	0.297076i	−0.987648	+	0.156687i	$0.949919\pi$
$984$	10329.5	−	7504.84i	0.334648	−	0.243136i
$985$	−37290.8	+	27093.4i	−1.20628	+	0.876413i
$986$	3411.55	+	10499.7i	0.110188	+	0.339125i
$987$	2907.23	−	8947.54i	0.0937571	−	0.288555i
$988$	−4659.94	−	3385.64i	−0.150053	−	0.109020i
$989$	25894.0			0.832539
$990$		0			0
$991$	−26728.0			−0.856754			−0.428377	−	0.903600i	$-0.640914\pi$
$991$	−26728.0			−0.856754			−0.428377	+	0.903600i	$0.640914\pi$
$992$	3028.96	+	2200.67i	0.0969451	+	0.0704348i
$993$	−20802.7	+	64024.2i	−0.664808	+	2.04607i
$994$	9630.21	+	29638.7i	0.307295	+	0.945758i
$995$	−6148.53	+	4467.17i	−0.195901	+	0.142330i
$996$	8109.59	−	5891.96i	0.257994	−	0.187444i
$997$	−4698.91	−	14461.8i	−0.149264	−	0.459387i	0.848271	−	0.529563i	$-0.177644\pi$
$997$	−4698.91	−	14461.8i	−0.149264	−	0.459387i	−0.997535	+	0.0701758i	$0.977644\pi$
$998$	−2459.78	+	7570.41i	−0.0780189	+	0.240117i
$999$	5691.43	+	4135.07i	0.180249	+	0.130959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.l.81.1		4
11.2	odd	10		242.4.c.e.27.1		4
11.3	even	5	inner	242.4.c.l.3.1		4
11.4	even	5	inner	242.4.c.l.9.1		4
11.5	even	5		22.4.a.a.1.1	✓	1
11.6	odd	10		242.4.a.d.1.1		1
11.7	odd	10		242.4.c.e.9.1		4
11.8	odd	10		242.4.c.e.3.1		4
11.9	even	5	inner	242.4.c.l.27.1		4
11.10	odd	2		242.4.c.e.81.1		4
33.5	odd	10		198.4.a.g.1.1		1
33.17	even	10		2178.4.a.l.1.1		1
44.27	odd	10		176.4.a.f.1.1		1
44.39	even	10		1936.4.a.n.1.1		1
55.27	odd	20		550.4.b.k.199.1		2
55.38	odd	20		550.4.b.k.199.2		2
55.49	even	10		550.4.a.n.1.1		1
77.27	odd	10		1078.4.a.d.1.1		1
88.5	even	10		704.4.a.l.1.1		1
88.27	odd	10		704.4.a.b.1.1		1
132.71	even	10		1584.4.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.a.a.1.1	✓	1	11.5	even	5
176.4.a.f.1.1		1	44.27	odd	10
198.4.a.g.1.1		1	33.5	odd	10
242.4.a.d.1.1		1	11.6	odd	10
242.4.c.e.3.1		4	11.8	odd	10
242.4.c.e.9.1		4	11.7	odd	10
242.4.c.e.27.1		4	11.2	odd	10
242.4.c.e.81.1		4	11.10	odd	2
242.4.c.l.3.1		4	11.3	even	5	inner
242.4.c.l.9.1		4	11.4	even	5	inner
242.4.c.l.27.1		4	11.9	even	5	inner
242.4.c.l.81.1		4	1.1	even	1	trivial
550.4.a.n.1.1		1	55.49	even	10
550.4.b.k.199.1		2	55.27	odd	20
550.4.b.k.199.2		2	55.38	odd	20
704.4.a.b.1.1		1	88.27	odd	10
704.4.a.l.1.1		1	88.5	even	10
1078.4.a.d.1.1		1	77.27	odd	10
1584.4.a.v.1.1		1	132.71	even	10
1936.4.a.n.1.1		1	44.39	even	10
2178.4.a.l.1.1		1	33.17	even	10

