LMFDB - Embedded newform 51.3.b.a.35.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,3,Mod(35,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("51.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 28x^{8} + 254x^{6} + 880x^{4} + 1249x^{2} + 612 $ x^10 + 28x^8 + 254x^6 + 880x^4 + 1249x^2 + 612
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.9
Root			$2.98570i$ of defining polynomial
Character	$\chi$	$=$	51.35
Dual form			51.3.b.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.98570i q^{2} +(-1.28836 + 2.70927i) q^{3} -4.91441 q^{4} -2.35897i q^{5} +(-8.08906 - 3.84667i) q^{6} +5.84735 q^{7} -2.73016i q^{8} +(-5.68024 - 6.98104i) q^{9} +O(q^{10})$	\(q+2.98570i q^{2} +(-1.28836 + 2.70927i) q^{3} -4.91441 q^{4} -2.35897i q^{5} +(-8.08906 - 3.84667i) q^{6} +5.84735 q^{7} -2.73016i q^{8} +(-5.68024 - 6.98104i) q^{9} +7.04319 q^{10} +13.8460i q^{11} +(6.33155 - 13.3144i) q^{12} +6.24865 q^{13} +17.4585i q^{14} +(6.39108 + 3.03921i) q^{15} -11.5062 q^{16} -4.12311i q^{17} +(20.8433 - 16.9595i) q^{18} +27.7294 q^{19} +11.5930i q^{20} +(-7.53352 + 15.8420i) q^{21} -41.3401 q^{22} -36.5288i q^{23} +(7.39674 + 3.51745i) q^{24} +19.4352 q^{25} +18.6566i q^{26} +(26.2317 - 6.39515i) q^{27} -28.7363 q^{28} -6.36395i q^{29} +(-9.07419 + 19.0819i) q^{30} -33.3709 q^{31} -45.2747i q^{32} +(-37.5126 - 17.8387i) q^{33} +12.3104 q^{34} -13.7937i q^{35} +(27.9150 + 34.3077i) q^{36} -59.7732 q^{37} +82.7917i q^{38} +(-8.05053 + 16.9292i) q^{39} -6.44038 q^{40} +19.5135i q^{41} +(-47.2996 - 22.4928i) q^{42} +65.4530 q^{43} -68.0451i q^{44} +(-16.4681 + 13.3995i) q^{45} +109.064 q^{46} +9.62349i q^{47} +(14.8242 - 31.1733i) q^{48} -14.8084 q^{49} +58.0278i q^{50} +(11.1706 + 5.31206i) q^{51} -30.7084 q^{52} -56.9577i q^{53} +(19.0940 + 78.3200i) q^{54} +32.6624 q^{55} -15.9642i q^{56} +(-35.7255 + 75.1263i) q^{57} +19.0008 q^{58} -45.4082i q^{59} +(-31.4084 - 14.9360i) q^{60} -22.1983 q^{61} -99.6355i q^{62} +(-33.2144 - 40.8206i) q^{63} +89.1520 q^{64} -14.7404i q^{65} +(53.2611 - 112.001i) q^{66} -23.8655 q^{67} +20.2626i q^{68} +(98.9661 + 47.0623i) q^{69} +41.1840 q^{70} +17.5378i q^{71} +(-19.0594 + 15.5080i) q^{72} +18.8867 q^{73} -178.465i q^{74} +(-25.0397 + 52.6552i) q^{75} -136.274 q^{76} +80.9626i q^{77} +(-50.5457 - 24.0365i) q^{78} -51.4312 q^{79} +27.1428i q^{80} +(-16.4698 + 79.3079i) q^{81} -58.2614 q^{82} +102.097i q^{83} +(37.0228 - 77.8543i) q^{84} -9.72629 q^{85} +195.423i q^{86} +(17.2416 + 8.19908i) q^{87} +37.8019 q^{88} +59.0852i q^{89} +(-40.0070 - 49.1688i) q^{90} +36.5380 q^{91} +179.517i q^{92} +(42.9938 - 90.4106i) q^{93} -28.7329 q^{94} -65.4129i q^{95} +(122.661 + 58.3303i) q^{96} -155.512 q^{97} -44.2136i q^{98} +(96.6596 - 78.6487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{3} - 16 q^{4} - 2 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 10 * q + 2 * q^3 - 16 * q^4 - 2 * q^6 - 4 * q^7 + 6 * q^9	$ 10 q + 2 q^{3} - 16 q^{4} - 2 q^{6} - 4 q^{7} + 6 q^{9} - 24 q^{10} - 46 q^{12} + 30 q^{13} + 30 q^{15} + 40 q^{16} + 80 q^{18} - 6 q^{19} - 40 q^{21} + 56 q^{22} - 30 q^{24} - 32 q^{25} - 10 q^{27} - 96 q^{28} - 20 q^{30} - 80 q^{31} - 26 q^{33} - 104 q^{37} - 24 q^{39} + 196 q^{40} + 122 q^{43} + 144 q^{45} + 324 q^{46} + 154 q^{48} - 154 q^{49} - 472 q^{52} + 70 q^{54} + 314 q^{55} - 232 q^{57} - 148 q^{58} - 244 q^{60} + 176 q^{61} - 304 q^{63} - 208 q^{64} + 320 q^{66} - 132 q^{67} + 294 q^{69} - 16 q^{70} - 480 q^{72} + 262 q^{75} + 248 q^{76} + 108 q^{78} - 92 q^{79} + 114 q^{81} - 76 q^{82} + 32 q^{84} + 34 q^{85} + 120 q^{87} + 52 q^{88} - 376 q^{90} + 156 q^{91} + 16 q^{93} + 216 q^{94} + 546 q^{96} + 464 q^{97} + 236 q^{99}+O(q^{100}) $ 10 * q + 2 * q^3 - 16 * q^4 - 2 * q^6 - 4 * q^7 + 6 * q^9 - 24 * q^10 - 46 * q^12 + 30 * q^13 + 30 * q^15 + 40 * q^16 + 80 * q^18 - 6 * q^19 - 40 * q^21 + 56 * q^22 - 30 * q^24 - 32 * q^25 - 10 * q^27 - 96 * q^28 - 20 * q^30 - 80 * q^31 - 26 * q^33 - 104 * q^37 - 24 * q^39 + 196 * q^40 + 122 * q^43 + 144 * q^45 + 324 * q^46 + 154 * q^48 - 154 * q^49 - 472 * q^52 + 70 * q^54 + 314 * q^55 - 232 * q^57 - 148 * q^58 - 244 * q^60 + 176 * q^61 - 304 * q^63 - 208 * q^64 + 320 * q^66 - 132 * q^67 + 294 * q^69 - 16 * q^70 - 480 * q^72 + 262 * q^75 + 248 * q^76 + 108 * q^78 - 92 * q^79 + 114 * q^81 - 76 * q^82 + 32 * q^84 + 34 * q^85 + 120 * q^87 + 52 * q^88 - 376 * q^90 + 156 * q^91 + 16 * q^93 + 216 * q^94 + 546 * q^96 + 464 * q^97 + 236 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.98570i			1.49285i	0.665469	+	0.746425i	$0.268232\pi$
$2$			2.98570i			1.49285i	−0.665469	+	0.746425i	$0.731768\pi$
$3$	−1.28836	+	2.70927i	−0.429455	+	0.903088i
$3$	−1.28836	+	2.70927i	−0.429455	+	0.903088i
$4$	−4.91441			−1.22860
$5$		−	2.35897i		−	0.471795i	−0.971778	−	0.235897i	$-0.924197\pi$
$5$		−	2.35897i		−	0.471795i	0.971778	−	0.235897i	$-0.0758029\pi$
$6$	−8.08906	−	3.84667i	−1.34818	−	0.641112i
$7$	5.84735			0.835336			0.417668	−	0.908600i	$-0.362847\pi$
$7$	5.84735			0.835336			0.417668	+	0.908600i	$0.362847\pi$
$8$		−	2.73016i		−	0.341271i
$9$	−5.68024	−	6.98104i	−0.631138	−	0.775671i
$10$	7.04319			0.704319
$11$			13.8460i			1.25873i	0.777110	+	0.629365i	$0.216685\pi$
$11$			13.8460i			1.25873i	−0.777110	+	0.629365i	$0.783315\pi$
$12$	6.33155	−	13.3144i	0.527629	−	1.10954i
$13$	6.24865			0.480665			0.240333	−	0.970691i	$-0.422744\pi$
$13$	6.24865			0.480665			0.240333	+	0.970691i	$0.422744\pi$
$14$			17.4585i			1.24703i
$15$	6.39108	+	3.03921i	0.426072	+	0.202614i
$16$	−11.5062			−0.719137
$17$		−	4.12311i		−	0.242536i
$17$		−	4.12311i		−	0.242536i
$18$	20.8433	−	16.9595i	1.15796	−	0.942194i
$19$	27.7294			1.45944			0.729721	−	0.683745i	$-0.239650\pi$
$19$	27.7294			1.45944			0.729721	+	0.683745i	$0.239650\pi$
$20$			11.5930i			0.579648i
$21$	−7.53352	+	15.8420i	−0.358739	+	0.754383i
$22$	−41.3401			−1.87910
$23$		−	36.5288i		−	1.58821i	−0.607782	−	0.794104i	$-0.707941\pi$
$23$		−	36.5288i		−	1.58821i	0.607782	−	0.794104i	$-0.292059\pi$
$24$	7.39674	+	3.51745i	0.308198	+	0.146560i
$25$	19.4352			0.777410
$26$			18.6566i			0.717561i
$27$	26.2317	−	6.39515i	0.971544	−	0.236858i
$28$	−28.7363			−1.02630
$29$		−	6.36395i		−	0.219446i	−0.993962	−	0.109723i	$-0.965004\pi$
$29$		−	6.36395i		−	0.219446i	0.993962	−	0.109723i	$-0.0349964\pi$
$30$	−9.07419	+	19.0819i	−0.302473	+	0.636062i
$31$	−33.3709			−1.07648			−0.538240	−	0.842792i	$-0.680911\pi$
$31$	−33.3709			−1.07648			−0.538240	+	0.842792i	$0.680911\pi$
$32$		−	45.2747i		−	1.41484i
$33$	−37.5126	−	17.8387i	−1.13674	−	0.540567i
$34$	12.3104			0.362069
$35$		−	13.7937i		−	0.394107i
$36$	27.9150	+	34.3077i	0.775418	+	0.952992i
$37$	−59.7732			−1.61549			−0.807746	−	0.589530i	$-0.799313\pi$
$37$	−59.7732			−1.61549			−0.807746	+	0.589530i	$0.799313\pi$
$38$			82.7917i			2.17873i
$39$	−8.05053	+	16.9292i	−0.206424	+	0.434083i
$40$	−6.44038			−0.161010
$41$			19.5135i			0.475938i	0.971273	+	0.237969i	$0.0764817\pi$
$41$			19.5135i			0.475938i	−0.971273	+	0.237969i	$0.923518\pi$
$42$	−47.2996	−	22.4928i	−1.12618	−	0.535544i
$43$	65.4530			1.52216			0.761082	−	0.648656i	$-0.224669\pi$
$43$	65.4530			1.52216			0.761082	+	0.648656i	$0.224669\pi$
$44$		−	68.0451i		−	1.54648i
$45$	−16.4681	+	13.3995i	−0.365957	+	0.297767i
$46$	109.064			2.37096
$47$			9.62349i			0.204755i	0.994746	+	0.102378i	$0.0326450\pi$
$47$			9.62349i			0.204755i	−0.994746	+	0.102378i	$0.967355\pi$
$48$	14.8242	−	31.1733i	0.308837	−	0.649445i
$49$	−14.8084			−0.302213
$50$			58.0278i			1.16056i
$51$	11.1706	+	5.31206i	0.219031	+	0.104158i
