LMFDB - Embedded newform 177.3.b.a.119.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.8
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} +O(q^{10})$	\(q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} -11.3055 q^{10} +3.60723i q^{11} +(-2.48568 + 11.1805i) q^{12} +6.03188 q^{13} -19.4495i q^{14} +(-11.8411 - 2.63255i) q^{15} -16.6955 q^{16} +27.5797i q^{17} +(-10.6622 + 22.7939i) q^{18} +11.5320 q^{19} +15.4371i q^{20} +(4.52891 - 20.3709i) q^{21} +10.0859 q^{22} -6.63792i q^{23} +(-1.49164 - 0.331625i) q^{24} +8.65080 q^{25} -16.8654i q^{26} +(-16.4750 + 21.3910i) q^{27} -26.5572 q^{28} +7.59974i q^{29} +(-7.36072 + 33.1083i) q^{30} +40.0199 q^{31} +44.6438i q^{32} +(10.5638 + 2.34856i) q^{33} +77.1139 q^{34} -28.1264i q^{35} +(31.1238 + 14.5586i) q^{36} -53.5956 q^{37} -32.2439i q^{38} +(3.92718 - 17.6643i) q^{39} -2.05952 q^{40} -33.0823i q^{41} +(-56.9578 - 12.6630i) q^{42} -19.3543 q^{43} -13.7718i q^{44} +(-15.4188 + 32.9628i) q^{45} -18.5599 q^{46} -51.4877i q^{47} +(-10.8700 + 48.8927i) q^{48} -0.612818 q^{49} -24.1880i q^{50} +(80.7671 + 17.9564i) q^{51} -23.0287 q^{52} -40.9324i q^{53} +(59.8101 + 46.0647i) q^{54} +14.5855 q^{55} -3.54310i q^{56} +(7.50816 - 33.7715i) q^{57} +21.2492 q^{58} +7.68115i q^{59} +(45.2075 + 10.0506i) q^{60} +48.9309 q^{61} -111.897i q^{62} +(-56.7075 - 26.5258i) q^{63} +58.0439 q^{64} -24.3894i q^{65} +(6.56667 - 29.5367i) q^{66} +85.3697 q^{67} -105.295i q^{68} +(-19.4391 - 4.32176i) q^{69} -78.6424 q^{70} -32.2458i q^{71} +(-1.94232 + 4.15235i) q^{72} +71.6167 q^{73} +149.855i q^{74} +(5.63229 - 25.3339i) q^{75} -44.0272 q^{76} +25.0922i q^{77} +(-49.3902 - 10.9806i) q^{78} -85.8602 q^{79} +67.5068i q^{80} +(51.9171 + 62.1741i) q^{81} -92.4993 q^{82} +131.770i q^{83} +(-17.2906 + 77.7727i) q^{84} +111.516 q^{85} +54.1152i q^{86} +(22.2558 + 4.94797i) q^{87} +1.83735 q^{88} -96.1523i q^{89} +(92.1652 + 43.1117i) q^{90} +41.9583 q^{91} +25.3425i q^{92} +(26.0558 - 117.198i) q^{93} -143.962 q^{94} -46.6287i q^{95} +(130.739 + 29.0663i) q^{96} -80.8331 q^{97} +1.71346i q^{98} +(13.7555 - 29.4069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.79604i		−	1.39802i	−0.715112	−	0.699010i	$-0.753624\pi$
$2$		−	2.79604i		−	1.39802i	0.715112	−	0.699010i	$-0.246376\pi$
$3$	0.651071	−	2.92850i	0.217024	−	0.976166i
$3$	0.651071	−	2.92850i	0.217024	−	0.976166i
$4$	−3.81783			−0.954458
$5$		−	4.04341i		−	0.808683i	−0.914608	−	0.404341i	$-0.867501\pi$
$5$		−	4.04341i		−	0.808683i	0.914608	−	0.404341i	$-0.132499\pi$
$6$	−8.18820	−	1.82042i	−1.36470	−	0.303403i
$7$	6.95609			0.993727			0.496864	−	0.867829i	$-0.334485\pi$
$7$	6.95609			0.993727			0.496864	+	0.867829i	$0.334485\pi$
$8$		−	0.509352i		−	0.0636690i
$9$	−8.15221	−	3.81332i	−0.905801	−	0.423703i
$10$	−11.3055			−1.13055
$11$			3.60723i			0.327930i	0.986466	+	0.163965i	$0.0524284\pi$
$11$			3.60723i			0.327930i	−0.986466	+	0.163965i	$0.947572\pi$
$12$	−2.48568	+	11.1805i	−0.207140	+	0.931709i
$13$	6.03188			0.463990			0.231995	−	0.972717i	$-0.425475\pi$
$13$	6.03188			0.463990			0.231995	+	0.972717i	$0.425475\pi$
$14$		−	19.4495i		−	1.38925i
$15$	−11.8411	−	2.63255i	−0.789409	−	0.175503i
$16$	−16.6955			−1.04347
$17$			27.5797i			1.62234i	0.584813	+	0.811168i	$0.301168\pi$
$17$			27.5797i			1.62234i	−0.584813	+	0.811168i	$0.698832\pi$
$18$	−10.6622	+	22.7939i	−0.592344	+	1.26633i
$19$	11.5320			0.606948			0.303474	−	0.952840i	$-0.401854\pi$
$19$	11.5320			0.606948			0.303474	+	0.952840i	$0.401854\pi$
$20$			15.4371i			0.771854i
$21$	4.52891	−	20.3709i	0.215662	−	0.970043i
$22$	10.0859			0.458452
$23$		−	6.63792i		−	0.288605i	−0.989534	−	0.144303i	$-0.953906\pi$
$23$		−	6.63792i		−	0.288605i	0.989534	−	0.144303i	$-0.0460939\pi$
$24$	−1.49164	−	0.331625i	−0.0621515	−	0.0138177i
$25$	8.65080			0.346032
$26$		−	16.8654i		−	0.648667i
$27$	−16.4750	+	21.3910i	−0.610185	+	0.792259i
$28$	−26.5572			−0.948470
$29$			7.59974i			0.262060i	0.991378	+	0.131030i	$0.0418284\pi$
$29$			7.59974i			0.262060i	−0.991378	+	0.131030i	$0.958172\pi$
$30$	−7.36072	+	33.1083i	−0.245357	+	1.10361i
$31$	40.0199			1.29096			0.645482	−	0.763776i	$-0.276657\pi$
$31$	40.0199			1.29096			0.645482	+	0.763776i	$0.276657\pi$
$32$			44.6438i			1.39512i
$33$	10.5638	+	2.34856i	0.320114	+	0.0711685i
$34$	77.1139			2.26806
$35$		−	28.1264i		−	0.803610i
$36$	31.1238	+	14.5586i	0.864549	+	0.404406i
$37$	−53.5956			−1.44853			−0.724264	−	0.689522i	$-0.757820\pi$
$37$	−53.5956			−1.44853			−0.724264	+	0.689522i	$0.757820\pi$
$38$		−	32.2439i		−	0.848524i
$39$	3.92718	−	17.6643i	0.100697	−	0.452932i
$40$	−2.05952			−0.0514880
$41$		−	33.0823i		−	0.806885i	−0.915005	−	0.403442i	$-0.867814\pi$
$41$		−	33.0823i		−	0.806885i	0.915005	−	0.403442i	$-0.132186\pi$
$42$	−56.9578	−	12.6630i	−1.35614	−	0.301500i
$43$	−19.3543			−0.450099			−0.225049	−	0.974347i	$-0.572254\pi$
$43$	−19.3543			−0.450099			−0.225049	+	0.974347i	$0.572254\pi$
$44$		−	13.7718i		−	0.312995i
$45$	−15.4188	+	32.9628i	−0.342641	+	0.732506i
$46$	−18.5599			−0.403476
$47$		−	51.4877i		−	1.09548i	−0.836647	−	0.547742i	$-0.815488\pi$
$47$		−	51.4877i		−	1.09548i	0.836647	−	0.547742i	$-0.184512\pi$
$48$	−10.8700	+	48.8927i	−0.226457	+	1.01860i
$49$	−0.612818			−0.0125065
$50$		−	24.1880i		−	0.483759i
$51$	80.7671	+	17.9564i	1.58367	+	0.352085i
$52$	−23.0287			−0.442859
$53$		−	40.9324i		−	0.772309i	−0.922434	−	0.386155i	$-0.873803\pi$
$53$		−	40.9324i		−	0.772309i	0.922434	−	0.386155i	$-0.126197\pi$
$54$	59.8101	+	46.0647i	1.10759	+	0.853050i
$55$	14.5855			0.265191
$56$		−	3.54310i		−	0.0632696i
$57$	7.50816	−	33.7715i	0.131722	−	0.592482i
$58$	21.2492			0.366365
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	45.2075	+	10.0506i	0.753458	+	0.167511i
$61$	48.9309			0.802146			0.401073	−	0.916046i	$-0.368637\pi$
$61$	48.9309			0.802146			0.401073	+	0.916046i	$0.368637\pi$
$62$		−	111.897i		−	1.80479i
$63$	−56.7075	−	26.5258i	−0.900119	−	0.421045i
$64$	58.0439			0.906936
$65$		−	24.3894i		−	0.375221i
$66$	6.56667	−	29.5367i	0.0994950	−	0.447525i
$67$	85.3697			1.27417			0.637087	−	0.770792i	$-0.280139\pi$
$67$	85.3697			1.27417			0.637087	+	0.770792i	$0.280139\pi$
$68$		−	105.295i		−	1.54845i
$69$	−19.4391	−	4.32176i	−0.281727	−	0.0626342i
$70$	−78.6424			−1.12346
$71$		−	32.2458i		−	0.454166i	−0.973875	−	0.227083i	$-0.927081\pi$
$71$		−	32.2458i		−	0.454166i	0.973875	−	0.227083i	$-0.0729188\pi$
$72$	−1.94232	+	4.15235i	−0.0269767	+	0.0576715i
$73$	71.6167			0.981050			0.490525	−	0.871427i	$-0.336805\pi$
$73$	71.6167			0.981050			0.490525	+	0.871427i	$0.336805\pi$
$74$			149.855i			2.02507i
$75$	5.63229	−	25.3339i	0.0750972	−	0.337785i
$76$	−44.0272			−0.579306
$77$			25.0922i			0.325873i
$78$	−49.3902	−	10.9806i	−0.633207	−	0.140776i
$79$	−85.8602			−1.08684			−0.543419	−	0.839462i	$-0.682871\pi$
$79$	−85.8602			−1.08684			−0.543419	+	0.839462i	$0.682871\pi$
$80$			67.5068i			0.843835i
$81$	51.9171	+	62.1741i	0.640952	+	0.767581i
$82$	−92.4993			−1.12804
