LMFDB - Embedded newform 177.5.b.a.119.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,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, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.35
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21543i q^{2} +(-2.46606 + 8.65555i) q^{3} +14.5227 q^{4} -2.20277i q^{5} +(10.5202 + 2.99733i) q^{6} +82.0188 q^{7} -37.0983i q^{8} +(-68.8371 - 42.6903i) q^{9} +O(q^{10})$	\(q-1.21543i q^{2} +(-2.46606 + 8.65555i) q^{3} +14.5227 q^{4} -2.20277i q^{5} +(10.5202 + 2.99733i) q^{6} +82.0188 q^{7} -37.0983i q^{8} +(-68.8371 - 42.6903i) q^{9} -2.67731 q^{10} -214.526i q^{11} +(-35.8140 + 125.702i) q^{12} +64.5985 q^{13} -99.6881i q^{14} +(19.0662 + 5.43216i) q^{15} +187.273 q^{16} +71.0494i q^{17} +(-51.8871 + 83.6667i) q^{18} -346.779 q^{19} -31.9902i q^{20} +(-202.264 + 709.917i) q^{21} -260.741 q^{22} -647.950i q^{23} +(321.106 + 91.4867i) q^{24} +620.148 q^{25} -78.5150i q^{26} +(539.264 - 490.546i) q^{27} +1191.14 q^{28} +909.033i q^{29} +(6.60242 - 23.1736i) q^{30} +115.190 q^{31} -821.190i q^{32} +(1856.84 + 529.035i) q^{33} +86.3557 q^{34} -180.668i q^{35} +(-999.702 - 619.979i) q^{36} -22.9249 q^{37} +421.486i q^{38} +(-159.304 + 559.135i) q^{39} -81.7188 q^{40} +830.984i q^{41} +(862.855 + 245.837i) q^{42} +1663.65 q^{43} -3115.50i q^{44} +(-94.0367 + 151.632i) q^{45} -787.539 q^{46} +2424.07i q^{47} +(-461.828 + 1620.95i) q^{48} +4326.08 q^{49} -753.747i q^{50} +(-614.972 - 175.212i) q^{51} +938.146 q^{52} -1372.64i q^{53} +(-596.224 - 655.439i) q^{54} -472.551 q^{55} -3042.75i q^{56} +(855.179 - 3001.56i) q^{57} +1104.87 q^{58} -453.188i q^{59} +(276.893 + 78.8899i) q^{60} -691.845 q^{61} -140.005i q^{62} +(-5645.93 - 3501.40i) q^{63} +1998.27 q^{64} -142.295i q^{65} +(643.005 - 2256.86i) q^{66} +6320.59 q^{67} +1031.83i q^{68} +(5608.37 + 1597.89i) q^{69} -219.590 q^{70} +2995.52i q^{71} +(-1583.74 + 2553.73i) q^{72} -9273.25 q^{73} +27.8637i q^{74} +(-1529.32 + 5367.72i) q^{75} -5036.17 q^{76} -17595.1i q^{77} +(679.590 + 193.623i) q^{78} -11789.5 q^{79} -412.519i q^{80} +(2916.08 + 5877.35i) q^{81} +1010.00 q^{82} +10058.1i q^{83} +(-2937.42 + 10309.9i) q^{84} +156.505 q^{85} -2022.06i q^{86} +(-7868.18 - 2241.73i) q^{87} -7958.54 q^{88} +7601.63i q^{89} +(184.298 + 114.295i) q^{90} +5298.29 q^{91} -9410.01i q^{92} +(-284.065 + 997.029i) q^{93} +2946.29 q^{94} +763.873i q^{95} +(7107.85 + 2025.11i) q^{96} -4999.76 q^{97} -5258.05i q^{98} +(-9158.17 + 14767.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * 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 $

$2$		−	1.21543i		−	0.303858i	−0.988391	−	0.151929i	$-0.951452\pi$
$2$		−	1.21543i		−	0.303858i	0.988391	−	0.151929i	$-0.0485485\pi$
$3$	−2.46606	+	8.65555i	−0.274007	+	0.961728i
$3$	−2.46606	+	8.65555i	−0.274007	+	0.961728i
$4$	14.5227			0.907671
$5$		−	2.20277i		−	0.0881107i	−0.999029	−	0.0440553i	$-0.985972\pi$
$5$		−	2.20277i		−	0.0881107i	0.999029	−	0.0440553i	$-0.0140278\pi$
$6$	10.5202	+	2.99733i	0.292228	+	0.0832592i
$7$	82.0188			1.67385			0.836926	−	0.547316i	$-0.184350\pi$
$7$	82.0188			1.67385			0.836926	+	0.547316i	$0.184350\pi$
$8$		−	37.0983i		−	0.579660i
$9$	−68.8371	−	42.6903i	−0.849840	−	0.527041i
$10$	−2.67731			−0.0267731
$11$		−	214.526i		−	1.77294i	−0.462785	−	0.886471i	$-0.653150\pi$
$11$		−	214.526i		−	1.77294i	0.462785	−	0.886471i	$-0.346850\pi$
$12$	−35.8140	+	125.702i	−0.248708	+	0.872932i
$13$	64.5985			0.382240			0.191120	−	0.981567i	$-0.438788\pi$
$13$	64.5985			0.382240			0.191120	+	0.981567i	$0.438788\pi$
$14$		−	99.6881i		−	0.508613i
$15$	19.0662	+	5.43216i	0.0847385	+	0.0241430i
$16$	187.273			0.731536
$17$			71.0494i			0.245846i	0.992416	+	0.122923i	$0.0392268\pi$
$17$			71.0494i			0.245846i	−0.992416	+	0.122923i	$0.960773\pi$
$18$	−51.8871	+	83.6667i	−0.160145	+	0.258230i
$19$	−346.779			−0.960606			−0.480303	−	0.877103i	$-0.659473\pi$
$19$	−346.779			−0.960606			−0.480303	+	0.877103i	$0.659473\pi$
$20$		−	31.9902i		−	0.0799755i
$21$	−202.264	+	709.917i	−0.458647	+	1.60979i
$22$	−260.741			−0.538722
$23$		−	647.950i		−	1.22486i	−0.790525	−	0.612429i	$-0.790192\pi$
$23$		−	647.950i		−	1.22486i	0.790525	−	0.612429i	$-0.209808\pi$
$24$	321.106	+	91.4867i	0.557475	+	0.158831i
$25$	620.148			0.992237
$26$		−	78.5150i		−	0.116146i
$27$	539.264	−	490.546i	0.739732	−	0.672902i
$28$	1191.14			1.51931
$29$			909.033i			1.08090i	0.841378	+	0.540448i	$0.181745\pi$
$29$			909.033i			1.08090i	−0.841378	+	0.540448i	$0.818255\pi$
$30$	6.60242	−	23.1736i	0.00733602	−	0.0257484i
$31$	115.190			0.119864			0.0599322	−	0.998202i	$-0.480912\pi$
$31$	115.190			0.119864			0.0599322	+	0.998202i	$0.480912\pi$
$32$		−	821.190i		−	0.801943i
$33$	1856.84	+	529.035i	1.70509	+	0.485799i
$34$	86.3557			0.0747021
$35$		−	180.668i		−	0.147484i
$36$	−999.702	−	619.979i	−0.771375	−	0.478379i
$37$	−22.9249			−0.0167457			−0.00837287	−	0.999965i	$-0.502665\pi$
$37$	−22.9249			−0.0167457			−0.00837287	+	0.999965i	$0.502665\pi$
$38$			421.486i			0.291888i
$39$	−159.304	+	559.135i	−0.104736	+	0.367610i
$40$	−81.7188			−0.0510743
$41$			830.984i			0.494339i	0.968972	+	0.247170i	$0.0795005\pi$
$41$			830.984i			0.494339i	−0.968972	+	0.247170i	$0.920500\pi$
$42$	862.855	+	245.837i	0.489147	+	0.139364i
$43$	1663.65			0.899759			0.449879	−	0.893089i	$-0.351467\pi$
$43$	1663.65			0.899759			0.449879	+	0.893089i	$0.351467\pi$
$44$		−	3115.50i		−	1.60925i
$45$	−94.0367	+	151.632i	−0.0464379	+	0.0748800i
$46$	−787.539			−0.372183
$47$			2424.07i			1.09736i	0.836032	+	0.548681i	$0.184870\pi$
$47$			2424.07i			1.09736i	−0.836032	+	0.548681i	$0.815130\pi$
$48$	−461.828	+	1620.95i	−0.200446	+	0.703539i
$49$	4326.08			1.80178
$50$		−	753.747i		−	0.301499i
$51$	−614.972	−	175.212i	−0.236437	−	0.0673635i
$52$	938.146			0.346948
$53$		−	1372.64i		−	0.488658i	−0.969692	−	0.244329i	$-0.921432\pi$
$53$		−	1372.64i		−	0.488658i	0.969692	−	0.244329i	$-0.0785677\pi$
$54$	−596.224	−	655.439i	−0.204466	−	0.224773i
$55$	−472.551			−0.156215
$56$		−	3042.75i		−	0.970266i
$57$	855.179	−	3001.56i	0.263213	−	0.923841i
$58$	1104.87			0.328438
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	276.893	+	78.8899i	0.0769146	+	0.0219138i
$61$	−691.845			−0.185930			−0.0929650	−	0.995669i	$-0.529634\pi$
$61$	−691.845			−0.185930			−0.0929650	+	0.995669i	$0.529634\pi$
$62$		−	140.005i		−	0.0364217i
$63$	−5645.93	−	3501.40i	−1.42251	−	0.882188i
$64$	1998.27			0.487860
$65$		−	142.295i		−	0.0336794i
$66$	643.005	−	2256.86i	0.147614	−	0.518104i
$67$	6320.59			1.40802			0.704009	−	0.710191i	$-0.251392\pi$