$52$	−30.7084			−0.590547
$53$		−	56.9577i		−	1.07467i	−0.843368	−	0.537336i	$-0.819431\pi$
$53$		−	56.9577i		−	1.07467i	0.843368	−	0.537336i	$-0.180569\pi$
$54$	19.0940	+	78.3200i	0.353593	+	1.45037i
$55$	32.6624			0.593862
$56$		−	15.9642i		−	0.285076i
$57$	−35.7255	+	75.1263i	−0.626764	+	1.31800i
$58$	19.0008			0.327601
$59$		−	45.4082i		−	0.769631i	−0.922994	−	0.384815i	$-0.874265\pi$
$59$		−	45.4082i		−	0.769631i	0.922994	−	0.384815i	$-0.125735\pi$
$60$	−31.4084	−	14.9360i	−0.523474	−	0.248933i
$61$	−22.1983			−0.363906			−0.181953	−	0.983307i	$-0.558242\pi$
$61$	−22.1983			−0.363906			−0.181953	+	0.983307i	$0.558242\pi$
$62$		−	99.6355i		−	1.60702i
$63$	−33.2144	−	40.8206i	−0.527212	−	0.647946i
$64$	89.1520			1.39300
$65$		−	14.7404i		−	0.226775i
$66$	53.2611	−	112.001i	0.806986	−	1.69699i
$67$	−23.8655			−0.356202			−0.178101	−	0.984012i	$-0.556995\pi$
$67$	−23.8655			−0.356202			−0.178101	+	0.984012i	$0.556995\pi$
$68$			20.2626i			0.297980i
$69$	98.9661	+	47.0623i	1.43429	+	0.682063i
$70$	41.1840			0.588343
$71$			17.5378i			0.247011i	0.992344	+	0.123505i	$0.0394136\pi$
$71$			17.5378i			0.247011i	−0.992344	+	0.123505i	$0.960586\pi$
$72$	−19.0594	+	15.5080i	−0.264714	+	0.215389i
$73$	18.8867			0.258722			0.129361	−	0.991598i	$-0.458707\pi$
$73$	18.8867			0.258722			0.129361	+	0.991598i	$0.458707\pi$
$74$		−	178.465i		−	2.41169i
$75$	−25.0397	+	52.6552i	−0.333862	+	0.702070i
$76$	−136.274			−1.79307
$77$			80.9626i			1.05146i
$78$	−50.5457	−	24.0365i	−0.648021	−	0.308160i
$79$	−51.4312			−0.651027			−0.325514	−	0.945537i	$-0.605537\pi$
$79$	−51.4312			−0.651027			−0.325514	+	0.945537i	$0.605537\pi$
$80$			27.1428i			0.339285i
$81$	−16.4698	+	79.3079i	−0.203331	+	0.979110i
$82$	−58.2614			−0.710504
$83$			102.097i			1.23008i	0.788496	+	0.615039i	$0.210860\pi$
$83$			102.097i			1.23008i	−0.788496	+	0.615039i	$0.789140\pi$
$84$	37.0228	−	77.8543i	0.440748	−	0.926837i
$85$	−9.72629			−0.114427
$86$			195.423i			2.27236i
$87$	17.2416	+	8.19908i	0.198180	+	0.0942423i
$88$	37.8019			0.429567
$89$			59.0852i			0.663879i	0.943301	+	0.331939i	$0.107703\pi$
$89$			59.0852i			0.663879i	−0.943301	+	0.331939i	$0.892297\pi$
$90$	−40.0070	−	49.1688i	−0.444522	−	0.546320i
$91$	36.5380			0.401517
$92$			179.517i			1.95128i
$93$	42.9938	−	90.4106i	0.462299	−	0.972157i
$94$	−28.7329			−0.305669
$95$		−	65.4129i		−	0.688557i
$96$	122.661	+	58.3303i	1.27772	+	0.607607i
$97$	−155.512			−1.60322			−0.801609	−	0.597849i	$-0.796022\pi$
$97$	−155.512			−1.60322			−0.801609	+	0.597849i	$0.796022\pi$
$98$		−	44.2136i		−	0.451159i
$99$	96.6596	−	78.6487i	0.976360	−	0.794431i
$100$	−95.5128			−0.955128
$101$		−	26.1517i		−	0.258928i	−0.991584	−	0.129464i	$-0.958674\pi$
$101$		−	26.1517i		−	0.258928i	0.991584	−	0.129464i	$-0.0413257\pi$
$102$	−15.8602	+	33.3520i	−0.155492	+	0.326981i
$103$	−48.9060			−0.474815			−0.237408	−	0.971410i	$-0.576298\pi$
$103$	−48.9060			−0.474815			−0.237408	+	0.971410i	$0.576298\pi$
$104$		−	17.0598i		−	0.164037i
$105$	37.3709	+	17.7714i	0.355914	+	0.169251i
$106$	170.059			1.60433
$107$		−	129.108i		−	1.20661i	−0.797510	−	0.603306i	$-0.793850\pi$
$107$		−	129.108i		−	1.20661i	0.797510	−	0.603306i	$-0.206150\pi$
$108$	−128.913	+	31.4284i	−1.19364	+	0.291004i
$109$	−10.2543			−0.0940765			−0.0470383	−	0.998893i	$-0.514978\pi$
$109$	−10.2543			−0.0940765			−0.0470383	+	0.998893i	$0.514978\pi$
$110$			97.5201i			0.886547i
$111$	77.0097	−	161.942i	0.693781	−	1.45893i
$112$	−67.2808			−0.600721
$113$		−	14.3234i		−	0.126756i	−0.997990	−	0.0633781i	$-0.979813\pi$
$113$		−	14.3234i		−	0.126756i	0.997990	−	0.0633781i	$-0.0201874\pi$
$114$	−224.305	−	106.666i	−1.96758	−	0.935665i
$115$	−86.1704			−0.749308
$116$			31.2751i			0.269613i
$117$	−35.4938	−	43.6220i	−0.303366	−	0.372838i
$118$	135.575			1.14894
$119$		−	24.1093i		−	0.202599i
$120$	8.29756	−	17.4487i	0.0691463	−	0.145406i
$121$	−70.7124			−0.584400
$122$		−	66.2774i		−	0.543257i
$123$	−52.8671	−	25.1404i	−0.429814	−	0.204394i
$124$	163.998			1.32257
$125$		−	104.822i		−	0.838572i
$126$	121.878	−	99.1682i	0.967287	−	0.787049i
$127$	166.807			1.31344			0.656719	−	0.754136i	$-0.271944\pi$
$127$	166.807			1.31344			0.656719	+	0.754136i	$0.271944\pi$
$128$			85.0824i			0.664707i
$129$	−84.3273	+	177.330i	−0.653700	+	1.37465i
$130$	44.0104			0.338541
$131$			188.137i			1.43616i	0.695959	+	0.718082i	$0.254980\pi$
$131$			188.137i			1.43616i	−0.695959	+	0.718082i	$0.745020\pi$
$132$	184.352	+	87.6668i	1.39661	+	0.664143i
$133$	162.144			1.21912
$134$		−	71.2554i		−	0.531757i
$135$	−15.0860	−	61.8799i	−0.111748	−	0.458369i
$136$	−11.2568			−0.0827703
$137$		−	166.226i		−	1.21333i	−0.794959	−	0.606663i	$-0.792508\pi$
$137$		−	166.226i		−	1.21333i	0.794959	−	0.606663i	$-0.207492\pi$
$138$	−140.514	+	295.483i	−1.01822	+	2.14118i
$139$	224.364			1.61413			0.807065	−	0.590463i	$-0.201055\pi$
$139$	224.364			1.61413			0.807065	+	0.590463i	$0.201055\pi$
$140$			67.7882i			0.484201i
$141$	−26.0726	−	12.3986i	−0.184912	−	0.0879331i
$142$	−52.3626			−0.368750
$143$			86.5189i			0.605027i
$144$	65.3579	+	80.3252i	0.453875	+	0.557814i
$145$	−15.0124			−0.103534
$146$			56.3901i			0.386234i
$147$	19.0787	−	40.1200i	0.129787	−	0.272925i
$148$	293.750			1.98480
$149$		−	22.5710i		−	0.151483i	−0.997127	−	0.0757415i	$-0.975868\pi$
$149$		−	22.5710i		−	0.151483i	0.997127	−	0.0757415i	$-0.0241324\pi$
$150$	−157.213	−	74.7610i	−1.04809	−	0.498407i
$151$	−210.631			−1.39491			−0.697454	−	0.716629i	$-0.745684\pi$
$151$	−210.631			−1.39491			−0.697454	+	0.716629i	$0.745684\pi$
$152$		−	75.7058i		−	0.498064i
$153$	−28.7836	+	23.4202i	−0.188128	+	0.153073i
$154$	−241.730			−1.56968
$155$			78.7210i			0.507878i
$156$	39.5636	−	83.1973i	0.253613	−	0.533316i
$157$	230.081			1.46549			0.732743	−	0.680505i	$-0.238240\pi$
$157$	230.081			1.46549			0.732743	+	0.680505i	$0.238240\pi$
$158$		−	153.558i		−	0.971886i
$159$	154.313	+	73.3822i	0.970525	+	0.461523i
$160$	−106.802			−0.667511
$161$		−	213.597i		−	1.32669i
$162$	−236.790	−	49.1739i	−1.46167	−	0.303543i
$163$	−6.04141			−0.0370639			−0.0185319	−	0.999828i	$-0.505899\pi$
$163$	−6.04141			−0.0370639			−0.0185319	+	0.999828i	$0.505899\pi$
$164$		−	95.8972i		−	0.584739i
$165$	−42.0810	+	88.4911i	−0.255037	+	0.536310i
$166$	−304.830			−1.83632
$167$			235.926i			1.41273i	0.707847	+	0.706366i	$0.249667\pi$
$167$			235.926i			1.41273i	−0.707847	+	0.706366i	$0.750333\pi$
$168$	43.2514	+	20.5677i	0.257449	+	0.122427i
$169$	−129.954			−0.768961
$170$		−	29.0398i		−	0.170822i
$171$	−157.510	−	193.580i	−0.921108	−	1.13205i
$172$	−321.663			−1.87014
$173$		−	43.2819i		−	0.250184i	−0.992145	−	0.125092i	$-0.960077\pi$
$173$		−	43.2819i		−	0.250184i	0.992145	−	0.125092i	$-0.0399227\pi$
$174$	−24.4800	+	51.4783i	−0.140690	+	0.295852i
$175$	113.645			0.649399
$176$		−	159.315i		−	0.905199i
$177$	123.023	+	58.5023i	0.695044	+	0.330521i
$178$	−176.411			−0.991072
$179$			273.240i			1.52648i	0.646116	+	0.763239i	$0.276392\pi$
$179$			273.240i			1.52648i	−0.646116	+	0.763239i	$0.723608\pi$
$180$	80.9309	−	65.8508i	0.449616	−	0.365838i
$181$	−130.136			−0.718984			−0.359492	−	0.933148i	$-0.617050\pi$
$181$	−130.136			−0.718984			−0.359492	+	0.933148i	$0.617050\pi$
$182$			109.092i			0.599405i
$183$	28.5994	−	60.1410i	0.156281	−	0.328639i
$184$	−99.7296			−0.542008
$185$			141.003i			0.762181i
$186$	269.939	+	128.367i	1.45129	+	0.690144i
$187$	57.0886			0.305287
$188$		−	47.2938i		−	0.251563i
$189$	153.386	−	37.3947i	0.811566	−	0.197856i
$190$	195.303			1.02791