$83$			131.770i			1.58759i	0.608185	+	0.793795i	$0.291898\pi$
$83$			131.770i			1.58759i	−0.608185	+	0.793795i	$0.708102\pi$
$84$	−17.2906	+	77.7727i	−0.205841	+	0.925865i
$85$	111.516			1.31196
$86$			54.1152i			0.629247i
$87$	22.2558	+	4.94797i	0.255814	+	0.0568732i
$88$	1.83735			0.0208790
$89$		−	96.1523i		−	1.08036i	−0.841549	−	0.540182i	$-0.818356\pi$
$89$		−	96.1523i		−	1.08036i	0.841549	−	0.540182i	$-0.181644\pi$
$90$	92.1652	+	43.1117i	1.02406	+	0.479019i
$91$	41.9583			0.461080
$92$			25.3425i			0.275462i
$93$	26.0558	−	117.198i	0.280170	−	1.26019i
$94$	−143.962			−1.53151
$95$		−	46.6287i		−	0.490828i
$96$	130.739	+	29.0663i	1.36187	+	0.302774i
$97$	−80.8331			−0.833331			−0.416665	−	0.909060i	$-0.636801\pi$
$97$	−80.8331			−0.833331			−0.416665	+	0.909060i	$0.636801\pi$
$98$			1.71346i			0.0174843i
$99$	13.7555	−	29.4069i	0.138945	−	0.297039i
$100$	−33.0273			−0.330273
$101$			106.431i			1.05378i	0.849935	+	0.526888i	$0.176641\pi$
$101$			106.431i			1.05378i	−0.849935	+	0.526888i	$0.823359\pi$
$102$	50.2067	−	225.828i	0.492222	−	2.21400i
$103$	−98.8938			−0.960134			−0.480067	−	0.877232i	$-0.659388\pi$
$103$	−98.8938			−0.960134			−0.480067	+	0.877232i	$0.659388\pi$
$104$		−	3.07235i		−	0.0295418i
$105$	−82.3680	−	18.3123i	−0.784457	−	0.174403i
$106$	−114.449			−1.07970
$107$			170.612i			1.59451i	0.603645	+	0.797253i	$0.293714\pi$
$107$			170.612i			1.59451i	−0.603645	+	0.797253i	$0.706286\pi$
$108$	62.8987	−	81.6672i	0.582396	−	0.756178i
$109$	158.872			1.45754			0.728769	−	0.684760i	$-0.240093\pi$
$109$	158.872			1.45754			0.728769	+	0.684760i	$0.240093\pi$
$110$		−	40.7817i		−	0.370742i
$111$	−34.8945	+	156.955i	−0.314365	+	1.41400i
$112$	−116.135			−1.03692
$113$			122.753i			1.08631i	0.839632	+	0.543156i	$0.182771\pi$
$113$			122.753i			1.08631i	−0.839632	+	0.543156i	$0.817229\pi$
$114$	−94.4263	−	20.9931i	−0.828301	−	0.184150i
$115$	−26.8399			−0.233390
$116$		−	29.0145i		−	0.250125i
$117$	−49.1731	−	23.0015i	−0.420283	−	0.196594i
$118$	21.4768			0.182007
$119$			191.847i			1.61216i
$120$	−1.34090	+	6.03131i	−0.0111741	+	0.0502609i
$121$	107.988			0.892462
$122$		−	136.813i		−	1.12142i
$123$	−96.8814	−	21.5389i	−0.787654	−	0.175113i
$124$	−152.789			−1.23217
$125$		−	136.064i		−	1.08851i
$126$	−74.1672	+	158.556i	−0.588629	+	1.25838i
$127$	−158.076			−1.24469			−0.622347	−	0.782742i	$-0.713821\pi$
$127$	−158.076			−1.24469			−0.622347	+	0.782742i	$0.713821\pi$
$128$			16.2824i			0.127206i
$129$	−12.6010	+	56.6789i	−0.0976822	+	0.439371i
$130$	−68.1936			−0.524566
$131$			164.456i			1.25539i	0.778459	+	0.627696i	$0.216002\pi$
$131$			164.456i			1.25539i	−0.778459	+	0.627696i	$0.783998\pi$
$132$	−40.3306	−	8.96641i	−0.305535	−	0.0679274i
$133$	80.2176			0.603140
$134$		−	238.697i		−	1.78132i
$135$	86.4927	+	66.6152i	0.640686	+	0.493446i
$136$	14.0478			0.103292
$137$		−	215.202i		−	1.57082i	−0.618977	−	0.785409i	$-0.712453\pi$
$137$		−	215.202i		−	1.57082i	0.618977	−	0.785409i	$-0.287547\pi$
$138$	−12.0838	+	54.3526i	−0.0875638	+	0.393859i
$139$	−74.2004			−0.533816			−0.266908	−	0.963722i	$-0.586002\pi$
$139$	−74.2004			−0.533816			−0.266908	+	0.963722i	$0.586002\pi$
$140$			107.382i			0.767012i
$141$	−150.782	−	33.5222i	−1.06937	−	0.237746i
$142$	−90.1604			−0.634932
$143$			21.7583i			0.152156i
$144$	136.105	+	63.6653i	0.945175	+	0.442120i
$145$	30.7289			0.211923
$146$		−	200.243i		−	1.37153i
$147$	−0.398988	+	1.79464i	−0.00271420	+	0.0122084i
$148$	204.619			1.38256
$149$			241.103i			1.61814i	0.587711	+	0.809071i	$0.300029\pi$
$149$			241.103i			1.61814i	−0.587711	+	0.809071i	$0.699971\pi$
$150$	−70.8344	−	15.7481i	−0.472230	−	0.104987i
$151$	30.4950			0.201954			0.100977	−	0.994889i	$-0.467803\pi$
$151$	30.4950			0.201954			0.100977	+	0.994889i	$0.467803\pi$
$152$		−	5.87385i		−	0.0386437i
$153$	105.170	−	224.836i	0.687388	−	1.46951i
$154$	70.1587			0.455576
$155$		−	161.817i		−	1.04398i
$156$	−14.9933	+	67.4395i	−0.0961110	+	0.432304i
$157$	65.8024			0.419124			0.209562	−	0.977795i	$-0.432796\pi$
$157$	65.8024			0.419124			0.209562	+	0.977795i	$0.432796\pi$
$158$			240.068i			1.51942i
$159$	−119.870	−	26.6499i	−0.753902	−	0.167609i
$160$	180.513			1.12821
$161$		−	46.1740i		−	0.286795i
$162$	173.841	−	145.162i	1.07309	−	0.896063i
$163$	−71.4607			−0.438409			−0.219205	−	0.975679i	$-0.570346\pi$
$163$	−71.4607			−0.438409			−0.219205	+	0.975679i	$0.570346\pi$
$164$			126.303i			0.770137i
$165$	9.49621	−	42.7137i	0.0575528	−	0.258871i
$166$	368.434			2.21948
$167$			94.7545i			0.567392i	0.958914	+	0.283696i	$0.0915607\pi$
$167$			94.7545i			0.567392i	−0.958914	+	0.283696i	$0.908439\pi$
$168$	−10.3760	−	2.30681i	−0.0617617	−	0.0137310i
$169$	−132.616			−0.784713
$170$		−	311.804i		−	1.83414i
$171$	−94.0113	−	43.9753i	−0.549774	−	0.257165i
$172$	73.8913			0.429600
$173$			92.2355i			0.533153i	0.963814	+	0.266576i	$0.0858925\pi$
$173$			92.2355i			0.533153i	−0.963814	+	0.266576i	$0.914108\pi$
$174$	13.8347	−	62.2281i	0.0795099	−	0.357633i
$175$	60.1757			0.343861
$176$		−	60.2244i		−	0.342184i
$177$	22.4942	+	5.00097i	0.127086	+	0.0282541i
$178$	−268.846			−1.51037
$179$		−	48.5009i		−	0.270955i	−0.990780	−	0.135477i	$-0.956743\pi$
$179$		−	48.5009i		−	0.270955i	0.990780	−	0.135477i	$-0.0432568\pi$
$180$	58.8666	−	125.846i	0.327036	−	0.699146i
$181$	177.194			0.978975			0.489487	−	0.872010i	$-0.337184\pi$
$181$	177.194			0.978975			0.489487	+	0.872010i	$0.337184\pi$
$182$		−	117.317i		−	0.644598i
$183$	31.8575	−	143.294i	0.174085	−	0.783028i
$184$	−3.38104			−0.0183752
$185$			216.709i			1.17140i
$186$	−327.690	−	72.8530i	−1.76178	−	0.391683i
$187$	−99.4863			−0.532012
$188$			196.572i			1.04559i
$189$	−114.601	+	148.798i	−0.606357	+	0.787289i
$190$	−130.376			−0.686187
$191$		−	137.245i		−	0.718559i	−0.933230	−	0.359279i	$-0.883023\pi$
$191$		−	137.245i		−	0.718559i	0.933230	−	0.359279i	$-0.116977\pi$
$192$	37.7907	−	169.981i	0.196827	−	0.885320i
$193$	363.765			1.88479			0.942396	−	0.334499i	$-0.108567\pi$
$193$	363.765			1.88479			0.942396	+	0.334499i	$0.108567\pi$
$194$			226.012i			1.16501i
$195$	−71.4242	−	15.8792i	−0.366278	−	0.0814319i
$196$	2.33963			0.0119369
$197$		−	117.106i		−	0.594445i	−0.954808	−	0.297223i	$-0.903940\pi$
$197$		−	117.106i		−	0.594445i	0.954808	−	0.297223i	$-0.0960603\pi$
$198$	−82.2228	−	38.4610i	−0.415266	−	0.194247i
$199$	−176.062			−0.884732			−0.442366	−	0.896835i	$-0.645861\pi$
$199$	−176.062			−0.884732			−0.442366	+	0.896835i	$0.645861\pi$
$200$		−	4.40630i		−	0.0220315i
$201$	55.5818	−	250.005i	0.276526	−	1.24381i
$202$	297.586			1.47320
$203$			52.8645i			0.260416i
$204$	−308.355	−	68.5543i	−1.51155	−	0.336051i
$205$	−133.765			−0.652514
$206$			276.511i			1.34229i
$207$	−25.3125	+	54.1137i	−0.122283	+	0.261419i
$208$	−100.705			−0.484159
$209$			41.5985i			0.199036i
$210$	−51.2018	+	230.304i	−0.243818	+	1.09669i
$211$	9.09339			0.0430966			0.0215483	−	0.999768i	$-0.493140\pi$
$211$	9.09339			0.0430966			0.0215483	+	0.999768i	$0.493140\pi$
$212$			156.273i			0.737136i
