LMFDB - Embedded newform 55.3.d.d.54.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(54,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("55.54");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.d (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:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{5}, \sqrt{-21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 41x^{2} - 40x + 505 $ x^4 - 2x^3 + 41x^2 - 40*x + 505
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			54.1
Root			$1.61803 - 4.58258i$ of defining polynomial
Character	$\chi$	$=$	55.54
Dual form			55.3.d.d.54.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.23607 q^{2} -4.58258i q^{3} +1.00000 q^{4} +(-2.00000 + 4.58258i) q^{5} +10.2470i q^{6} -11.1803 q^{7} +6.70820 q^{8} -12.0000 q^{9} +(4.47214 - 10.2470i) q^{10} +(-4.00000 - 10.2470i) q^{11} -4.58258i q^{12} -8.94427 q^{13} +25.0000 q^{14} +(21.0000 + 9.16515i) q^{15} -19.0000 q^{16} +15.6525 q^{17} +26.8328 q^{18} -10.2470i q^{19} +(-2.00000 + 4.58258i) q^{20} +51.2348i q^{21} +(8.94427 + 22.9129i) q^{22} -27.4955i q^{23} -30.7409i q^{24} +(-17.0000 - 18.3303i) q^{25} +20.0000 q^{26} +13.7477i q^{27} -11.1803 q^{28} +10.2470i q^{29} +(-46.9574 - 20.4939i) q^{30} -3.00000 q^{31} +15.6525 q^{32} +(-46.9574 + 18.3303i) q^{33} -35.0000 q^{34} +(22.3607 - 51.2348i) q^{35} -12.0000 q^{36} -4.58258i q^{37} +22.9129i q^{38} +40.9878i q^{39} +(-13.4164 + 30.7409i) q^{40} +20.4939i q^{41} -114.564i q^{42} -22.3607 q^{43} +(-4.00000 - 10.2470i) q^{44} +(24.0000 - 54.9909i) q^{45} +61.4817i q^{46} +64.1561i q^{47} +87.0689i q^{48} +76.0000 q^{49} +(38.0132 + 40.9878i) q^{50} -71.7287i q^{51} -8.94427 q^{52} -4.58258i q^{53} -30.7409i q^{54} +(54.9574 + 2.16360i) q^{55} -75.0000 q^{56} -46.9574 q^{57} -22.9129i q^{58} -18.0000 q^{59} +(21.0000 + 9.16515i) q^{60} -71.7287i q^{61} +6.70820 q^{62} +134.164 q^{63} +41.0000 q^{64} +(17.8885 - 40.9878i) q^{65} +(105.000 - 40.9878i) q^{66} -27.4955i q^{67} +15.6525 q^{68} -126.000 q^{69} +(-50.0000 + 114.564i) q^{70} +27.0000 q^{71} -80.4984 q^{72} -58.1378 q^{73} +10.2470i q^{74} +(-84.0000 + 77.9038i) q^{75} -10.2470i q^{76} +(44.7214 + 114.564i) q^{77} -91.6515i q^{78} +61.4817i q^{79} +(38.0000 - 87.0689i) q^{80} -45.0000 q^{81} -45.8258i q^{82} +71.5542 q^{83} +51.2348i q^{84} +(-31.3050 + 71.7287i) q^{85} +50.0000 q^{86} +46.9574 q^{87} +(-26.8328 - 68.7386i) q^{88} +37.0000 q^{89} +(-53.6656 + 122.963i) q^{90} +100.000 q^{91} -27.4955i q^{92} +13.7477i q^{93} -143.457i q^{94} +(46.9574 + 20.4939i) q^{95} -71.7287i q^{96} -119.147i q^{97} -169.941 q^{98} +(48.0000 + 122.963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 8 q^{5} - 48 q^{9} - 16 q^{11} + 100 q^{14} + 84 q^{15} - 76 q^{16} - 8 q^{20} - 68 q^{25} + 80 q^{26} - 12 q^{31} - 140 q^{34} - 48 q^{36} - 16 q^{44} + 96 q^{45} + 304 q^{49} + 32 q^{55}+ \cdots + 192 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 8 * q^5 - 48 * q^9 - 16 * q^11 + 100 * q^14 + 84 * q^15 - 76 * q^16 - 8 * q^20 - 68 * q^25 + 80 * q^26 - 12 * q^31 - 140 * q^34 - 48 * q^36 - 16 * q^44 + 96 * q^45 + 304 * q^49 + 32 * q^55 - 300 * q^56 - 72 * q^59 + 84 * q^60 + 164 * q^64 + 420 * q^66 - 504 * q^69 - 200 * q^70 + 108 * q^71 - 336 * q^75 + 152 * q^80 - 180 * q^81 + 200 * q^86 + 148 * q^89 + 400 * q^91 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.23607			−1.11803			−0.559017	−	0.829156i	$-0.688821\pi$
$2$	−2.23607			−1.11803			−0.559017	+	0.829156i	$0.688821\pi$
$3$		−	4.58258i		−	1.52753i	−0.645497	−	0.763763i	$-0.723350\pi$
$3$		−	4.58258i		−	1.52753i	0.645497	−	0.763763i	$-0.276650\pi$
$4$	1.00000			0.250000
$5$	−2.00000	+	4.58258i	−0.400000	+	0.916515i
$5$	−2.00000	+	4.58258i	−0.400000	+	0.916515i
$6$			10.2470i			1.70783i
$7$	−11.1803			−1.59719			−0.798596	−	0.601868i	$-0.794423\pi$
$7$	−11.1803			−1.59719			−0.798596	+	0.601868i	$0.794423\pi$
$8$	6.70820			0.838525
$9$	−12.0000			−1.33333
$10$	4.47214	−	10.2470i	0.447214	−	1.02470i
$11$	−4.00000	−	10.2470i	−0.363636	−	0.931541i
$11$	−4.00000	−	10.2470i	−0.363636	−	0.931541i
$12$		−	4.58258i		−	0.381881i
$13$	−8.94427			−0.688021			−0.344010	−	0.938966i	$-0.611786\pi$
$13$	−8.94427			−0.688021			−0.344010	+	0.938966i	$0.611786\pi$
$14$	25.0000			1.78571
$15$	21.0000	+	9.16515i	1.40000	+	0.611010i
$16$	−19.0000			−1.18750
$17$	15.6525			0.920734			0.460367	−	0.887729i	$-0.347718\pi$
$17$	15.6525			0.920734			0.460367	+	0.887729i	$0.347718\pi$
$18$	26.8328			1.49071
$19$		−	10.2470i		−	0.539313i	−0.962957	−	0.269657i	$-0.913090\pi$
$19$		−	10.2470i		−	0.539313i	0.962957	−	0.269657i	$-0.0869102\pi$
$20$	−2.00000	+	4.58258i	−0.100000	+	0.229129i
$21$			51.2348i			2.43975i
$22$	8.94427	+	22.9129i	0.406558	+	1.04149i
$23$		−	27.4955i		−	1.19545i	−0.801700	−	0.597727i	$-0.796071\pi$
$23$		−	27.4955i		−	1.19545i	0.801700	−	0.597727i	$-0.203929\pi$
$24$		−	30.7409i		−	1.28087i
$25$	−17.0000	−	18.3303i	−0.680000	−	0.733212i
$26$	20.0000			0.769231
$27$			13.7477i			0.509175i
$28$	−11.1803			−0.399298
$29$			10.2470i			0.353343i	0.984270	+	0.176672i	$0.0565330\pi$
$29$			10.2470i			0.353343i	−0.984270	+	0.176672i	$0.943467\pi$
$30$	−46.9574	−	20.4939i	−1.56525	−	0.683130i
$31$	−3.00000			−0.0967742			−0.0483871	−	0.998829i	$-0.515408\pi$
$31$	−3.00000			−0.0967742			−0.0483871	+	0.998829i	$0.515408\pi$
$32$	15.6525			0.489140
$33$	−46.9574	+	18.3303i	−1.42295	+	0.555464i
$34$	−35.0000			−1.02941
$35$	22.3607	−	51.2348i	0.638877	−	1.46385i
$36$	−12.0000			−0.333333
$37$		−	4.58258i		−	0.123853i	−0.998081	−	0.0619267i	$-0.980275\pi$
$37$		−	4.58258i		−	0.123853i	0.998081	−	0.0619267i	$-0.0197245\pi$
$38$			22.9129i			0.602970i
$39$			40.9878i			1.05097i
$40$	−13.4164	+	30.7409i	−0.335410	+	0.768521i
$41$			20.4939i			0.499851i	0.968265	+	0.249926i	$0.0804062\pi$
$41$			20.4939i			0.499851i	−0.968265	+	0.249926i	$0.919594\pi$
$42$		−	114.564i		−	2.72772i
$43$	−22.3607			−0.520016			−0.260008	−	0.965606i	$-0.583725\pi$
$43$	−22.3607			−0.520016			−0.260008	+	0.965606i	$0.583725\pi$
$44$	−4.00000	−	10.2470i	−0.0909091	−	0.232885i
$45$	24.0000	−	54.9909i	0.533333	−	1.22202i
$46$			61.4817i			1.33656i
$47$			64.1561i			1.36502i	0.730875	+	0.682511i	$0.239112\pi$
$47$			64.1561i			1.36502i	−0.730875	+	0.682511i	$0.760888\pi$
$48$			87.0689i			1.81394i
$49$	76.0000			1.55102
$50$	38.0132	+	40.9878i	0.760263	+	0.819756i
$51$		−	71.7287i		−	1.40644i
$52$	−8.94427			−0.172005
$53$		−	4.58258i		−	0.0864637i	−0.999065	−	0.0432318i	$-0.986235\pi$
$53$		−	4.58258i		−	0.0864637i	0.999065	−	0.0432318i	$-0.0137654\pi$
$54$		−	30.7409i		−	0.569275i
$55$	54.9574	+	2.16360i	0.999226	+	0.0393382i
$56$	−75.0000			−1.33929
$57$	−46.9574			−0.823815
$58$		−	22.9129i		−	0.395050i
$59$	−18.0000			−0.305085			−0.152542	−	0.988297i	$-0.548746\pi$
$59$	−18.0000			−0.305085			−0.152542	+	0.988297i	$0.548746\pi$
$60$	21.0000	+	9.16515i	0.350000	+	0.152753i
$61$		−	71.7287i		−	1.17588i	−0.808905	−	0.587940i	$-0.799939\pi$
$61$		−	71.7287i		−	1.17588i	0.808905	−	0.587940i	$-0.200061\pi$
$62$	6.70820			0.108197
$63$	134.164			2.12959
$64$	41.0000			0.640625
$65$	17.8885	−	40.9878i	0.275208	−	0.630582i
$66$	105.000	−	40.9878i	1.59091	−	0.621027i