$191$		−	207.182i		−	1.08472i	−0.840145	−	0.542362i	$-0.817530\pi$
$191$		−	207.182i		−	1.08472i	0.840145	−	0.542362i	$-0.182470\pi$
$192$	−114.860	+	241.536i	−0.598230	+	1.25800i
$193$	194.604			1.00831			0.504154	−	0.863614i	$-0.331804\pi$
$193$	194.604			1.00831			0.504154	+	0.863614i	$0.331804\pi$
$194$		−	464.313i		−	2.39337i
$195$	39.9356	+	18.9910i	0.204798	+	0.0973896i
$196$	72.7748			0.371300
$197$			57.7426i			0.293110i	0.989203	+	0.146555i	$0.0468185\pi$
$197$			57.7426i			0.293110i	−0.989203	+	0.146555i	$0.953182\pi$
$198$	234.822	+	288.597i	1.18597	+	1.45756i
$199$	−103.821			−0.521715			−0.260858	−	0.965377i	$-0.584005\pi$
$199$	−103.821			−0.521715			−0.260858	+	0.965377i	$0.584005\pi$
$200$		−	53.0614i		−	0.265307i
$201$	30.7475	−	64.6581i	0.152973	−	0.321682i
$202$	78.0813			0.386541
$203$		−	37.2123i		−	0.183312i
$204$	−54.8969	−	26.1057i	−0.269102	−	0.127969i
$205$	46.0317			0.224545
$206$		−	146.019i		−	0.708828i
$207$	−255.009	+	207.492i	−1.23193	+	1.00238i
$208$	−71.8982			−0.345664
$209$			383.942i			1.83704i
$210$	−53.0600	+	111.578i	−0.252667	+	0.531326i
$211$	−33.5801			−0.159148			−0.0795738	−	0.996829i	$-0.525356\pi$
$211$	−33.5801			−0.159148			−0.0795738	+	0.996829i	$0.525356\pi$
$212$			279.913i			1.32035i
$213$	−47.5145	−	22.5950i	−0.223073	−	0.106080i
$214$	385.477			1.80129
$215$		−	154.402i		−	0.718149i
$216$	−17.4598	−	71.6169i	−0.0808325	−	0.331560i
$217$	−195.131			−0.899223
$218$		−	30.6164i		−	0.140442i
$219$	−24.3330	+	51.1691i	−0.111109	+	0.233649i
$220$	−160.516			−0.729620
$221$		−	25.7638i		−	0.116578i
$222$	483.509	+	229.928i	2.17797	+	1.03571i
$223$	−71.4935			−0.320599			−0.160299	−	0.987068i	$-0.551246\pi$
$223$	−71.4935			−0.320599			−0.160299	+	0.987068i	$0.551246\pi$
$224$		−	264.737i		−	1.18186i
$225$	−110.397	−	135.678i	−0.490653	−	0.603014i
$226$	42.7655			0.189228
$227$			246.800i			1.08722i	0.839337	+	0.543611i	$0.182943\pi$
$227$			246.800i			1.08722i	−0.839337	+	0.543611i	$0.817057\pi$
$228$	175.570	−	369.202i	0.770044	−	1.61931i
$229$	163.776			0.715179			0.357589	−	0.933879i	$-0.383599\pi$
$229$	163.776			0.715179			0.357589	+	0.933879i	$0.383599\pi$
$230$		−	257.279i		−	1.11860i
$231$	−219.349	−	104.309i	−0.949564	−	0.451555i
$232$	−17.3746			−0.0748906
$233$		−	368.733i		−	1.58254i	−0.611465	−	0.791272i	$-0.709419\pi$
$233$		−	368.733i		−	1.58254i	0.611465	−	0.791272i	$-0.290581\pi$
$234$	130.242	−	105.974i	0.556591	−	0.452880i
$235$	22.7016			0.0966024
$236$			223.155i			0.945571i
$237$	66.2620	−	139.341i	0.279587	−	0.587935i
$238$	71.9831			0.302450
$239$			116.550i			0.487657i	0.969818	+	0.243829i	$0.0784034\pi$
$239$			116.550i			0.487657i	−0.969818	+	0.243829i	$0.921597\pi$
$240$	−73.5371	−	34.9698i	−0.306404	−	0.145708i
$241$	−121.122			−0.502583			−0.251291	−	0.967911i	$-0.580855\pi$
$241$	−121.122			−0.502583			−0.251291	+	0.967911i	$0.580855\pi$
$242$		−	211.126i		−	0.872422i
$243$	−193.647	−	146.799i	−0.796902	−	0.604109i
$244$	109.091			0.447096
$245$			34.9327i			0.142583i
$246$	75.0618	−	157.845i	0.305129	−	0.641648i
$247$	173.271			0.701503
$248$			91.1080i			0.367371i
$249$	−276.607	−	131.538i	−1.11087	−	0.528263i
$250$	312.966			1.25186
$251$			164.056i			0.653608i	0.945092	+	0.326804i	$0.105972\pi$
$251$			164.056i			0.653608i	−0.945092	+	0.326804i	$0.894028\pi$
$252$	163.229	+	200.609i	0.647735	+	0.796069i
$253$	505.778			1.99912
$254$			498.034i			1.96077i
$255$	12.5310	−	26.3511i	0.0491412	−	0.103338i
$256$	102.577			0.400693
$257$		−	132.852i		−	0.516932i	−0.966020	−	0.258466i	$-0.916783\pi$
$257$		−	132.852i		−	0.516932i	0.966020	−	0.258466i	$-0.0832170\pi$
$258$	−529.453	−	251.776i	−2.05214	−	0.975877i
$259$	−349.515			−1.34948
$260$			72.4403i			0.278617i
$261$	−44.4270	+	36.1487i	−0.170218	+	0.138501i
$262$	−561.722			−2.14398
$263$		−	214.012i		−	0.813732i	−0.913488	−	0.406866i	$-0.866622\pi$
$263$		−	214.012i		−	0.813732i	0.913488	−	0.406866i	$-0.133378\pi$
$264$	−48.7026	+	102.415i	−0.184480	+	0.387937i
$265$	−134.362			−0.507025
$266$			484.112i			1.81997i
$267$	−160.078	−	76.1233i	−0.599541	−	0.285106i
$268$	117.285			0.437631
$269$		−	67.9688i		−	0.252672i	−0.991988	−	0.126336i	$-0.959678\pi$
$269$		−	67.9688i		−	0.252672i	0.991988	−	0.126336i	$-0.0403218\pi$
$270$	184.755	−	45.0423i	0.684277	−	0.166823i
$271$	−267.663			−0.987685			−0.493843	−	0.869551i	$-0.664408\pi$
$271$	−267.663			−0.987685			−0.493843	+	0.869551i	$0.664408\pi$
$272$			47.4413i			0.174416i
$273$	−47.0743	+	98.9913i	−0.172433	+	0.362605i
$274$	496.300			1.81131
$275$			269.101i			0.978549i
$276$	−486.361	−	231.284i	−1.76218	−	0.837985i
$277$	−114.349			−0.412811			−0.206406	−	0.978467i	$-0.566177\pi$
$277$	−114.349			−0.412811			−0.206406	+	0.978467i	$0.566177\pi$
$278$			669.884i			2.40966i
$279$	189.555	+	232.963i	0.679407	+	0.834995i
$280$	−37.6592			−0.134497
$281$		−	98.4027i		−	0.350188i	−0.984552	−	0.175094i	$-0.943977\pi$
$281$		−	98.4027i		−	0.350188i	0.984552	−	0.175094i	$-0.0560229\pi$
$282$	37.0184	−	77.8450i	0.131271	−	0.276046i
$283$	48.6905			0.172051			0.0860255	−	0.996293i	$-0.472583\pi$
$283$	48.6905			0.172051			0.0860255	+	0.996293i	$0.472583\pi$
$284$		−	86.1879i		−	0.303478i
$285$	177.221	+	84.2756i	0.621827	+	0.295704i
$286$	−258.320			−0.903215
$287$			114.102i			0.397568i
$288$	−316.065	+	257.171i	−1.09745	+	0.892956i
$289$	−17.0000			−0.0588235
$290$		−	44.8225i		−	0.154560i
$291$	200.356	−	421.324i	0.688509	−	1.44785i
$292$	−92.8172			−0.317867
$293$		−	103.064i		−	0.351756i	−0.984412	−	0.175878i	$-0.943724\pi$
$293$		−	103.064i		−	0.351756i	0.984412	−	0.175878i	$-0.0562764\pi$
$294$	119.786	+	56.9632i	0.407437	+	0.193752i
$295$	−107.117			−0.363107
$296$			163.191i			0.551320i
$297$	88.5475	+	363.205i	0.298140	+	1.22291i
$298$	67.3902			0.226142
$299$		−	228.255i		−	0.763396i
$300$	123.055	−	258.770i	0.410184	−	0.862565i
$301$	382.727			1.27152
$302$		−	628.882i		−	2.08239i
$303$	70.8520	+	33.6929i	0.233835	+	0.111198i
$304$	−319.060			−1.04954
$305$			52.3651i			0.171689i
$306$	−69.9258	−	85.9391i	−0.228516	−	0.280847i
$307$	36.3733			0.118480			0.0592400	−	0.998244i	$-0.481132\pi$
$307$	36.3733			0.118480			0.0592400	+	0.998244i	$0.481132\pi$
$308$		−	397.884i		−	1.29183i
$309$	63.0087	−	132.499i	0.203912	−	0.428800i
$310$	−235.037			−0.758185
$311$			441.551i			1.41978i	0.704313	+	0.709890i	$0.251255\pi$
$311$			441.551i			1.41978i	−0.704313	+	0.709890i	$0.748745\pi$
$312$	46.2196	+	21.9793i	0.148140	+	0.0704464i
$313$	−134.895			−0.430974			−0.215487	−	0.976507i	$-0.569134\pi$
$313$	−134.895			−0.430974			−0.215487	+	0.976507i	$0.569134\pi$
$314$			686.954i			2.18775i
$315$	−96.2947	+	78.3518i	−0.305697	+	0.248736i
$316$	252.754			0.799854
$317$		−	21.0947i		−	0.0665449i	−0.999446	−	0.0332725i	$-0.989407\pi$
$317$		−	21.0947i		−	0.0665449i	0.999446	−	0.0332725i	$-0.0105929\pi$
$318$	−219.097	+	460.734i	−0.688985	+	1.44885i
$319$	88.1154			0.276224
$320$		−	210.307i		−	0.657210i
$321$	349.787	+	166.337i	1.08968	+	0.518185i
$322$	637.736			1.98055
$323$		−	114.331i		−	0.353967i
$324$	80.9394	−	389.752i	0.249813	−	1.20294i
$325$	121.444			0.373674
$326$		−	18.0378i		−	0.0553308i
$327$	13.2113	−	27.7817i	0.0404016	−	0.0849594i
$328$	53.2750			0.162424
$329$			56.2720i			0.171039i
$330$	−264.208	−	125.641i	−0.800630	−	0.380732i
$331$	−620.732			−1.87532			−0.937662	−	0.347548i	$-0.887014\pi$
$331$	−620.732			−1.87532			−0.937662	+	0.347548i	$0.887014\pi$
$332$		−	501.745i		−	1.51128i
$333$	339.526	+	417.279i	1.01960	+	1.25309i
$334$	−704.405			−2.10900
$335$			56.2982i			0.168054i