$213$	−94.4317	−	20.9943i	−0.443341	−	0.0985648i
$214$	477.038			2.22915
$215$			78.2573i			0.363987i
$216$	10.8955	+	8.39157i	0.0504423	+	0.0388498i
$217$	278.382			1.28287
$218$		−	444.211i		−	2.03767i
$219$	46.6276	−	209.729i	0.212911	−	0.957668i
$220$	−55.6850			−0.253114
$221$			166.357i			0.752748i
$222$	438.851	+	97.5665i	1.97681	+	0.439489i
$223$	244.350			1.09574			0.547869	−	0.836564i	$-0.315439\pi$
$223$	244.350			1.09574			0.547869	+	0.836564i	$0.315439\pi$
$224$			310.546i			1.38637i
$225$	−70.5232	−	32.9883i	−0.313436	−	0.146615i
$226$	343.223			1.51868
$227$			46.8646i			0.206452i	0.994658	+	0.103226i	$0.0329165\pi$
$227$			46.8646i			0.206452i	−0.994658	+	0.103226i	$0.967084\pi$
$228$	−28.6649	+	128.934i	−0.125723	+	0.565499i
$229$	−142.421			−0.621925			−0.310963	−	0.950422i	$-0.600651\pi$
$229$	−142.421			−0.621925			−0.310963	+	0.950422i	$0.600651\pi$
$230$			75.0453i			0.326284i
$231$	73.4825	+	16.3368i	0.318106	+	0.0707221i
$232$	3.87094			0.0166851
$233$		−	226.548i		−	0.972308i	−0.873873	−	0.486154i	$-0.838399\pi$
$233$		−	226.548i		−	0.972308i	0.873873	−	0.486154i	$-0.161601\pi$
$234$	−64.3131	+	137.490i	−0.274842	+	0.587564i
$235$	−208.186			−0.885899
$236$		−	29.3253i		−	0.124260i
$237$	−55.9011	+	251.442i	−0.235870	+	1.06093i
$238$	536.411			2.25383
$239$			50.3598i			0.210711i	0.994435	+	0.105355i	$0.0335980\pi$
$239$			50.3598i			0.210711i	−0.994435	+	0.105355i	$0.966402\pi$
$240$	197.694	+	43.9517i	0.823723	+	0.183132i
$241$	−252.513			−1.04777			−0.523887	−	0.851788i	$-0.675519\pi$
$241$	−252.513			−1.04777			−0.523887	+	0.851788i	$0.675519\pi$
$242$		−	301.938i		−	1.24768i
$243$	215.878	−	111.559i	0.888388	−	0.459093i
$244$	−186.810			−0.765614
$245$			2.47788i			0.0101138i
$246$	−60.2237	+	270.884i	−0.244812	+	1.10116i
$247$	69.5596			0.281618
$248$		−	20.3842i		−	0.0821943i
$249$	385.888	+	85.7917i	1.54975	+	0.344545i
$250$	−380.441			−1.52176
$251$		−	115.362i		−	0.459610i	−0.973237	−	0.229805i	$-0.926191\pi$
$251$		−	115.362i		−	0.459610i	0.973237	−	0.229805i	$-0.0738088\pi$
$252$	216.500	+	101.271i	0.859126	+	0.401869i
$253$	23.9445			0.0946422
$254$			441.987i			1.74011i
$255$	72.6050	−	326.575i	0.284726	−	1.28069i
$256$	277.702			1.08477
$257$			67.7037i			0.263439i	0.991287	+	0.131719i	$0.0420498\pi$
$257$			67.7037i			0.263439i	−0.991287	+	0.131719i	$0.957950\pi$
$258$	158.476	+	35.2329i	0.614250	+	0.136562i
$259$	−372.816			−1.43944
$260$			93.1145i			0.358133i
$261$	28.9803	−	61.9547i	0.111035	−	0.237374i
$262$	459.826			1.75506
$263$			295.997i			1.12546i	0.826639	+	0.562732i	$0.190250\pi$
$263$			295.997i			1.12546i	−0.826639	+	0.562732i	$0.809750\pi$
$264$	1.19624	−	5.38067i	0.00453123	−	0.0203813i
$265$	−165.507			−0.624553
$266$		−	224.292i		−	0.843202i
$267$	−281.582	−	62.6020i	−1.05461	−	0.234465i
$268$	−325.927			−1.21615
$269$			446.809i			1.66100i	0.557019	+	0.830500i	$0.311945\pi$
$269$			446.809i			1.66100i	−0.557019	+	0.830500i	$0.688055\pi$
$270$	186.259	−	241.837i	0.689847	−	0.895692i
$271$	111.864			0.412781			0.206391	−	0.978470i	$-0.433828\pi$
$271$	111.864			0.412781			0.206391	+	0.978470i	$0.433828\pi$
$272$		−	460.457i		−	1.69286i
$273$	27.3178	−	122.875i	0.100065	−	0.450091i
$274$	−601.713			−2.19603
$275$			31.2054i			0.113474i
$276$	74.2154	+	16.4998i	0.268896	+	0.0597817i
$277$	−245.137			−0.884970			−0.442485	−	0.896776i	$-0.645903\pi$
$277$	−245.137			−0.884970			−0.442485	+	0.896776i	$0.645903\pi$
$278$			207.467i			0.746285i
$279$	−326.250	−	152.609i	−1.16936	−	0.546985i
$280$	−14.3262			−0.0511650
$281$		−	197.586i		−	0.703153i	−0.936159	−	0.351576i	$-0.885646\pi$
$281$		−	197.586i		−	0.703153i	0.936159	−	0.351576i	$-0.114354\pi$
$282$	−93.7294	+	421.592i	−0.332374	+	1.49501i
$283$	−355.505			−1.25620			−0.628101	−	0.778132i	$-0.716168\pi$
$283$	−355.505			−1.25620			−0.628101	+	0.778132i	$0.716168\pi$
$284$			123.109i			0.433482i
$285$	−136.552	−	30.3586i	−0.479130	−	0.106521i
$286$	60.8372			0.212717
$287$		−	230.123i		−	0.801823i
$288$	170.241	−	363.946i	0.591116	−	1.26370i
$289$	−471.640			−1.63197
$290$		−	85.9192i		−	0.296273i
$291$	−52.6281	+	236.720i	−0.180853	+	0.813469i
$292$	−273.420			−0.936371
$293$		−	438.814i		−	1.49766i	−0.662762	−	0.748830i	$-0.730616\pi$
$293$		−	438.814i		−	1.49766i	0.662762	−	0.748830i	$-0.269384\pi$
$294$	5.01787	+	1.11559i	0.0170676	+	0.00379451i
$295$	31.0581			0.105282
$296$			27.2990i			0.0922264i
$297$	−77.1622	−	59.4290i	−0.259805	−	0.200098i
$298$	674.134			2.26219
$299$		−	40.0391i		−	0.133910i
$300$	−21.5031	+	96.7204i	−0.0716771	+	0.322401i
$301$	−134.630			−0.447276
$302$		−	85.2652i		−	0.282335i
$303$	311.684	+	69.2944i	1.02866	+	0.228694i
$304$	−192.532			−0.633330
$305$		−	197.848i		−	0.648682i
$306$	−628.649	−	294.060i	−2.05441	−	0.960982i
$307$	−519.064			−1.69076			−0.845381	−	0.534163i	$-0.820627\pi$
$307$	−519.064			−1.69076			−0.845381	+	0.534163i	$0.820627\pi$
$308$		−	95.7977i		−	0.311032i
$309$	−64.3869	+	289.610i	−0.208372	+	0.937250i
$310$	−452.446			−1.45950
$311$		−	327.149i		−	1.05193i	−0.850507	−	0.525963i	$-0.823705\pi$
$311$		−	327.149i		−	1.05193i	0.850507	−	0.525963i	$-0.176295\pi$
$312$	−8.99737	−	2.00032i	−0.0288377	−	0.00641127i
$313$	−309.990			−0.990383			−0.495191	−	0.868784i	$-0.664902\pi$
$313$	−309.990			−0.990383			−0.495191	+	0.868784i	$0.664902\pi$
$314$		−	183.986i		−	0.585943i
$315$	−107.255	+	229.292i	−0.340492	+	0.727911i
$316$	327.800			1.03734
$317$		−	335.223i		−	1.05749i	−0.848782	−	0.528743i	$-0.822664\pi$
$317$		−	335.223i		−	1.05749i	0.848782	−	0.528743i	$-0.177336\pi$
$318$	−74.5142	+	335.162i	−0.234321	+	1.05397i
$319$	−27.4140			−0.0859372
$320$		−	234.696i		−	0.733423i
$321$	499.637	+	111.081i	1.55650	+	0.346046i
$322$	−129.104			−0.400945
$323$			318.049i			0.984673i
$324$	−198.211	−	237.370i	−0.611762	−	0.732623i
$325$	52.1805			0.160556
$326$			199.807i			0.612904i
$327$	103.437	−	465.255i	0.316320	−	1.42280i
$328$	−16.8505			−0.0513735
$329$		−	358.153i		−	1.08861i
$330$	−119.429	−	26.5518i	−0.361906	−	0.0804599i
$331$	379.087			1.14528			0.572639	−	0.819808i	$-0.305920\pi$
$331$	379.087			1.14528			0.572639	+	0.819808i	$0.305920\pi$
$332$		−	503.076i		−	1.51529i
$333$	436.922	+	204.377i	1.31208	+	0.613745i
$334$	264.937			0.793225
$335$		−	345.185i		−	1.03040i
$336$	−75.6124	+	340.102i	−0.225037	+	1.01221i
$337$	308.875			0.916542			0.458271	−	0.888813i	$-0.348469\pi$
$337$	308.875			0.916542			0.458271	+	0.888813i	$0.348469\pi$
$338$			370.801i			1.09704i
$339$	359.483	+	79.9211i	1.06042	+	0.235756i
$340$	−425.750			−1.25221
$341$			144.361i			0.423345i
$342$	−122.957	+	262.859i	−0.359522	+	0.768594i
$343$	−345.111			−1.00616
$344$			9.85813i			0.0286573i
$345$	−17.4747	+	78.6005i	−0.0506512	+	0.227828i
$346$	257.894			0.745358
$347$			515.591i			1.48585i	0.669373	+	0.742926i	$0.266563\pi$
$347$			515.591i			1.48585i	−0.669373	+	0.742926i	$0.733437\pi$
$348$	−84.9690	−	18.8905i	−0.244164	−	0.0542831i
$349$	540.605			1.54901			0.774506	−	0.632567i	$-0.217999\pi$