$67$		−	27.4955i		−	0.410380i	−0.978722	−	0.205190i	$-0.934219\pi$
$67$		−	27.4955i		−	0.410380i	0.978722	−	0.205190i	$-0.0657812\pi$
$68$	15.6525			0.230183
$69$	−126.000			−1.82609
$70$	−50.0000	+	114.564i	−0.714286	+	1.63663i
$71$	27.0000			0.380282			0.190141	−	0.981757i	$-0.439106\pi$
$71$	27.0000			0.380282			0.190141	+	0.981757i	$0.439106\pi$
$72$	−80.4984			−1.11803
$73$	−58.1378			−0.796408			−0.398204	−	0.917297i	$-0.630366\pi$
$73$	−58.1378			−0.796408			−0.398204	+	0.917297i	$0.630366\pi$
$74$			10.2470i			0.138472i
$75$	−84.0000	+	77.9038i	−1.12000	+	1.03872i
$76$		−	10.2470i		−	0.134828i
$77$	44.7214	+	114.564i	0.580797	+	1.48785i
$78$		−	91.6515i		−	1.17502i
$79$			61.4817i			0.778249i	0.921185	+	0.389125i	$0.127222\pi$
$79$			61.4817i			0.778249i	−0.921185	+	0.389125i	$0.872778\pi$
$80$	38.0000	−	87.0689i	0.475000	−	1.08836i
$81$	−45.0000			−0.555556
$82$		−	45.8258i		−	0.558851i
$83$	71.5542			0.862098			0.431049	−	0.902328i	$-0.358144\pi$
$83$	71.5542			0.862098			0.431049	+	0.902328i	$0.358144\pi$
$84$			51.2348i			0.609938i
$85$	−31.3050	+	71.7287i	−0.368294	+	0.843867i
$86$	50.0000			0.581395
$87$	46.9574			0.539741
$88$	−26.8328	−	68.7386i	−0.304918	−	0.781121i
$89$	37.0000			0.415730			0.207865	−	0.978157i	$-0.433348\pi$
$89$	37.0000			0.415730			0.207865	+	0.978157i	$0.433348\pi$
$90$	−53.6656	+	122.963i	−0.596285	+	1.36626i
$91$	100.000			1.09890
$92$		−	27.4955i		−	0.298864i
$93$			13.7477i			0.147825i
$94$		−	143.457i		−	1.52614i
$95$	46.9574	+	20.4939i	0.494289	+	0.215725i
$96$		−	71.7287i		−	0.747173i
$97$		−	119.147i		−	1.22832i	−0.789182	−	0.614160i	$-0.789495\pi$
$97$		−	119.147i		−	1.22832i	0.789182	−	0.614160i	$-0.210505\pi$
$98$	−169.941			−1.73409
$99$	48.0000	+	122.963i	0.484848	+	1.24205i
$100$	−17.0000	−	18.3303i	−0.170000	−	0.183303i
$101$		−	102.470i		−	1.01455i	−0.861784	−	0.507275i	$-0.830653\pi$
$101$		−	102.470i		−	1.01455i	0.861784	−	0.507275i	$-0.169347\pi$
$102$			160.390i			1.57245i
$103$			18.3303i			0.177964i	0.996033	+	0.0889821i	$0.0283614\pi$
$103$			18.3303i			0.177964i	−0.996033	+	0.0889821i	$0.971639\pi$
$104$	−60.0000			−0.576923
$105$	−234.787	−	102.470i	−2.23607	−	0.975900i
$106$			10.2470i			0.0966693i
$107$	−156.525			−1.46285			−0.731424	−	0.681923i	$-0.761144\pi$
$107$	−156.525			−1.46285			−0.731424	+	0.681923i	$0.761144\pi$
$108$			13.7477i			0.127294i
$109$			20.4939i			0.188017i	0.995571	+	0.0940087i	$0.0299682\pi$
$109$			20.4939i			0.188017i	−0.995571	+	0.0940087i	$0.970032\pi$
$110$	−122.889	−	4.83795i	−1.11717	−	0.0439814i
$111$	−21.0000			−0.189189
$112$	212.426			1.89666
$113$		−	164.973i		−	1.45994i	−0.683482	−	0.729968i	$-0.739535\pi$
$113$		−	164.973i		−	1.45994i	0.683482	−	0.729968i	$-0.260465\pi$
$114$	105.000			0.921053
$115$	126.000	+	54.9909i	1.09565	+	0.478182i
$116$			10.2470i			0.0883358i
$117$	107.331			0.917361
$118$	40.2492			0.341095
$119$	−175.000			−1.47059
$120$	140.872	+	61.4817i	1.17394	+	0.512348i
$121$	−89.0000	+	81.9756i	−0.735537	+	0.677484i
$122$			160.390i			1.31467i
$123$	93.9149			0.763535
$124$	−3.00000			−0.0241935
$125$	118.000	−	41.2432i	0.944000	−	0.329945i
$126$	−300.000			−2.38095
$127$	31.3050			0.246496			0.123248	−	0.992376i	$-0.460669\pi$
$127$	31.3050			0.246496			0.123248	+	0.992376i	$0.460669\pi$
$128$	−154.289			−1.20538
$129$			102.470i			0.794337i
$130$	−40.0000	+	91.6515i	−0.307692	+	0.705012i
$131$		−	215.186i		−	1.64264i	−0.570467	−	0.821320i	$-0.693238\pi$
$131$		−	215.186i		−	1.64264i	0.570467	−	0.821320i	$-0.306762\pi$
$132$	−46.9574	+	18.3303i	−0.355738	+	0.138866i
$133$			114.564i			0.861386i
$134$			61.4817i			0.458819i
$135$	−63.0000	−	27.4955i	−0.466667	−	0.203670i
$136$	105.000			0.772059
$137$			64.1561i			0.468292i	0.972201	+	0.234146i	$0.0752294\pi$
$137$			64.1561i			0.468292i	−0.972201	+	0.234146i	$0.924771\pi$
$138$	281.745			2.04163
$139$		−	225.433i		−	1.62182i	−0.585171	−	0.810910i	$-0.698973\pi$
$139$		−	225.433i		−	1.62182i	0.585171	−	0.810910i	$-0.301027\pi$
$140$	22.3607	−	51.2348i	0.159719	−	0.365963i
$141$	294.000			2.08511
$142$	−60.3738			−0.425168
$143$	35.7771	+	91.6515i	0.250189	+	0.640920i
$144$	228.000			1.58333
$145$	−46.9574	−	20.4939i	−0.323844	−	0.141337i
$146$	130.000			0.890411
$147$		−	348.276i		−	2.36922i
$148$		−	4.58258i		−	0.0309633i
$149$			153.704i			1.03157i	0.856717	+	0.515786i	$0.172500\pi$
$149$			153.704i			1.03157i	−0.856717	+	0.515786i	$0.827500\pi$
$150$	187.830	−	174.198i	1.25220	−	1.16132i
$151$			102.470i			0.678606i	0.940677	+	0.339303i	$0.110191\pi$
$151$			102.470i			0.678606i	−0.940677	+	0.339303i	$0.889809\pi$
$152$		−	68.7386i		−	0.452228i
$153$	−187.830			−1.22765
$154$	−100.000	−	256.174i	−0.649351	−	1.66347i
$155$	6.00000	−	13.7477i	0.0387097	−	0.0886950i
$156$			40.9878i			0.262742i
$157$		−	50.4083i		−	0.321072i	−0.987030	−	0.160536i	$-0.948678\pi$
$157$		−	50.4083i		−	0.321072i	0.987030	−	0.160536i	$-0.0513223\pi$
$158$		−	137.477i		−	0.870109i
$159$	−21.0000			−0.132075
$160$	−31.3050	+	71.7287i	−0.195656	+	0.448304i
$161$			307.409i			1.90937i
$162$	100.623			0.621130
$163$			270.372i			1.65872i	0.558712	+	0.829362i	$0.311296\pi$
$163$			270.372i			1.65872i	−0.558712	+	0.829362i	$0.688704\pi$
$164$			20.4939i			0.124963i
$165$	9.91486	−	251.847i	0.0600900	−	1.52634i
$166$	−160.000			−0.963855
$167$	−297.397			−1.78082			−0.890410	−	0.455159i	$-0.849583\pi$
$167$	−297.397			−1.78082			−0.890410	+	0.455159i	$0.849583\pi$
$168$			343.693i			2.04579i
$169$	−89.0000			−0.526627
$170$	70.0000	−	160.390i	0.411765	−	0.943471i
$171$			122.963i			0.719084i
$172$	−22.3607			−0.130004
$173$	143.108			0.827216			0.413608	−	0.910455i	$-0.364268\pi$
$173$	143.108			0.827216			0.413608	+	0.910455i	$0.364268\pi$
$174$	−105.000			−0.603448
$175$	190.066	+	204.939i	1.08609	+	1.17108i
$176$	76.0000	+	194.692i	0.431818	+	1.10620i
$177$			82.4864i			0.466025i
$178$	−82.7345			−0.464801
$179$	242.000			1.35196			0.675978	−	0.736922i	$-0.263722\pi$
$179$	242.000			1.35196			0.675978	+	0.736922i	$0.263722\pi$
$180$	24.0000	−	54.9909i	0.133333	−	0.305505i
$181$	−258.000			−1.42541			−0.712707	−	0.701462i	$-0.752531\pi$
$181$	−258.000			−1.42541			−0.712707	+	0.701462i	$0.752531\pi$
$182$	−223.607			−1.22861
$183$	−328.702			−1.79619
$184$		−	184.445i		−	1.00242i
$185$	21.0000	+	9.16515i	0.113514	+	0.0495414i
$186$		−	30.7409i		−	0.165273i
$187$	−62.6099	−	160.390i	−0.334812	−	0.857701i
$188$			64.1561i			0.341256i
$189$		−	153.704i		−	0.813250i
$190$	−105.000	−	45.8258i	−0.552632	−	0.241188i
$191$	−278.000			−1.45550			−0.727749	−	0.685844i	$-0.759433\pi$
$191$	−278.000			−1.45550			−0.727749	+	0.685844i	$0.759433\pi$
$192$		−	187.886i		−	0.978571i
$193$	78.2624			0.405505			0.202752	−	0.979230i	$-0.435011\pi$
$193$	78.2624			0.405505			0.202752	+	0.979230i	$0.435011\pi$
$194$			266.421i			1.37330i
$195$	−187.830	−	81.9756i	−0.963229	−	0.420388i
$196$	76.0000			0.387755
$197$	196.774			0.998853			0.499426	−	0.866356i	$-0.333544\pi$
$197$	196.774			0.998853			0.499426	+	0.866356i	$0.333544\pi$
$198$	−107.331	−	274.955i	−0.542077	−	1.38866i
$199$	−53.0000			−0.266332			−0.133166	−	0.991094i	$-0.542514\pi$
$199$	−53.0000			−0.266332			−0.133166	+	0.991094i	$0.542514\pi$