$336$	86.6822	−	182.282i	0.257983	−	0.542505i
$337$	−206.305			−0.612180			−0.306090	−	0.952003i	$-0.599021\pi$
$337$	−206.305			−0.612180			−0.306090	+	0.952003i	$0.599021\pi$
$338$		−	388.005i		−	1.14794i
$339$	38.8060	+	18.4538i	0.114472	+	0.0544360i
$340$	47.7990			0.140585
$341$		−	462.054i		−	1.35500i
$342$	577.972	−	470.276i	1.68998	−	1.37508i
$343$	−373.111			−1.08779
$344$		−	178.698i		−	0.519470i
$345$	111.019	−	233.458i	0.321794	−	0.676691i
$346$	129.227			0.373488
$347$		−	274.248i		−	0.790339i	−0.918608	−	0.395170i	$-0.870686\pi$
$347$		−	274.248i		−	0.790339i	0.918608	−	0.395170i	$-0.129314\pi$
$348$	−84.7325	−	40.2937i	−0.243484	−	0.115786i
$349$	417.800			1.19714			0.598568	−	0.801072i	$-0.295737\pi$
$349$	417.800			1.19714			0.598568	+	0.801072i	$0.295737\pi$
$350$			339.309i			0.969455i
$351$	163.913	−	39.9611i	0.466987	−	0.113849i
$352$	626.875			1.78089
$353$			270.614i			0.766613i	0.923621	+	0.383306i	$0.125215\pi$
$353$			270.614i			0.766613i	−0.923621	+	0.383306i	$0.874785\pi$
$354$	−174.670	+	367.310i	−0.493419	+	1.03760i
$355$	41.3711			0.116538
$356$		−	290.369i		−	0.815644i
$357$	65.3184	+	31.0615i	0.182965	+	0.0870070i
$358$	−815.812			−2.27880
$359$			602.350i			1.67785i	0.544244	+	0.838927i	$0.316817\pi$
$359$			602.350i			1.67785i	−0.544244	+	0.838927i	$0.683183\pi$
$360$	36.5829	+	44.9606i	0.101619	+	0.124890i
$361$	407.919			1.12997
$362$		−	388.548i		−	1.07334i
$363$	91.1033	−	191.579i	0.250973	−	0.527765i
$364$	−179.563			−0.493305
$365$		−	44.5533i		−	0.122064i
$366$	179.563	+	85.3894i	0.490609	+	0.233304i
$367$	648.676			1.76751			0.883754	−	0.467951i	$-0.155008\pi$
$367$	648.676			1.76751			0.883754	+	0.467951i	$0.155008\pi$
$368$			420.307i			1.14214i
$369$	136.224	−	110.841i	0.369171	−	0.300382i
$370$	−420.994			−1.13782
$371$		−	333.052i		−	0.897713i
$372$	−211.290	+	444.315i	−0.567983	+	1.19440i
$373$	−583.590			−1.56458			−0.782292	−	0.622912i	$-0.785949\pi$
$373$	−583.590			−1.56458			−0.782292	+	0.622912i	$0.785949\pi$
$374$			170.450i			0.455748i
$375$	283.989	+	135.048i	0.757305	+	0.360129i
$376$	26.2737			0.0698769
$377$		−	39.7661i		−	0.105480i
$378$	111.650	+	457.965i	0.295369	+	1.21155i
$379$	167.591			0.442193			0.221097	−	0.975252i	$-0.429036\pi$
$379$	167.591			0.442193			0.221097	+	0.975252i	$0.429036\pi$
$380$			321.466i			0.845963i
$381$	−214.907	+	451.923i	−0.564062	+	1.18615i
$382$	618.585			1.61933
$383$		−	172.679i		−	0.450859i	−0.974260	−	0.225429i	$-0.927622\pi$
$383$		−	172.679i		−	0.450859i	0.974260	−	0.225429i	$-0.0723785\pi$
$384$	−230.511	−	109.617i	−0.600289	−	0.285461i
$385$	190.989			0.496074
$386$			581.028i			1.50525i
$387$	−371.789	−	456.930i	−0.960695	−	1.18070i
$388$	764.251			1.96972
$389$		−	471.766i		−	1.21277i	−0.795173	−	0.606383i	$-0.792620\pi$
$389$		−	471.766i		−	1.21277i	0.795173	−	0.606383i	$-0.207380\pi$
$390$	−56.7014	+	119.236i	−0.145388	+	0.305733i
$391$	−150.612			−0.385197
$392$			40.4295i			0.103136i
$393$	−509.714	−	242.389i	−1.29698	−	0.616767i
$394$	−172.402			−0.437569
$395$			121.325i			0.307151i
$396$	−475.025	+	386.512i	−1.19956	+	0.976041i
$397$	8.74802			0.0220353			0.0110177	−	0.999939i	$-0.496493\pi$
$397$	8.74802			0.0220353			0.0110177	+	0.999939i	$0.496493\pi$
$398$		−	309.979i		−	0.778843i
$399$	−208.900	+	439.290i	−0.523559	+	1.10098i
$400$	−223.626			−0.559064
$401$			600.230i			1.49683i	0.663229	+	0.748416i	$0.269185\pi$
$401$			600.230i			1.49683i	−0.663229	+	0.748416i	$0.730815\pi$
$402$	193.050	+	91.8029i	0.480223	+	0.228365i
$403$	−208.523			−0.517427
$404$			128.520i			0.318120i
$405$	187.085	+	38.8518i	0.461939	+	0.0959304i
$406$	111.105			0.273657
$407$		−	827.622i		−	2.03347i
$408$	14.5028	−	30.4975i	0.0355461	−	0.0747489i
$409$	−271.610			−0.664083			−0.332041	−	0.943265i	$-0.607737\pi$
$409$	−271.610			−0.664083			−0.332041	+	0.943265i	$0.607737\pi$
$410$			137.437i			0.335212i
$411$	450.349	+	214.159i	1.09574	+	0.521068i
$412$	240.344			0.583360
$413$		−	265.518i		−	0.642900i
$414$	−619.510	−	761.380i	−1.49640	−	1.83908i
$415$	240.843			0.580345
$416$		−	282.906i		−	0.680062i
$417$	−289.063	+	607.862i	−0.693196	+	1.45770i
$418$	−1146.34			−2.74243
$419$		−	28.3184i		−	0.0675856i	−0.999429	−	0.0337928i	$-0.989241\pi$
$419$		−	28.3184i		−	0.0675856i	0.999429	−	0.0337928i	$-0.0107586\pi$
$420$	−183.656	−	87.3358i	−0.437277	−	0.207942i
$421$	486.603			1.15583			0.577914	−	0.816098i	$-0.303867\pi$
$421$	486.603			1.15583			0.577914	+	0.816098i	$0.303867\pi$
$422$		−	100.260i		−	0.237584i
$423$	67.1820	−	54.6637i	0.158823	−	0.129229i
$424$	−155.504			−0.366754
$425$		−	80.1336i		−	0.188550i
$426$	67.4620	−	141.864i	0.158362	−	0.333014i
$427$	−129.801			−0.303984
$428$			634.488i			1.48245i
$429$	−234.403	−	111.468i	−0.546393	−	0.259832i
$430$	460.998			1.07209
$431$			247.572i			0.574414i	0.957869	+	0.287207i	$0.0927267\pi$
$431$			247.572i			0.574414i	−0.957869	+	0.287207i	$0.907273\pi$
$432$	−301.827	+	73.5839i	−0.698674	+	0.170333i
$433$	53.1928			0.122847			0.0614236	−	0.998112i	$-0.480436\pi$
$433$	53.1928			0.122847			0.0614236	+	0.998112i	$0.480436\pi$
$434$		−	582.604i		−	1.34241i
$435$	19.3414	−	40.6725i	0.0444630	−	0.0935000i
$436$	50.3941			0.115583
$437$		−	1012.92i		−	2.31790i
$438$	−152.776	−	72.6510i	−0.348803	−	0.165870i
$439$	−411.902			−0.938274			−0.469137	−	0.883125i	$-0.655435\pi$
$439$	−411.902			−0.938274			−0.469137	+	0.883125i	$0.655435\pi$
$440$		−	89.1737i		−	0.202668i
$441$	84.1155	+	103.378i	0.190738	+	0.234418i
$442$	76.9231			0.174034
$443$			67.5908i			0.152575i	0.997086	+	0.0762876i	$0.0243067\pi$
$443$			67.5908i			0.152575i	−0.997086	+	0.0762876i	$0.975693\pi$
$444$	−378.457	+	795.848i	−0.852381	+	1.79245i
$445$	139.380			0.313214
$446$		−	213.458i		−	0.478606i
$447$	61.1508	+	29.0796i	0.136803	+	0.0650551i
$448$	521.303			1.16362
$449$		−	264.181i		−	0.588375i	−0.955748	−	0.294188i	$-0.904951\pi$
$449$		−	264.181i		−	0.588375i	0.955748	−	0.294188i	$-0.0950491\pi$
$450$	405.095	−	329.612i	0.900210	−	0.732471i
$451$	−270.184			−0.599077
$452$			70.3913i			0.155733i
$453$	271.370	−	570.656i	0.599050	−	1.25973i
$454$	−736.870			−1.62306
$455$		−	86.1923i		−	0.189434i
$456$	205.107	+	97.5366i	0.449796	+	0.213896i
$457$	−624.410			−1.36632			−0.683162	−	0.730267i	$-0.739396\pi$
$457$	−624.410			−1.36632			−0.683162	+	0.730267i	$0.739396\pi$
$458$			488.986i			1.06765i
$459$	−26.3679	−	108.156i	−0.0574464	−	0.235634i
$460$	423.477			0.920602
$461$			335.753i			0.728315i	0.931337	+	0.364158i	$0.118643\pi$
$461$			335.753i			0.728315i	−0.931337	+	0.364158i	$0.881357\pi$
$462$	311.436	−	654.911i	0.674105	−	1.41756i
$463$	264.145			0.570507			0.285253	−	0.958452i	$-0.407922\pi$
$463$	264.145			0.570507			0.285253	+	0.958452i	$0.407922\pi$
$464$			73.2248i			0.157812i
$465$	−213.276	−	101.421i	−0.458658	−	0.218110i
$466$	1100.93			2.36250
$467$			56.6007i			0.121201i	0.998162	+	0.0606003i	$0.0193015\pi$
$467$			56.6007i			0.121201i	−0.998162	+	0.0606003i	$0.980698\pi$
$468$	174.431	+	214.377i	0.372716	+	0.458070i
$469$	−139.550			−0.297549
$470$			67.7801i			0.144213i
$471$	−296.429	+	623.352i	−0.629360	+	1.32346i
$472$	−123.972			−0.262652
$473$			906.264i			1.91599i
$474$	416.030	+	197.839i	0.877699	+	0.417381i
$475$	538.928			1.13458
$476$			118.483i			0.248914i
$477$	−397.624	+	323.533i	−0.833593	+	0.678266i
$478$	−347.984			−0.727999
$479$		−	279.086i		−	0.582642i	−0.956625	−	0.291321i	$-0.905905\pi$
$479$		−	279.086i		−	0.582642i	0.956625	−	0.291321i	$-0.0940948\pi$