$349$	540.605			1.54901			0.774506	+	0.632567i	$0.217999\pi$
$350$		−	168.254i		−	0.480725i
$351$	−99.3751	+	129.028i	−0.283120	+	0.367601i
$352$	−161.040			−0.457501
$353$		−	34.9577i		−	0.0990304i	−0.998773	−	0.0495152i	$-0.984232\pi$
$353$		−	34.9577i		−	0.0990304i	0.998773	−	0.0495152i	$-0.0157676\pi$
$354$	13.9829	−	62.8947i	0.0394998	−	0.177669i
$355$	−130.383			−0.367276
$356$			367.093i			1.03116i
$357$	561.823	+	124.906i	1.57374	+	0.349877i
$358$	−135.610			−0.378800
$359$			474.613i			1.32204i	0.750368	+	0.661021i	$0.229876\pi$
$359$			474.613i			1.32204i	−0.750368	+	0.661021i	$0.770124\pi$
$360$	16.7897	+	7.85362i	0.0466379	+	0.0218156i
$361$	−228.013			−0.631615
$362$		−	495.442i		−	1.36863i
$363$	70.3078	−	316.242i	0.193686	−	0.871191i
$364$	−160.190			−0.440081
$365$		−	289.576i		−	0.793359i
$366$	−400.656	−	89.0748i	−1.09469	−	0.243374i
$367$	−573.939			−1.56387			−0.781934	−	0.623362i	$-0.785767\pi$
$367$	−573.939			−1.56387			−0.781934	+	0.623362i	$0.785767\pi$
$368$			110.823i			0.301150i
$369$	−126.153	+	269.694i	−0.341879	+	0.730877i
$370$	605.927			1.63764
$371$		−	284.729i		−	0.767465i
$372$	−99.4766	+	447.443i	−0.267410	+	1.20280i
$373$	485.686			1.30211			0.651053	−	0.759032i	$-0.274327\pi$
$373$	485.686			1.30211			0.651053	+	0.759032i	$0.274327\pi$
$374$			278.167i			0.743763i
$375$	−398.464	−	88.5875i	−1.06257	−	0.236233i
$376$	−26.2254			−0.0697484
$377$			45.8407i			0.121593i
$378$	416.044	+	320.430i	1.10065	+	0.847699i
$379$	−599.727			−1.58239			−0.791196	−	0.611562i	$-0.790541\pi$
$379$	−599.727			−1.58239			−0.791196	+	0.611562i	$0.790541\pi$
$380$			178.020i			0.468475i
$381$	−102.919	+	462.926i	−0.270128	+	1.21503i
$382$	−383.742			−1.00456
$383$		−	51.7725i		−	0.135176i	−0.997713	−	0.0675881i	$-0.978470\pi$
$383$		−	51.7725i		−	0.135176i	0.997713	−	0.0675881i	$-0.0215304\pi$
$384$	47.6829	+	10.6010i	0.124174	+	0.0276067i
$385$	101.458			0.263528
$386$		−	1017.10i		−	2.63498i
$387$	157.780	+	73.8040i	0.407700	+	0.190708i
$388$	308.607			0.795379
$389$			505.152i			1.29859i	0.760536	+	0.649296i	$0.224936\pi$
$389$			505.152i			1.29859i	−0.760536	+	0.649296i	$0.775064\pi$
$390$	−44.3989	+	199.705i	−0.113843	+	0.512064i
$391$	183.072			0.468215
$392$			0.312140i			0.000796275i
$393$	481.610	+	107.073i	1.22547	+	0.272450i
$394$	−327.432			−0.831046
$395$			347.168i			0.878908i
$396$	−52.5163	+	112.270i	−0.132617	+	0.283511i
$397$	372.570			0.938465			0.469232	−	0.883075i	$-0.344531\pi$
$397$	372.570			0.938465			0.469232	+	0.883075i	$0.344531\pi$
$398$			492.275i			1.23687i
$399$	52.2274	−	234.917i	0.130896	−	0.588765i
$400$	−144.429			−0.361073
$401$			420.779i			1.04933i	0.851310	+	0.524663i	$0.175809\pi$
$401$			420.779i			1.04933i	−0.851310	+	0.524663i	$0.824191\pi$
$402$	−699.024	−	155.409i	−1.73887	−	0.386589i
$403$	241.395			0.598995
$404$		−	406.337i		−	1.00578i
$405$	251.395	−	209.922i	0.620730	−	0.518327i
$406$	147.811			0.364067
$407$		−	193.331i		−	0.475016i
$408$	9.14611	−	41.1389i	0.0224169	−	0.100831i
$409$	392.844			0.960500			0.480250	−	0.877132i	$-0.340546\pi$
$409$	392.844			0.960500			0.480250	+	0.877132i	$0.340546\pi$
$410$			374.013i			0.912227i
$411$	−630.219	−	140.112i	−1.53338	−	0.340905i
$412$	377.560			0.916407
$413$			53.4307i			0.129372i
$414$	151.304	+	70.7748i	0.365469	+	0.170954i
$415$	532.801			1.28386
$416$			269.286i			0.647322i
$417$	−48.3098	+	217.296i	−0.115851	+	0.521093i
$418$	116.311			0.278256
$419$			286.270i			0.683223i	0.939841	+	0.341612i	$0.110973\pi$
$419$			286.270i			0.683223i	−0.939841	+	0.341612i	$0.889027\pi$
$420$	314.467	+	69.9131i	0.748731	+	0.166460i
$421$	629.689			1.49570			0.747849	−	0.663869i	$-0.231087\pi$
$421$	629.689			1.49570			0.747849	+	0.663869i	$0.231087\pi$
$422$		−	25.4255i		−	0.0602499i
$423$	−196.339	+	419.739i	−0.464159	+	0.992291i
$424$	−20.8490			−0.0491721
$425$			238.587i			0.561380i
$426$	−58.7009	+	264.035i	−0.137795	+	0.619800i
$427$	340.368			0.797114
$428$		−	651.368i		−	1.52189i
$429$	63.7193	+	14.1662i	0.148530	+	0.0330215i
$430$	218.810			0.508861
$431$		−	125.145i		−	0.290359i	−0.989405	−	0.145179i	$-0.953624\pi$
$431$		−	125.145i		−	0.290359i	0.989405	−	0.145179i	$-0.0463759\pi$
$432$	275.058	−	357.133i	0.636708	−	0.826697i
$433$	−336.848			−0.777941			−0.388970	−	0.921250i	$-0.627169\pi$
$433$	−336.848			−0.777941			−0.388970	+	0.921250i	$0.627169\pi$
$434$		−	778.366i		−	1.79347i
$435$	20.0067	−	89.9895i	0.0459924	−	0.206872i
$436$	−606.545			−1.39116
$437$		−	76.5485i		−	0.175168i
$438$	−586.411	−	130.372i	−1.33884	−	0.297654i
$439$	204.185			0.465115			0.232557	−	0.972583i	$-0.425291\pi$
$439$	204.185			0.465115			0.232557	+	0.972583i	$0.425291\pi$
$440$		−	7.42916i		−	0.0168845i
$441$	4.99582	+	2.33687i	0.0113284	+	0.00529903i
$442$	465.142			1.05236
$443$			367.998i			0.830695i	0.909663	+	0.415348i	$0.136340\pi$
$443$			367.998i			0.830695i	−0.909663	+	0.415348i	$0.863660\pi$
$444$	133.221	−	599.226i	0.300048	−	1.34961i
$445$	−388.784			−0.873671
$446$		−	683.211i		−	1.53186i
$447$	706.070	+	156.975i	1.57958	+	0.351175i
$448$	403.758			0.901247
$449$			42.2232i			0.0940384i	0.998894	+	0.0470192i	$0.0149722\pi$
$449$			42.2232i			0.0940384i	−0.998894	+	0.0470192i	$0.985028\pi$
$450$	−92.2366	+	197.185i	−0.204970	+	0.438190i
$451$	119.335			0.264601
$452$		−	468.651i		−	1.03684i
$453$	19.8544	−	89.3046i	0.0438288	−	0.197140i
$454$	131.035			0.288624
$455$		−	169.655i		−	0.372867i
$456$	−17.2016	−	3.82429i	−0.0377227	−	0.00838661i
$457$	−454.706			−0.994981			−0.497491	−	0.867469i	$-0.665745\pi$
$457$	−454.706			−0.994981			−0.497491	+	0.867469i	$0.665745\pi$
$458$			398.214i			0.869464i
$459$	−589.957	−	454.375i	−1.28531	−	0.989925i
$460$	102.470			0.222761
$461$			101.873i			0.220984i	0.993877	+	0.110492i	$0.0352426\pi$
$461$			101.873i			0.220984i	−0.993877	+	0.110492i	$0.964757\pi$
$462$	45.6783	−	205.460i	0.0988709	−	0.444718i
$463$	835.368			1.80425			0.902125	−	0.431475i	$-0.142007\pi$
$463$	835.368			1.80425			0.902125	+	0.431475i	$0.142007\pi$
$464$		−	126.881i		−	0.273451i
$465$	−473.881	−	105.354i	−1.01910	−	0.226568i
$466$	−633.436			−1.35931
$467$			5.68550i			0.0121745i	0.999981	+	0.00608726i	$0.00193765\pi$
$467$			5.68550i			0.0121745i	−0.999981	+	0.00608726i	$0.998062\pi$
$468$	187.735	+	87.8158i	0.401142	+	0.187641i
$469$	593.839			1.26618
$470$			582.097i			1.23850i
$471$	42.8421	−	192.702i	0.0909598	−	0.409134i
$472$	3.91241			0.00828900
$473$		−	69.8152i		−	0.147601i
$474$	703.040	+	156.302i	1.48321	+	0.329751i
$475$	99.7610			0.210023
$476$		−	732.439i		−	1.53874i
$477$	−156.088	+	333.689i	−0.327229	+	0.699559i
$478$	140.808			0.294577
$479$		−	565.886i		−	1.18139i	−0.806895	−	0.590695i	$-0.798853\pi$
$479$		−	565.886i		−	1.18139i	0.806895	−	0.590695i	$-0.201147\pi$
$480$	117.527	−	528.634i	0.244848	−	1.10132i
$481$	−323.282			−0.672103
$482$			706.037i			1.46481i
$483$	−135.220	−	30.0626i	−0.279959	−	0.0622413i
$484$	−412.280			−0.851817