$200$	−114.039	−	122.963i	−0.570197	−	0.614817i
$201$	−126.000			−0.626866
$202$			229.129i			1.13430i
$203$		−	114.564i		−	0.564357i
$204$		−	71.7287i		−	0.351611i
$205$	−93.9149	−	40.9878i	−0.458121	−	0.199941i
$206$		−	40.9878i		−	0.198970i
$207$			329.945i			1.59394i
$208$	169.941			0.817025
$209$	−105.000	+	40.9878i	−0.502392	+	0.196114i
$210$	525.000	+	229.129i	2.50000	+	1.09109i
$211$		−	174.198i		−	0.825584i	−0.910825	−	0.412792i	$-0.864554\pi$
$211$		−	174.198i		−	0.825584i	0.910825	−	0.412792i	$-0.135446\pi$
$212$		−	4.58258i		−	0.0216159i
$213$		−	123.730i		−	0.580890i
$214$	350.000			1.63551
$215$	44.7214	−	102.470i	0.208006	−	0.476602i
$216$			92.2226i			0.426956i
$217$	33.5410			0.154567
$218$		−	45.8258i		−	0.210210i
$219$			266.421i			1.21653i
$220$	54.9574	+	2.16360i	0.249806	+	0.00983454i
$221$	−140.000			−0.633484
$222$	46.9574			0.211520
$223$		−	394.102i		−	1.76727i	−0.468175	−	0.883636i	$-0.655088\pi$
$223$		−	394.102i		−	1.76727i	0.468175	−	0.883636i	$-0.344912\pi$
$224$	−175.000			−0.781250
$225$	204.000	+	219.964i	0.906667	+	0.977616i
$226$			368.890i			1.63226i
$227$	277.272			1.22146			0.610732	−	0.791837i	$-0.290875\pi$
$227$	277.272			1.22146			0.610732	+	0.791837i	$0.290875\pi$
$228$	−46.9574			−0.205954
$229$	292.000			1.27511			0.637555	−	0.770405i	$-0.279946\pi$
$229$	292.000			1.27511			0.637555	+	0.770405i	$0.279946\pi$
$230$	−281.745	−	122.963i	−1.22498	−	0.534624i
$231$	525.000	−	204.939i	2.27273	−	0.887182i
$232$			68.7386i			0.296287i
$233$	172.177			0.738958			0.369479	−	0.929239i	$-0.379536\pi$
$233$	172.177			0.738958			0.369479	+	0.929239i	$0.379536\pi$
$234$	−240.000			−1.02564
$235$	−294.000	−	128.312i	−1.25106	−	0.546009i
$236$	−18.0000			−0.0762712
$237$	281.745			1.18880
$238$	391.312			1.64417
$239$		−	225.433i		−	0.943234i	−0.881804	−	0.471617i	$-0.843671\pi$
$239$		−	225.433i		−	0.943234i	0.881804	−	0.471617i	$-0.156329\pi$
$240$	−399.000	−	174.138i	−1.66250	−	0.725574i
$241$			327.902i			1.36059i	0.732938	+	0.680295i	$0.238149\pi$
$241$			327.902i			1.36059i	−0.732938	+	0.680295i	$0.761851\pi$
$242$	199.010	−	183.303i	0.822356	−	0.757451i
$243$			329.945i			1.35780i
$244$		−	71.7287i		−	0.293970i
$245$	−152.000	+	348.276i	−0.620408	+	1.42153i
$246$	−210.000			−0.853659
$247$			91.6515i			0.371059i
$248$	−20.1246			−0.0811476
$249$		−	327.902i		−	1.31688i
$250$	−263.856	+	92.2226i	−1.05542	+	0.368890i
$251$	282.000			1.12351			0.561753	−	0.827305i	$-0.310127\pi$
$251$	282.000			1.12351			0.561753	+	0.827305i	$0.310127\pi$
$252$	134.164			0.532397
$253$	−281.745	+	109.982i	−1.11361	+	0.434711i
$254$	−70.0000			−0.275591
$255$	328.702	+	143.457i	1.28903	+	0.562578i
$256$	181.000			0.707031
$257$			64.1561i			0.249634i	0.992180	+	0.124817i	$0.0398345\pi$
$257$			64.1561i			0.249634i	−0.992180	+	0.124817i	$0.960166\pi$
$258$		−	229.129i		−	0.888096i
$259$			51.2348i			0.197818i
$260$	17.8885	−	40.9878i	0.0688021	−	0.157645i
$261$		−	122.963i		−	0.471124i
$262$			481.170i			1.83653i
$263$	−199.010			−0.756692			−0.378346	−	0.925664i	$-0.623507\pi$
$263$	−199.010			−0.756692			−0.378346	+	0.925664i	$0.623507\pi$
$264$	−315.000	+	122.963i	−1.19318	+	0.465770i
$265$	21.0000	+	9.16515i	0.0792453	+	0.0345855i
$266$		−	256.174i		−	0.963059i
$267$		−	169.555i		−	0.635039i
$268$		−	27.4955i		−	0.102595i
$269$	162.000			0.602230			0.301115	−	0.953588i	$-0.402641\pi$
$269$	162.000			0.602230			0.301115	+	0.953588i	$0.402641\pi$
$270$	140.872	+	61.4817i	0.521749	+	0.227710i
$271$		−	245.927i		−	0.907479i	−0.891134	−	0.453740i	$-0.850090\pi$
$271$		−	245.927i		−	0.907479i	0.891134	−	0.453740i	$-0.149910\pi$
$272$	−297.397			−1.09337
$273$		−	458.258i		−	1.67860i
$274$		−	143.457i		−	0.523567i
$275$	−119.830	+	247.519i	−0.435744	+	0.900070i
$276$	−126.000			−0.456522
$277$	−58.1378			−0.209884			−0.104942	−	0.994478i	$-0.533466\pi$
$277$	−58.1378			−0.209884			−0.104942	+	0.994478i	$0.533466\pi$
$278$			504.083i			1.81325i
$279$	36.0000			0.129032
$280$	150.000	−	343.693i	0.535714	−	1.22748i
$281$		−	163.951i		−	0.583456i	−0.956501	−	0.291728i	$-0.905770\pi$
$281$		−	163.951i		−	0.583456i	0.956501	−	0.291728i	$-0.0942303\pi$
$282$	−657.404			−2.33122
$283$	250.440			0.884946			0.442473	−	0.896782i	$-0.354101\pi$
$283$	250.440			0.884946			0.442473	+	0.896782i	$0.354101\pi$
$284$	27.0000			0.0950704
$285$	93.9149	−	215.186i	0.329526	−	0.755038i
$286$	−80.0000	−	204.939i	−0.279720	−	0.716570i
$287$		−	229.129i		−	0.798358i
$288$	−187.830			−0.652186
$289$	−44.0000			−0.152249
$290$	105.000	+	45.8258i	0.362069	+	0.158020i
$291$	−546.000			−1.87629
$292$	−58.1378			−0.199102
$293$	447.214			1.52633			0.763163	−	0.646206i	$-0.223645\pi$
$293$	447.214			1.52633			0.763163	+	0.646206i	$0.223645\pi$
$294$			778.768i			2.64887i
$295$	36.0000	−	82.4864i	0.122034	−	0.279615i
$296$		−	30.7409i		−	0.103854i
$297$	140.872	−	54.9909i	0.474317	−	0.185155i
$298$		−	343.693i		−	1.15333i
$299$			245.927i			0.822498i
$300$	−84.0000	+	77.9038i	−0.280000	+	0.259679i
$301$	250.000			0.830565
$302$		−	229.129i		−	0.758705i
$303$	−469.574			−1.54975
$304$			194.692i			0.640434i
$305$	328.702	+	143.457i	1.07771	+	0.470352i
$306$	420.000			1.37255
$307$	−447.214			−1.45672			−0.728361	−	0.685194i	$-0.759718\pi$
$307$	−447.214			−1.45672			−0.728361	+	0.685194i	$0.759718\pi$
$308$	44.7214	+	114.564i	0.145199	+	0.371962i
$309$	84.0000			0.271845
$310$	−13.4164	+	30.7409i	−0.0432787	+	0.0991640i
$311$	87.0000			0.279743			0.139871	−	0.990170i	$-0.455331\pi$
$311$	87.0000			0.279743			0.139871	+	0.990170i	$0.455331\pi$
$312$			274.955i			0.881265i
$313$			293.285i			0.937012i	0.883460	+	0.468506i	$0.155208\pi$
$313$			293.285i			0.937012i	−0.883460	+	0.468506i	$0.844792\pi$
$314$			112.716i			0.358970i
$315$	−268.328	+	614.817i	−0.851835	+	1.95180i
$316$			61.4817i			0.194562i
$317$		−	50.4083i		−	0.159017i	−0.996834	−	0.0795084i	$-0.974665\pi$
$317$		−	50.4083i		−	0.159017i	0.996834	−	0.0795084i	$-0.0253351\pi$
$318$	46.9574			0.147665
$319$	105.000	−	40.9878i	0.329154	−	0.128488i
$320$	−82.0000	+	187.886i	−0.256250	+	0.587143i
$321$			717.287i			2.23454i
$322$		−	687.386i		−	2.13474i
$323$		−	160.390i		−	0.496564i
$324$	−45.0000			−0.138889
$325$	152.053	+	163.951i	0.467854	+	0.504465i
$326$		−	604.570i		−	1.85451i
$327$	93.9149			0.287201
$328$			137.477i			0.419138i
$329$		−	717.287i		−	2.18020i
$330$	−22.1703	+	563.146i	−0.0671827	+	1.70650i
$331$	−138.000			−0.416918			−0.208459	−	0.978031i	$-0.566845\pi$
$331$	−138.000			−0.416918			−0.208459	+	0.978031i	$0.566845\pi$
$332$	71.5542			0.215525
$333$			54.9909i			0.165138i
$334$	665.000			1.99102
$335$	126.000	+	54.9909i	0.376119	+	0.164152i
$336$		−	973.460i		−	2.89720i
$337$	−243.731			−0.723239			−0.361619	−	0.932326i	$-0.617776\pi$
$337$	−243.731			−0.723239			−0.361619	+	0.932326i	$0.617776\pi$
$338$	199.010			0.588787
$339$	−756.000			−2.23009
$340$	−31.3050	+	71.7287i	−0.0920734	+	0.210967i
$341$	12.0000	+	30.7409i	0.0351906	+	0.0901491i
$342$		−	274.955i		−	0.803961i
$343$	−301.869			−0.880085
$344$	−150.000			−0.436047
$345$	252.000	−	577.405i	0.730435	−	1.67364i
$346$	−320.000			−0.924855