$480$	137.600	−	289.355i	0.286666	−	0.602822i
$481$	−373.502			−0.776511
$482$		−	361.636i		−	0.750281i
$483$	578.690	+	275.190i	1.19812	+	0.569752i
$484$	347.510			0.717996
$485$			366.849i			0.756390i
$486$	438.297	−	578.172i	0.901845	−	1.18966i
$487$	597.908			1.22774			0.613869	−	0.789408i	$-0.289612\pi$
$487$	597.908			1.22774			0.613869	+	0.789408i	$0.289612\pi$
$488$			60.6049i			0.124190i
$489$	7.78353	−	16.3678i	0.0159172	−	0.0334719i
$490$	−104.299			−0.212854
$491$			619.056i			1.26081i	0.776268	+	0.630403i	$0.217111\pi$
$491$			619.056i			1.26081i	−0.776268	+	0.630403i	$0.782889\pi$
$492$	259.811	+	123.550i	0.528071	+	0.251119i
$493$	−26.2392			−0.0532236
$494$			517.336i			1.04724i
$495$	−185.530	−	228.017i	−0.374808	−	0.460641i
$496$	383.972			0.774137
$497$			102.550i			0.206337i
$498$	392.732	−	825.865i	0.788618	−	1.65836i
$499$	264.488			0.530036			0.265018	−	0.964244i	$-0.414622\pi$
$499$	264.488			0.530036			0.265018	+	0.964244i	$0.414622\pi$
$500$			515.136i			1.03027i
$501$	−639.187	−	303.959i	−1.27582	−	0.606704i
$502$	−489.821			−0.975740
$503$		−	805.942i		−	1.60227i	−0.598484	−	0.801135i	$-0.704230\pi$
$503$		−	805.942i		−	1.60227i	0.598484	−	0.801135i	$-0.295770\pi$
$504$	−111.447	+	90.6807i	−0.221125	+	0.179922i
$505$	−61.6912			−0.122161
$506$			1510.10i			2.98439i
$507$	167.429	−	352.081i	0.330234	−	0.694440i
$508$	−819.756			−1.61369
$509$		−	333.533i		−	0.655272i	−0.944804	−	0.327636i	$-0.893748\pi$
$509$		−	333.533i		−	0.655272i	0.944804	−	0.327636i	$-0.106252\pi$
$510$	78.6765	+	37.4138i	0.154268	+	0.0733605i
$511$	110.437			0.216120
$512$			646.595i			1.26288i
$513$	727.389	−	177.334i	1.41791	−	0.345680i
$514$	396.655			0.771703
$515$			115.368i			0.224015i
$516$	414.419	−	871.471i	0.803138	−	1.68890i
$517$	−133.247			−0.257731
$518$		−	1043.55i		−	2.01457i
$519$	117.262	+	55.7629i	0.225939	+	0.107443i
$520$	−40.2437			−0.0773917
$521$		−	200.988i		−	0.385773i	−0.981221	−	0.192887i	$-0.938215\pi$
$521$		−	200.988i		−	0.385773i	0.981221	−	0.192887i	$-0.0617849\pi$
$522$	−107.929	−	132.646i	−0.206761	−	0.254110i
$523$	472.640			0.903709			0.451855	−	0.892092i	$-0.350763\pi$
$523$	472.640			0.903709			0.451855	+	0.892092i	$0.350763\pi$
$524$		−	924.585i		−	1.76448i
$525$	−146.416	+	307.894i	−0.278887	+	0.586465i
$526$	638.975			1.21478
$527$			137.592i			0.261085i
$528$	431.627	+	205.256i	0.817475	+	0.388742i
$529$	−805.351			−1.52240
$530$		−	401.164i		−	0.756912i
$531$	−316.996	+	257.929i	−0.596980	+	0.485743i
$532$	−796.840			−1.49782
$533$			121.933i			0.228767i
$534$	227.281	−	477.944i	0.425620	−	0.895026i
$535$	−304.561			−0.569273
$536$			65.1569i			0.121561i
$537$	−740.279	−	352.032i	−1.37855	−	0.655553i
$538$	202.934			0.377202
$539$		−	205.038i		−	0.380405i
$540$	74.1388	+	304.103i	0.137294	+	0.563154i
$541$	−554.686			−1.02530			−0.512649	−	0.858598i	$-0.671336\pi$
$541$	−554.686			−1.02530			−0.512649	+	0.858598i	$0.671336\pi$
$542$		−	799.161i		−	1.47447i
$543$	167.663	−	352.573i	0.308771	−	0.649306i
$544$	−186.672			−0.343148
$545$			24.1897i			0.0443848i
$546$	−295.558	−	140.550i	−0.541316	−	0.257417i
$547$	−283.508			−0.518297			−0.259148	−	0.965838i	$-0.583442\pi$
$547$	−283.508			−0.518297			−0.259148	+	0.965838i	$0.583442\pi$
$548$			816.901i			1.49070i
$549$	126.091	+	154.967i	0.229675	+	0.282271i
$550$	−803.455			−1.46083
$551$		−	176.468i		−	0.320269i
$552$	128.488	−	270.194i	0.232768	−	0.489482i
$553$	−300.736			−0.543827
$554$		−	341.411i		−	0.616266i
$555$	−382.016	−	181.664i	−0.688317	−	0.327322i
$556$	−1102.62			−1.98313
$557$			907.265i			1.62884i	0.580274	+	0.814421i	$0.302945\pi$
$557$			907.265i			1.62884i	−0.580274	+	0.814421i	$0.697055\pi$
$558$	−695.559	+	565.953i	−1.24652	+	1.01425i
$559$	408.993			0.731651
$560$			158.714i			0.283417i
$561$	−73.5509	+	154.668i	−0.131107	+	0.275701i
$562$	293.801			0.522778
$563$			666.582i			1.18398i	0.805945	+	0.591991i	$0.201658\pi$
$563$			666.582i			1.18398i	−0.805945	+	0.591991i	$0.798342\pi$
$564$	128.132	+	60.9316i	0.227184	+	0.108035i
$565$	−33.7886			−0.0598029
$566$			145.375i			0.256847i
$567$	−96.3048	+	463.741i	−0.169850	+	0.817886i
$568$	47.8810			0.0842976
$569$		−	247.464i		−	0.434910i	−0.976070	−	0.217455i	$-0.930224\pi$
$569$		−	247.464i		−	0.434910i	0.976070	−	0.217455i	$-0.0697756\pi$
$570$	−251.622	+	529.128i	−0.441442	+	0.928296i
$571$	148.196			0.259538			0.129769	−	0.991544i	$-0.458576\pi$
$571$	148.196			0.259538			0.129769	+	0.991544i	$0.458576\pi$
$572$		−	425.190i		−	0.743339i
$573$	561.312	+	266.926i	0.979602	+	0.465840i
$574$	−340.675			−0.593510
$575$		−	709.946i		−	1.23469i
$576$	−506.405	−	622.374i	−0.879175	−	1.08051i
$577$	809.739			1.40336			0.701680	−	0.712492i	$-0.252433\pi$
$577$	809.739			1.40336			0.701680	+	0.712492i	$0.252433\pi$
$578$		−	50.7569i		−	0.0878147i
$579$	−250.720	+	527.233i	−0.433023	+	0.910592i
$580$	73.7770			0.127202
$581$			596.995i			1.02753i
$582$	1257.95	+	598.204i	2.16142	+	1.02784i
$583$	788.637			1.35272
$584$		−	51.5639i		−	0.0882943i
$585$	−102.903	+	83.7289i	−0.175903	+	0.143126i
$586$	307.719			0.525119
$587$			812.999i			1.38501i	0.721415	+	0.692503i	$0.243492\pi$
$587$			812.999i			1.38501i	−0.721415	+	0.692503i	$0.756508\pi$
$588$	−93.7605	+	197.166i	−0.159457	+	0.335317i
$589$	−925.354			−1.57106
$590$		−	319.819i		−	0.542065i
$591$	−156.440	−	74.3935i	−0.264704	−	0.125877i
$592$	687.763			1.16176
$593$		−	360.231i		−	0.607473i	−0.952756	−	0.303737i	$-0.901766\pi$
$593$		−	360.231i		−	0.607473i	0.952756	−	0.303737i	$-0.0982343\pi$
$594$	−1084.42	+	264.376i	−1.82562	+	0.445078i
$595$	−56.8731			−0.0955850
$596$			110.923i			0.186113i
$597$	133.760	−	281.280i	0.224053	−	0.471155i
$598$	681.502			1.13964
$599$			15.4101i			0.0257264i	0.999917	+	0.0128632i	$0.00409460\pi$
$599$			15.4101i			0.0257264i	−0.999917	+	0.0128632i	$0.995905\pi$
$600$	143.757	+	68.3624i	0.239596	+	0.113937i
$601$	−127.926			−0.212854			−0.106427	−	0.994320i	$-0.533941\pi$
$601$	−127.926			−0.212854			−0.106427	+	0.994320i	$0.533941\pi$
$602$			1142.71i			1.89819i
$603$	135.562	+	166.606i	0.224813	+	0.276296i
$604$	1035.13			1.71379
$605$			166.809i			0.275717i
$606$	−100.597	+	211.543i	−0.166002	+	0.349081i
$607$	925.983			1.52551			0.762754	−	0.646689i	$-0.223847\pi$
$607$	925.983			1.52551			0.762754	+	0.646689i	$0.223847\pi$
$608$		−	1255.44i		−	2.06487i
$609$	100.818	+	47.9429i	0.165547	+	0.0787240i
$610$	−156.347			−0.256306
$611$			60.1338i			0.0984187i
$612$	141.454	−	115.097i	0.231134	−	0.188066i
$613$	−54.7142			−0.0892565			−0.0446282	−	0.999004i	$-0.514210\pi$
$613$	−54.7142			−0.0892565			−0.0446282	+	0.999004i	$0.514210\pi$
$614$			108.600i			0.176873i
$615$	−59.3056	+	124.712i	−0.0964319	+	0.202784i
$616$	221.041			0.358833
$617$			254.443i			0.412388i	0.978511	+	0.206194i	$0.0661078\pi$
$617$			254.443i			0.412388i	−0.978511	+	0.206194i	$0.933892\pi$
$618$	395.603	+	188.125i	0.640135	+	0.304410i
$619$	615.519			0.994376			0.497188	−	0.867643i	$-0.334366\pi$
$619$	615.519			0.994376			0.497188	+	0.867643i	$0.334366\pi$
$620$		−	386.868i		−	0.623980i
$621$	−233.607	−	958.212i	−0.376179	−	1.54301i
$622$	−1318.34			−2.11952
$623$			345.492i			0.554562i
$624$	92.6310	−	194.791i	0.148447	−	0.312165i
$625$	238.610			0.381776
$626$		−	402.756i		−	0.643381i
$627$	−1040.20	−	494.657i	−1.65901	−	0.788926i
$628$	−1130.72			−1.80050
$629$			246.451i			0.391815i
$630$	−233.935	−	287.507i	−0.371325	−	0.456361i
$631$	−221.177			−0.350519			−0.175259	−	0.984522i	$-0.556076\pi$