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 + 1.17557i) q^{2} +(-2.16312 + 6.65740i) q^{3} +(1.23607 + 3.80423i) q^{4} +(15.3713 - 11.1679i) q^{5} +(-11.3262 + 8.22899i) q^{6} +(4.32624 + 13.3148i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-17.7984 - 12.9313i) q^{9} +O(q^{10})\)	\(q+(1.61803 + 1.17557i) q^{2} +(-2.16312 + 6.65740i) q^{3} +(1.23607 + 3.80423i) q^{4} +(15.3713 - 11.1679i) q^{5} +(-11.3262 + 8.22899i) q^{6} +(4.32624 + 13.3148i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-17.7984 - 12.9313i) q^{9} +38.0000 q^{10} -28.0000 q^{12} +(58.2492 + 42.3205i) q^{13} +(-8.65248 + 26.6296i) q^{14} +(41.0993 + 126.491i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(37.2148 - 27.0381i) q^{17} +(-13.5967 - 41.8465i) q^{18} +(-6.18034 + 19.0211i) q^{19} +(61.4853 + 44.6717i) q^{20} -98.0000 q^{21} -107.000 q^{23} +(-45.3050 - 32.9160i) q^{24} +(72.9280 - 224.449i) q^{25} +(44.4984 + 136.952i) q^{26} +(-28.3156 + 20.5725i) q^{27} +(-45.3050 + 32.9160i) q^{28} +(37.0820 + 114.127i) q^{29} +(-82.1985 + 252.981i) q^{30} +(-94.6550 - 68.7709i) q^{31} -32.0000 q^{32} +92.0000 q^{34} +(215.199 + 156.351i) q^{35} +(27.1935 - 83.6930i) q^{36} +(-62.1124 - 191.162i) q^{37} +(-32.3607 + 23.5114i) q^{38} +(-407.745 + 296.244i) q^{39} +(46.9706 + 144.561i) q^{40} +(-70.4559 + 216.841i) q^{41} +(-158.567 - 115.206i) q^{42} -242.000 q^{43} -418.000 q^{45} +(-173.130 - 125.786i) q^{46} +(-29.6656 + 91.3014i) q^{47} +(-34.6099 - 106.518i) q^{48} +(118.925 - 86.4044i) q^{49} +(381.856 - 277.435i) q^{50} +(99.5035 + 306.240i) q^{51} +(-88.9969 + 273.904i) q^{52} +(-370.530 - 269.206i) q^{53} -70.0000 q^{54} -112.000 q^{56} +(-113.262 - 82.2899i) q^{57} +(-74.1641 + 228.254i) q^{58} +(134.422 + 413.710i) q^{59} +(-430.397 + 312.702i) q^{60} +(540.423 - 392.641i) q^{61} +(-72.3100 - 222.547i) q^{62} +(95.1772 - 292.925i) q^{63} +(-51.7771 - 37.6183i) q^{64} +1368.00 q^{65} +439.000 q^{67} +(148.859 + 108.152i) q^{68} +(231.454 - 712.341i) q^{69} +(164.397 + 505.962i) q^{70} +(900.436 - 654.205i) q^{71} +(142.387 - 103.450i) q^{72} +(-22.2492 - 68.4761i) q^{73} +(124.225 - 382.325i) q^{74} +(1336.50 + 971.021i) q^{75} -80.0000 q^{76} -1008.00 q^{78} +(56.6312 + 41.1450i) q^{79} +(-93.9412 + 289.121i) q^{80} +(-259.265 - 797.936i) q^{81} +(-368.912 + 268.030i) q^{82} +(-289.628 + 210.427i) q^{83} +(-121.135 - 372.814i) q^{84} +(270.081 - 831.223i) q^{85} +(-391.564 - 284.488i) q^{86} -840.000 q^{87} +895.000 q^{89} +(-676.338 - 491.388i) q^{90} +(-311.489 + 958.665i) q^{91} +(-132.259 - 407.052i) q^{92} +(662.585 - 481.396i) q^{93} +(-155.331 + 112.855i) q^{94} +(117.426 + 361.401i) q^{95} +(69.2198 - 213.037i) q^{96} +(-330.888 - 240.404i) q^{97} +294.