$347$	−4.47214			−0.0128880			−0.00644400	−	0.999979i	$-0.502051\pi$
$347$	−4.47214			−0.0128880			−0.00644400	+	0.999979i	$0.502051\pi$
$348$	46.9574			0.134935
$349$		−	512.348i		−	1.46804i	−0.679125	−	0.734022i	$-0.737641\pi$
$349$		−	512.348i		−	1.46804i	0.679125	−	0.734022i	$-0.262359\pi$
$350$	−425.000	−	458.258i	−1.21429	−	1.30931i
$351$		−	122.963i		−	0.350323i
$352$	−62.6099	−	160.390i	−0.177869	−	0.455654i
$353$			293.285i			0.830835i	0.909631	+	0.415418i	$0.136365\pi$
$353$			293.285i			0.830835i	−0.909631	+	0.415418i	$0.863635\pi$
$354$		−	184.445i		−	0.521031i
$355$	−54.0000	+	123.730i	−0.152113	+	0.348534i
$356$	37.0000			0.103933
$357$			801.951i			2.24636i
$358$	−541.128			−1.51153
$359$			635.311i			1.76967i	0.465906	+	0.884834i	$0.345728\pi$
$359$			635.311i			1.76967i	−0.465906	+	0.884834i	$0.654272\pi$
$360$	160.997	−	368.890i	0.447214	−	1.02470i
$361$	256.000			0.709141
$362$	576.906			1.59366
$363$	375.659	+	407.849i	1.03487	+	1.12355i
$364$	100.000			0.274725
$365$	116.276	−	266.421i	0.318563	−	0.729920i
$366$	735.000			2.00820
$367$			430.762i			1.17374i	0.809682	+	0.586869i	$0.199640\pi$
$367$			430.762i			1.17374i	−0.809682	+	0.586869i	$0.800360\pi$
$368$			522.414i			1.41960i
$369$		−	245.927i		−	0.666468i
$370$	−46.9574	−	20.4939i	−0.126912	−	0.0553889i
$371$			51.2348i			0.138099i
$372$			13.7477i			0.0369563i
$373$	545.601			1.46274			0.731368	−	0.681983i	$-0.238882\pi$
$373$	545.601			1.46274			0.731368	+	0.681983i	$0.238882\pi$
$374$	140.000	+	358.643i	0.374332	+	0.958939i
$375$	−189.000	−	540.744i	−0.504000	−	1.44198i
$376$			430.372i			1.14461i
$377$		−	91.6515i		−	0.243107i
$378$			343.693i			0.909241i
$379$	−428.000			−1.12929			−0.564644	−	0.825335i	$-0.690986\pi$
$379$	−428.000			−1.12929			−0.564644	+	0.825335i	$0.690986\pi$
$380$	46.9574	+	20.4939i	0.123572	+	0.0539313i
$381$		−	143.457i		−	0.376528i
$382$	621.627			1.62730
$383$		−	164.973i		−	0.430738i	−0.976533	−	0.215369i	$-0.930905\pi$
$383$		−	164.973i		−	0.430738i	0.976533	−	0.215369i	$-0.0690955\pi$
$384$			707.040i			1.84125i
$385$	−614.443	−	24.1898i	−1.59596	−	0.0628306i
$386$	−175.000			−0.453368
$387$	268.328			0.693354
$388$		−	119.147i		−	0.307080i
$389$	−228.000			−0.586118			−0.293059	−	0.956094i	$-0.594673\pi$
$389$	−228.000			−0.586118			−0.293059	+	0.956094i	$0.594673\pi$
$390$	420.000	+	183.303i	1.07692	+	0.470008i
$391$		−	430.372i		−	1.10070i
$392$	509.823			1.30057
$393$	−986.106			−2.50918
$394$	−440.000			−1.11675
$395$	−281.745	−	122.963i	−0.713277	−	0.311300i
$396$	48.0000	+	122.963i	0.121212	+	0.310514i
$397$		−	669.056i		−	1.68528i	−0.538478	−	0.842640i	$-0.681000\pi$
$397$		−	669.056i		−	1.68528i	0.538478	−	0.842640i	$-0.319000\pi$
$398$	118.512			0.297768
$399$	525.000			1.31579
$400$	323.000	+	348.276i	0.807500	+	0.870689i
$401$	107.000			0.266833			0.133416	−	0.991060i	$-0.457405\pi$
$401$	107.000			0.266833			0.133416	+	0.991060i	$0.457405\pi$
$402$	281.745			0.700857
$403$	26.8328			0.0665827
$404$		−	102.470i		−	0.253637i
$405$	90.0000	−	206.216i	0.222222	−	0.509175i
$406$			256.174i			0.630970i
$407$	−46.9574	+	18.3303i	−0.115375	+	0.0450376i
$408$		−	481.170i		−	1.17934i
$409$			327.902i			0.801717i	0.916140	+	0.400859i	$0.131288\pi$
$409$			327.902i			0.801717i	−0.916140	+	0.400859i	$0.868712\pi$
$410$	210.000	+	91.6515i	0.512195	+	0.223540i
$411$	294.000			0.715328
$412$			18.3303i			0.0444910i
$413$	201.246			0.487279
$414$		−	737.780i		−	1.78208i
$415$	−143.108	+	327.902i	−0.344839	+	0.790126i
$416$	−140.000			−0.336538
$417$	−1033.06			−2.47737
$418$	234.787	−	91.6515i	0.561692	−	0.219262i
$419$	722.000			1.72315			0.861575	−	0.507630i	$-0.169478\pi$
$419$	722.000			1.72315			0.861575	+	0.507630i	$0.169478\pi$
$420$	−234.787	−	102.470i	−0.559017	−	0.243975i
$421$	−408.000			−0.969121			−0.484561	−	0.874758i	$-0.661020\pi$
$421$	−408.000			−0.969121			−0.484561	+	0.874758i	$0.661020\pi$
$422$			389.519i			0.923031i
$423$		−	769.873i		−	1.82003i
$424$		−	30.7409i		−	0.0725020i
$425$	−266.092	−	286.915i	−0.626099	−	0.675093i
$426$			276.668i			0.649455i
$427$			801.951i			1.87810i
$428$	−156.525			−0.365712
$429$	420.000	−	163.951i	0.979021	−	0.382171i
$430$	−100.000	+	229.129i	−0.232558	+	0.532858i
$431$		−	61.4817i		−	0.142649i	−0.997453	−	0.0713245i	$-0.977277\pi$
$431$		−	61.4817i		−	0.142649i	0.997453	−	0.0713245i	$-0.0227226\pi$
$432$		−	261.207i		−	0.604645i
$433$			247.459i			0.571499i	0.958304	+	0.285750i	$0.0922425\pi$
$433$			247.459i			0.571499i	−0.958304	+	0.285750i	$0.907757\pi$
$434$	−75.0000			−0.172811
$435$	−93.9149	+	215.186i	−0.215896	+	0.494680i
$436$			20.4939i			0.0470044i
$437$	−281.745			−0.644724
$438$		−	595.735i		−	1.36013i
$439$		−	430.372i		−	0.980346i	−0.871625	−	0.490173i	$-0.836934\pi$
$439$		−	430.372i		−	0.980346i	0.871625	−	0.490173i	$-0.163066\pi$
$440$	368.666	+	14.5139i	0.837876	+	0.0329860i
$441$	−912.000			−2.06803
$442$	313.050			0.708257
$443$		−	302.450i		−	0.682731i	−0.939931	−	0.341366i	$-0.889111\pi$
$443$		−	302.450i		−	0.682731i	0.939931	−	0.341366i	$-0.110889\pi$
$444$	−21.0000			−0.0472973
$445$	−74.0000	+	169.555i	−0.166292	+	0.381023i
$446$			881.238i			1.97587i
$447$	704.361			1.57575
$448$	−458.394			−1.02320
$449$	22.0000			0.0489978			0.0244989	−	0.999700i	$-0.492201\pi$
$449$	22.0000			0.0489978			0.0244989	+	0.999700i	$0.492201\pi$
$450$	−456.158	−	491.854i	−1.01368	−	1.09301i
$451$	210.000	−	81.9756i	0.465632	−	0.181764i
$452$		−	164.973i		−	0.364984i
$453$	469.574			1.03659
$454$	−620.000			−1.36564
$455$	−200.000	+	458.258i	−0.439560	+	1.00716i
$456$	−315.000			−0.690789
$457$	−346.591			−0.758404			−0.379202	−	0.925314i	$-0.623801\pi$
$457$	−346.591			−0.758404			−0.379202	+	0.925314i	$0.623801\pi$
$458$	−652.932			−1.42562
$459$			215.186i			0.468815i
$460$	126.000	+	54.9909i	0.273913	+	0.119545i
$461$			338.149i			0.733513i	0.930317	+	0.366756i	$0.119532\pi$
$461$			338.149i			0.733513i	−0.930317	+	0.366756i	$0.880468\pi$
$462$	−1173.94	+	458.258i	−2.54099	+	0.991900i
$463$		−	623.230i		−	1.34607i	−0.739611	−	0.673035i	$-0.764990\pi$
$463$		−	623.230i		−	1.34607i	0.739611	−	0.673035i	$-0.235010\pi$
$464$		−	194.692i		−	0.419595i
$465$	−63.0000	−	27.4955i	−0.135484	−	0.0591300i
$466$	−385.000			−0.826180
$467$		−	554.492i		−	1.18735i	−0.804706	−	0.593674i	$-0.797677\pi$
$467$		−	554.492i		−	1.18735i	0.804706	−	0.593674i	$-0.202323\pi$
$468$	107.331			0.229340
$469$			307.409i			0.655455i
$470$	657.404	+	286.915i	1.39873	+	0.610457i
$471$	−231.000			−0.490446
$472$	−120.748			−0.255821
$473$	89.4427	+	229.129i	0.189097	+	0.484416i
$474$	−630.000			−1.32911
$475$	−187.830	+	174.198i	−0.395431	+	0.366733i
$476$	−175.000			−0.367647
$477$			54.9909i			0.115285i
$478$			504.083i			1.05457i
$479$		−	40.9878i		−	0.0855695i	−0.999084	−	0.0427848i	$-0.986377\pi$
$479$		−	40.9878i		−	0.0855695i	0.999084	−	0.0427848i	$-0.0136230\pi$
$480$	328.702	+	143.457i	0.684796	+	0.298869i
$481$			40.9878i			0.0852137i
$482$		−	733.212i		−	1.52119i
$483$	1408.72			2.91661
$484$	−89.0000	+	81.9756i	−0.183884	+	0.169371i
$485$	546.000	+	238.294i	1.12577	+	0.491328i
$486$		−	737.780i		−	1.51807i
$487$			339.111i			0.696326i	0.937434	+	0.348163i	$0.113194\pi$