$631$	−221.177			−0.350519			−0.175259	+	0.984522i	$0.556076\pi$
$632$			140.416i			0.222176i
$633$	43.2634	−	90.9775i	0.0683467	−	0.143724i
$634$	62.9826			0.0993416
$635$		−	393.492i		−	0.619672i
$636$	−758.360	−	360.630i	−1.19239	−	0.567029i
$637$	−92.5328			−0.145263
$638$			263.086i			0.412361i
$639$	122.432	−	99.6187i	0.191599	−	0.155898i
$640$	200.707			0.313605
$641$			518.088i			0.808250i	0.914704	+	0.404125i	$0.132424\pi$
$641$			518.088i			0.808250i	−0.914704	+	0.404125i	$0.867576\pi$
$642$	−496.634	+	1044.36i	−0.773573	+	1.62673i
$643$	−473.954			−0.737098			−0.368549	−	0.929608i	$-0.620145\pi$
$643$	−473.954			−0.737098			−0.368549	+	0.929608i	$0.620145\pi$
$644$			1049.70i			1.62997i
$645$	418.316	+	198.926i	0.648552	+	0.308412i
$646$	341.359			0.528419
$647$		−	905.524i		−	1.39957i	−0.714352	−	0.699787i	$-0.753278\pi$
$647$		−	905.524i		−	1.39957i	0.714352	−	0.699787i	$-0.246722\pi$
$648$	216.524	+	44.9653i	0.334141	+	0.0693908i
$649$	628.723			0.968757
$650$			362.596i			0.557839i
$651$	251.400	−	528.663i	0.386175	−	0.812078i
$652$	29.6900			0.0455368
$653$		−	461.531i		−	0.706786i	−0.935475	−	0.353393i	$-0.885028\pi$
$653$		−	461.531i		−	0.706786i	0.935475	−	0.353393i	$-0.114972\pi$
$654$	82.9479	+	39.4451i	0.126832	+	0.0603135i
$655$	443.811			0.677574
$656$		−	224.526i		−	0.342265i
$657$	−107.281	−	131.849i	−0.163289	−	0.200683i
$658$	−168.011			−0.255336
$659$		−	1013.12i		−	1.53735i	−0.639637	−	0.768677i	$-0.720915\pi$
$659$		−	1013.12i		−	1.53735i	0.639637	−	0.768677i	$-0.279085\pi$
$660$	206.804	−	434.882i	0.313339	−	0.658912i
$661$	1013.26			1.53292			0.766460	−	0.642292i	$-0.222017\pi$
$661$	1013.26			1.53292			0.766460	+	0.642292i	$0.222017\pi$
$662$		−	1853.32i		−	2.79958i
$663$	69.8010	+	33.1932i	0.105281	+	0.0500651i
$664$	278.740			0.419790
$665$		−	382.492i		−	0.575176i
$666$	−1245.87	+	1013.72i	−1.87068	+	1.52211i
$667$	−232.467			−0.348527
$668$		−	1159.44i		−	1.73569i
$669$	92.1096	−	193.695i	0.137683	−	0.289529i
$670$	−168.090			−0.250880
$671$		−	307.358i		−	0.458059i
$672$	717.244	+	341.078i	1.06733	+	0.507557i
$673$	1071.19			1.59166			0.795829	−	0.605522i	$-0.207036\pi$
$673$	1071.19			1.59166			0.795829	+	0.605522i	$0.207036\pi$
$674$		−	615.964i		−	0.913894i
$675$	509.820	−	124.291i	0.755288	−	0.184135i
$676$	638.650			0.944748
$677$			1256.39i			1.85582i	0.372798	+	0.927912i	$0.378398\pi$
$677$			1256.39i			1.85582i	−0.372798	+	0.927912i	$0.621602\pi$
$678$	−55.0976	+	115.863i	−0.0812648	+	0.170890i
$679$	−909.335			−1.33923
$680$			26.5544i			0.0390506i
$681$	−668.646	−	317.968i	−0.981859	−	0.466913i
$682$	1379.56			2.02281
$683$		−	336.900i		−	0.493265i	−0.969109	−	0.246632i	$-0.920676\pi$
$683$		−	336.900i		−	0.493265i	0.969109	−	0.246632i	$-0.0793240\pi$
$684$	774.067	+	951.332i	1.13168	+	1.39084i
$685$	−392.122			−0.572440
$686$		−	1114.00i		−	1.62390i
$687$	−211.003	+	443.712i	−0.307137	+	0.645870i
$688$	−753.116			−1.09464
$689$		−	355.908i		−	0.516558i
$690$	697.037	+	331.469i	1.01020	+	0.480390i
$691$	596.888			0.863803			0.431902	−	0.901921i	$-0.357843\pi$
$691$	596.888			0.863803			0.431902	+	0.901921i	$0.357843\pi$
$692$			212.705i			0.307377i
$693$	565.203	−	459.887i	0.815589	−	0.663617i
$694$	818.822			1.17986
$695$		−	529.269i		−	0.761538i
$696$	22.3848	−	47.0725i	0.0321621	−	0.0676329i
$697$	80.4561			0.115432
$698$			1247.43i			1.78714i
$699$	998.994	+	475.062i	1.42918	+	0.679630i
$700$	−558.497			−0.797853
$701$			496.025i			0.707597i	0.935322	+	0.353798i	$0.115110\pi$
$701$			496.025i			0.707597i	−0.935322	+	0.353798i	$0.884890\pi$
$702$	119.312	+	489.394i	0.169960	+	0.697143i
$703$	−1657.48			−2.35772
$704$			1234.40i			1.75341i
$705$	−29.2479	+	61.5045i	−0.0414863	+	0.0872405i
$706$	−807.974			−1.14444
$707$		−	152.918i		−	0.216292i
$708$	−604.585	−	287.504i	−0.853934	−	0.406080i
$709$	−904.662			−1.27597			−0.637985	−	0.770049i	$-0.720232\pi$
$709$	−904.662			−1.27597			−0.637985	+	0.770049i	$0.720232\pi$
$710$			123.522i			0.173974i
$711$	292.141	+	359.043i	0.410888	+	0.504983i
$712$	161.312			0.226562
$713$			1219.00i			1.70967i
$714$	−92.7404	+	195.021i	−0.129888	+	0.273139i
$715$	204.096			0.285449
$716$		−	1342.81i		−	1.87544i
$717$	−315.765	−	150.159i	−0.440398	−	0.209427i
$718$	−1798.44			−2.50479
$719$		−	295.637i		−	0.411178i	−0.978638	−	0.205589i	$-0.934089\pi$
$719$		−	295.637i		−	0.411178i	0.978638	−	0.205589i	$-0.0659111\pi$
$720$	189.485	−	154.178i	0.263174	−	0.214136i
$721$	−285.971			−0.396630
$722$			1217.92i			1.68688i
$723$	156.050	−	328.153i	0.215837	−	0.453877i
$724$	639.543			0.883346
$725$		−	123.685i		−	0.170600i
$726$	571.996	+	272.007i	0.787874	+	0.374665i
$727$	−588.858			−0.809983			−0.404991	−	0.914320i	$-0.632726\pi$
$727$	−588.858			−0.809983			−0.404991	+	0.914320i	$0.632726\pi$
$728$		−	99.7549i		−	0.137026i
$729$	647.204	−	335.511i	0.887797	−	0.460235i
$730$	133.023			0.182223
$731$		−	269.870i		−	0.369179i
$732$	−140.549	+	295.558i	−0.192007	+	0.403767i
$733$	1190.69			1.62440			0.812201	−	0.583378i	$-0.198269\pi$
$733$	1190.69			1.62440			0.812201	+	0.583378i	$0.198269\pi$
$734$			1936.75i			2.63863i
$735$	−94.6420	−	45.0061i	−0.128765	−	0.0612327i
$736$	−1653.83			−2.24705
$737$		−	330.443i		−	0.448362i
$738$	330.938	+	406.725i	0.448426	+	0.551118i
$739$	−509.472			−0.689407			−0.344704	−	0.938712i	$-0.612021\pi$
$739$	−509.472			−0.689407			−0.344704	+	0.938712i	$0.612021\pi$
$740$		−	692.949i		−	0.936418i
$741$	−223.236	+	469.438i	−0.301264	+	0.633519i
$742$	994.393			1.34015
$743$		−	239.192i		−	0.321928i	−0.986960	−	0.160964i	$-0.948540\pi$
$743$		−	239.192i		−	0.321928i	0.986960	−	0.160964i	$-0.0514603\pi$
$744$	−246.836	−	117.380i	−0.331769	−	0.157769i
$745$	−53.2443			−0.0714689
$746$		−	1742.42i		−	2.33569i
$747$	712.740	−	579.933i	0.954137	−	0.776349i
$748$	−280.557			−0.375076
$749$		−	754.937i		−	1.00793i
$750$	−403.214	+	847.907i	−0.537618	+	1.13054i
$751$	391.193			0.520897			0.260448	−	0.965488i	$-0.416130\pi$
$751$	391.193			0.520897			0.260448	+	0.965488i	$0.416130\pi$
$752$		−	110.730i		−	0.147247i
$753$	−444.470	−	211.363i	−0.590266	−	0.280695i
$754$	118.730			0.157466
$755$			496.873i			0.658110i
$756$	−753.802	+	183.773i	−0.997093	+	0.243086i
$757$	−671.860			−0.887530			−0.443765	−	0.896143i	$-0.646357\pi$
$757$	−671.860			−0.887530			−0.443765	+	0.896143i	$0.646357\pi$
$758$			500.377i			0.660128i
$759$	−651.626	+	1370.29i	−0.858533	+	1.80539i
$760$	−178.588			−0.234984
$761$			392.828i			0.516199i	0.966118	+	0.258100i	$0.0830963\pi$
$761$			392.828i			0.516199i	−0.966118	+	0.258100i	$0.916904\pi$
$762$	−1349.31	−	641.650i	−1.77074	−	0.842060i
$763$	−59.9608			−0.0785855
$764$			1018.18i			1.33270i
$765$	55.2477	+	67.8996i	0.0722192	+	0.0887577i
$766$	515.568			0.673065
$767$		−	283.740i		−	0.369935i
$768$	−132.157	+	277.909i	−0.172079	+	0.361861i
$769$	−452.671			−0.588649			−0.294325	−	0.955705i	$-0.595095\pi$
$769$	−452.671			−0.588649			−0.294325	+	0.955705i	$0.595095\pi$
$770$			570.235i			0.740565i
$771$	359.930	+	171.161i	0.466836	+	0.221999i
$772$	−956.362			−1.23881
$773$			1123.88i			1.45393i	0.686677	+	0.726963i	$0.259069\pi$
$773$			1123.88i			1.45393i	−0.686677	+	0.726963i	$0.740931\pi$
$774$	1364.26	−	1110.05i	1.76261	−	1.43417i
$775$	−648.572			−0.836866
$776$			424.574i			0.547131i
$777$	450.303	−	946.930i	0.579540	−	1.21870i
$778$	1408.55			1.81048
$779$			541.096i			0.694604i
$780$	−196.260	−	93.3295i	−0.251616	−	0.119653i
$781$	−242.828			−0.310920
$782$		−	449.682i		−	0.575041i
$783$	−40.6984	−	166.937i	−0.0519775	−	0.213202i