$67$	6320.59			1.40802			0.704009	+	0.710191i	$0.251392\pi$
$68$			1031.83i			0.223147i
$69$	5608.37	+	1597.89i	1.17798	+	0.335620i
$70$	−219.590			−0.0448142
$71$			2995.52i			0.594232i	0.954841	+	0.297116i	$0.0960248\pi$
$71$			2995.52i			0.594232i	−0.954841	+	0.297116i	$0.903975\pi$
$72$	−1583.74	+	2553.73i	−0.305504	+	0.492619i
$73$	−9273.25			−1.74015			−0.870074	−	0.492921i	$-0.835929\pi$
$73$	−9273.25			−1.74015			−0.870074	+	0.492921i	$0.835929\pi$
$74$			27.8637i			0.00508832i
$75$	−1529.32	+	5367.72i	−0.271880	+	0.954261i
$76$	−5036.17			−0.871914
$77$		−	17595.1i		−	2.96764i
$78$	679.590	+	193.623i	0.111701	+	0.0318250i
$79$	−11789.5			−1.88903			−0.944517	−	0.328463i	$-0.893469\pi$
$79$	−11789.5			−1.88903			−0.944517	+	0.328463i	$0.893469\pi$
$80$		−	412.519i		−	0.0644562i
$81$	2916.08	+	5877.35i	0.444457	+	0.895800i
$82$	1010.00			0.150209
$83$			10058.1i			1.46003i	0.683431	+	0.730015i	$0.260487\pi$
$83$			10058.1i			1.46003i	−0.683431	+	0.730015i	$0.739513\pi$
$84$	−2937.42	+	10309.9i	−0.416301	+	1.46116i
$85$	156.505			0.0216616
$86$		−	2022.06i		−	0.273399i
$87$	−7868.18	−	2241.73i	−1.03953	−	0.296173i
$88$	−7958.54			−1.02770
$89$			7601.63i			0.959680i	0.877356	+	0.479840i	$0.159305\pi$
$89$			7601.63i			0.959680i	−0.877356	+	0.479840i	$0.840695\pi$
$90$	184.298	+	114.295i	0.0227529	+	0.0141105i
$91$	5298.29			0.639812
$92$		−	9410.01i		−	1.11177i
$93$	−284.065	+	997.029i	−0.0328437	+	0.115277i
$94$	2946.29			0.333442
$95$			763.873i			0.0846397i
$96$	7107.85	+	2025.11i	0.771251	+	0.219738i
$97$	−4999.76			−0.531380			−0.265690	−	0.964058i	$-0.585600\pi$
$97$	−4999.76			−0.531380			−0.265690	+	0.964058i	$0.585600\pi$
$98$		−	5258.05i		−	0.547485i
$99$	−9158.17	+	14767.3i	−0.934412	+	1.50672i
$100$	9006.24			0.900624
$101$			10783.4i			1.05709i	0.848904	+	0.528547i	$0.177263\pi$
$101$			10783.4i			1.05709i	−0.848904	+	0.528547i	$0.822737\pi$
$102$	−212.959	+	747.456i	−0.0204689	+	0.0718431i
$103$	−4925.34			−0.464261			−0.232130	−	0.972685i	$-0.574570\pi$
$103$	−4925.34			−0.464261			−0.232130	+	0.972685i	$0.574570\pi$
$104$		−	2396.49i		−	0.221569i
$105$	1563.78	+	445.539i	0.141840	+	0.0404117i
$106$	−1668.35			−0.148483
$107$		−	320.878i		−	0.0280267i	−0.999902	−	0.0140134i	$-0.995539\pi$
$107$		−	320.878i		−	0.0280267i	0.999902	−	0.0140134i	$-0.00446074\pi$
$108$	7831.59	−	7124.06i	0.671433	−	0.610773i
$109$	19779.8			1.66482			0.832412	−	0.554157i	$-0.186959\pi$
$109$	19779.8			1.66482			0.832412	+	0.554157i	$0.186959\pi$
$110$			574.352i			0.0474671i
$111$	56.5343	−	198.428i	0.00458845	−	0.0161048i
$112$	15359.9			1.22448
$113$		−	5391.62i		−	0.422243i	−0.977460	−	0.211121i	$-0.932288\pi$
$113$		−	5391.62i		−	0.422243i	0.977460	−	0.211121i	$-0.0677116\pi$
$114$	−3648.19	−	1039.41i	−0.280716	−	0.0799793i
$115$	−1427.28			−0.107923
$116$			13201.6i			0.981097i
$117$	−4446.77	−	2757.73i	−0.324843	−	0.201456i
$118$	−550.818			−0.0395589
$119$			5827.39i			0.411509i
$120$	201.524	−	707.321i	0.0139947	−	0.0491195i
$121$	−31380.4			−2.14332
$122$			840.890i			0.0564962i
$123$	−7192.63	−	2049.26i	−0.475420	−	0.135452i
$124$	1672.87			0.108797
$125$		−	2742.77i		−	0.175537i
$126$	−4255.71	+	6862.24i	−0.268060	+	0.432240i
$127$	−14703.8			−0.911635			−0.455817	−	0.890073i	$-0.650653\pi$
$127$	−14703.8			−0.911635			−0.455817	+	0.890073i	$0.650653\pi$
$128$		−	15567.8i		−	0.950183i
$129$	−4102.68	+	14399.8i	−0.246540	+	0.865323i
$130$	−172.950			−0.0102337
$131$		−	17431.2i		−	1.01574i	−0.861432	−	0.507872i	$-0.830432\pi$
$131$		−	17431.2i		−	1.01574i	0.861432	−	0.507872i	$-0.169568\pi$
$132$	26966.4	+	7683.03i	1.54766	+	0.440945i
$133$	−28442.4			−1.60791
$134$		−	7682.24i		−	0.427837i
$135$	−1080.56	−	1187.87i	−0.0592898	−	0.0651783i
$136$	2635.81			0.142507
$137$		−	17662.4i		−	0.941040i	−0.882389	−	0.470520i	$-0.844066\pi$
$137$		−	17662.4i		−	0.941040i	0.882389	−	0.470520i	$-0.155934\pi$
$138$	1942.12	−	6816.58i	0.101981	−	0.357938i
$139$	−29045.7			−1.50332			−0.751660	−	0.659550i	$-0.770747\pi$
$139$	−29045.7			−1.50332			−0.751660	+	0.659550i	$0.770747\pi$
$140$		−	2623.80i		−	0.133867i
$141$	−20981.7	−	5977.92i	−1.05536	−	0.300685i
$142$	3640.85			0.180562
$143$		−	13858.0i		−	0.677688i
$144$	−12891.3	−	7994.75i	−0.621689	−	0.385549i
$145$	2002.39			0.0952384
$146$			11271.0i			0.528757i
$147$	−10668.4	+	37444.6i	−0.493701	+	1.73282i
$148$	−332.932			−0.0151996
$149$		−	7250.60i		−	0.326589i	−0.986577	−	0.163294i	$-0.947788\pi$
$149$		−	7250.60i		−	0.326589i	0.986577	−	0.163294i	$-0.0522121\pi$
$150$	6524.09	+	1858.79i	0.289960	+	0.0826128i
$151$	34873.1			1.52946			0.764728	−	0.644354i	$-0.222873\pi$
$151$	34873.1			1.52946			0.764728	+	0.644354i	$0.222873\pi$
$152$			12864.9i			0.556825i
$153$	3033.12	−	4890.83i	0.129571	−	0.208930i
$154$	−21385.7			−0.901741
$155$		−	253.736i		−	0.0105613i
$156$	−2313.53	+	8120.17i	−0.0950661	+	0.333669i
$157$	25637.9			1.04012			0.520060	−	0.854130i	$-0.325909\pi$
$157$	25637.9			1.04012			0.520060	+	0.854130i	$0.325909\pi$
$158$			14329.3i			0.573997i
$159$	11881.0	+	3385.02i	0.469956	+	0.133896i
$160$	−1808.89			−0.0706598
$161$		−	53144.1i		−	2.05023i
$162$	7143.51	−	3544.29i	0.272196	−	0.135052i
$163$	215.000			0.00809213			0.00404606	−	0.999992i	$-0.498712\pi$
$163$	215.000			0.00809213			0.00404606	+	0.999992i	$0.498712\pi$
$164$			12068.2i			0.448697i
$165$	1165.34	−	4090.18i	0.0428040	−	0.150236i
$166$	12225.0			0.443641
$167$		−	4036.80i		−	0.144745i	−0.997378	−	0.0723726i	$-0.976943\pi$
$167$		−	4036.80i		−	0.144745i	0.997378	−	0.0723726i	$-0.0230571\pi$
$168$	26336.7	+	7503.62i	0.933131	+	0.265860i
$169$	−24388.0			−0.853893
$170$		−	190.221i		−	0.00658205i
$171$	23871.2	+	14804.1i	0.816362	+	0.506278i
$172$	24160.8			0.816685
$173$		−	15914.9i		−	0.531754i	−0.964007	−	0.265877i	$-0.914339\pi$
$173$		−	15914.9i		−	0.531754i	0.964007	−	0.265877i	$-0.0856615\pi$
$174$	−2724.67	+	9563.23i	−0.0899944	+	0.315868i
$175$	50863.8			1.66086
$176$		−	40175.0i		−	1.29697i
$177$	3922.59	+	1117.59i	0.125206	+	0.0356727i
$178$	9239.25			0.291606
$179$		−	33455.0i		−	1.04413i	−0.852905	−	0.522066i	$-0.825162\pi$
$179$		−	33455.0i		−	1.04413i	0.852905	−	0.522066i	$-0.174838\pi$
$180$	−1365.67	+	2202.11i	−0.0421503	+	0.0679664i
$181$	−11493.3			−0.350824			−0.175412	−	0.984495i	$-0.556126\pi$
$181$	−11493.3			−0.350824			−0.175412	+	0.984495i	$0.556126\pi$
$182$		−	6439.70i		−	0.194412i
$183$	1706.13	−	5988.30i	0.0509461	−	0.178814i
$184$	−24037.8			−0.710002
$185$			50.4983i			0.00147548i