$485$			326.842i			0.673900i
$486$	−311.925	−	603.604i	−0.641820	−	1.24198i
$487$	−576.100			−1.18296			−0.591478	−	0.806321i	$-0.701455\pi$
$487$	−576.100			−1.18296			−0.591478	+	0.806321i	$0.701455\pi$
$488$		−	24.9230i		−	0.0510718i
$489$	−46.5260	+	209.273i	−0.0951452	+	0.427960i
$490$	6.92824			0.0141393
$491$			475.446i			0.968321i	0.874979	+	0.484161i	$0.160875\pi$
$491$			475.446i			0.968321i	−0.874979	+	0.484161i	$0.839125\pi$
$492$	369.877	+	82.2320i	0.751782	+	0.167138i
$493$	−209.599			−0.425149
$494$		−	194.491i		−	0.393707i
$495$	−118.904	−	55.6193i	−0.240210	−	0.112362i
$496$	−668.151			−1.34708
$497$		−	224.304i		−	0.451317i
$498$	239.877	−	1078.96i	0.481681	−	2.16658i
$499$	61.4468			0.123140			0.0615699	−	0.998103i	$-0.480389\pi$
$499$	61.4468			0.123140			0.0615699	+	0.998103i	$0.480389\pi$
$500$			519.470i			1.03894i
$501$	277.488	+	61.6919i	0.553869	+	0.123138i
$502$	−322.557			−0.642543
$503$		−	838.880i		−	1.66775i	−0.551951	−	0.833876i	$-0.686117\pi$
$503$		−	838.880i		−	1.66775i	0.551951	−	0.833876i	$-0.313883\pi$
$504$	−13.5110	+	28.8841i	−0.0268075	+	0.0573097i
$505$	430.346			0.852171
$506$		−	66.9497i		−	0.132312i
$507$	−86.3428	+	388.367i	−0.170301	+	0.766010i
$508$	603.508			1.18801
$509$		−	877.915i		−	1.72478i	−0.506242	−	0.862391i	$-0.668966\pi$
$509$		−	877.915i		−	1.72478i	0.506242	−	0.862391i	$-0.331034\pi$
$510$	−913.116	−	203.006i	−1.79042	−	0.398052i
$511$	498.172			0.974896
$512$		−	711.335i		−	1.38933i
$513$	−189.990	+	246.681i	−0.370350	+	0.480860i
$514$	189.302			0.368292
$515$			399.869i			0.776444i
$516$	48.1085	−	216.391i	0.0932335	−	0.419361i
$517$	185.728			0.359242
$518$			1042.41i			2.01237i
$519$	270.111	+	60.0519i	0.520446	+	0.115707i
$520$	−12.4228			−0.0238899
$521$		−	868.672i		−	1.66732i	−0.552281	−	0.833658i	$-0.686242\pi$
$521$		−	868.672i		−	1.66732i	0.552281	−	0.833658i	$-0.313758\pi$
$522$	−173.228	−	81.0299i	−0.331854	−	0.155230i
$523$	−971.738			−1.85801			−0.929004	−	0.370070i	$-0.879334\pi$
$523$	−971.738			−1.85801			−0.929004	+	0.370070i	$0.879334\pi$
$524$		−	627.866i		−	1.19822i
$525$	39.1787	−	176.225i	0.0746261	−	0.335666i
$526$	827.619			1.57342
$527$			1103.74i			2.09438i
$528$	−176.367	−	39.2104i	−0.334029	−	0.0742621i
$529$	484.938			0.916707
$530$			462.763i			0.873137i
$531$	29.2907	−	62.6183i	0.0551614	−	0.117925i
$532$	−306.257			−0.575672
$533$		−	199.548i		−	0.374387i
$534$	−175.038	+	787.314i	−0.327786	+	1.47437i
$535$	689.856			1.28945
$536$		−	43.4832i		−	0.0811254i
$537$	−142.035	−	31.5775i	−0.264497	−	0.0588036i
$538$	1249.29			2.32211
$539$		−	2.21057i		−	0.00410125i
$540$	−330.214	−	254.326i	−0.611508	−	0.470973i
$541$	349.329			0.645710			0.322855	−	0.946448i	$-0.395357\pi$
$541$	349.329			0.645710			0.322855	+	0.946448i	$0.395357\pi$
$542$		−	312.775i		−	0.577076i
$543$	115.366	−	518.914i	0.212461	−	0.955642i
$544$	−1231.26			−2.26335
$545$		−	642.384i		−	1.17869i
$546$	−343.562	−	76.3817i	−0.629235	−	0.139893i
$547$	−97.0056			−0.177341			−0.0886706	−	0.996061i	$-0.528262\pi$
$547$	−97.0056			−0.177341			−0.0886706	+	0.996061i	$0.528262\pi$
$548$			821.605i			1.49928i
$549$	−398.895	−	186.589i	−0.726585	−	0.339871i
$550$	87.2515			0.158639
$551$			87.6402i			0.159057i
$552$	−2.20130	+	9.90137i	−0.00398786	+	0.0179373i
$553$	−597.251			−1.08002
$554$			685.412i			1.23721i
$555$	634.632	+	141.093i	1.14348	+	0.254222i
$556$	283.285			0.509505
$557$			670.323i			1.20345i	0.798703	+	0.601726i	$0.205520\pi$
$557$			670.323i			1.20345i	−0.798703	+	0.601726i	$0.794480\pi$
$558$	−426.700	+	912.209i	−0.764695	+	1.63478i
$559$	−116.742			−0.208842
$560$			469.583i			0.838542i
$561$	−64.7727	+	291.345i	−0.115459	+	0.519332i
$562$	−552.458			−0.983021
$563$		−	354.081i		−	0.628919i	−0.949271	−	0.314459i	$-0.898177\pi$
$563$		−	354.081i		−	0.628919i	0.949271	−	0.314459i	$-0.101823\pi$
$564$	575.659	+	127.982i	1.02067	+	0.226919i
$565$	496.342			0.878482
$566$			994.006i			1.75620i
$567$	361.140	+	432.488i	0.636931	+	0.762766i
$568$	−16.4244			−0.0289163
$569$		−	923.710i		−	1.62339i	−0.584080	−	0.811696i	$-0.698545\pi$
$569$		−	923.710i		−	1.62339i	0.584080	−	0.811696i	$-0.301455\pi$
$570$	−84.8838	+	381.805i	−0.148919	+	0.669833i
$571$	−95.5951			−0.167417			−0.0837085	−	0.996490i	$-0.526676\pi$
$571$	−95.5951			−0.167417			−0.0837085	+	0.996490i	$0.526676\pi$
$572$		−	83.0697i		−	0.145227i
$573$	−401.921	−	89.3561i	−0.701433	−	0.155944i
$574$	−643.434			−1.12096
$575$		−	57.4233i		−	0.0998666i
$576$	−473.186	−	221.340i	−0.821504	−	0.384271i
$577$	−709.681			−1.22995			−0.614975	−	0.788546i	$-0.710834\pi$
$577$	−709.681			−1.22995			−0.614975	+	0.788546i	$0.710834\pi$
$578$			1318.72i			2.28153i
$579$	236.837	−	1065.29i	0.409045	−	1.83987i
$580$	−117.318			−0.202272
$581$			916.604i			1.57763i
$582$	661.877	+	147.150i	1.13725	+	0.252835i
$583$	147.652			0.253263
$584$		−	36.4781i		−	0.0624625i
$585$	−93.0046	+	198.827i	−0.158982	+	0.339876i
$586$	−1226.94			−2.09376
$587$			305.912i			0.521144i	0.965454	+	0.260572i	$0.0839112\pi$
$587$			305.912i			0.521144i	−0.965454	+	0.260572i	$0.916089\pi$
$588$	1.52327	−	6.85162i	0.00259059	−	0.0116524i
$589$	461.509			0.783547
$590$		−	86.8395i		−	0.147186i
$591$	−342.944	−	76.2442i	−0.580277	−	0.129009i
$592$	894.804			1.51149
$593$		−	485.726i		−	0.819100i	−0.912288	−	0.409550i	$-0.865686\pi$
$593$		−	485.726i		−	0.819100i	0.912288	−	0.409550i	$-0.134314\pi$
$594$	−166.166	+	215.748i	−0.279740	+	0.363213i
$595$	775.717			1.30373
$596$		−	920.491i		−	1.54445i
$597$	−114.629	+	515.596i	−0.192008	+	0.863646i
$598$	−111.951			−0.187209
$599$			1115.58i			1.86240i	0.364513	+	0.931198i	$0.381235\pi$
$599$			1115.58i			1.86240i	−0.364513	+	0.931198i	$0.618765\pi$
$600$	−12.9038	−	2.86882i	−0.0215064	−	0.00478136i
$601$	−447.398			−0.744423			−0.372212	−	0.928148i	$-0.621400\pi$
$601$	−447.398			−0.744423			−0.372212	+	0.928148i	$0.621400\pi$
$602$			376.430i			0.625300i
$603$	−695.952	−	325.542i	−1.15415	−	0.539871i
$604$	−116.425			−0.192756
$605$		−	436.640i		−	0.721719i
$606$	193.750	−	871.481i	0.319719	−	1.43809i
$607$	717.432			1.18193			0.590965	−	0.806697i	$-0.298747\pi$
$607$	717.432			1.18193			0.590965	+	0.806697i	$0.298747\pi$
$608$			514.833i			0.846764i
$609$	154.814	+	34.4185i	0.254209	+	0.0565165i
$610$	−553.190			−0.906869
$611$		−	310.568i		−	0.508294i
$612$	−401.523	+	858.384i	−0.656083	+	1.40259i
$613$	−1101.82			−1.79743			−0.898715	−	0.438534i	$-0.855498\pi$
$613$	−1101.82			−1.79743			−0.898715	+	0.438534i	$0.855498\pi$
$614$			1451.32i			2.36372i
$615$	−87.0908	+	391.732i	−0.141611	+	0.636962i
$616$	12.7808			0.0207480
$617$		−	150.603i		−	0.244089i	−0.992525	−	0.122044i	$-0.961055\pi$
$617$		−	150.603i		−	0.244089i	0.992525	−	0.122044i	$-0.0389450\pi$
$618$	809.762	+	180.028i	1.31029	+	0.291308i
$619$	−621.716			−1.00439			−0.502193	−	0.864755i	$-0.667473\pi$
$619$	−621.716			−1.00439			−0.502193	+	0.864755i	$0.667473\pi$
$620$			617.789i			0.996435i