$784$	170.389			0.217333
$785$		−	542.756i		−	0.691409i
$786$	723.702	−	1521.85i	0.920741	−	1.93620i
$787$	−244.866			−0.311138			−0.155569	−	0.987825i	$-0.549721\pi$
$787$	−244.866			−0.311138			−0.155569	+	0.987825i	$0.549721\pi$
$788$		−	283.771i		−	0.360116i
$789$	579.814	+	275.725i	0.734872	+	0.349461i
$790$	−362.239			−0.458531
$791$		−	83.7543i		−	0.105884i
$792$	−214.724	−	263.897i	−0.271116	−	0.333203i
$793$	−138.709			−0.174917
$794$			26.1190i			0.0328954i
$795$	173.107	−	364.021i	0.217744	−	0.457888i
$796$	510.221			0.640981
$797$			1383.05i			1.73532i	0.497160	+	0.867659i	$0.334376\pi$
$797$			1383.05i			1.73532i	−0.497160	+	0.867659i	$0.665624\pi$
$798$	−1311.59	−	623.713i	−1.64359	−	0.781595i
$799$	39.6787			0.0496604
$800$		−	879.926i		−	1.09991i
$801$	412.476	−	335.618i	0.514952	−	0.418999i
$802$	−1792.11			−2.23455
$803$			261.506i			0.325661i
$804$	−151.106	+	317.757i	−0.187943	+	0.395220i
$805$	−503.869			−0.625924
$806$		−	622.587i		−	0.772441i
$807$	184.145	+	87.5685i	0.228185	+	0.108511i
$808$	−71.3985			−0.0883645
$809$		−	425.627i		−	0.526115i	−0.964780	−	0.263057i	$-0.915269\pi$
$809$		−	425.627i		−	0.526115i	0.964780	−	0.263057i	$-0.0847308\pi$
$810$	−116.000	+	558.581i	−0.143210	+	0.689606i
$811$	589.005			0.726270			0.363135	−	0.931737i	$-0.381706\pi$
$811$	589.005			0.726270			0.363135	+	0.931737i	$0.381706\pi$
$812$			182.876i			0.225217i
$813$	344.847	−	725.169i	0.424166	−	0.891967i
$814$	2471.03			3.03566
$815$			14.2515i			0.0174865i
$816$	−128.531	−	61.1216i	−0.157513	−	0.0749039i
$817$	1814.97			2.22151
$818$		−	810.946i		−	0.991376i
$819$	−207.545	−	255.074i	−0.253412	−	0.311445i
$820$	−226.219			−0.275877
$821$		−	628.803i		−	0.765899i	−0.923769	−	0.382950i	$-0.874908\pi$
$821$		−	628.803i		−	0.765899i	0.923769	−	0.382950i	$-0.125092\pi$
$822$	−639.415	+	1344.61i	−0.777877	+	1.63578i
$823$	−597.267			−0.725720			−0.362860	−	0.931844i	$-0.618200\pi$
$823$	−597.267			−0.725720			−0.362860	+	0.931844i	$0.618200\pi$
$824$			133.521i			0.162040i
$825$	−729.066	−	346.700i	−0.883716	−	0.420242i
$826$	792.757			0.959754
$827$			719.598i			0.870131i	0.900399	+	0.435065i	$0.143275\pi$
$827$			719.598i			0.870131i	−0.900399	+	0.435065i	$0.856725\pi$
$828$	1253.22	−	1019.70i	1.51355	−	1.23152i
$829$	−357.388			−0.431108			−0.215554	−	0.976492i	$-0.569156\pi$
$829$	−357.388			−0.431108			−0.215554	+	0.976492i	$0.569156\pi$
$830$			719.085i			0.866368i
$831$	147.323	−	309.801i	0.177284	−	0.372805i
$832$	557.079			0.669567
$833$			61.0568i			0.0732975i
$834$	−1814.89	−	863.054i	−2.17613	−	1.03484i
$835$	556.543			0.666519
$836$		−	1886.85i		−	2.25700i
$837$	−875.375	+	213.412i	−1.04585	+	0.254972i
$838$	84.5502			0.100895
$839$			201.403i			0.240052i	0.992771	+	0.120026i	$0.0382978\pi$
$839$			201.403i			0.240052i	−0.992771	+	0.120026i	$0.961702\pi$
$840$	48.5188	−	102.029i	0.0577604	−	0.121463i
$841$	800.500			0.951843
$842$			1452.85i			1.72548i
$843$	266.599	+	126.779i	0.316250	+	0.150390i
$844$	165.027			0.195529
$845$			306.559i			0.362792i
$846$	163.210	+	200.585i	0.192919	+	0.237099i
$847$	−413.480			−0.488170
$848$			655.366i			0.772837i
$849$	−62.7310	+	131.915i	−0.0738881	+	0.155377i
$850$	239.255			0.281476
$851$			2183.44i			2.56574i
$852$	233.506	+	111.041i	0.274068	+	0.130330i
$853$	−519.978			−0.609587			−0.304794	−	0.952418i	$-0.598588\pi$
$853$	−519.978			−0.609587			−0.304794	+	0.952418i	$0.598588\pi$
$854$		−	387.547i		−	0.453802i
$855$	−456.650	+	371.561i	−0.534093	+	0.434574i
$856$	−352.485			−0.411781
$857$		−	84.6174i		−	0.0987367i	−0.998781	−	0.0493684i	$-0.984279\pi$
$857$		−	84.6174i		−	0.0987367i	0.998781	−	0.0493684i	$-0.0157208\pi$
$858$	332.810	−	699.856i	0.387890	−	0.815683i
$859$	−5.07382			−0.00590665			−0.00295333	−	0.999996i	$-0.500940\pi$
$859$	−5.07382			−0.00590665			−0.00295333	+	0.999996i	$0.500940\pi$
$860$			758.795i			0.882320i
$861$	−309.133	−	147.005i	−0.359039	−	0.170738i
$862$	−739.177			−0.857514
$863$			393.960i			0.456501i	0.973602	+	0.228250i	$0.0733005\pi$
$863$			393.960i			0.456501i	−0.973602	+	0.228250i	$0.926699\pi$
$864$	−289.539	−	1187.63i	−0.335114	−	1.37458i
$865$	−102.101			−0.118036
$866$			158.818i			0.183392i
$867$	21.9022	−	46.0575i	0.0252620	−	0.0531229i
$868$	958.956			1.10479
$869$		−	712.117i		−	0.819467i
$870$	121.436	+	57.7477i	0.139582	+	0.0663766i
$871$	−149.127			−0.171214
$872$			27.9960i			0.0321055i
$873$	883.346	+	1085.64i	1.01185	+	1.24357i
$874$	3024.28			3.46027
$875$		−	612.929i		−	0.700490i
$876$	119.582	−	251.466i	0.136509	−	0.287062i
$877$	490.073			0.558806			0.279403	−	0.960174i	$-0.409863\pi$
$877$	490.073			0.558806			0.279403	+	0.960174i	$0.409863\pi$
$878$		−	1229.82i		−	1.40070i
$879$	279.229	+	132.784i	0.317666	+	0.151063i
$880$	−375.820			−0.427068
$881$		−	248.887i		−	0.282505i	−0.989974	−	0.141252i	$-0.954887\pi$
$881$		−	248.887i		−	0.282505i	0.989974	−	0.141252i	$-0.0451129\pi$
$882$	−308.657	+	251.144i	−0.349951	+	0.284744i
$883$	−780.857			−0.884323			−0.442161	−	0.896936i	$-0.645788\pi$
$883$	−780.857			−0.884323			−0.442161	+	0.896936i	$0.645788\pi$
$884$			126.614i			0.143229i
$885$	138.005	−	290.208i	0.155938	−	0.327918i
$886$	−201.806			−0.227772
$887$			674.605i			0.760547i	0.924874	+	0.380273i	$0.124170\pi$
$887$			674.605i			0.760547i	−0.924874	+	0.380273i	$0.875830\pi$
$888$	−442.127	−	210.249i	−0.497891	−	0.236767i
$889$	975.377			1.09716
$890$			416.148i			0.467582i
$891$	−1098.10	−	228.041i	−1.23243	−	0.255939i
$892$	351.349			0.393889
$893$			266.854i			0.298828i
$894$	−86.8231	+	182.578i	−0.0971175	+	0.204226i
$895$	644.565			0.720184
$896$			497.507i			0.555254i
$897$	618.404	+	294.076i	0.689414	+	0.327844i
$898$	788.764			0.878357
$899$			212.371i			0.236230i
$900$	542.536	+	666.779i	0.602817	+	0.740865i
$901$	−234.842			−0.260646
$902$		−	806.688i		−	0.894333i
$903$	−493.092	+	1036.91i	−0.546060	+	1.14829i
$904$	−39.1054			−0.0432581
$905$			306.988i			0.339213i
$906$	1703.81	+	810.229i	1.88058	+	0.894292i
$907$	673.025			0.742034			0.371017	−	0.928626i	$-0.379009\pi$
$907$	673.025			0.742034			0.371017	+	0.928626i	$0.379009\pi$
$908$		−	1212.88i		−	1.33577i
$909$	−182.566	+	148.548i	−0.200843	+	0.163419i
$910$	257.344			0.282796
$911$		−	1355.16i		−	1.48755i	−0.668428	−	0.743777i	$-0.733033\pi$
$911$		−	1355.16i		−	1.48755i	0.668428	−	0.743777i	$-0.266967\pi$
$912$	411.065	−	864.418i	0.450729	−	0.947826i
$913$	−1413.63			−1.54834
$914$		−	1864.30i		−	2.03972i
$915$	−141.871	−	67.4653i	−0.155050	−	0.0737326i
$916$	−804.862			−0.878671
$917$			1100.11i			1.19968i
$918$	322.922	−	78.7267i	0.351767	−	0.0857589i
$919$	277.389			0.301838			0.150919	−	0.988546i	$-0.451777\pi$
$919$	277.389			0.301838			0.150919	+	0.988546i	$0.451777\pi$
$920$			235.259i			0.255717i
$921$	−46.8621	+	98.5451i	−0.0508818	+	0.106998i
$922$	−1002.46			−1.08727
$923$			109.587i			0.118730i
$924$	1077.97	+	512.619i	1.16664	+	0.554782i
$925$	−1161.71			−1.25590
$926$			788.657i			0.851682i
$927$	277.798	+	341.415i	0.299674	+	0.368300i
$928$	−288.126			−0.310481
$929$		−	706.589i		−	0.760591i	−0.924865	−	0.380295i	$-0.875822\pi$
$929$		−	706.589i		−	0.760591i	0.924865	−	0.380295i	$-0.124178\pi$
$930$	302.814	−	636.779i	0.325606	−	0.684708i
$931$	−410.629			−0.441063
$932$			1812.10i			1.94432i
$933$	−1196.28	−	568.879i	−1.28219	−	0.609731i
$934$	−168.993			−0.180935
$935$		−	134.670i		−	0.144033i
$936$	−119.095	+	96.9039i	−0.127239	+	0.103530i
$937$	−777.272			−0.829532			−0.414766	−	0.909928i	$-0.636137\pi$