$186$	1211.82	+	345.261i	0.0350278	+	0.00997981i
$187$	15241.9			0.435870
$188$			35204.2i			0.996043i
$189$	44229.8	−	40233.9i	1.23820	−	1.12634i
$190$	928.435			0.0257184
$191$		−	21256.8i		−	0.582681i	−0.956619	−	0.291340i	$-0.905899\pi$
$191$		−	21256.8i		−	0.582681i	0.956619	−	0.291340i	$-0.0941012\pi$
$192$	−4927.87	+	17296.2i	−0.133677	+	0.469188i
$193$	−43172.8			−1.15903			−0.579516	−	0.814961i	$-0.696758\pi$
$193$	−43172.8			−1.15903			−0.579516	+	0.814961i	$0.696758\pi$
$194$			6076.86i			0.161464i
$195$	1231.64	+	350.910i	0.0323904	+	0.00922839i
$196$	62826.4			1.63542
$197$			29358.4i			0.756484i	0.925707	+	0.378242i	$0.123471\pi$
$197$			29358.4i			0.756484i	−0.925707	+	0.378242i	$0.876529\pi$
$198$	17948.7	+	11131.1i	0.457827	+	0.283928i
$199$	43519.2			1.09894			0.549471	−	0.835513i	$-0.314829\pi$
$199$	43519.2			1.09894			0.549471	+	0.835513i	$0.314829\pi$
$200$		−	23006.4i		−	0.575160i
$201$	−15587.0	+	54708.2i	−0.385807	+	1.35413i
$202$	13106.5			0.321206
$203$			74557.7i			1.80926i
$204$	−8931.07	−	2544.56i	−0.214607	−	0.0611439i
$205$	1830.46			0.0435566
$206$			5986.41i			0.141069i
$207$	−27661.2	+	44603.0i	−0.645550	+	1.04093i
$208$	12097.6			0.279622
$209$			74393.0i			1.70310i
$210$	541.522	−	1900.67i	0.0122794	−	0.0430991i
$211$	43467.3			0.976333			0.488166	−	0.872751i	$-0.337666\pi$
$211$	43467.3			0.976333			0.488166	+	0.872751i	$0.337666\pi$
$212$		−	19934.5i		−	0.443541i
$213$	−25927.9	−	7387.15i	−0.571489	−	0.162824i
$214$	−390.005			−0.00851613
$215$		−	3664.64i		−	0.0792784i
$216$	−18198.4	−	20005.8i	−0.390055	−	0.428793i
$217$	9447.71			0.200635
$218$		−	24040.9i		−	0.505870i
$219$	22868.4	−	80265.1i	0.476813	−	1.67355i
$220$	−6862.72			−0.141792
$221$			4589.69i			0.0939720i
$222$	−241.175	−	68.7136i	−0.00489358	−	0.00139424i
$223$	3730.90			0.0750245			0.0375123	−	0.999296i	$-0.488057\pi$
$223$	3730.90			0.0750245			0.0375123	+	0.999296i	$0.488057\pi$
$224$		−	67353.0i		−	1.34233i
$225$	−42689.1	−	26474.3i	−0.843242	−	0.522949i
$226$	−6553.14			−0.128302
$227$			76853.4i			1.49146i	0.666249	+	0.745730i	$0.267899\pi$
$227$			76853.4i			1.49146i	−0.666249	+	0.745730i	$0.732101\pi$
$228$	12419.5	−	43590.9i	0.238911	−	0.838544i
$229$	−55040.5			−1.04957			−0.524785	−	0.851235i	$-0.675854\pi$
$229$	−55040.5			−1.04957			−0.524785	+	0.851235i	$0.675854\pi$
$230$			1734.76i			0.0327933i
$231$	152296.	+	43390.8i	2.85406	+	0.813155i
$232$	33723.5			0.626552
$233$			44490.4i			0.819511i	0.912195	+	0.409755i	$0.134386\pi$
$233$			44490.4i			0.819511i	−0.912195	+	0.409755i	$0.865614\pi$
$234$	−3351.83	+	5404.74i	−0.0612139	+	0.0987059i
$235$	5339.67			0.0966893
$236$		−	6581.52i		−	0.118169i
$237$	29073.6	−	102044.i	0.517609	−	1.81674i
$238$	7082.78			0.125040
$239$		−	77312.2i		−	1.35348i	−0.736221	−	0.676741i	$-0.763392\pi$
$239$		−	77312.2i		−	1.35348i	0.736221	−	0.676741i	$-0.236608\pi$
$240$	3570.58	+	1017.30i	0.0619893	+	0.0176614i
$241$	−49043.4			−0.844397			−0.422198	−	0.906504i	$-0.638741\pi$
$241$	−49043.4			−0.844397			−0.422198	+	0.906504i	$0.638741\pi$
$242$			38140.7i			0.651265i
$243$	−58062.9	+	10746.4i	−0.983300	+	0.181991i
$244$	−10047.5			−0.168763
$245$		−	9529.34i		−	0.158756i
$246$	−2490.73	+	8742.14i	−0.0411583	+	0.144460i
$247$	−22401.4			−0.367182
$248$		−	4273.33i		−	0.0694806i
$249$	−87058.7	−	24804.0i	−1.40415	−	0.400058i
$250$	−3333.65			−0.0533384
$251$			93490.5i			1.48395i	0.670426	+	0.741977i	$0.266111\pi$
$251$			93490.5i			1.48395i	−0.670426	+	0.741977i	$0.733889\pi$
$252$	−81994.3	−	50849.9i	−1.29117	−	0.800736i
$253$	−139002.			−2.17160
$254$			17871.4i			0.277007i
$255$	−385.952	+	1354.64i	−0.00593544	+	0.0208326i
$256$	13050.8			0.199139
$257$			64723.4i			0.979930i	0.871742	+	0.489965i	$0.162991\pi$
$257$			64723.4i			0.979930i	−0.871742	+	0.489965i	$0.837009\pi$
$258$	17502.0	+	4986.52i	0.262935	+	0.0749132i
$259$	−1880.27			−0.0280299
$260$		−	2066.52i		−	0.0305698i
$261$	38806.9	−	62575.1i	0.569676	−	0.918588i
$262$	−21186.4			−0.308642
$263$		−	50164.2i		−	0.725242i	−0.931937	−	0.362621i	$-0.881882\pi$
$263$		−	50164.2i		−	0.725242i	0.931937	−	0.362621i	$-0.118118\pi$
$264$	19626.3	−	68885.5i	0.281598	−	0.988371i
$265$	−3023.61			−0.0430560
$266$			34569.7i			0.488577i
$267$	−65796.3	−	18746.1i	−0.922951	−	0.262959i
$268$	91792.2			1.27802
$269$			27158.5i			0.375319i	0.982234	+	0.187660i	$0.0600902\pi$
$269$			27158.5i			0.375319i	−0.982234	+	0.187660i	$0.939910\pi$
$270$	−1443.78	+	1313.34i	−0.0198049	+	0.0180157i
$271$	−31247.5			−0.425478			−0.212739	−	0.977109i	$-0.568238\pi$
$271$	−31247.5			−0.425478			−0.212739	+	0.977109i	$0.568238\pi$
$272$			13305.7i			0.179845i
$273$	−13065.9	+	45859.6i	−0.175313	+	0.615325i
$274$	−21467.4			−0.285942
$275$		−	133038.i		−	1.75918i
$276$	81448.8	+	23205.7i	1.06922	+	0.304632i
$277$	57707.8			0.752099			0.376049	−	0.926600i	$-0.377282\pi$
$277$	57707.8			0.752099			0.376049	+	0.926600i	$0.377282\pi$
$278$			35303.0i			0.456796i
$279$	−7929.31	−	4917.48i	−0.101866	−	0.0631734i
$280$	−6702.48			−0.0854908
$281$			141489.i			1.79189i	0.444169	+	0.895943i	$0.353499\pi$
$281$			141489.i			1.79189i	−0.444169	+	0.895943i	$0.646501\pi$
$282$	−7265.75	+	25501.8i	−0.0913655	+	0.320680i
$283$	−87019.3			−1.08653			−0.543266	−	0.839561i	$-0.682812\pi$
$283$	−87019.3			−1.08653			−0.543266	+	0.839561i	$0.682812\pi$
$284$			43503.2i			0.539367i
$285$	−6611.74	−	1883.76i	−0.0814003	−	0.0231919i
$286$	−16843.5			−0.205921
$287$			68156.3i			0.827451i
$288$	−35056.8	+	56528.3i	−0.422657	+	0.681524i
$289$	78473.0			0.939560
$290$		−	2433.76i		−	0.0289389i
$291$	12329.7	−	43275.7i	0.145602	−	0.511043i
$292$	−134673.			−1.57948
$293$		−	16368.4i		−	0.190665i	−0.995445	−	0.0953324i	$-0.969609\pi$
$293$		−	16368.4i		−	0.190665i	0.995445	−	0.0953324i	$-0.0303914\pi$
$294$	45511.3	+	12966.7i	0.526531	+	0.150015i
$295$	−998.267			−0.0114710
$296$			850.475i			0.00970684i
$297$	−105235.	−	115686.i	−1.19302	−	1.31150i
$298$	−8812.60			−0.0992366
$299$		−	41856.6i		−	0.468190i
$300$	−22210.0	+	77953.9i	−0.246777	+	0.866155i
$301$	136451.			1.50606
$302$		−	42385.9i		−	0.464737i
$303$	−93336.3	−	26592.6i	−1.01664	−	0.289651i
$304$	−64942.4			−0.702718
$305$			1523.97i			0.0163824i
$306$	−5944.47	−	3686.55i	−0.0634849	−	0.0393710i
$307$	151300.			1.60532			0.802659	−	0.596439i	$-0.203418\pi$
$307$	151300.			1.60532			0.802659	+	0.596439i	$0.203418\pi$
$308$		−	255530.i		−	2.69364i
$309$	12146.2	−	42631.5i	0.127211	−	0.446492i
$310$	−308.398			−0.00320914