$621$	141.992	+	109.360i	0.228650	+	0.176103i
$622$	−914.722			−1.47061
$623$		−	668.844i		−	1.07359i
$624$	−65.5662	+	294.915i	−0.105074	+	0.472620i
$625$	−333.894			−0.534230
$626$			866.743i			1.38457i
$627$	121.821	+	27.0836i	0.194292	+	0.0431956i
$628$	−251.222			−0.400036
$629$		−	1478.15i		−	2.35000i
$630$	641.109	+	299.889i	1.01763	+	0.476014i
$631$	310.615			0.492259			0.246129	−	0.969237i	$-0.420841\pi$
$631$	310.615			0.492259			0.246129	+	0.969237i	$0.420841\pi$
$632$			43.7331i			0.0691979i
$633$	5.92044	−	26.6300i	0.00935299	−	0.0420695i
$634$	−937.296			−1.47838
$635$			639.167i			1.00656i
$636$	457.645	+	101.745i	0.719568	+	0.159976i
$637$	−3.69644			−0.00580289
$638$			76.6505i			0.120142i
$639$	−122.964	+	262.874i	−0.192431	+	0.411384i
$640$	65.8363			0.102869
$641$			184.355i			0.287606i	0.989606	+	0.143803i	$0.0459331\pi$
$641$			184.355i			0.287606i	−0.989606	+	0.143803i	$0.954067\pi$
$642$	310.586	−	1397.01i	0.483779	−	2.17602i
$643$	−428.215			−0.665964			−0.332982	−	0.942933i	$-0.608055\pi$
$643$	−428.215			−0.665964			−0.332982	+	0.942933i	$0.608055\pi$
$644$			176.284i			0.273734i
$645$	229.176	+	50.9511i	0.355312	+	0.0789939i
$646$	889.278			1.37659
$647$			516.078i			0.797648i	0.917028	+	0.398824i	$0.130581\pi$
$647$			516.078i			0.797648i	−0.917028	+	0.398824i	$0.869419\pi$
$648$	31.6685	−	26.4441i	0.0488711	−	0.0408088i
$649$	−27.7076			−0.0426928
$650$		−	145.899i		−	0.224460i
$651$	181.246	−	815.241i	0.278412	−	1.25229i
$652$	272.825			0.418443
$653$		−	983.392i		−	1.50596i	−0.658044	−	0.752980i	$-0.728616\pi$
$653$		−	983.392i		−	1.50596i	0.658044	−	0.752980i	$-0.271384\pi$
$654$	−1300.87	−	289.213i	−1.98910	−	0.442222i
$655$	664.965			1.01521
$656$			552.325i			0.841959i
$657$	−583.834	−	273.098i	−0.888637	−	0.415674i
$658$	−1001.41			−1.52190
$659$		−	152.558i		−	0.231499i	−0.993278	−	0.115749i	$-0.963073\pi$
$659$		−	152.558i		−	0.231499i	0.993278	−	0.115749i	$-0.0369270\pi$
$660$	−36.2549	+	163.074i	−0.0549317	+	0.247081i
$661$	−585.844			−0.886300			−0.443150	−	0.896447i	$-0.646139\pi$
$661$	−585.844			−0.886300			−0.443150	+	0.896447i	$0.646139\pi$
$662$		−	1059.94i		−	1.60112i
$663$	487.177	+	108.311i	0.734807	+	0.163364i
$664$	67.1173			0.101080
$665$		−	324.353i		−	0.487749i
$666$	571.447	−	1221.65i	0.858028	−	1.83431i
$667$	50.4465			0.0756319
$668$		−	361.757i		−	0.541552i
$669$	159.089	−	715.577i	0.237801	−	1.06962i
$670$	−965.151			−1.44052
$671$			176.505i			0.263047i
$672$	909.435	+	202.188i	1.35333	+	0.300875i
$673$	742.833			1.10376			0.551882	−	0.833922i	$-0.313910\pi$
$673$	742.833			1.10376			0.551882	+	0.833922i	$0.313910\pi$
$674$		−	863.625i		−	1.28134i
$675$	−142.522	+	185.049i	−0.211143	+	0.274147i
$676$	506.307			0.748975
$677$		−	514.809i		−	0.760427i	−0.924899	−	0.380213i	$-0.875851\pi$
$677$		−	514.809i		−	0.760427i	0.924899	−	0.380213i	$-0.124149\pi$
$678$	223.463	−	1005.13i	0.329591	−	1.48249i
$679$	−562.282			−0.828103
$680$		−	56.8010i		−	0.0835309i
$681$	137.243	+	30.5122i	0.201531	+	0.0448050i
$682$	403.638			0.591845
$683$		−	387.873i		−	0.567896i	−0.958840	−	0.283948i	$-0.908356\pi$
$683$		−	387.873i		−	0.567896i	0.958840	−	0.283948i	$-0.0916444\pi$
$684$	358.919	+	167.890i	0.524736	+	0.245453i
$685$	−870.151			−1.27029
$686$			964.944i			1.40662i
$687$	−92.7262	+	417.080i	−0.134973	+	0.607103i
$688$	323.129			0.469664
$689$		−	246.899i		−	0.358344i
$690$	219.770	+	48.8598i	0.318507	+	0.0708114i
$691$	1208.04			1.74826			0.874128	−	0.485696i	$-0.161434\pi$
$691$	1208.04			1.74826			0.874128	+	0.485696i	$0.161434\pi$
$692$		−	352.139i		−	0.508872i
$693$	95.6847	−	204.557i	0.138073	−	0.295176i
$694$	1441.61			2.07725
$695$			300.023i			0.431688i
$696$	2.52026	−	11.3360i	0.00362106	−	0.0162874i
$697$	912.399			1.30904
$698$		−	1511.55i		−	2.16555i
$699$	−663.445	−	147.499i	−0.949134	−	0.211014i
$700$	−229.741			−0.328201
$701$			370.498i			0.528527i	0.964451	+	0.264264i	$0.0851289\pi$
$701$			370.498i			0.528527i	−0.964451	+	0.264264i	$0.914871\pi$
$702$	360.767	+	277.857i	0.513913	+	0.395807i
$703$	−618.064			−0.879181
$704$			209.377i			0.297411i
$705$	−135.544	+	609.673i	−0.192261	+	0.864785i
$706$	−97.7432			−0.138446
$707$			740.346i			1.04717i
$708$	−85.8792	−	19.0929i	−0.121298	−	0.0269673i
$709$	−1040.67			−1.46779			−0.733897	−	0.679260i	$-0.762301\pi$
$709$	−1040.67			−1.46779			−0.733897	+	0.679260i	$0.762301\pi$
$710$			364.556i			0.513459i
$711$	699.951	+	327.413i	0.984460	+	0.460496i
$712$	−48.9754			−0.0687856
$713$		−	265.649i		−	0.372579i
$714$	349.242	−	1570.88i	0.489135	−	2.20011i
$715$	87.9780			0.123046
$716$			185.168i			0.258615i
$717$	147.479	+	32.7878i	0.205689	+	0.0457292i
$718$	1327.04			1.84824
$719$		−	760.116i		−	1.05719i	−0.848876	−	0.528593i	$-0.822720\pi$
$719$		−	760.116i		−	1.05719i	0.848876	−	0.528593i	$-0.177280\pi$
$720$	257.425	−	550.330i	0.357535	−	0.764347i
$721$	−687.914			−0.954111
$722$			637.533i			0.883009i
$723$	−164.404	+	739.485i	−0.227392	+	1.02280i
$724$	−676.498			−0.934390
$725$			65.7438i			0.0906811i
$726$	−884.226	−	196.583i	−1.21794	−	0.270776i
$727$	−683.054			−0.939552			−0.469776	−	0.882786i	$-0.655665\pi$
$727$	−683.054			−0.939552			−0.469776	+	0.882786i	$0.655665\pi$
$728$		−	21.3715i		−	0.0293565i
$729$	−186.150	−	704.833i	−0.255349	−	0.966849i
$730$	−809.665			−1.10913
$731$		−	533.785i		−	0.730212i
$732$	−121.627	+	547.072i	−0.166157	+	0.747367i
$733$	−1050.25			−1.43282			−0.716408	−	0.697681i	$-0.754215\pi$
$733$	−1050.25			−1.43282			−0.716408	+	0.697681i	$0.754215\pi$
$734$			1604.76i			2.18632i
$735$	7.25646	+	1.61327i	0.00987273	+	0.00219493i
$736$	296.342			0.402639
$737$			307.948i			0.417840i
$738$	754.074	+	352.730i	1.02178	+	0.477954i
$739$	−863.855			−1.16895			−0.584476	−	0.811411i	$-0.698700\pi$
$739$	−863.855			−1.16895			−0.584476	+	0.811411i	$0.698700\pi$
$740$		−	827.359i		−	1.11805i
$741$	45.2883	−	203.705i	0.0611178	−	0.274906i
$742$	−796.114			−1.07293
$743$		−	604.163i		−	0.813140i	−0.913620	−	0.406570i	$-0.866725\pi$
$743$		−	604.163i		−	0.813140i	0.913620	−	0.406570i	$-0.133275\pi$
$744$	−59.6951	−	13.2716i	−0.0802353	−	0.0178381i
$745$	974.880			1.30856
$746$		−	1358.00i		−	1.82037i
$747$	502.482	−	1074.22i	0.672667	−	1.43804i
$748$	379.822			0.507783
$749$			1186.79i			1.58450i
$750$	−247.694	+	1114.12i	−0.330259	+	1.48549i
$751$	7.84121			0.0104410			0.00522051	−	0.999986i	$-0.498338\pi$
$751$	7.84121			0.0104410			0.00522051	+	0.999986i	$0.498338\pi$
$752$			859.613i			1.14310i
$753$	−337.838	−	75.1089i	−0.448656	−	0.0997463i
$754$	128.172			0.169990
$755$		−	123.304i		−	0.163317i
$756$	437.529	−	568.084i	0.578742	−	0.751434i
$757$	483.558			0.638782			0.319391	−	0.947623i	$-0.396522\pi$
$757$	483.558			0.638782			0.319391	+	0.947623i	$0.396522\pi$
$758$			1676.86i			2.21222i
$759$	15.5896	−	70.1214i	0.0205396	−	0.0923866i
$760$	−23.7504			−0.0312505
$761$			951.213i			1.24995i	0.780644	+	0.624976i	$0.214891\pi$
$761$			951.213i			1.24995i	−0.780644	+	0.624976i	$0.785109\pi$