$487$			339.111i			0.696326i	−0.937434	+	0.348163i	$0.886806\pi$
$488$		−	481.170i		−	0.986005i
$489$	1239.00			2.53374
$490$	339.882	−	778.768i	0.693637	−	1.58932i
$491$			584.076i			1.18956i	0.803887	+	0.594782i	$0.202762\pi$
$491$			584.076i			1.18956i	−0.803887	+	0.594782i	$0.797238\pi$
$492$	93.9149			0.190884
$493$			160.390i			0.325335i
$494$		−	204.939i		−	0.414856i
$495$	−659.489	−	25.9632i	−1.33230	−	0.0524509i
$496$	57.0000			0.114919
$497$	−301.869			−0.607383
$498$			733.212i			1.47231i
$499$	−268.000			−0.537074			−0.268537	−	0.963269i	$-0.586540\pi$
$499$	−268.000			−0.537074			−0.268537	+	0.963269i	$0.586540\pi$
$500$	118.000	−	41.2432i	0.236000	−	0.0824864i
$501$			1362.84i			2.72025i
$502$	−630.571			−1.25612
$503$	−541.128			−1.07580			−0.537901	−	0.843008i	$-0.680783\pi$
$503$	−541.128			−1.07580			−0.537901	+	0.843008i	$0.680783\pi$
$504$	900.000			1.78571
$505$	469.574	+	204.939i	0.929850	+	0.405820i
$506$	630.000	−	245.927i	1.24506	−	0.486021i
$507$			407.849i			0.804436i
$508$	31.3050			0.0616239
$509$	−828.000			−1.62672			−0.813360	−	0.581761i	$-0.802364\pi$
$509$	−828.000			−1.62672			−0.813360	+	0.581761i	$0.802364\pi$
$510$	−735.000	−	320.780i	−1.44118	−	0.628981i
$511$	650.000			1.27202
$512$	212.426			0.414895
$513$	140.872			0.274605
$514$		−	143.457i		−	0.279100i
$515$	−84.0000	−	36.6606i	−0.163107	−	0.0711856i
$516$			102.470i			0.198584i
$517$	657.404	−	256.624i	1.27157	−	0.496372i
$518$		−	114.564i		−	0.221167i
$519$		−	655.805i		−	1.26359i
$520$	120.000	−	274.955i	0.230769	−	0.528759i
$521$	242.000			0.464491			0.232246	−	0.972657i	$-0.425393\pi$
$521$	242.000			0.464491			0.232246	+	0.972657i	$0.425393\pi$
$522$			274.955i			0.526733i
$523$	143.108			0.273630			0.136815	−	0.990597i	$-0.456313\pi$
$523$	143.108			0.273630			0.136815	+	0.990597i	$0.456313\pi$
$524$		−	215.186i		−	0.410660i
$525$	939.149	−	870.991i	1.78885	−	1.65903i
$526$	445.000			0.846008
$527$	−46.9574			−0.0891033
$528$	892.191	−	348.276i	1.68976	−	0.659613i
$529$	−227.000			−0.429112
$530$	−46.9574	−	20.4939i	−0.0885989	−	0.0386677i
$531$	216.000			0.406780
$532$			114.564i			0.215347i
$533$		−	183.303i		−	0.343908i
$534$			379.137i			0.709995i
$535$	313.050	−	717.287i	0.585139	−	1.34072i
$536$		−	184.445i		−	0.344114i
$537$		−	1108.98i		−	2.06515i
$538$	−362.243			−0.673314
$539$	−304.000	−	778.768i	−0.564007	−	1.44484i
$540$	−63.0000	−	27.4955i	−0.116667	−	0.0509175i
$541$		−	440.619i		−	0.814453i	−0.913327	−	0.407226i	$-0.866496\pi$
$541$		−	440.619i		−	0.814453i	0.913327	−	0.407226i	$-0.133504\pi$
$542$			549.909i			1.01459i
$543$			1182.30i			2.17736i
$544$	245.000			0.450368
$545$	−93.9149	−	40.9878i	−0.172321	−	0.0752070i
$546$			1024.70i			1.87673i
$547$	398.020			0.727642			0.363821	−	0.931469i	$-0.381472\pi$
$547$	398.020			0.727642			0.363821	+	0.931469i	$0.381472\pi$
$548$			64.1561i			0.117073i
$549$			860.744i			1.56784i
$550$	267.947	−	553.470i	0.487177	−	1.00631i
$551$	105.000			0.190563
$552$	−845.234			−1.53122
$553$		−	687.386i		−	1.24301i
$554$	130.000			0.234657
$555$	42.0000	−	96.2341i	0.0756757	−	0.173395i
$556$		−	225.433i		−	0.405455i
$557$	−156.525			−0.281014			−0.140507	−	0.990080i	$-0.544873\pi$
$557$	−156.525			−0.281014			−0.140507	+	0.990080i	$0.544873\pi$
$558$	−80.4984			−0.144262
$559$	200.000			0.357782
$560$	−424.853	+	973.460i	−0.758666	+	1.73832i
$561$	−735.000	+	286.915i	−1.31016	+	0.511434i
$562$			366.606i			0.652324i
$563$	−881.011			−1.56485			−0.782425	−	0.622745i	$-0.786018\pi$
$563$	−881.011			−1.56485			−0.782425	+	0.622745i	$0.786018\pi$
$564$	294.000			0.521277
$565$	756.000	+	329.945i	1.33805	+	0.583974i
$566$	−560.000			−0.989399
$567$	503.115			0.887329
$568$	181.122			0.318876
$569$			143.457i			0.252122i	0.992023	+	0.126061i	$0.0402335\pi$
$569$			143.457i			0.252122i	−0.992023	+	0.126061i	$0.959767\pi$
$570$	−210.000	+	481.170i	−0.368421	+	0.844159i
$571$		−	604.570i		−	1.05879i	−0.848375	−	0.529396i	$-0.822419\pi$
$571$		−	604.570i		−	1.05879i	0.848375	−	0.529396i	$-0.177581\pi$
$572$	35.7771	+	91.6515i	0.0625474	+	0.160230i
$573$			1273.96i			2.22331i
$574$			512.348i			0.892592i
$575$	−504.000	+	467.423i	−0.876522	+	0.812909i
$576$	−492.000			−0.854167
$577$		−	164.973i		−	0.285915i	−0.989729	−	0.142957i	$-0.954339\pi$
$577$		−	164.973i		−	0.285915i	0.989729	−	0.142957i	$-0.0456612\pi$
$578$	98.3870			0.170220
$579$		−	358.643i		−	0.619418i
$580$	−46.9574	−	20.4939i	−0.0809611	−	0.0353343i
$581$	−800.000			−1.37694
$582$	1220.89			2.09775
$583$	−46.9574	+	18.3303i	−0.0805445	+	0.0314413i
$584$	−390.000			−0.667808
$585$	−214.663	+	491.854i	−0.366944	+	0.840775i
$586$	−1000.00			−1.70648
$587$		−	875.272i		−	1.49109i	−0.666453	−	0.745547i	$-0.732188\pi$
$587$		−	875.272i		−	1.49109i	0.666453	−	0.745547i	$-0.267812\pi$
$588$		−	348.276i		−	0.592306i
$589$			30.7409i			0.0521916i
$590$	−80.4984	+	184.445i	−0.136438	+	0.312619i
$591$		−	901.732i		−	1.52577i
$592$			87.0689i			0.147076i
$593$	111.803			0.188539			0.0942693	−	0.995547i	$-0.469949\pi$
$593$	111.803			0.188539			0.0942693	+	0.995547i	$0.469949\pi$
$594$	−315.000	+	122.963i	−0.530303	+	0.207009i
$595$	350.000	−	801.951i	0.588235	−	1.34782i
$596$			153.704i			0.257893i
$597$			242.877i			0.406828i
$598$		−	549.909i		−	0.919580i
$599$	−493.000			−0.823038			−0.411519	−	0.911401i	$-0.635002\pi$
$599$	−493.000			−0.823038			−0.411519	+	0.911401i	$0.635002\pi$
$600$	−563.489	+	522.594i	−0.939149	+	0.870991i
$601$			102.470i			0.170498i	0.996360	+	0.0852492i	$0.0271686\pi$
$601$			102.470i			0.170498i	−0.996360	+	0.0852492i	$0.972831\pi$
$602$	−559.017			−0.928600
$603$			329.945i			0.547173i
$604$			102.470i			0.169652i
$605$	−197.659	−	571.800i	−0.326710	−	0.945125i
$606$	1050.00			1.73267
$607$	816.165			1.34459			0.672294	−	0.740284i	$-0.265309\pi$
$607$	816.165			1.34459			0.672294	+	0.740284i	$0.265309\pi$
$608$		−	160.390i		−	0.263800i
$609$	−525.000			−0.862069
$610$	−735.000	−	320.780i	−1.20492	−	0.525869i
$611$		−	573.829i		−	0.939164i
$612$	−187.830			−0.306911
$613$	−881.011			−1.43721			−0.718606	−	0.695418i	$-0.755219\pi$
$613$	−881.011			−1.43721			−0.718606	+	0.695418i	$0.755219\pi$
$614$	1000.00			1.62866
$615$	−187.830	+	430.372i	−0.305414	+	0.699792i
$616$	300.000	+	768.521i	0.487013	+	1.24760i
$617$			293.285i			0.475340i	0.971346	+	0.237670i	$0.0763837\pi$
$617$			293.285i			0.475340i	−0.971346	+	0.237670i	$0.923616\pi$
$618$	−187.830			−0.303932
$619$	972.000			1.57027			0.785137	−	0.619322i	$-0.212592\pi$
$619$	972.000			1.57027			0.785137	+	0.619322i	$0.212592\pi$
$620$	6.00000	−	13.7477i	0.00967742	−	0.0221738i
$621$	378.000			0.608696
$622$	−194.538			−0.312762
$623$	−413.673			−0.664001
$624$		−	778.768i		−	1.24803i
$625$	−47.0000	+	623.230i	−0.0752000	+	0.997168i
$626$		−	655.805i		−	1.04761i
$627$	187.830	+	481.170i	0.299569	+	0.767417i
$628$		−	50.4083i		−	0.0802680i
$629$		−	71.7287i		−	0.114036i
$630$	600.000	−	1374.77i	0.952381	−	2.18218i
$631$	−113.000			−0.179081			−0.0895404	−	0.995983i	$-0.528540\pi$
$631$	−113.000			−0.179081			−0.0895404	+	0.995983i	$0.528540\pi$
$632$			412.432i			0.652582i
$633$	−798.276			−1.26110
$634$			112.716i			0.177786i