$311$		−	65535.7i		−	0.677575i	−0.940863	−	0.338787i	$-0.889983\pi$
$311$		−	65535.7i		−	0.677575i	0.940863	−	0.338787i	$-0.110017\pi$
$312$	20742.9	+	5909.90i	0.213089	+	0.0607115i
$313$	−78300.4			−0.799237			−0.399618	−	0.916682i	$-0.630857\pi$
$313$	−78300.4			−0.799237			−0.399618	+	0.916682i	$0.630857\pi$
$314$		−	31161.1i		−	0.316049i
$315$	−7712.78	+	12436.7i	−0.0777302	+	0.125338i
$316$	−171215.			−1.71462
$317$			175687.i			1.74832i	0.485639	+	0.874160i	$0.338587\pi$
$317$			175687.i			1.74832i	−0.485639	+	0.874160i	$0.661413\pi$
$318$	4114.26	−	14440.5i	0.0406853	−	0.142800i
$319$	195011.			1.91636
$320$		−	4401.73i		−	0.0429856i
$321$	2777.37	+	791.306i	0.0269541	+	0.00767952i
$322$	−64592.9			−0.622979
$323$		−	24638.4i		−	0.236161i
$324$	42349.4	+	85355.1i	0.403420	+	0.813092i
$325$	40060.6			0.379272
$326$		−	261.317i		−	0.00245886i
$327$	−48778.2	+	171205.i	−0.456174	+	1.60111i
$328$	30828.1			0.286549
$329$			198819.i			1.83682i
$330$	−4971.34	−	1416.39i	−0.0456505	−	0.0130063i
$331$	−28653.0			−0.261525			−0.130763	−	0.991414i	$-0.541743\pi$
$331$	−28653.0			−0.261525			−0.130763	+	0.991414i	$0.541743\pi$
$332$			146072.i			1.32523i
$333$	1578.08	+	978.671i	0.0142312	+	0.00882568i
$334$	−4906.45			−0.0439819
$335$		−	13922.8i		−	0.124061i
$336$	−37878.6	+	132949.i	−0.335517	+	1.17762i
$337$	−26575.1			−0.233999			−0.117000	−	0.993132i	$-0.537328\pi$
$337$	−26575.1			−0.233999			−0.117000	+	0.993132i	$0.537328\pi$
$338$			29642.0i			0.259462i
$339$	46667.4	+	13296.1i	0.406083	+	0.115698i
$340$	2272.88			0.0196616
$341$		−	24711.2i		−	0.212512i
$342$	17993.3	−	29013.8i	0.153837	−	0.248058i
$343$	157892.			1.34206
$344$		−	61718.7i		−	0.521554i
$345$	3519.77	−	12353.9i	0.0295717	−	0.103793i
$346$	−19343.4			−0.161577
$347$			168421.i			1.39874i	0.714757	+	0.699372i	$0.246537\pi$
$347$			168421.i			1.39874i	−0.714757	+	0.699372i	$0.753463\pi$
$348$	−114267.	−	32556.1i	−0.943548	−	0.268828i
$349$	−67634.2			−0.555284			−0.277642	−	0.960685i	$-0.589553\pi$
$349$	−67634.2			−0.555284			−0.277642	+	0.960685i	$0.589553\pi$
$350$		−	61821.4i		−	0.504664i
$351$	34835.7	−	31688.5i	0.282755	−	0.257210i
$352$	−176166.			−1.42180
$353$		−	232429.i		−	1.86527i	−0.360824	−	0.932634i	$-0.617504\pi$
$353$		−	232429.i		−	1.86527i	0.360824	−	0.932634i	$-0.382496\pi$
$354$	1358.35	−	4767.63i	0.0108394	−	0.0380449i
$355$	6598.44			0.0523582
$356$			110396.i			0.871073i
$357$	−50439.2	−	14370.7i	−0.395760	−	0.112757i
$358$	−40662.2			−0.317267
$359$			224734.i			1.74373i	0.489744	+	0.871866i	$0.337090\pi$
$359$			224734.i			1.74373i	−0.489744	+	0.871866i	$0.662910\pi$
$360$	5625.28	+	3488.60i	0.0434050	+	0.0269182i
$361$	−10065.5			−0.0772360
$362$			13969.4i			0.106601i
$363$	77386.0	−	271614.i	0.587285	−	2.06129i
$364$	76945.6			0.580739
$365$			20426.8i			0.153326i
$366$	−7278.36	−	2073.69i	−0.0543340	−	0.0154804i
$367$	−80990.7			−0.601317			−0.300658	−	0.953732i	$-0.597206\pi$
$367$	−80990.7			−0.601317			−0.300658	+	0.953732i	$0.597206\pi$
$368$		−	121344.i		−	0.896029i
$369$	35475.0	−	57202.5i	0.260537	−	0.420109i
$370$	61.3771			0.000448336
$371$		−	112582.i		−	0.817942i
$372$	−4125.40	+	14479.6i	−0.0298112	+	0.104633i
$373$	−93827.9			−0.674395			−0.337198	−	0.941434i	$-0.609479\pi$
$373$	−93827.9			−0.674395			−0.337198	+	0.941434i	$0.609479\pi$
$374$		−	18525.5i		−	0.132442i
$375$	23740.2	+	6763.85i	0.168819	+	0.0480985i
$376$	89928.9			0.636097
$377$			58722.1i			0.413161i
$378$	−48901.6	−	53758.3i	−0.342247	−	0.376237i
$379$	−151090.			−1.05186			−0.525930	−	0.850528i	$-0.676283\pi$
$379$	−151090.			−1.05186			−0.525930	+	0.850528i	$0.676283\pi$
$380$			11093.5i			0.0768249i
$381$	36260.4	−	127269.i	0.249794	−	0.876744i
$382$	−25836.1			−0.177052
$383$			154064.i			1.05028i	0.851017	+	0.525139i	$0.175987\pi$
$383$			154064.i			1.05028i	−0.851017	+	0.525139i	$0.824013\pi$
$384$	134748.	+	38391.2i	0.913817	+	0.260357i
$385$	−38758.0			−0.261481
$386$			52473.5i			0.352181i
$387$	−114521.	−	71021.9i	−0.764651	−	0.474209i
$388$	−72610.1			−0.482318
$389$		−	160924.i		−	1.06346i	−0.846913	−	0.531731i	$-0.821542\pi$
$389$		−	160924.i		−	1.06346i	0.846913	−	0.531731i	$-0.178458\pi$
$390$	426.506	−	1496.98i	0.00280412	−	0.00984207i
$391$	46036.5			0.301126
$392$		−	160490.i		−	1.04442i
$393$	150877.	+	42986.4i	0.976870	+	0.278321i
$394$	35683.1			0.229863
$395$			25969.4i			0.166444i
$396$	−133002.	+	214462.i	−0.848138	+	1.36760i
$397$	11224.1			0.0712151			0.0356076	−	0.999366i	$-0.488663\pi$
$397$	11224.1			0.0712151			0.0356076	+	0.999366i	$0.488663\pi$
$398$		−	52894.6i		−	0.333922i
$399$	70140.7	−	246184.i	0.440580	−	1.54637i
$400$	116137.			0.725857
$401$			86704.8i			0.539205i	0.962972	+	0.269603i	$0.0868924\pi$
$401$			86704.8i			0.539205i	−0.962972	+	0.269603i	$0.913108\pi$
$402$	66494.0	+	18944.9i	0.411463	+	0.117230i
$403$	7441.08			0.0458169
$404$			156605.i			0.959492i
$405$	12946.4	−	6423.44i	0.0789296	−	0.0391614i
$406$	90619.8			0.549757
$407$			4917.99i			0.0296892i
$408$	−6500.08	+	22814.4i	−0.0390479	+	0.137053i
$409$	93858.7			0.561084			0.280542	−	0.959842i	$-0.409486\pi$
$409$	93858.7			0.561084			0.280542	+	0.959842i	$0.409486\pi$
$410$		−	2224.80i		−	0.0132350i
$411$	152878.	+	43556.6i	0.905024	+	0.257852i
$412$	−71529.4			−0.421396
$413$		−	37169.9i		−	0.217917i
$414$	54211.8	+	33620.2i	0.316296	+	0.196155i
$415$	22155.7			0.128644
$416$		−	53047.6i		−	0.306534i
$417$	71628.5	−	251406.i	0.411921	−	1.44579i
$418$	90419.6			0.517499
$419$			278133.i			1.58425i	0.610358	+	0.792125i	$0.291025\pi$
$419$			278133.i			1.58425i	−0.610358	+	0.792125i	$0.708975\pi$
$420$	22710.4	+	6470.45i	0.128744	+	0.0366805i
$421$	281754.			1.58967			0.794833	−	0.606828i	$-0.207558\pi$
$421$	281754.			1.58967			0.794833	+	0.606828i	$0.207558\pi$
$422$		−	52831.5i		−	0.296666i
$423$	103484.	−	166866.i	0.578354	−	0.932583i
$424$	−50922.6			−0.283256
$425$			44061.1i			0.243937i
$426$	−8978.57	+	31513.6i	−0.0494752	+	0.173651i
$427$	−56744.3			−0.311219
$428$		−	4660.02i		−	0.0254390i
$429$	119949.	+	34174.8i	0.651752	+	0.185691i
$430$	−4454.12			−0.0240893
$431$		−	275231.i		−	1.48164i	−0.671704	−	0.740820i	$-0.734437\pi$
$431$		−	275231.i		−	1.48164i	0.671704	−	0.740820i	$-0.265563\pi$
$432$	100990.	−	91866.1i	0.541141	−	0.492252i
$433$	26656.4			0.142176			0.0710880	−	0.997470i	$-0.477353\pi$
$433$	26656.4			0.142176			0.0710880	+	0.997470i	$0.477353\pi$
$434$		−	11483.0i		−	0.0609645i
$435$	−4938.02	+	17331.8i	−0.0260960	+	0.0915934i
$436$	287256.			1.51111
$437$			224695.i			1.17661i