$762$	1294.36	+	287.765i	1.69863	+	0.377644i
$763$	1105.12			1.44839
$764$			523.977i			0.685834i
$765$	−909.104	−	425.247i	−1.18837	−	0.555879i
$766$	−144.758			−0.188979
$767$			46.3317i			0.0604064i
$768$	180.804	−	813.249i	0.235421	−	1.05892i
$769$	−650.550			−0.845969			−0.422985	−	0.906137i	$-0.639018\pi$
$769$	−650.550			−0.845969			−0.422985	+	0.906137i	$0.639018\pi$
$770$		−	283.681i		−	0.368417i
$771$	198.270	+	44.0800i	0.257160	+	0.0571725i
$772$	−1388.79			−1.79895
$773$			992.020i			1.28334i	0.766982	+	0.641669i	$0.221758\pi$
$773$			992.020i			1.28334i	−0.766982	+	0.641669i	$0.778242\pi$
$774$	206.359	−	441.159i	0.266614	−	0.569973i
$775$	346.204			0.446715
$776$			41.1725i			0.0530573i
$777$	−242.730	+	1091.79i	−0.312393	+	1.40513i
$778$	1412.42			1.81546
$779$		−	381.505i		−	0.489737i
$780$	272.686	+	60.6242i	0.349597	+	0.0777233i
$781$	116.318			0.148934
$782$		−	511.876i		−	0.654573i
$783$	−162.566	−	125.206i	−0.207619	−	0.159905i
$784$	10.2313			0.0130501
$785$		−	266.066i		−	0.338938i
$786$	299.380	−	1346.60i	0.380890	−	1.71323i
$787$	−1242.88			−1.57926			−0.789630	−	0.613583i	$-0.789728\pi$
$787$	−1242.88			−1.57926			−0.789630	+	0.613583i	$0.789728\pi$
$788$			447.090i			0.567373i
$789$	866.827	+	192.715i	1.09864	+	0.244253i
$790$	970.696			1.22873
$791$			853.882i			1.07950i
$792$	−14.9784	−	7.00640i	−0.0189122	−	0.00884647i
$793$	295.145			0.372188
$794$		−	1041.72i		−	1.31199i
$795$	−107.757	+	484.686i	−0.135543	+	0.609668i
$796$	672.174			0.844439
$797$		−	572.779i		−	0.718669i	−0.933209	−	0.359335i	$-0.883004\pi$
$797$		−	572.779i		−	0.718669i	0.933209	−	0.359335i	$-0.116996\pi$
$798$	−656.838	−	146.030i	−0.823105	−	0.182995i
$799$	1420.02			1.77724
$800$			386.205i			0.482756i
$801$	−366.660	+	783.854i	−0.457753	+	0.978594i
$802$	1176.52			1.46698
$803$			258.338i			0.321716i
$804$	−212.202	+	954.477i	−0.263933	+	1.18716i
$805$	−186.701			−0.231926
$806$		−	674.949i		−	0.837406i
$807$	1308.48	+	290.904i	1.62141	+	0.360476i
$808$	54.2110			0.0670929
$809$			534.139i			0.660246i	0.943938	+	0.330123i	$0.107090\pi$
$809$			534.139i			0.660246i	−0.943938	+	0.330123i	$0.892910\pi$
$810$	−586.951	−	702.911i	−0.724631	−	0.867792i
$811$	1153.16			1.42190			0.710948	−	0.703244i	$-0.248266\pi$
$811$	1153.16			1.42190			0.710948	+	0.703244i	$0.248266\pi$
$812$		−	201.828i		−	0.248556i
$813$	72.8313	−	327.593i	0.0895834	−	0.402943i
$814$	−540.562			−0.664081
$815$			288.945i			0.354534i
$816$	−1348.45	−	299.790i	−1.65251	−	0.367390i
$817$	−223.193			−0.273186
$818$		−	1098.41i		−	1.34280i
$819$	−342.053	−	160.000i	−0.417647	−	0.195361i
$820$	510.693			0.622797
$821$		−	238.118i		−	0.290034i	−0.989429	−	0.145017i	$-0.953676\pi$
$821$		−	238.118i		−	0.290034i	0.989429	−	0.145017i	$-0.0463238\pi$
$822$	−391.758	+	1762.12i	−0.476592	+	2.14369i
$823$	1325.63			1.61073			0.805365	−	0.592779i	$-0.201969\pi$
$823$	1325.63			1.61073			0.805365	+	0.592779i	$0.201969\pi$
$824$			50.3717i			0.0611308i
$825$	91.3850	+	20.3169i	0.110770	+	0.0246266i
$826$	149.394			0.180865
$827$		−	933.439i		−	1.12870i	−0.825534	−	0.564352i	$-0.809126\pi$
$827$		−	933.439i		−	1.12870i	0.825534	−	0.564352i	$-0.190874\pi$
$828$	96.6390	−	206.597i	0.116714	−	0.249513i
$829$	−234.018			−0.282289			−0.141144	−	0.989989i	$-0.545078\pi$
$829$	−234.018			−0.282289			−0.141144	+	0.989989i	$0.545078\pi$
$830$		−	1489.73i		−	1.79486i
$831$	−159.602	+	717.883i	−0.192060	+	0.863878i
$832$	350.114			0.420809
$833$		−	16.9013i		−	0.0202897i
$834$	607.567	+	135.076i	0.728498	+	0.161962i
$835$	383.132			0.458840
$836$		−	158.816i		−	0.189972i
$837$	−659.327	+	856.065i	−0.787726	+	1.02278i
$838$	800.423			0.955159
$839$			646.303i			0.770325i	0.922849	+	0.385162i	$0.125855\pi$
$839$			646.303i			0.770325i	−0.922849	+	0.385162i	$0.874145\pi$
$840$	−9.32739	+	41.9543i	−0.0111040	+	0.0499456i
$841$	783.244			0.931325
$842$		−	1760.63i		−	2.09101i
$843$	−578.630	−	128.643i	−0.686394	−	0.152601i
$844$	−34.7170			−0.0411339
$845$			536.223i			0.634584i
$846$	1173.61	+	548.973i	1.38724	+	0.648904i
$847$	751.174			0.886864
$848$			683.386i			0.805880i
$849$	−231.459	+	1041.10i	−0.272626	+	1.22626i
$850$	667.097			0.784820
$851$			355.763i			0.418053i
$852$	360.524	+	80.1527i	0.423150	+	0.0940759i
$853$	−24.1394			−0.0282994			−0.0141497	−	0.999900i	$-0.504504\pi$
$853$	−24.1394			−0.0282994			−0.0141497	+	0.999900i	$0.504504\pi$
$854$		−	951.681i		−	1.11438i
$855$	−177.810	+	380.127i	−0.207965	+	0.444593i
$856$	86.9016			0.101521
$857$			135.299i			0.157875i	0.996880	+	0.0789373i	$0.0251527\pi$
$857$			135.299i			0.157875i	−0.996880	+	0.0789373i	$0.974847\pi$
$858$	39.6093	−	178.162i	0.0461647	−	0.207647i
$859$	−491.575			−0.572264			−0.286132	−	0.958190i	$-0.592370\pi$
$859$	−491.575			−0.572264			−0.286132	+	0.958190i	$0.592370\pi$
$860$		−	298.773i		−	0.347411i
$861$	−673.916	−	149.827i	−0.782713	−	0.174015i
$862$	−349.909			−0.405927
$863$		−	51.2585i		−	0.0593957i	−0.999559	−	0.0296979i	$-0.990545\pi$
$863$		−	51.2585i		−	0.0593957i	0.999559	−	0.0296979i	$-0.00945452\pi$
$864$	−954.976	−	735.506i	−1.10530	−	0.851281i
$865$	372.946			0.431152
$866$			941.841i			1.08758i
$867$	−307.072	+	1381.20i	−0.354177	+	1.59308i
$868$	−1062.81			−1.22444
$869$		−	309.717i		−	0.356407i
$870$	−251.614	−	55.9395i	−0.289212	−	0.0642983i
$871$	514.939			0.591205
$872$		−	80.9215i		−	0.0927999i
$873$	658.968	+	308.243i	0.754832	+	0.353084i
$874$	−214.033			−0.244889
$875$		−	946.474i		−	1.08168i
$876$	−178.016	+	800.711i	−0.203215	+	0.914054i
$877$	−1387.61			−1.58222			−0.791110	−	0.611674i	$-0.790496\pi$
$877$	−1387.61			−1.58222			−0.791110	+	0.611674i	$0.790496\pi$
$878$		−	570.910i		−	0.650240i
$879$	−1285.07	−	285.700i	−1.46197	−	0.325028i
$880$	−243.512			−0.276718
$881$		−	698.452i		−	0.792795i	−0.918079	−	0.396398i	$-0.870260\pi$
$881$		−	698.452i		−	0.792795i	0.918079	−	0.396398i	$-0.129740\pi$
$882$	6.53399	−	13.9685i	0.00740815	−	0.0158373i
$883$	−1111.31			−1.25856			−0.629279	−	0.777179i	$-0.716650\pi$
$883$	−1111.31			−1.25856			−0.629279	+	0.777179i	$0.716650\pi$
$884$		−	635.124i		−	0.718466i
$885$	20.2210	−	90.9535i	0.0228486	−	0.102772i
$886$	1028.94			1.16133
$887$			771.311i			0.869573i	0.900534	+	0.434787i	$0.143176\pi$
$887$			771.311i			0.869573i	−0.900534	+	0.434787i	$0.856824\pi$
$888$	79.9451	+	17.7736i	0.0900283	+	0.0200153i
$889$	−1099.59			−1.23689
$890$			1087.05i			1.22141i
$891$	−224.276	+	187.277i	−0.251713	+	0.210187i
$892$	−932.885			−1.04584
$893$		−	593.757i		−	0.664901i
$894$	438.909	−	1974.20i	0.490950	−	2.20828i
$895$	−196.109			−0.219116
$896$			113.262i			0.126408i
$897$	−117.254	−	26.0683i	−0.130718	−	0.0290617i
$898$	118.058			0.131467
$899$			304.140i			0.338310i
$900$	269.245	+	125.944i	0.299162	+	0.139938i
$901$	1128.90			1.25294
$902$		−	333.666i		−	0.369918i
$903$	−87.6537	+	394.264i	−0.0970694	+	0.436615i
$904$	62.5246			0.0691644
$905$		−	716.470i		−	0.791680i
$906$	−249.699	−	55.5138i	−0.275606	−	0.0612735i