$635$	−62.6099	+	143.457i	−0.0985983	+	0.225917i
$636$	−21.0000			−0.0330189
$637$	−679.765			−1.06713
$638$	−234.787	+	91.6515i	−0.368005	+	0.143654i
$639$	−324.000			−0.507042
$640$	308.577	−	707.040i	0.482152	−	1.10475i
$641$	1007.00			1.57098			0.785491	−	0.618873i	$-0.212410\pi$
$641$	1007.00			1.57098			0.785491	+	0.618873i	$0.212410\pi$
$642$		−	1603.90i		−	2.49829i
$643$			270.372i			0.420485i	0.977649	+	0.210243i	$0.0674254\pi$
$643$			270.372i			0.420485i	−0.977649	+	0.210243i	$0.932575\pi$
$644$			307.409i			0.477342i
$645$	−469.574	−	204.939i	−0.728022	−	0.317735i
$646$			358.643i			0.555175i
$647$			18.3303i			0.0283312i	0.999900	+	0.0141656i	$0.00450921\pi$
$647$			18.3303i			0.0283312i	−0.999900	+	0.0141656i	$0.995491\pi$
$648$	−301.869			−0.465847
$649$	72.0000	+	184.445i	0.110940	+	0.284199i
$650$	−340.000	−	366.606i	−0.523077	−	0.564009i
$651$		−	153.704i		−	0.236105i
$652$			270.372i			0.414681i
$653$		−	691.969i		−	1.05968i	−0.848099	−	0.529838i	$-0.822253\pi$
$653$		−	691.969i		−	1.05968i	0.848099	−	0.529838i	$-0.177747\pi$
$654$	−210.000			−0.321101
$655$	986.106	+	430.372i	1.50551	+	0.657056i
$656$		−	389.384i		−	0.593573i
$657$	697.653			1.06188
$658$			1603.90i			2.43754i
$659$			1096.42i			1.66377i	0.554949	+	0.831884i	$0.312738\pi$
$659$			1096.42i			1.66377i	−0.554949	+	0.831884i	$0.687262\pi$
$660$	9.91486	−	251.847i	0.0150225	−	0.381586i
$661$	862.000			1.30408			0.652042	−	0.758183i	$-0.273912\pi$
$661$	862.000			1.30408			0.652042	+	0.758183i	$0.273912\pi$
$662$	308.577			0.466129
$663$			641.561i			0.967663i
$664$	480.000			0.722892
$665$	−525.000	−	229.129i	−0.789474	−	0.344555i
$666$		−	122.963i		−	0.184630i
$667$	281.745			0.422406
$668$	−297.397			−0.445205
$669$	−1806.00			−2.69955
$670$	−281.745	−	122.963i	−0.420514	−	0.183527i
$671$	−735.000	+	286.915i	−1.09538	+	0.427593i
$672$			801.951i			1.19338i
$673$	713.306			1.05989			0.529945	−	0.848032i	$-0.322213\pi$
$673$	713.306			1.05989			0.529945	+	0.848032i	$0.322213\pi$
$674$	545.000			0.808605
$675$	252.000	−	233.711i	0.373333	−	0.346239i
$676$	−89.0000			−0.131657
$677$	31.3050			0.0462407			0.0231203	−	0.999733i	$-0.492640\pi$
$677$	31.3050			0.0462407			0.0231203	+	0.999733i	$0.492640\pi$
$678$	1690.47			2.49331
$679$			1332.10i			1.96186i
$680$	−210.000	+	481.170i	−0.308824	+	0.707604i
$681$		−	1270.62i		−	1.86582i
$682$	−26.8328	−	68.7386i	−0.0393443	−	0.100790i
$683$		−	600.317i		−	0.878942i	−0.898257	−	0.439471i	$-0.855166\pi$
$683$		−	600.317i		−	0.878942i	0.898257	−	0.439471i	$-0.144834\pi$
$684$			122.963i			0.179771i
$685$	−294.000	−	128.312i	−0.429197	−	0.187317i
$686$	675.000			0.983965
$687$		−	1338.11i		−	1.94776i
$688$	424.853			0.617519
$689$			40.9878i			0.0594888i
$690$	−563.489	+	1291.12i	−0.816651	+	1.87118i
$691$	872.000			1.26194			0.630970	−	0.775808i	$-0.282657\pi$
$691$	872.000			1.26194			0.630970	+	0.775808i	$0.282657\pi$
$692$	143.108			0.206804
$693$	−536.656	−	1374.77i	−0.774396	−	1.98380i
$694$	10.0000			0.0144092
$695$	1033.06	+	450.866i	1.48642	+	0.648728i
$696$	315.000			0.452586
$697$			320.780i			0.460230i
$698$			1145.64i			1.64132i
$699$		−	789.015i		−	1.12878i
$700$	190.066	+	204.939i	0.271523	+	0.292770i
$701$			870.991i			1.24250i	0.783613	+	0.621249i	$0.213374\pi$
$701$			870.991i			1.24250i	−0.783613	+	0.621249i	$0.786626\pi$
$702$			274.955i			0.391673i
$703$	−46.9574			−0.0667958
$704$	−164.000	−	420.125i	−0.232955	−	0.596768i
$705$	−588.000	+	1347.28i	−0.834043	+	1.91103i
$706$		−	655.805i		−	0.928902i
$707$			1145.64i			1.62043i
$708$			82.4864i			0.116506i
$709$	−768.000			−1.08322			−0.541608	−	0.840631i	$-0.682184\pi$
$709$	−768.000			−1.08322			−0.541608	+	0.840631i	$0.682184\pi$
$710$	120.748	−	276.668i	0.170067	−	0.389673i
$711$		−	737.780i		−	1.03767i
$712$	248.204			0.348600
$713$			82.4864i			0.115689i
$714$		−	1793.22i		−	2.51151i
$715$	−491.554	−	19.3518i	−0.687488	−	0.0270655i
$716$	242.000			0.337989
$717$	−1033.06			−1.44081
$718$		−	1420.60i		−	1.97855i
$719$	−263.000			−0.365786			−0.182893	−	0.983133i	$-0.558546\pi$
$719$	−263.000			−0.365786			−0.182893	+	0.983133i	$0.558546\pi$
$720$	−456.000	+	1044.83i	−0.633333	+	1.45115i
$721$		−	204.939i		−	0.284243i
$722$	−572.433			−0.792844
$723$	1502.64			2.07834
$724$	−258.000			−0.356354
$725$	187.830	−	174.198i	0.259075	−	0.240273i
$726$	−840.000	−	911.979i	−1.15702	−	1.25617i
$727$			293.285i			0.403418i	0.979446	+	0.201709i	$0.0646495\pi$
$727$			293.285i			0.403418i	−0.979446	+	0.201709i	$0.935350\pi$
$728$	670.820			0.921457
$729$	1107.00			1.51852
$730$	−260.000	+	595.735i	−0.356164	+	0.816075i
$731$	−350.000			−0.478796
$732$	−328.702			−0.449046
$733$	−219.135			−0.298956			−0.149478	−	0.988765i	$-0.547759\pi$
$733$	−219.135			−0.298956			−0.149478	+	0.988765i	$0.547759\pi$
$734$		−	963.213i		−	1.31228i
$735$	1596.00	+	696.552i	2.17143	+	0.947689i
$736$		−	430.372i		−	0.584744i
$737$	−281.745	+	109.982i	−0.382286	+	0.149229i
$738$			549.909i			0.745134i
$739$			389.384i			0.526907i	0.964672	+	0.263453i	$0.0848615\pi$
$739$			389.384i			0.526907i	−0.964672	+	0.263453i	$0.915138\pi$
$740$	21.0000	+	9.16515i	0.0283784	+	0.0123853i
$741$	420.000			0.566802
$742$		−	114.564i		−	0.154399i
$743$	−682.001			−0.917901			−0.458951	−	0.888462i	$-0.651775\pi$
$743$	−682.001			−0.917901			−0.458951	+	0.888462i	$0.651775\pi$
$744$			92.2226i			0.123955i
$745$	−704.361	−	307.409i	−0.945452	−	0.412629i
$746$	−1220.00			−1.63539
$747$	−858.650			−1.14946
$748$	−62.6099	−	160.390i	−0.0837031	−	0.214425i
$749$	1750.00			2.33645
$750$	422.617	+	1209.14i	0.563489	+	1.61219i
$751$	−1003.00			−1.33555			−0.667776	−	0.744362i	$-0.732754\pi$
$751$	−1003.00			−1.33555			−0.667776	+	0.744362i	$0.732754\pi$
$752$		−	1218.97i		−	1.62096i
$753$		−	1292.29i		−	1.71618i
$754$			204.939i			0.271802i
$755$	−469.574	−	204.939i	−0.621953	−	0.271442i
$756$		−	153.704i		−	0.203313i
$757$		−	1218.97i		−	1.61026i	−0.593100	−	0.805129i	$-0.702096\pi$
$757$		−	1218.97i		−	1.61026i	0.593100	−	0.805129i	$-0.297904\pi$
$758$	957.037			1.26258
$759$	504.000	+	1291.12i	0.664032	+	1.70107i
$760$	315.000	+	137.477i	0.414474	+	0.180891i
$761$			184.445i			0.242372i	0.992630	+	0.121186i	$0.0386698\pi$
$761$			184.445i			0.242372i	−0.992630	+	0.121186i	$0.961330\pi$
$762$			320.780i			0.420972i
$763$		−	229.129i		−	0.300300i
$764$	−278.000			−0.363874
$765$	375.659	−	860.744i	0.491058	−	1.12516i
$766$			368.890i			0.481580i
$767$	160.997			0.209905
$768$		−	829.446i		−	1.08001i
$769$			245.927i			0.319801i	0.987133	+	0.159900i	$0.0511173\pi$
$769$			245.927i			0.319801i	−0.987133	+	0.159900i	$0.948883\pi$
$770$	1373.94	+	54.0900i	1.78433	+	0.0702467i
$771$	294.000			0.381323
$772$	78.2624			0.101376
$773$		−	279.537i		−	0.361626i	−0.983517	−	0.180813i	$-0.942127\pi$
$773$		−	279.537i		−	0.361626i	0.983517	−	0.180813i	$-0.0578729\pi$
$774$	−600.000			−0.775194
$775$	51.0000	+	54.9909i	0.0658065	+	0.0709560i
$776$		−	799.262i		−	1.02998i
$777$	234.787			0.302171
$778$	509.823			0.655300
$779$	210.000			0.269576
$780$	−187.830	−	81.9756i	−0.240807	−	0.105097i
$781$	−108.000	−	276.668i	−0.138284	−	0.354248i
$782$			962.341i			1.23061i