$438$	−97556.6	−	27795.0i	−0.508520	−	0.144883i
$439$	148386.			0.769954			0.384977	−	0.922926i	$-0.374209\pi$
$439$	148386.			0.769954			0.384977	+	0.922926i	$0.374209\pi$
$440$			17530.8i			0.0905517i
$441$	−297794.	−	184681.i	−1.53123	−	0.949612i
$442$	5578.44			0.0285541
$443$			101722.i			0.518331i	0.965833	+	0.259165i	$0.0834474\pi$
$443$			101722.i			0.518331i	−0.965833	+	0.259165i	$0.916553\pi$
$444$	821.033	−	2881.71i	0.00416480	−	0.0146179i
$445$	16744.6			0.0845581
$446$		−	4534.64i		−	0.0227968i
$447$	62757.9	+	17880.4i	0.314090	+	0.0894877i
$448$	163896.			0.816605
$449$		−	53811.9i		−	0.266923i	−0.991054	−	0.133461i	$-0.957391\pi$
$449$		−	53811.9i		−	0.266923i	0.991054	−	0.133461i	$-0.0426092\pi$
$450$	−32177.7	+	51885.7i	−0.158902	+	0.256226i
$451$	178268.			0.876435
$452$		−	78301.0i		−	0.383258i
$453$	−85999.3	+	301846.i	−0.419082	+	1.47092i
$454$	93410.0			0.453191
$455$		−	11670.9i		−	0.0563743i
$456$	−111353.	−	31725.6i	−0.535514	−	0.152574i
$457$	−164243.			−0.786421			−0.393210	−	0.919448i	$-0.628636\pi$
$457$	−164243.			−0.786421			−0.393210	+	0.919448i	$0.628636\pi$
$458$			66897.9i			0.318920i
$459$	34853.0	+	38314.4i	0.165430	+	0.181860i
$460$	−20728.1			−0.0979587
$461$		−	287867.i		−	1.35453i	−0.735737	−	0.677267i	$-0.763164\pi$
$461$		−	287867.i		−	1.35453i	0.735737	−	0.677267i	$-0.236836\pi$
$462$	52738.5	−	185105.i	0.247083	−	0.867229i
$463$	−394931.			−1.84229			−0.921147	−	0.389215i	$-0.872746\pi$
$463$	−394931.			−1.84229			−0.921147	+	0.389215i	$0.872746\pi$
$464$			170238.i			0.790714i
$465$	2196.22	+	625.729i	0.0101571	+	0.00289388i
$466$	54075.0			0.249015
$467$			137557.i			0.630739i	0.948969	+	0.315370i	$0.102129\pi$
$467$			137557.i			0.630739i	−0.948969	+	0.315370i	$0.897871\pi$
$468$	−64579.2	−	40049.7i	−0.294850	−	0.182855i
$469$	518407.			2.35681
$470$		−	6490.00i		−	0.0293798i
$471$	−63224.8	+	221910.i	−0.285001	+	1.00031i
$472$	−16812.5			−0.0754653
$473$		−	356897.i		−	1.59522i
$474$	−124028.	−	35336.9i	−0.552029	−	0.157279i
$475$	−215054.			−0.953148
$476$			84629.5i			0.373515i
$477$	−58598.4	+	94488.6i	−0.257543	+	0.415281i
$478$	−93967.7			−0.411266
$479$		−	367171.i		−	1.60029i	−0.599809	−	0.800143i	$-0.704757\pi$
$479$		−	367171.i		−	1.60029i	0.599809	−	0.800143i	$-0.295243\pi$
$480$	4460.84	−	15656.9i	0.0193613	−	0.0679554i
$481$	−1480.92			−0.00640088
$482$			59608.9i			0.256576i
$483$	459991.	+	131057.i	1.97177	+	0.561778i
$484$	−455728.			−1.94543
$485$			11013.3i			0.0468203i
$486$	13061.5	+	70571.4i	0.0552992	+	0.298783i
$487$	119891.			0.505508			0.252754	−	0.967531i	$-0.418664\pi$
$487$	119891.			0.505508			0.252754	+	0.967531i	$0.418664\pi$
$488$			25666.3i			0.107776i
$489$	−530.203	+	1860.94i	−0.00221730	+	0.00778242i
$490$	−11582.2			−0.0482393
$491$			383372.i			1.59022i	0.606464	+	0.795111i	$0.292588\pi$
$491$			383372.i			1.59022i	−0.606464	+	0.795111i	$0.707412\pi$
$492$	−104457.	−	29760.9i	−0.431525	−	0.122946i
$493$	−64586.3			−0.265733
$494$			27227.3i			0.111571i
$495$	32529.0	+	20173.3i	0.132758	+	0.0823317i
$496$	21571.9			0.0876851
$497$			245689.i			0.994656i
$498$	−30147.6	+	105814.i	−0.121561	+	0.426662i
$499$	318251.			1.27811			0.639056	−	0.769160i	$-0.279325\pi$
$499$	318251.			1.27811			0.639056	+	0.769160i	$0.279325\pi$
$500$		−	39832.5i		−	0.159330i
$501$	34940.7	+	9955.00i	0.139205	+	0.0396612i
$502$	113631.			0.450911
$503$		−	177262.i		−	0.700614i	−0.936635	−	0.350307i	$-0.886077\pi$
$503$		−	177262.i		−	0.700614i	0.936635	−	0.350307i	$-0.113923\pi$
$504$	−129896.	+	209454.i	−0.511369	+	0.824571i
$505$	23753.3			0.0931412
$506$			168947.i			0.659858i
$507$	60142.5	−	211092.i	0.233973	−	0.821212i
$508$	−213539.			−0.827464
$509$			35995.6i			0.138936i	0.997584	+	0.0694679i	$0.0221301\pi$
$509$			35995.6i			0.138936i	−0.997584	+	0.0694679i	$0.977870\pi$
$510$	1646.47	+	469.098i	0.00633014	+	0.00180353i
$511$	−760580.			−2.91275
$512$		−	264947.i		−	1.01069i
$513$	−187005.	+	170111.i	−0.710591	+	0.646394i
$514$	78666.8			0.297759
$515$			10849.4i			0.0409063i
$516$	−59582.1	+	209125.i	−0.223777	+	0.785428i
$517$	520027.			1.94556
$518$			2285.34i			0.00851710i
$519$	137752.	+	39247.1i	0.511402	+	0.145704i
$520$	−5278.91			−0.0195226
$521$		−	429560.i		−	1.58252i	−0.611483	−	0.791258i	$-0.709427\pi$
$521$		−	429560.i		−	1.58252i	0.611483	−	0.791258i	$-0.290573\pi$
$522$	−76055.7	−	47167.1i	−0.279120	−	0.173100i
$523$	330192.			1.20716			0.603578	−	0.797304i	$-0.293741\pi$
$523$	330192.			1.20716			0.603578	+	0.797304i	$0.293741\pi$
$524$		−	253149.i		−	0.921962i
$525$	−125433.	+	440254.i	−0.455087	+	1.59729i
$526$	−60971.2			−0.220370
$527$			8184.16i			0.0294681i
$528$	347736.	+	99074.1i	1.24733	+	0.355379i
$529$	−139999.			−0.500279
$530$			3674.99i			0.0130829i
$531$	−19346.7	+	31196.1i	−0.0686148	+	0.110640i
$532$	−413061.			−1.45945
$533$			53680.3i			0.188956i
$534$	−22784.6	+	79970.8i	−0.0799022	+	0.280446i
$535$	−706.819			−0.00246945
$536$		−	234483.i		−	0.816172i
$537$	289571.	+	82502.2i	1.00417	+	0.286099i
$538$	33009.3			0.114044
$539$		−	928055.i		−	3.19445i
$540$	−15692.6	−	17251.2i	−0.0538156	−	0.0591604i
$541$	−414323.			−1.41561			−0.707806	−	0.706407i	$-0.750315\pi$
$541$	−414323.			−1.41561			−0.707806	+	0.706407i	$0.750315\pi$
$542$			37979.2i			0.129285i
$543$	28343.3	−	99481.2i	0.0961282	−	0.337397i
$544$	58345.1			0.197154
$545$		−	43570.2i		−	0.146689i
$546$	55739.1	+	15880.7i	0.186971	+	0.0532703i
$547$	378149.			1.26383			0.631915	−	0.775038i	$-0.282269\pi$
$547$	378149.			1.26383			0.631915	+	0.775038i	$0.282269\pi$
$548$		−	256506.i		−	0.854154i
$549$	47624.6	+	29535.1i	0.158011	+	0.0979926i
$550$	−161698.			−0.534539
$551$		−	315233.i		−	1.03831i
$552$	59278.8	−	208061.i	0.194546	−	0.682829i
$553$	−966957.			−3.16196
$554$		−	70139.8i		−	0.228531i
$555$	−437.090	−	124.532i	−0.00141901	−	0.000404292i
$556$	−421822.			−1.36452
$557$			539510.i			1.73896i	0.493969	+	0.869479i	$0.335545\pi$
$557$			539510.i			1.73896i	−0.493969	+	0.869479i	$0.664455\pi$
$558$	−5976.85	+	9637.53i	−0.0191957	+	0.0309526i
$559$	107470.			0.343923
$560$		−	33834.3i		−	0.107890i
$561$	−37587.6	+	131927.i	−0.119432	+	0.419188i
$562$	171970.			0.544478
$563$		−	203932.i		−	0.643382i	−0.946845	−	0.321691i	$-0.895749\pi$
$563$		−	203932.i		−	0.643382i	0.946845	−	0.321691i	$-0.104251\pi$
$564$	−304711.	−	86815.7i	−0.957922	−	0.272923i
$565$	−11876.5			−0.0372041
$566$			105766.i			0.330151i
$567$	239173.	+	482053.i	0.743955	+	1.49944i
$568$	111129.			0.344453