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 7 q^{3} - 4 q^{4} + 19 q^{5} - 14 q^{6} - 14 q^{7} + 8 q^{8} - 22 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 7 * q^3 - 4 * q^4 + 19 * q^5 - 14 * q^6 - 14 * q^7 + 8 * q^8 - 22 * q^9	\( 4 q + 2 q^{2} + 7 q^{3} - 4 q^{4} + 19 q^{5} - 14 q^{6} - 14 q^{7} + 8 q^{8} - 22 q^{9} + 152 q^{10} - 112 q^{12} + 72 q^{13} + 28 q^{14} - 133 q^{15} - 16 q^{16} + 46 q^{17} + 44 q^{18} + 20 q^{19} + 76 q^{20} - 392 q^{21} - 428 q^{23} - 56 q^{24} - 236 q^{25} - 144 q^{26} - 35 q^{27} - 56 q^{28} - 120 q^{29} + 266 q^{30} - 117 q^{31} - 128 q^{32} + 368 q^{34} + 266 q^{35} - 88 q^{36} + 201 q^{37} - 40 q^{38} - 504 q^{39} - 152 q^{40} + 228 q^{41} - 196 q^{42} - 968 q^{43} - 1672 q^{45} - 214 q^{46} + 96 q^{47} + 112 q^{48} + 147 q^{49} + 472 q^{50} - 322 q^{51} + 288 q^{52} - 458 q^{53} - 280 q^{54} - 448 q^{56} - 140 q^{57} + 240 q^{58} - 435 q^{59} - 532 q^{60} + 668 q^{61} + 234 q^{62} - 308 q^{63} - 64 q^{64} + 5472 q^{65} + 1756 q^{67} + 184 q^{68} - 749 q^{69} - 532 q^{70} + 1113 q^{71} + 176 q^{72} + 72 q^{73} - 402 q^{74} + 1652 q^{75} - 320 q^{76} - 4032 q^{78} + 70 q^{79} + 304 q^{80} + 839 q^{81} - 456 q^{82} - 358 q^{83} + 392 q^{84} - 874 q^{85} - 484 q^{86} - 3360 q^{87} + 3580 q^{89} - 836 q^{90} + 1008 q^{91} + 428 q^{92} + 819 q^{93} - 192 q^{94} - 380 q^{95} - 224 q^{96} - 409 q^{97} + 1176 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 7 * q^3 - 4 * q^4 + 19 * q^5 - 14 * q^6 - 14 * q^7 + 8 * q^8 - 22 * q^9 + 152 * q^10 - 112 * q^12 + 72 * q^13 + 28 * q^14 - 133 * q^15 - 16 * q^16 + 46 * q^17 + 44 * q^18 + 20 * q^19 + 76 * q^20 - 392 * q^21 - 428 * q^23 - 56 * q^24 - 236 * q^25 - 144 * q^26 - 35 * q^27 - 56 * q^28 - 120 * q^29 + 266 * q^30 - 117 * q^31 - 128 * q^32 + 368 * q^34 + 266 * q^35 - 88 * q^36 + 201 * q^37 - 40 * q^38 - 504 * q^39 - 152 * q^40 + 228 * q^41 - 196 * q^42 - 968 * q^43 - 1672 * q^45 - 214 * q^46 + 96 * q^47 + 112 * q^48 + 147 * q^49 + 472 * q^50 - 322 * q^51 + 288 * q^52 - 458 * q^53 - 280 * q^54 - 448 * q^56 - 140 * q^57 + 240 * q^58 - 435 * q^59 - 532 * q^60 + 668 * q^61 + 234 * q^62 - 308 * q^63 - 64 * q^64 + 5472 * q^65 + 1756 * q^67 + 184 * q^68 - 749 * q^69 - 532 * q^70 + 1113 * q^71 + 176 * q^72 + 72 * q^73 - 402 * q^74 + 1652 * q^75 - 320 * q^76 - 4032 * q^78 + 70 * q^79 + 304 * q^80 + 839 * q^81 - 456 * q^82 - 358 * q^83 + 392 * q^84 - 874 * q^85 - 484 * q^86 - 3360 * q^87 + 3580 * q^89 - 836 * q^90 + 1008 * q^91 + 428 * q^92 + 819 * q^93 - 192 * q^94 - 380 * q^95 - 224 * q^96 - 409 * q^97 + 1176 * q^98

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