$783$	−140.872			−0.179914
$784$	−1444.00			−1.84184
$785$	231.000	+	100.817i	0.294268	+	0.128429i
$786$	2205.00			2.80534
$787$	−746.847			−0.948979			−0.474490	−	0.880261i	$-0.657367\pi$
$787$	−746.847			−0.948979			−0.474490	+	0.880261i	$0.657367\pi$
$788$	196.774			0.249713
$789$			911.979i			1.15587i
$790$	630.000	+	274.955i	0.797468	+	0.348044i
$791$			1844.45i			2.33180i
$792$	321.994	+	824.864i	0.406558	+	1.04149i
$793$			641.561i			0.809030i
$794$			1496.05i			1.88420i
$795$	42.0000	−	96.2341i	0.0528302	−	0.121049i
$796$	−53.0000			−0.0665829
$797$			705.717i			0.885466i	0.896653	+	0.442733i	$0.145991\pi$
$797$			705.717i			0.885466i	−0.896653	+	0.442733i	$0.854009\pi$
$798$	−1173.94			−1.47110
$799$			1004.20i			1.25682i
$800$	−266.092	−	286.915i	−0.332615	−	0.358643i
$801$	−444.000			−0.554307
$802$	−239.259			−0.298328
$803$	232.551	+	595.735i	0.289603	+	0.741886i
$804$	−126.000			−0.156716
$805$	−1408.72	−	614.817i	−1.74997	−	0.763748i
$806$	−60.0000			−0.0744417
$807$		−	742.377i		−	0.919922i
$808$		−	687.386i		−	0.850726i
$809$		−	1209.14i		−	1.49461i	−0.664481	−	0.747305i	$-0.731347\pi$
$809$		−	1209.14i		−	1.49461i	0.664481	−	0.747305i	$-0.268653\pi$
$810$	−201.246	+	461.113i	−0.248452	+	0.569275i
$811$		−	1096.42i		−	1.35194i	−0.736929	−	0.675970i	$-0.763725\pi$
$811$		−	1096.42i		−	1.35194i	0.736929	−	0.675970i	$-0.236275\pi$
$812$		−	114.564i		−	0.141089i
$813$	−1126.98			−1.38620
$814$	105.000	−	40.9878i	0.128993	−	0.0503536i
$815$	−1239.00	−	540.744i	−1.52025	−	0.663489i
$816$			1362.84i			1.67015i
$817$			229.129i			0.280451i
$818$		−	733.212i		−	0.896347i
$819$	−1200.00			−1.46520
$820$	−93.9149	−	40.9878i	−0.114530	−	0.0499851i
$821$		−	758.274i		−	0.923598i	−0.886984	−	0.461799i	$-0.847204\pi$
$821$		−	758.274i		−	0.923598i	0.886984	−	0.461799i	$-0.152796\pi$
$822$	−657.404			−0.799762
$823$			293.285i			0.356361i	0.983998	+	0.178180i	$0.0570210\pi$
$823$			293.285i			0.356361i	−0.983998	+	0.178180i	$0.942979\pi$
$824$			122.963i			0.149227i
$825$	1134.28	+	549.129i	1.37488	+	0.665611i
$826$	−450.000			−0.544794
$827$	−594.794			−0.719219			−0.359609	−	0.933103i	$-0.617090\pi$
$827$	−594.794			−0.719219			−0.359609	+	0.933103i	$0.617090\pi$
$828$			329.945i			0.398485i
$829$	102.000			0.123040			0.0615199	−	0.998106i	$-0.480405\pi$
$829$	102.000			0.123040			0.0615199	+	0.998106i	$0.480405\pi$
$830$	320.000	−	733.212i	0.385542	−	0.883388i
$831$			266.421i			0.320603i
$832$	−366.715			−0.440763
$833$	1189.59			1.42808
$834$	2310.00			2.76978
$835$	594.794	−	1362.84i	0.712328	−	1.63215i
$836$	−105.000	+	40.9878i	−0.125598	+	0.0490285i
$837$		−	41.2432i		−	0.0492750i
$838$	−1614.44			−1.92654
$839$	−138.000			−0.164482			−0.0822408	−	0.996612i	$-0.526208\pi$
$839$	−138.000			−0.164482			−0.0822408	+	0.996612i	$0.526208\pi$
$840$	−1575.00	−	687.386i	−1.87500	−	0.818317i
$841$	736.000			0.875149
$842$	912.316			1.08351
$843$	−751.319			−0.891244
$844$		−	174.198i		−	0.206396i
$845$	178.000	−	407.849i	0.210651	−	0.482662i
$846$			1721.49i			2.03486i
$847$	995.050	−	916.515i	1.17479	−	1.08207i
$848$			87.0689i			0.102676i
$849$		−	1147.66i		−	1.35178i
$850$	595.000	+	641.561i	0.700000	+	0.754777i
$851$	−126.000			−0.148061
$852$		−	123.730i		−	0.145222i
$853$	532.184			0.623897			0.311949	−	0.950099i	$-0.399018\pi$
$853$	532.184			0.623897			0.311949	+	0.950099i	$0.399018\pi$
$854$		−	1793.22i		−	2.09978i
$855$	−563.489	−	245.927i	−0.659052	−	0.287634i
$856$	−1050.00			−1.22664
$857$	950.329			1.10890			0.554451	−	0.832216i	$-0.312928\pi$
$857$	950.329			1.10890			0.554451	+	0.832216i	$0.312928\pi$
$858$	−939.149	+	366.606i	−1.09458	+	0.427280i
$859$	−1068.00			−1.24331			−0.621653	−	0.783293i	$-0.713539\pi$
$859$	−1068.00			−1.24331			−0.621653	+	0.783293i	$0.713539\pi$
$860$	44.7214	−	102.470i	0.0520016	−	0.119151i
$861$	−1050.00			−1.21951
$862$			137.477i			0.159486i
$863$		−	73.3212i		−	0.0849608i	−0.999097	−	0.0424804i	$-0.986474\pi$
$863$		−	73.3212i		−	0.0849608i	0.999097	−	0.0424804i	$-0.0135260\pi$
$864$			215.186i			0.249058i
$865$	−286.217	+	655.805i	−0.330886	+	0.758156i
$866$		−	553.335i		−	0.638955i
$867$			201.633i			0.232564i
$868$	33.5410			0.0386417
$869$	630.000	−	245.927i	0.724971	−	0.283000i
$870$	210.000	−	481.170i	0.241379	−	0.553069i
$871$			245.927i			0.282350i
$872$			137.477i			0.157657i
$873$			1429.76i			1.63776i
$874$	630.000			0.720824
$875$	−1319.28	+	461.113i	−1.50775	+	0.526986i
$876$			266.421i			0.304133i
$877$	−169.941			−0.193776			−0.0968878	−	0.995295i	$-0.530889\pi$
$877$	−169.941			−0.193776			−0.0968878	+	0.995295i	$0.530889\pi$
$878$			962.341i			1.09606i
$879$		−	2049.39i		−	2.33150i
$880$	−1044.19	−	41.1084i	−1.18658	−	0.0467141i
$881$	−78.0000			−0.0885358			−0.0442679	−	0.999020i	$-0.514096\pi$
$881$	−78.0000			−0.0885358			−0.0442679	+	0.999020i	$0.514096\pi$
$882$	2039.29			2.31212
$883$			1553.49i			1.75934i	0.475589	+	0.879668i	$0.342235\pi$
$883$			1553.49i			1.75934i	−0.475589	+	0.879668i	$0.657765\pi$
$884$	−140.000			−0.158371
$885$	−378.000	−	164.973i	−0.427119	−	0.186410i
$886$			676.299i			0.763317i
$887$	−299.633			−0.337805			−0.168903	−	0.985633i	$-0.554022\pi$
$887$	−299.633			−0.337805			−0.168903	+	0.985633i	$0.554022\pi$
$888$	−140.872			−0.158640
$889$	−350.000			−0.393701
$890$	165.469	−	379.137i	0.185920	−	0.425997i
$891$	180.000	+	461.113i	0.202020	+	0.517523i
$892$		−	394.102i		−	0.441818i
$893$	657.404			0.736175
$894$	−1575.00			−1.76174
$895$	−484.000	+	1108.98i	−0.540782	+	1.23909i
$896$	1725.00			1.92522
$897$	1126.98			1.25639
$898$	−49.1935			−0.0547812
$899$		−	30.7409i		−	0.0341945i
$900$	204.000	+	219.964i	0.226667	+	0.244404i
$901$		−	71.7287i		−	0.0796101i
$902$	−469.574	+	183.303i	−0.520592	+	0.203218i
$903$		−	1145.64i		−	1.26871i
$904$		−	1106.67i		−	1.22419i
$905$	516.000	−	1182.30i	0.570166	−	1.30641i
$906$	−1050.00			−1.15894
$907$		−	691.969i		−	0.762921i	−0.924385	−	0.381460i	$-0.875421\pi$
$907$		−	691.969i		−	0.762921i	0.924385	−	0.381460i	$-0.124579\pi$
$908$	277.272			0.305366
$909$			1229.63i			1.35273i
$910$	447.214	−	1024.70i	0.491444	−	1.12604i
$911$	1037.00			1.13831			0.569155	−	0.822230i	$-0.307271\pi$
$911$	1037.00			1.13831			0.569155	+	0.822230i	$0.307271\pi$
$912$	892.191			0.978280
$913$	−286.217	−	733.212i	−0.313490	−	0.803080i
$914$	775.000			0.847921
$915$	657.404	−	1506.30i	0.718474	−	1.64623i
$916$	292.000			0.318777
$917$			2405.85i			2.62361i
$918$		−	481.170i		−	0.524151i
$919$			1782.97i			1.94012i	0.242867	+	0.970060i	$0.421912\pi$
$919$			1782.97i			1.94012i	−0.242867	+	0.970060i	$0.578088\pi$
$920$	845.234	+	368.890i	0.918732	+	0.400968i
$921$			2049.39i			2.22518i
$922$		−	756.125i		−	0.820092i
$923$	−241.495			−0.261642
$924$	525.000	−	204.939i	0.568182	−	0.221795i
$925$	−84.0000	+	77.9038i	−0.0908108	+	0.0842203i
$926$			1393.59i			1.50495i
$927$		−	219.964i		−	0.237285i
$928$			160.390i			0.172834i
$929$	−633.000			−0.681378			−0.340689	−	0.940176i	$-0.610660\pi$
$929$	−633.000			−0.681378			−0.340689	+	0.940176i	$0.610660\pi$
$930$	140.872	+	61.4817i	0.151476	+	0.0661094i
$931$		−	778.768i		−	0.836486i
$932$	172.177			0.184740
$933$		−	398.684i		−	0.427314i