$937$	−777.272			−0.829532			−0.414766	+	0.909928i	$0.636137\pi$
$938$		−	416.656i		−	0.444196i
$939$	173.794	−	365.466i	0.185084	−	0.389208i
$940$	−111.565			−0.118686
$941$		−	1244.77i		−	1.32282i	−0.750024	−	0.661411i	$-0.769958\pi$
$941$		−	1244.77i		−	1.32282i	0.750024	−	0.661411i	$-0.230042\pi$
$942$	−1861.14	−	885.047i	−1.97573	−	0.939541i
$943$	712.803			0.755888
$944$			522.476i			0.553470i
$945$	−88.2131	−	361.833i	−0.0933472	−	0.382893i
$946$	−2705.83			−2.86029
$947$			1073.95i			1.13405i	0.823699	+	0.567027i	$0.191906\pi$
$947$			1073.95i			1.13405i	−0.823699	+	0.567027i	$0.808094\pi$
$948$	−325.639	+	684.777i	−0.343501	+	0.722339i
$949$	118.016			0.124359
$950$			1609.08i			1.69377i
$951$	57.1513	+	27.1777i	0.0600960	+	0.0285780i
$952$	−65.8222			−0.0691410
$953$			433.160i			0.454522i	0.973834	+	0.227261i	$0.0729771\pi$
$953$			433.160i			0.454522i	−0.973834	+	0.227261i	$0.927023\pi$
$954$	−965.973	−	1187.19i	−1.01255	−	1.24443i
$955$	−488.738			−0.511767
$956$		−	572.775i		−	0.599137i
$957$	−113.525	+	238.728i	−0.118626	+	0.249454i
$958$	833.266			0.869798
$959$		−	971.980i		−	1.01353i
$960$	569.778	+	270.952i	0.593519	+	0.282242i
$961$	152.616			0.158810
$962$		−	1115.16i		−	1.15922i
$963$	−901.305	+	733.361i	−0.935934	+	0.761538i
$964$	595.246			0.617475
$965$		−	459.064i		−	0.475714i
$966$	−821.636	+	1727.80i	−0.850555	+	1.78861i
$967$	−810.085			−0.837731			−0.418865	−	0.908048i	$-0.637572\pi$
$967$	−810.085			−0.837731			−0.418865	+	0.908048i	$0.637572\pi$
$968$			193.056i			0.199438i
$969$	309.754	+	147.300i	0.319663	+	0.152013i
$970$	−1095.30			−1.12918
$971$		−	778.577i		−	0.801830i	−0.916115	−	0.400915i	$-0.868692\pi$
$971$		−	778.577i		−	0.801830i	0.916115	−	0.400915i	$-0.131308\pi$
$972$	951.662	+	721.429i	0.979076	+	0.742210i
$973$	1311.94			1.34834
$974$			1785.18i			1.83283i
$975$	−156.464	+	329.024i	−0.160476	+	0.337461i
$976$	255.418			0.261698
$977$		−	1409.92i		−	1.44311i	−0.692357	−	0.721555i	$-0.743428\pi$
$977$		−	1409.92i		−	1.44311i	0.692357	−	0.721555i	$-0.256572\pi$
$978$	48.8693	+	23.2393i	0.0499686	+	0.0237621i
$979$	−818.095			−0.835644
$980$		−	171.674i		−	0.175177i
$981$	58.2471	+	71.5859i	0.0593752	+	0.0729724i
$982$	−1848.32			−1.88220
$983$		−	1307.60i		−	1.33022i	−0.746746	−	0.665109i	$-0.768385\pi$
$983$		−	1307.60i		−	1.33022i	0.746746	−	0.665109i	$-0.231615\pi$
$984$	−68.6375	+	144.336i	−0.0697536	+	0.146683i
$985$	136.213			0.138288
$986$		−	78.3425i		−	0.0794549i
$987$	−152.456	−	72.4988i	−0.154464	−	0.0734537i
$988$	−851.526			−0.861868
$989$		−	2390.92i		−	2.41751i
$990$	680.792	−	553.938i	0.687669	−	0.559533i
$991$	−276.670			−0.279182			−0.139591	−	0.990209i	$-0.544579\pi$
$991$	−276.670			−0.279182			−0.139591	+	0.990209i	$0.544579\pi$
$992$			1510.86i			1.52304i
$993$	799.729	−	1681.73i	0.805367	−	1.69358i
$994$	−306.182			−0.308031
$995$			244.912i			0.246142i
$996$	1359.36	+	646.430i	1.36482	+	0.649026i
$997$	1100.90			1.10421			0.552105	−	0.833775i	$-0.313825\pi$
$997$	1100.90			1.10421			0.552105	+	0.833775i	$0.313825\pi$
$998$			789.682i			0.791264i
$999$	−1567.95	+	382.259i	−1.56952	+	0.382642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.b.a.35.9	yes	10
3.2	odd	2	inner	51.3.b.a.35.2	✓	10
4.3	odd	2		816.3.g.b.545.7		10
12.11	even	2		816.3.g.b.545.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.b.a.35.2	✓	10	3.2	odd	2	inner
51.3.b.a.35.9	yes	10	1.1	even	1	trivial
816.3.g.b.545.7		10	4.3	odd	2
816.3.g.b.545.8		10	12.11	even	2

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.98570i q^{2} +(-1.28836 + 2.70927i) q^{3} -4.91441 q^{4} -2.35897i q^{5} +(-8.08906 - 3.84667i) q^{6} +5.84735 q^{7} -2.73016i q^{8} +(-5.68024 - 6.98104i) q^{9} +O(q^{10})\)	\(q+2.98570i q^{2} +(-1.28836 + 2.70927i) q^{3} -4.91441 q^{4} -2.35897i q^{5} +(-8.08906 - 3.84667i) q^{6} +5.84735 q^{7} -2.73016i q^{8} +(-5.68024 - 6.98104i) q^{9} +7.04319 q^{10} +13.8460i q^{11} +(6.33155 - 13.3144i) q^{12} +6.24865 q^{13} +17.4585i q^{14} +(6.39108 + 3.03921i) q^{15} -11.5062 q^{16} -4.12311i q^{17} +(20.8433 - 16.9595i) q^{18} +27.7294 q^{19} +11.5930i q^{20} +(-7.53352 + 15.8420i) q^{21} -41.3401 q^{22} -36.5288i q^{23} +(7.39674 + 3.51745i) q^{24} +19.4352 q^{25} +18.6566i q^{26} +(26.2317 - 6.39515i) q^{27} -28.7363 q^{28} -6.36395i q^{29} +(-9.07419 + 19.0819i) q^{30} -33.3709 q^{31} -45.2747i q^{32} +(-37.5126 - 17.8387i) q^{33} +12.3104 q^{34} -13.7937i q^{35} +(27.9150 + 34.3077i) q^{36} -59.7732 q^{37} +82.7917i q^{38} +(-8.05053 + 16.9292i) q^{39} -6.44038 q^{40} +19.5135i q^{41} +(-47.2996 - 22.4928i) q^{42} +65.4530 q^{43} -68.0451i q^{44} +(-16.4681 + 13.3995i) q^{45} +109.064 q^{46} +9.62349i q^{47} +(14.8242 - 31.1733i) q^{48} -14.8084 q^{49} +58.0278i q^{50} +(11.1706 + 5.31206i) q^{51} -30.7084 q^{52} -56.9577i q^{53} +(19.0940 + 78.3200i) q^{54} +32.6624 q^{55} -15.9642i q^{56} +(-35.7255 + 75.1263i) q^{57} +19.0008 q^{58} -45.4082i q^{59} +(-31.4084 - 14.9360i) q^{60} -22.1983 q^{61} -99.6355i q^{62} +(-33.2144 - 40.8206i) q^{63} +89.1520 q^{64} -14.7404i q^{65} +(53.2611 - 112.001i) q^{66} -23.8655 q^{67} +20.2626i q^{68} +(98.9661 + 47.0623i) q^{69} +41.1840 q^{70} +17.5378i q^{71} +(-19.0594 + 15.5080i) q^{72} +18.8867 q^{73} -178.465i q^{74} +(-25.0397 + 52.6552i) q^{75} -136.274 q^{76} +80.9626i q^{77} +(-50.5457 - 24.0365i) q^{78} -51.4312 q^{79} +27.1428i q^{80} +(-16.4698 + 79.3079i) q^{81} -58.2614 q^{82} +102.097i q^{83} +(37.0228 - 77.8543i) q^{84} -9.72629 q^{85} +195.423i q^{86} +(17.2416 + 8.19908i) q^{87} +37.8019 q^{88} +59.0852i q^{89} +(-40.0070 - 49.1688i) q^{90} +36.5380 q^{91} +179.517i q^{92} +(42.9938 - 90.4106i) q^{93} -28.7329 q^{94} -65.4129i q^{95} +(122.661 + 58.3303i) q^{96} -155.512 q^{97} -44.2136i q^{98} +(96.6596 - 78.6487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{3} - 16 q^{4} - 2 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 10 * q + 2 * q^3 - 16 * q^4 - 2 * q^6 - 4 * q^7 + 6 * q^9	\( 10 q + 2 q^{3} - 16 q^{4} - 2 q^{6} - 4 q^{7} + 6 q^{9} - 24 q^{10} - 46 q^{12} + 30 q^{13} + 30 q^{15} + 40 q^{16} + 80 q^{18} - 6 q^{19} - 40 q^{21} + 56 q^{22} - 30 q^{24} - 32 q^{25} - 10 q^{27} - 96 q^{28} - 20 q^{30} - 80 q^{31} - 26 q^{33} - 104 q^{37} - 24 q^{39} + 196 q^{40} + 122 q^{43} + 144 q^{45} + 324 q^{46} + 154 q^{48} - 154 q^{49} - 472 q^{52} + 70 q^{54} + 314 q^{55} - 232 q^{57} - 148 q^{58} - 244 q^{60} + 176 q^{61} - 304 q^{63} - 208 q^{64} + 320 q^{66} - 132 q^{67} + 294 q^{69} - 16 q^{70} - 480 q^{72} + 262 q^{75} + 248 q^{76} + 108 q^{78} - 92 q^{79} + 114 q^{81} - 76 q^{82} + 32 q^{84} + 34 q^{85} + 120 q^{87} + 52 q^{88} - 376 q^{90} + 156 q^{91} + 16 q^{93} + 216 q^{94} + 546 q^{96} + 464 q^{97} + 236 q^{99}+O(q^{100}) \) 10 * q + 2 * q^3 - 16 * q^4 - 2 * q^6 - 4 * q^7 + 6 * q^9 - 24 * q^10 - 46 * q^12 + 30 * q^13 + 30 * q^15 + 40 * q^16 + 80 * q^18 - 6 * q^19 - 40 * q^21 + 56 * q^22 - 30 * q^24 - 32 * q^25 - 10 * q^27 - 96 * q^28 - 20 * q^30 - 80 * q^31 - 26 * q^33 - 104 * q^37 - 24 * q^39 + 196 * q^40 + 122 * q^43 + 144 * q^45 + 324 * q^46 + 154 * q^48 - 154 * q^49 - 472 * q^52 + 70 * q^54 + 314 * q^55 - 232 * q^57 - 148 * q^58 - 244 * q^60 + 176 * q^61 - 304 * q^63 - 208 * q^64 + 320 * q^66 - 132 * q^67 + 294 * q^69 - 16 * q^70 - 480 * q^72 + 262 * q^75 + 248 * q^76 + 108 * q^78 - 92 * q^79 + 114 * q^81 - 76 * q^82 + 32 * q^84 + 34 * q^85 + 120 * q^87 + 52 * q^88 - 376 * q^90 + 156 * q^91 + 16 * q^93 + 216 * q^94 + 546 * q^96 + 464 * q^97 + 236 * q^99

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