$907$	924.774			1.01960			0.509798	−	0.860294i	$-0.329720\pi$
$907$	924.774			1.01960			0.509798	+	0.860294i	$0.329720\pi$
$908$		−	178.921i		−	0.197050i
$909$	405.857	−	867.651i	0.446488	−	0.954512i
$910$	−474.361			−0.521276
$911$			884.822i			0.971265i	0.874163	+	0.485632i	$0.161411\pi$
$911$			884.822i			0.971265i	−0.874163	+	0.485632i	$0.838589\pi$
$912$	−125.352	+	563.831i	−0.137448	+	0.618236i
$913$	−475.324			−0.520618
$914$			1271.38i			1.39100i
$915$	−579.397	−	128.813i	−0.633221	−	0.140779i
$916$	543.739			0.593602
$917$			1143.97i			1.24752i
$918$	−1270.45	+	1649.54i	−1.38393	+	1.79689i
$919$	−624.037			−0.679039			−0.339520	−	0.940599i	$-0.610265\pi$
$919$	−624.037			−0.679039			−0.339520	+	0.940599i	$0.610265\pi$
$920$			13.6709i			0.0148597i
$921$	−337.948	+	1520.08i	−0.366936	+	1.65047i
$922$	284.842			0.308939
$923$		−	194.502i		−	0.210728i
$924$	−280.544	−	62.3712i	−0.303619	−	0.0675013i
$925$	−463.644			−0.501237
$926$		−	2335.72i		−	2.52238i
$927$	806.203	+	377.114i	0.869691	+	0.406811i
$928$	−339.281			−0.365605
$929$			584.667i			0.629351i	0.949199	+	0.314675i	$0.101896\pi$
$929$			584.667i			0.629351i	−0.949199	+	0.314675i	$0.898104\pi$
$930$	−294.575	+	1324.99i	−0.316747	+	1.42472i
$931$	−7.06702			−0.00759078
$932$			864.921i			0.928027i
$933$	−958.056	−	212.997i	−1.02686	−	0.228293i
$934$	15.8969			0.0170202
$935$			402.264i			0.430229i
$936$	−11.7159	+	25.0464i	−0.0125169	+	0.0267590i
$937$	−980.559			−1.04649			−0.523244	−	0.852183i	$-0.675278\pi$
$937$	−980.559			−1.04649			−0.523244	+	0.852183i	$0.675278\pi$
$938$		−	1660.40i		−	1.77015i
$939$	−201.825	+	907.805i	−0.214937	+	0.966778i
$940$	794.820			0.845553
$941$			186.524i			0.198219i	0.995077	+	0.0991095i	$0.0315994\pi$
$941$			186.524i			0.198219i	−0.995077	+	0.0991095i	$0.968401\pi$
$942$	−538.803	−	119.788i	−0.571978	−	0.127164i
$943$	−219.598			−0.232871
$944$		−	128.240i		−	0.135848i
$945$	601.651	+	463.381i	0.636667	+	0.490351i
$946$	−195.206			−0.206349
$947$		−	787.251i		−	0.831311i	−0.909522	−	0.415655i	$-0.863552\pi$
$947$		−	787.251i		−	0.831311i	0.909522	−	0.415655i	$-0.136448\pi$
$948$	213.421	−	959.961i	0.225128	−	1.01262i
$949$	431.983			0.455198
$950$		−	278.936i		−	0.293617i
$951$	−981.700	−	218.254i	−1.03228	−	0.229500i
$952$	97.7176			0.102645
$953$		−	542.842i		−	0.569613i	−0.958585	−	0.284807i	$-0.908071\pi$
$953$		−	542.842i		−	0.569613i	0.958585	−	0.284807i	$-0.0919294\pi$
$954$	933.009	+	436.429i	0.977996	+	0.457473i
$955$	−554.937			−0.581086
$956$		−	192.265i		−	0.201114i
$957$	−17.8485	+	80.2818i	−0.0186504	+	0.0838890i
$958$	−1582.24			−1.65161
$959$		−	1496.96i		−	1.56096i
$960$	−687.306	−	152.804i	−0.715943	−	0.159170i
$961$	640.589			0.666586
$962$			903.908i			0.939613i
$963$	650.599	−	1390.87i	0.675596	−	1.44431i
$964$	964.054			1.00006
$965$		−	1470.85i		−	1.52420i
$966$	−84.0561	+	378.082i	−0.0870146	+	0.391389i
$967$	468.018			0.483989			0.241995	−	0.970278i	$-0.422198\pi$
$967$	468.018			0.483989			0.241995	+	0.970278i	$0.422198\pi$
$968$		−	55.0039i		−	0.0568222i
$969$	931.407	+	207.073i	0.961204	+	0.213697i
$970$	913.862			0.942126
$971$		−	828.213i		−	0.852949i	−0.904500	−	0.426474i	$-0.859755\pi$
$971$		−	828.213i		−	0.852949i	0.904500	−	0.426474i	$-0.140245\pi$
$972$	−824.187	+	425.915i	−0.847929	+	0.438184i
$973$	−516.145			−0.530467
$974$			1610.80i			1.65380i
$975$	33.9733	−	152.811i	0.0348444	−	0.156729i
$976$	−816.925			−0.837014
$977$		−	5.87085i		−	0.00600906i	−0.999995	−	0.00300453i	$-0.999044\pi$
$977$		−	5.87085i		−	0.00600906i	0.999995	−	0.00300453i	$-0.000956373\pi$
$978$	585.134	+	130.089i	0.598297	+	0.133015i
$979$	346.843			0.354283
$980$		−	9.46011i		−	0.00965317i
$981$	−1295.15	−	605.829i	−1.32024	−	0.617562i
$982$	1329.36			1.35373
$983$		−	687.595i		−	0.699486i	−0.936846	−	0.349743i	$-0.886269\pi$
$983$		−	687.595i		−	0.699486i	0.936846	−	0.349743i	$-0.113731\pi$
$984$	−10.9709	+	49.3467i	−0.0111493	+	0.0501491i
$985$	−473.507			−0.480718
$986$			586.046i			0.594367i
$987$	−1048.85	−	233.183i	−1.06267	−	0.236255i
$988$	−265.567			−0.268792
$989$			128.472i			0.129901i
$990$	−155.514	+	332.461i	−0.157084	+	0.335819i
$991$	184.476			0.186151			0.0930755	−	0.995659i	$-0.470330\pi$
$991$	184.476			0.186151			0.0930755	+	0.995659i	$0.470330\pi$
$992$			1786.64i			1.80105i
$993$	246.813	−	1110.16i	0.248553	−	1.11798i
$994$	−627.164			−0.630949
$995$			711.890i			0.715468i
$996$	−1473.26	−	327.538i	−1.47917	−	0.328854i
$997$	294.205			0.295091			0.147545	−	0.989055i	$-0.452863\pi$
$997$	294.205			0.295091			0.147545	+	0.989055i	$0.452863\pi$
$998$		−	171.808i		−	0.172152i
$999$	882.986	−	1146.46i	0.883870	−	1.14761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.8	✓	38
3.2	odd	2	inner	177.3.b.a.119.31	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.8	✓	38	1.1	even	1	trivial
177.3.b.a.119.31	yes	38	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} +O(q^{10})\)	\(q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} -11.3055 q^{10} +3.60723i q^{11} +(-2.48568 + 11.1805i) q^{12} +6.03188 q^{13} -19.4495i q^{14} +(-11.8411 - 2.63255i) q^{15} -16.6955 q^{16} +27.5797i q^{17} +(-10.6622 + 22.7939i) q^{18} +11.5320 q^{19} +15.4371i q^{20} +(4.52891 - 20.3709i) q^{21} +10.0859 q^{22} -6.63792i q^{23} +(-1.49164 - 0.331625i) q^{24} +8.65080 q^{25} -16.8654i q^{26} +(-16.4750 + 21.3910i) q^{27} -26.5572 q^{28} +7.59974i q^{29} +(-7.36072 + 33.1083i) q^{30} +40.0199 q^{31} +44.6438i q^{32} +(10.5638 + 2.34856i) q^{33} +77.1139 q^{34} -28.1264i q^{35} +(31.1238 + 14.5586i) q^{36} -53.5956 q^{37} -32.2439i q^{38} +(3.92718 - 17.6643i) q^{39} -2.05952 q^{40} -33.0823i q^{41} +(-56.9578 - 12.6630i) q^{42} -19.3543 q^{43} -13.7718i q^{44} +(-15.4188 + 32.9628i) q^{45} -18.5599 q^{46} -51.4877i q^{47} +(-10.8700 + 48.8927i) q^{48} -0.612818 q^{49} -24.1880i q^{50} +(80.7671 + 17.9564i) q^{51} -23.0287 q^{52} -40.9324i q^{53} +(59.8101 + 46.0647i) q^{54} +14.5855 q^{55} -3.54310i q^{56} +(7.50816 - 33.7715i) q^{57} +21.2492 q^{58} +7.68115i q^{59} +(45.2075 + 10.0506i) q^{60} +48.9309 q^{61} -111.897i q^{62} +(-56.7075 - 26.5258i) q^{63} +58.0439 q^{64} -24.3894i q^{65} +(6.56667 - 29.5367i) q^{66} +85.3697 q^{67} -105.295i q^{68} +(-19.4391 - 4.32176i) q^{69} -78.6424 q^{70} -32.2458i q^{71} +(-1.94232 + 4.15235i) q^{72} +71.6167 q^{73} +149.855i q^{74} +(5.63229 - 25.3339i) q^{75} -44.0272 q^{76} +25.0922i q^{77} +(-49.3902 - 10.9806i) q^{78} -85.8602 q^{79} +67.5068i q^{80} +(51.9171 + 62.1741i) q^{81} -92.4993 q^{82} +131.770i q^{83} +(-17.2906 + 77.7727i) q^{84} +111.516 q^{85} +54.1152i q^{86} +(22.2558 + 4.94797i) q^{87} +1.83735 q^{88} -96.1523i q^{89} +(92.1652 + 43.1117i) q^{90} +41.9583 q^{91} +25.3425i q^{92} +(26.0558 - 117.198i) q^{93} -143.962 q^{94} -46.6287i q^{95} +(130.739 + 29.0663i) q^{96} -80.8331 q^{97} +1.71346i q^{98} +(13.7555 - 29.4069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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