$934$			1239.88i			1.32750i
$935$	860.220	+	33.8657i	0.920021	+	0.0362200i
$936$	720.000			0.769231
$937$	728.958			0.777970			0.388985	−	0.921244i	$-0.372826\pi$
$937$	728.958			0.777970			0.388985	+	0.921244i	$0.372826\pi$
$938$		−	687.386i		−	0.732821i
$939$	1344.00			1.43131
$940$	−294.000	−	128.312i	−0.312766	−	0.136502i
$941$		−	850.497i		−	0.903822i	−0.892063	−	0.451911i	$-0.850742\pi$
$941$		−	850.497i		−	0.903822i	0.892063	−	0.451911i	$-0.149258\pi$
$942$	516.532			0.548335
$943$	563.489			0.597549
$944$	342.000			0.362288
$945$	704.361	+	307.409i	0.745356	+	0.325300i
$946$	−200.000	−	512.348i	−0.211416	−	0.541594i
$947$			911.933i			0.962970i	0.876454	+	0.481485i	$0.159902\pi$
$947$			911.933i			0.962970i	−0.876454	+	0.481485i	$0.840098\pi$
$948$	281.745			0.297199
$949$	520.000			0.547945
$950$	420.000	−	389.519i	0.442105	−	0.410020i
$951$	−231.000			−0.242902
$952$	−1173.94			−1.23313
$953$	1236.55			1.29753			0.648765	−	0.760989i	$-0.275286\pi$
$953$	1236.55			1.29753			0.648765	+	0.760989i	$0.275286\pi$
$954$		−	122.963i		−	0.128892i
$955$	556.000	−	1273.96i	0.582199	−	1.33399i
$956$		−	225.433i		−	0.235808i
$957$	−187.830	−	481.170i	−0.196269	−	0.502790i
$958$			91.6515i			0.0956696i
$959$		−	717.287i		−	0.747953i
$960$	861.000	+	375.771i	0.896875	+	0.391428i
$961$	−952.000			−0.990635
$962$		−	91.6515i		−	0.0952718i
$963$	1878.30			1.95046
$964$			327.902i			0.340148i
$965$	−156.525	+	358.643i	−0.162202	+	0.371651i
$966$	−3150.00			−3.26087
$967$	−431.561			−0.446289			−0.223144	−	0.974785i	$-0.571632\pi$
$967$	−431.561			−0.446289			−0.223144	+	0.974785i	$0.571632\pi$
$968$	−597.030	+	549.909i	−0.616767	+	0.568088i
$969$	−735.000			−0.758514
$970$	−1220.89	−	532.841i	−1.25865	−	0.549321i
$971$	−1048.00			−1.07930			−0.539650	−	0.841890i	$-0.681443\pi$
$971$	−1048.00			−1.07930			−0.539650	+	0.841890i	$0.681443\pi$
$972$			329.945i			0.339450i
$973$			2520.42i			2.59036i
$974$		−	758.274i		−	0.778516i
$975$	751.319	−	696.793i	0.770583	−	0.714659i
$976$			1362.84i			1.39636i
$977$			247.459i			0.253285i	0.991948	+	0.126642i	$0.0404200\pi$
$977$			247.459i			0.253285i	−0.991948	+	0.126642i	$0.959580\pi$
$978$	−2770.49			−2.83281
$979$	−148.000	−	379.137i	−0.151175	−	0.387270i
$980$	−152.000	+	348.276i	−0.155102	+	0.355383i
$981$		−	245.927i		−	0.250690i
$982$		−	1306.03i		−	1.32997i
$983$		−	27.4955i		−	0.0279710i	−0.999902	−	0.0139855i	$-0.995548\pi$
$983$		−	27.4955i		−	0.0279710i	0.999902	−	0.0139855i	$-0.00445186\pi$
$984$	630.000			0.640244
$985$	−393.548	+	901.732i	−0.399541	+	0.915464i
$986$		−	358.643i		−	0.363736i
$987$	−3287.02			−3.33031
$988$			91.6515i			0.0927647i
$989$			614.817i			0.621655i
$990$	1474.66	+	58.0554i	1.48956	+	0.0586419i
$991$	1182.00			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$991$	1182.00			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$992$	−46.9574			−0.0473361
$993$			632.395i			0.636853i
$994$	675.000			0.679074
$995$	106.000	−	242.877i	0.106533	−	0.244097i
$996$		−	327.902i		−	0.329219i
$997$	1694.94			1.70004			0.850020	−	0.526751i	$-0.176590\pi$
$997$	1694.94			1.70004			0.850020	+	0.526751i	$0.176590\pi$
$998$	599.266			0.600467
$999$	63.0000			0.0630631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.d.d.54.1	✓	4
3.2	odd	2		495.3.h.d.109.3		4
4.3	odd	2		880.3.i.d.769.4		4
5.2	odd	4		275.3.c.e.76.1		4
5.3	odd	4		275.3.c.e.76.4		4
5.4	even	2	inner	55.3.d.d.54.4	yes	4
11.10	odd	2	inner	55.3.d.d.54.3	yes	4
15.14	odd	2		495.3.h.d.109.2		4
20.19	odd	2		880.3.i.d.769.1		4
33.32	even	2		495.3.h.d.109.1		4
44.43	even	2		880.3.i.d.769.3		4
55.32	even	4		275.3.c.e.76.3		4
55.43	even	4		275.3.c.e.76.2		4
55.54	odd	2	inner	55.3.d.d.54.2	yes	4
165.164	even	2		495.3.h.d.109.4		4
220.219	even	2		880.3.i.d.769.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.d.d.54.1	✓	4	1.1	even	1	trivial
55.3.d.d.54.2	yes	4	55.54	odd	2	inner
55.3.d.d.54.3	yes	4	11.10	odd	2	inner
55.3.d.d.54.4	yes	4	5.4	even	2	inner
275.3.c.e.76.1		4	5.2	odd	4
275.3.c.e.76.2		4	55.43	even	4
275.3.c.e.76.3		4	55.32	even	4
275.3.c.e.76.4		4	5.3	odd	4
495.3.h.d.109.1		4	33.32	even	2
495.3.h.d.109.2		4	15.14	odd	2
495.3.h.d.109.3		4	3.2	odd	2
495.3.h.d.109.4		4	165.164	even	2
880.3.i.d.769.1		4	20.19	odd	2
880.3.i.d.769.2		4	220.219	even	2
880.3.i.d.769.3		4	44.43	even	2
880.3.i.d.769.4		4	4.3	odd	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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} -4.58258i q^{3} +1.00000 q^{4} +(-2.00000 + 4.58258i) q^{5} +10.2470i q^{6} -11.1803 q^{7} +6.70820 q^{8} -12.0000 q^{9} +(4.47214 - 10.2470i) q^{10} +(-4.00000 - 10.2470i) q^{11} -4.58258i q^{12} -8.94427 q^{13} +25.0000 q^{14} +(21.0000 + 9.16515i) q^{15} -19.0000 q^{16} +15.6525 q^{17} +26.8328 q^{18} -10.2470i q^{19} +(-2.00000 + 4.58258i) q^{20} +51.2348i q^{21} +(8.94427 + 22.9129i) q^{22} -27.4955i q^{23} -30.7409i q^{24} +(-17.0000 - 18.3303i) q^{25} +20.0000 q^{26} +13.7477i q^{27} -11.1803 q^{28} +10.2470i q^{29} +(-46.9574 - 20.4939i) q^{30} -3.00000 q^{31} +15.6525 q^{32} +(-46.9574 + 18.3303i) q^{33} -35.0000 q^{34} +(22.3607 - 51.2348i) q^{35} -12.0000 q^{36} -4.58258i q^{37} +22.9129i q^{38} +40.9878i q^{39} +(-13.4164 + 30.7409i) q^{40} +20.4939i q^{41} -114.564i q^{42} -22.3607 q^{43} +(-4.00000 - 10.2470i) q^{44} +(24.0000 - 54.9909i) q^{45} +61.4817i q^{46} +64.1561i q^{47} +87.0689i q^{48} +76.0000 q^{49} +(38.0132 + 40.9878i) q^{50} -71.7287i q^{51} -8.94427 q^{52} -4.58258i q^{53} -30.7409i q^{54} +(54.9574 + 2.16360i) q^{55} -75.0000 q^{56} -46.9574 q^{57} -22.9129i q^{58} -18.0000 q^{59} +(21.0000 + 9.16515i) q^{60} -71.7287i q^{61} +6.70820 q^{62} +134.164 q^{63} +41.0000 q^{64} +(17.8885 - 40.9878i) q^{65} +(105.000 - 40.9878i) q^{66} -27.4955i q^{67} +15.6525 q^{68} -126.000 q^{69} +(-50.0000 + 114.564i) q^{70} +27.0000 q^{71} -80.4984 q^{72} -58.1378 q^{73} +10.2470i q^{74} +(-84.0000 + 77.9038i) q^{75} -10.2470i q^{76} +(44.7214 + 114.564i) q^{77} -91.6515i q^{78} +61.4817i q^{79} +(38.0000 - 87.0689i) q^{80} -45.0000 q^{81} -45.8258i q^{82} +71.5542 q^{83} +51.2348i q^{84} +(-31.3050 + 71.7287i) q^{85} +50.0000 q^{86} +46.9574 q^{87} +(-26.8328 - 68.7386i) q^{88} +37.0000 q^{89} +(-53.6656 + 122.963i) q^{90} +100.000 q^{91} -27.4955i q^{92} +13.7477i q^{93} -143.457i q^{94} +(46.9574 + 20.4939i) q^{95} -71.7287i q^{96} -119.147i q^{97} -169.941 q^{98} +(48.0000 + 122.963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 8 q^{5} - 48 q^{9} - 16 q^{11} + 100 q^{14} + 84 q^{15} - 76 q^{16} - 8 q^{20} - 68 q^{25} + 80 q^{26} - 12 q^{31} - 140 q^{34} - 48 q^{36} - 16 q^{44} + 96 q^{45} + 304 q^{49} + 32 q^{55}+ \cdots + 192 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 8 * q^5 - 48 * q^9 - 16 * q^11 + 100 * q^14 + 84 * q^15 - 76 * q^16 - 8 * q^20 - 68 * q^25 + 80 * q^26 - 12 * q^31 - 140 * q^34 - 48 * q^36 - 16 * q^44 + 96 * q^45 + 304 * q^49 + 32 * q^55 - 300 * q^56 - 72 * q^59 + 84 * q^60 + 164 * q^64 + 420 * q^66 - 504 * q^69 - 200 * q^70 + 108 * q^71 - 336 * q^75 + 152 * q^80 - 180 * q^81 + 200 * q^86 + 148 * q^89 + 400 * q^91 + 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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