$569$			120352.i			0.371730i	0.982575	+	0.185865i	$0.0595088\pi$
$569$			120352.i			0.371730i	−0.982575	+	0.185865i	$0.940491\pi$
$570$	−2289.58	+	8036.11i	−0.00704703	+	0.0247341i
$571$	455194.			1.39613			0.698063	−	0.716037i	$-0.254046\pi$
$571$	455194.			1.39613			0.698063	+	0.716037i	$0.254046\pi$
$572$		−	201257.i		−	0.615118i
$573$	183989.	+	52420.6i	0.560380	+	0.159659i
$574$	82839.3			0.251427
$575$		−	401825.i		−	1.21535i
$576$	−137555.	−	85306.8i	−0.414603	−	0.257122i
$577$	−313776.			−0.942470			−0.471235	−	0.882008i	$-0.656192\pi$
$577$	−313776.			−0.942470			−0.471235	+	0.882008i	$0.656192\pi$
$578$		−	95378.5i		−	0.285492i
$579$	106467.	−	373684.i	0.317583	−	1.11467i
$580$	29080.1			0.0864451
$581$			824956.i			2.44387i
$582$	−52598.6	−	14985.9i	−0.155284	−	0.0442423i
$583$	−294467.			−0.866362
$584$			344021.i			1.00869i
$585$	−6074.63	+	9795.20i	−0.0177504	+	0.0286221i
$586$	−19894.6			−0.0579350
$587$		−	71975.2i		−	0.208885i	−0.994531	−	0.104442i	$-0.966694\pi$
$587$		−	71975.2i		−	0.208885i	0.994531	−	0.104442i	$-0.0333058\pi$
$588$	−154934.	+	543797.i	−0.448118	+	1.57283i
$589$	−39945.3			−0.115142
$590$			1213.32i			0.00348556i
$591$	−254113.	−	72399.7i	−0.727531	−	0.207282i
$592$	−4293.23			−0.0122501
$593$			166539.i			0.473594i	0.971559	+	0.236797i	$0.0760977\pi$
$593$			166539.i			0.473594i	−0.971559	+	0.236797i	$0.923902\pi$
$594$	−140609.	+	127906.i	−0.398510	+	0.362507i
$595$	12836.4			0.0362584
$596$		−	105299.i		−	0.296435i
$597$	−107321.	+	376683.i	−0.301118	+	1.05688i
$598$	−50873.8			−0.142263
$599$			492294.i			1.37205i	0.727576	+	0.686027i	$0.240647\pi$
$599$			492294.i			1.37205i	−0.727576	+	0.686027i	$0.759353\pi$
$600$	199133.	+	56735.3i	0.553147	+	0.157598i
$601$	87508.3			0.242270			0.121135	−	0.992636i	$-0.461347\pi$
$601$	87508.3			0.242270			0.121135	+	0.992636i	$0.461347\pi$
$602$		−	165847.i		−	0.457629i
$603$	−435091.	−	269828.i	−1.19659	−	0.742082i
$604$	506453.			1.38824
$605$			69123.6i			0.188849i
$606$	−32321.4	+	113444.i	−0.0880127	+	0.308913i
$607$	330632.			0.897363			0.448681	−	0.893692i	$-0.351894\pi$
$607$	330632.			0.897363			0.448681	+	0.893692i	$0.351894\pi$
$608$			284771.i			0.770352i
$609$	−645338.	−	183864.i	−1.74001	−	0.495750i
$610$	1852.28			0.00497792
$611$			156591.i			0.419455i
$612$	44049.2	−	71028.2i	0.117607	−	0.189639i
$613$	−333860.			−0.888471			−0.444236	−	0.895910i	$-0.646525\pi$
$613$	−333860.			−0.888471			−0.444236	+	0.895910i	$0.646525\pi$
$614$		−	183894.i		−	0.487788i
$615$	−4514.04	+	15843.7i	−0.0119348	+	0.0418896i
$616$	−652749.			−1.72022
$617$		−	610711.i		−	1.60422i	−0.597173	−	0.802112i	$-0.703709\pi$
$617$		−	610711.i		−	1.60422i	0.597173	−	0.802112i	$-0.296291\pi$
$618$	−51815.7	−	14762.9i	−0.135670	−	0.0386540i
$619$	−46781.8			−0.122094			−0.0610472	−	0.998135i	$-0.519444\pi$
$619$	−46781.8			−0.122094			−0.0610472	+	0.998135i	$0.519444\pi$
$620$		−	3684.94i		−	0.00958621i
$621$	−317849.	−	349417.i	−0.824210	−	0.906067i
$622$	−79654.1			−0.205886
$623$			623476.i			1.60636i
$624$	−29833.4	+	104711.i	−0.0766185	+	0.268920i
$625$	381551.			0.976770
$626$			95168.8i			0.242854i
$627$	−643913.	−	183458.i	−1.63792	−	0.466661i
$628$	372333.			0.944087
$629$		−	1628.80i		−	0.00411687i
$630$	15115.9	+	9374.34i	0.0380849	+	0.0236189i
$631$	235618.			0.591767			0.295883	−	0.955224i	$-0.404386\pi$
$631$	235618.			0.591767			0.295883	+	0.955224i	$0.404386\pi$
$632$			437368.i			1.09500i
$633$	−107193.	+	376233.i	−0.267522	+	0.938966i
$634$	213535.			0.531240
$635$			32389.0i			0.0803248i
$636$	172544.	+	49159.7i	0.426565	+	0.121533i
$637$	279458.			0.688712
$638$		−	237022.i		−	0.582302i
$639$	127880.	−	206203.i	0.313184	−	0.505002i
$640$	−34292.2			−0.0837213
$641$			277801.i			0.676111i	0.941126	+	0.338056i	$0.109769\pi$
$641$			277801.i			0.676111i	−0.941126	+	0.338056i	$0.890231\pi$
$642$	961.777	−	3375.71i	0.00233348	−	0.00819020i
$643$	−433332.			−1.04809			−0.524045	−	0.851690i	$-0.675578\pi$
$643$	−433332.			−1.04809			−0.524045	+	0.851690i	$0.675578\pi$
$644$		−	771797.i		−	1.86094i
$645$	31719.5	+	9037.24i	0.0762442	+	0.0217228i
$646$	−29946.3			−0.0717593
$647$		−	629544.i		−	1.50390i	−0.659223	−	0.751948i	$-0.729115\pi$
$647$		−	629544.i		−	1.50390i	0.659223	−	0.751948i	$-0.270885\pi$
$648$	218039.	−	108181.i	0.519260	−	0.257634i
$649$	−97220.5			−0.230817
$650$		−	48690.9i		−	0.115245i
$651$	−23298.7	+	81775.1i	−0.0549755	+	0.192956i
$652$	3122.38			0.00734499
$653$		−	176659.i		−	0.414296i	−0.978310	−	0.207148i	$-0.933582\pi$
$653$		−	176659.i		−	0.414296i	0.978310	−	0.207148i	$-0.0664181\pi$
$654$	208088.	+	59286.5i	0.486509	+	0.138612i
$655$	−38396.9			−0.0894980
$656$			155621.i			0.361627i
$657$	638343.	+	395878.i	1.47885	+	0.917128i
$658$	241651.			0.558133
$659$			145776.i			0.335671i	0.985815	+	0.167836i	$0.0536778\pi$
$659$			145776.i			0.335671i	−0.985815	+	0.167836i	$0.946322\pi$
$660$	16923.9	−	59400.6i	0.0388520	−	0.136365i
$661$	−87225.2			−0.199636			−0.0998180	−	0.995006i	$-0.531826\pi$
$661$	−87225.2			−0.199636			−0.0998180	+	0.995006i	$0.531826\pi$
$662$			34825.7i			0.0794665i
$663$	−39726.2	−	11318.5i	−0.0903754	−	0.0257490i
$664$	373140.			0.846321
$665$			62651.9i			0.141674i
$666$	1189.51	−	1918.05i	0.00268175	−	0.00432426i
$667$	589008.			1.32394
$668$		−	58625.3i		−	0.131381i
$669$	−9200.63	+	32292.9i	−0.0205573	+	0.0721532i
$670$	−16922.2			−0.0376970
$671$			148419.i			0.329643i
$672$	582977.	+	166097.i	1.29096	+	0.367809i
$673$	−586965.			−1.29593			−0.647966	−	0.761669i	$-0.724380\pi$
$673$	−586965.			−1.29593			−0.647966	+	0.761669i	$0.724380\pi$
$674$			32300.2i			0.0711025i
$675$	334424.	−	304211.i	0.733989	−	0.667678i
$676$	−354181.			−0.775053
$677$			366982.i			0.800695i	0.916363	+	0.400348i	$0.131111\pi$
$677$			366982.i			0.800695i	−0.916363	+	0.400348i	$0.868889\pi$
$678$	16160.5	−	56721.0i	0.0351556	−	0.123391i
$679$	−410074.			−0.889452
$680$		−	5806.08i		−	0.0125564i
$681$	−665208.	−	189525.i	−1.43438	−	0.408670i
$682$	−30034.7			−0.0645735
$683$		−	139267.i		−	0.298543i	−0.988796	−	0.149272i	$-0.952307\pi$
$683$		−	139267.i		−	0.298543i	0.988796	−	0.149272i	$-0.0476929\pi$
$684$	346675.	+	214996.i	0.740987	+	0.459534i
$685$	−38906.1			−0.0829157
$686$		−	191907.i		−	0.407796i
$687$	135733.	−	476406.i	0.287590	−	1.00940i
$688$	311558.			0.658206
$689$		−	88670.5i		−	0.186785i
$690$	−15015.3	−	4278.04i	−0.0315382	−	0.00898559i
$691$	−413976.			−0.866999			−0.433500	−	0.901154i	$-0.642721\pi$
$691$	−413976.			−0.866999			−0.433500	+	0.901154i	$0.642721\pi$
$692$		−	231127.i		−	0.482657i
$693$	−751142.	+	1.21120e6i	−1.56407	+	2.52202i
$694$	204705.			0.425019
$695$			63980.8i			0.132459i
$696$	−83164.4	+	291896.i	−0.171680	+	0.602572i
$697$	−59041.0			−0.121531
$698$			82204.7i			0.168727i
$699$	−385089.	−	109716.i	−0.788146	−	0.224552i
$700$	738680.			1.50751
$701$		−	282729.i		−	0.575353i	−0.957728	−	0.287676i	$-0.907117\pi$
$701$		−	282729.i		−	0.575353i	0.957728	−	0.287676i	$-0.0928827\pi$
$702$	−38515.2	−	42340.3i	−0.0781552	−	0.0859172i
$703$	7949.88			0.0160861
$704$		−	428681.i		−	0.864947i
$705$	−13168.0	+	46217.8i	−0.0264936	+	0.0929888i
$706$	−282502.			−0.566776
$707$			884442.i			1.76942i
$708$	56966.7	+	16230.5i	0.113646	+	0.0323791i
$709$	603036.			1.19964			0.599820	−	0.800135i	$-0.295239\pi$
$709$	603036.			1.19964			0.599820	+	0.800135i	$0.295239\pi$
$710$		−	8019.94i		−	0.0159094i
$711$	811552.	+	503295.i	1.60538	+	0.995597i
$712$	282007.			0.556289
$713$		−	74637.2i		−	0.146817i
$714$	−17466.6	+	61305.4i	−0.0342619	+	0.120255i
$715$	−30526.1			−0.0597116
$716$		−	485858.i		−	0.947727i
$717$	669180.	+	190657.i	1.30168	+	0.370864i
$718$	273149.			0.529847
$719$		−	327772.i		−	0.634036i	−0.948419	−	0.317018i	$-0.897318\pi$
$719$		−	327772.i		−	0.634036i	0.948419	−	0.317018i	$-0.102682\pi$
$720$	−17610.6	+	28396.6i	−0.0339710	+	0.0547774i
$721$	−403970.			−0.777104
$722$			12233.9i			0.0234687i
$723$	120944.	−	424498.i	0.231371	−	0.812080i
$724$	−166915.			−0.318432
$725$			563735.i			1.07250i
$726$	−330128.	−	94057.3i	−0.626339	−	0.178451i
$727$	432025.			0.817410			0.408705	−	0.912667i	$-0.365981\pi$
$727$	432025.			0.817410			0.408705	+	0.912667i	$0.365981\pi$
$728$		−	196557.i		−	0.370874i
$729$	50171.2	−	529067.i	0.0944060	−	0.995534i
$730$	24827.4			0.0465892
$731$			118202.i			0.221202i
$732$	24777.7	−	86966.5i	0.0462423	−	0.162304i
$733$	−766148.			−1.42595			−0.712976	−	0.701188i	$-0.752653\pi$
$733$	−766148.			−1.42595			−0.712976	+	0.701188i	$0.752653\pi$
$734$			98438.6i			0.182715i
$735$	82481.6	+	23500.0i	0.152680	+	0.0435003i
$736$	−532090.			−0.982267
$737$		−	1.35593e6i		−	2.49633i
$738$	−69525.7	−	43117.3i	−0.127653	−	0.0791661i
$739$	243072.			0.445088			0.222544	−	0.974923i	$-0.428564\pi$
$739$	243072.			0.445088			0.222544	+	0.974923i	$0.428564\pi$
$740$			733.372i			0.00133925i
$741$	55243.3	−	193896.i	0.100610	−	0.353129i
$742$	−136836.			−0.248538
$743$			979859.i			1.77495i	0.460857	+	0.887474i	$0.347542\pi$
$743$			979859.i			1.77495i	−0.460857	+	0.887474i	$0.652458\pi$
$744$	36988.1	+	10538.3i	0.0668214	+	0.0190382i
$745$	−15971.4			−0.0287760
$746$			114041.i			0.204920i
$747$	429385.	−	692373.i	0.769495	−	1.24079i
$748$	221355.			0.395626
$749$		−	26318.0i		−	0.0469126i
$750$	8220.99	−	28854.5i	0.0146151	−	0.0512970i
$751$	−215652.			−0.382361			−0.191180	−	0.981555i	$-0.561232\pi$
$751$	−215652.			−0.382361			−0.191180	+	0.981555i	$0.561232\pi$
$752$			453964.i			0.802760i
$753$	−809212.	−	230554.i	−1.42716	−	0.406614i
$754$	71372.7			0.125542
$755$		−	76817.3i		−	0.134761i
$756$	642337.	−	584306.i	1.12388	−	1.02234i
$757$	−692690.			−1.20878			−0.604390	−	0.796688i	$-0.706583\pi$
$757$	−692690.			−1.20878			−0.604390	+	0.796688i	$0.706583\pi$
$758$			183640.i			0.319616i
$759$	342788.	−	1.20314e6i	0.595035	−	2.08849i
$760$	28338.4			0.0490622
$761$		−	651643.i		−	1.12523i	−0.826720	−	0.562614i	$-0.809796\pi$
$761$		−	651643.i		−	1.12523i	0.826720	−	0.562614i	$-0.190204\pi$
$762$	−154687.	−	44072.0i	−0.266406	−	0.0759020i
$763$	1.62231e6			2.78667
$764$		−	308706.i		−	0.528882i
$765$	−10773.4	−	6681.26i	−0.0184089	−	0.0114166i
$766$	187254.			0.319135
$767$		−	29275.2i		−	0.0497634i
$768$	−32184.1	+	112962.i	−0.0545656	+	0.191518i
$769$	227812.			0.385234			0.192617	−	0.981274i	$-0.438303\pi$
$769$	227812.			0.385234			0.192617	+	0.981274i	$0.438303\pi$
$770$			47107.7i			0.0794530i
$771$	−560217.	−	159612.i	−0.942426	−	0.268508i
$772$	−626986.			−1.05202
$773$		−	1.13056e6i		−	1.89206i	−0.324073	−	0.946032i	$-0.605052\pi$
$773$		−	1.13056e6i		−	1.89206i	0.324073	−	0.946032i	$-0.394948\pi$
$774$	−86322.1	+	139192.i	−0.144092	+	0.232345i
$775$	71434.6			0.118934
$776$			185482.i			0.308020i
$777$	4636.88	−	16274.8i	0.00768039	−	0.0269571i
$778$	−195592.			−0.323141
$779$		−	288168.i		−	0.474865i
$780$	17886.8	+	5096.17i	0.0293998	+	0.00837634i
$781$	642617.			1.05354
$782$		−	55954.2i		−	0.0914996i
$783$	445922.	+	490209.i	0.727336	+	0.799572i
$784$	810158.			1.31807
$785$		−	56474.4i		−	0.0916457i
$786$	52247.0	−	183380.i	0.0845701	−	0.296829i
$787$	688498.			1.11161			0.555806	−	0.831312i	$-0.312410\pi$
$787$	688498.			1.11161			0.555806	+	0.831312i	$0.312410\pi$
$788$			426364.i			0.686638i
$789$	434199.	+	123708.i	0.697485	+	0.198721i
$790$	31564.0			0.0505753
$791$		−	442214.i		−	0.706772i
$792$	547842.	+	339752.i	0.873384	+	0.541642i
$793$	−44692.2			−0.0710698
$794$		−	13642.2i		−	0.0216393i
$795$	7456.41	−	26171.0i	0.0117977	−	0.0414082i
$796$	632018.			0.997478
$797$			184085.i			0.289803i	0.989446	+	0.144901i	$0.0462865\pi$
$797$			184085.i			0.289803i	−0.989446	+	0.144901i	$0.953713\pi$
$798$	−299220.	−	85251.2i	−0.469878	−	0.133873i
$799$	−172229.			−0.269782
$800$		−	509259.i		−	0.795717i
$801$	324516.	−	523274.i	0.505790	−	0.815575i
$802$	105384.			0.163842
$803$			1.98935e6i			3.08518i
$804$	−226366.	+	794512.i	−0.350186	+	1.22910i
$805$	−117064.			−0.180647
$806$		−	9044.11i		−	0.0139218i
$807$	−235072.	−	66974.6i	−0.360955	−	0.102840i
$808$	400046.			0.612755
$809$			573172.i			0.875766i	0.899032	+	0.437883i	$0.144272\pi$
$809$			573172.i			0.875766i	−0.899032	+	0.437883i	$0.855728\pi$
$810$	−7807.25	−	15735.5i	−0.0118995	−	0.0239834i
$811$	624102.			0.948886			0.474443	−	0.880286i	$-0.342649\pi$
$811$	624102.			0.948886			0.474443	+	0.880286i	$0.342649\pi$
$812$			1.08278e6i			1.64221i
$813$	77058.4	−	270464.i	0.116584	−	0.409194i
$814$	5977.48			0.00902130
$815$		−	473.594i		−	0.000713003i
$816$	−115168.	−	32812.6i	−0.172962	−	0.0492788i
$817$	−576920.			−0.864314
$818$		−	114079.i		−	0.170490i
$819$	−364718.	−	226185.i	−0.543738	−	0.337207i
$820$	26583.3			0.0395350
$821$		−	284003.i		−	0.421344i	−0.977557	−	0.210672i	$-0.932435\pi$
$821$		−	284003.i		−	0.421344i	0.977557	−	0.210672i	$-0.0675652\pi$
$822$	52940.0	−	185812.i	0.0783502	−	0.274999i
$823$	−186913.			−0.275956			−0.137978	−	0.990435i	$-0.544060\pi$
$823$	−186913.			−0.275956			−0.137978	+	0.990435i	$0.544060\pi$
$824$			182722.i			0.269114i
$825$	1.15151e6	+	328080.i	1.69185	+	0.482027i
$826$	−45177.4			−0.0662157
$827$		−	960638.i		−	1.40459i	−0.711887	−	0.702294i	$-0.752159\pi$
$827$		−	960638.i		−	1.40459i	0.711887	−	0.702294i	$-0.247841\pi$
$828$	−401716.	+	647757.i	−0.585947	+	0.944825i
$829$	−487952.			−0.710016			−0.355008	−	0.934863i	$-0.615522\pi$
$829$	−487952.			−0.710016			−0.355008	+	0.934863i	$0.615522\pi$
$830$		−	26928.8i		−	0.0390895i
$831$	−142311.	+	499493.i	−0.206080	+	0.723314i
$832$	129085.			0.186479
$833$			307365.i			0.442960i
$834$	−305567.	−	87059.5i	−0.439313	−	0.125165i
$835$	−8892.13			−0.0127536
$836$			1.08039e6i			1.54585i
$837$	62117.7	−	56505.8i	0.0886674	−	0.0806569i
$838$	338051.			0.481387
$839$			964236.i			1.36981i	0.728634	+	0.684904i	$0.240156\pi$
$839$			964236.i			1.36981i	−0.728634	+	0.684904i	$0.759844\pi$
$840$	16528.7	−	58013.6i	0.0234251	−	0.0822188i
$841$	−119060.			−0.168334
$842$		−	342453.i		−	0.483032i
$843$	−1.22467e6	−	348921.i	−1.72331	−	0.490990i
$844$	631264.			0.886188
$845$			53721.2i			0.0752371i
$846$	−202814.	−	125778.i	−0.283372	−	0.175737i
$847$	−2.57378e6			−3.58760
$848$		−	257059.i		−	0.357471i
$849$	214595.	−	753200.i	0.297718	−	1.04495i
$850$	53553.3			0.0741222
$851$			14854.2i			0.0205112i
$852$	−376544.	−	107282.i	−0.518724	−	0.147790i
$853$	−1.13482e6			−1.55965			−0.779827	−	0.625995i	$-0.784693\pi$
$853$	−1.13482e6			−1.55965			−0.779827	+	0.625995i	$0.784693\pi$
$854$			68968.7i			0.0945663i
$855$	32609.9	−	52582.8i	0.0446085	−	0.0719302i
$856$	−11904.0			−0.0162460
$857$			19870.1i			0.0270544i	0.999909	+	0.0135272i	$0.00430598\pi$
$857$			19870.1i			0.0270544i	−0.999909	+	0.0135272i	$0.995694\pi$
$858$	41537.1	−	145790.i	0.0564238	−	0.198040i
$859$	1.29296e6			1.75226			0.876128	−	0.482079i	$-0.160118\pi$
$859$	1.29296e6			1.75226			0.876128	+	0.482079i	$0.160118\pi$
$860$		−	53220.6i		−	0.0719586i
$861$	−589930.	−	168078.i	−0.795782	−	0.226727i
$862$	−334524.			−0.450208
$863$			489254.i			0.656920i	0.944518	+	0.328460i	$0.106530\pi$
$863$			489254.i			0.656920i	−0.944518	+	0.328460i	$0.893470\pi$
$864$	−402831.	−	442838.i	−0.539629	−	0.593223i
$865$	−35056.7			−0.0468532
$866$		−	32399.1i		−	0.0432013i
$867$	−193519.	+	679227.i	−0.257446	+	0.903601i
$868$	137207.			0.182111
$869$			2.52914e6i			3.34915i
$870$	21065.6	+	6001.82i	0.0278314	+	0.00792947i
$871$	408301.			0.538200
$872$		−	733795.i		−	0.965033i
$873$	344169.	+	213441.i	0.451588	+	0.280059i
$874$	273102.			0.357521
$875$		−	224959.i		−	0.293823i
$876$	332112.	−	1.16567e6i	0.432789	−	1.51903i
$877$	−533017.			−0.693014			−0.346507	−	0.938047i	$-0.612632\pi$
$877$	−533017.			−0.693014			−0.346507	+	0.938047i	$0.612632\pi$
$878$		−	180353.i		−	0.233956i
$879$	141677.	+	40365.5i	0.183368	+	0.0522435i
$880$	−88496.1			−0.114277
$881$			818217.i			1.05418i	0.849808	+	0.527092i	$0.176718\pi$
$881$			818217.i			1.05418i	−0.849808	+	0.527092i	$0.823282\pi$
$882$	−224467.	+	361948.i	−0.288547	+	0.465275i
$883$	−622062.			−0.797834			−0.398917	−	0.916987i	$-0.630614\pi$
$883$	−622062.			−0.797834			−0.398917	+	0.916987i	$0.630614\pi$
$884$			66654.8i			0.0852956i
$885$	2461.79	−	8640.55i	0.00314315	−	0.0110320i
$886$	123636.			0.157499
$887$			704902.i			0.895946i	0.894047	+	0.447973i	$0.147854\pi$
$887$			704902.i			0.895946i	−0.894047	+	0.447973i	$0.852146\pi$
$888$	−7361.33	−	2097.33i	−0.00933534	−	0.00265974i
$889$	−1.20598e6			−1.52594
$890$		−	20351.9i		−	0.0256936i
$891$	1.26084e6	−	625575.i	1.58820	−	0.787996i
$892$	54182.8			0.0680976
$893$		−	840617.i		−	1.05413i
$894$	21732.4	−	76277.9i	0.0271915	−	0.0954385i
$895$	−73693.6			−0.0919991
$896$		−	1.27685e6i		−	1.59047i
$897$	362292.	+	103221.i	0.450271	+	0.128287i
$898$	−65404.6			−0.0811065
$899$			104711.i			0.129561i
$900$	−619963.	−	384479.i	−0.765386	−	0.474665i
$901$	97525.4			0.120135
$902$		−	216672.i		−	0.266311i
$903$	−336497.	+	1.18106e6i	−0.412672	+	1.44842i
$904$	−200020.			−0.244758
$905$			25317.2i			0.0309113i
$906$	366873.	+	104526.i	0.446950	+	0.127341i
$907$	−118084.			−0.143541			−0.0717707	−	0.997421i	$-0.522865\pi$
$907$	−118084.			−0.143541			−0.0717707	+	0.997421i	$0.522865\pi$
$908$			1.11612e6i			1.35375i
$909$	460347.	−	742298.i	0.557131	−	0.898360i
$910$	−14185.2			−0.0171298
$911$			744970.i			0.897640i	0.893622	+	0.448820i	$0.148155\pi$
$911$			744970.i			0.897640i	−0.893622	+	0.448820i	$0.851845\pi$
$912$	160152.	−	562112.i	0.192550	−	0.675824i
$913$	2.15773e6			2.58855
$914$			199626.i			0.238960i
$915$	−13190.8	−	3758.22i	−0.0157554	−	0.00448890i
$916$	−799338.			−0.952663
$917$		−	1.42968e6i		−	1.70021i
$918$	46568.5	−	42361.4i	0.0552595	−	0.0502672i
$919$	640238.			0.758072			0.379036	−	0.925382i	$-0.376256\pi$
$919$	640238.			0.758072			0.379036	+	0.925382i	$0.376256\pi$
$920$			52949.7i			0.0625588i
$921$	−373114.	+	1.30958e6i	−0.439868	+	1.54388i
$922$	−349883.			−0.411586
$923$			193506.i			0.227139i
$924$	2.21175e6	+	630152.i	2.59055	+	0.738077i
$925$	−14216.8			−0.0166157
$926$			480011.i			0.559795i
$927$	339046.	+	210264.i	0.394547	+	0.244684i
$928$	746489.			0.866817
$929$		−	1.23729e6i		−	1.43364i	−0.697259	−	0.716820i	$-0.745597\pi$
$929$		−	1.23729e6i		−	1.43364i	0.697259	−	0.716820i	$-0.254403\pi$
$930$	760.530	−	2669.36i	0.000879327	−	0.00308632i
$931$	−1.50019e6			−1.73080
$932$			646122.i			0.743846i
$933$	567248.	+	161615.i	0.651643	+	0.185660i
$934$	167191.			0.191655
$935$		−	33574.4i		−	0.0384048i
$936$	−102307.	+	164967.i	−0.116776	+	0.188298i
$937$	−574329.			−0.654157			−0.327078	−	0.944997i	$-0.606064\pi$
$937$	−574329.			−0.654157			−0.327078	+	0.944997i	$0.606064\pi$
$938$		−	630088.i		−	0.716136i
$939$	193094.	−	677733.i	0.218997	−	0.768648i
$940$	77546.6			0.0877621
$941$			1.35247e6i			1.52738i	0.645581	+	0.763691i	$0.276615\pi$
$941$			1.35247e6i			1.52738i	−0.645581	+	0.763691i	$0.723385\pi$
$942$	269717.	+	76845.4i	0.303953	+	0.0865996i
$943$	538437.			0.605496
$944$		−	84869.9i		−	0.0952379i
$945$	−88626.0	−	97427.9i	−0.0992424	−	0.109099i
$946$	−433783.			−0.484720
$947$		−	283995.i		−	0.316673i	−0.987385	−	0.158337i	$-0.949387\pi$
$947$		−	283995.i		−	0.316673i	0.987385	−	0.158337i	$-0.0506131\pi$
$948$	422228.	−	1.48196e6i	0.469818	−	1.64900i
$949$	−599038.			−0.665153
$950$			261383.i			0.289621i
$951$	−1.52067e6	−	433255.i	−1.68141	−	0.479052i
$952$	216186.			0.238536
$953$		−	300012.i		−	0.330334i	−0.986266	−	0.165167i	$-0.947184\pi$
$953$		−	300012.i		−	0.330334i	0.986266	−	0.165167i	$-0.0528163\pi$
$954$	114844.	+	71222.3i	0.126186	+	0.0782563i
$955$	−46823.7			−0.0513404
$956$		−	1.12278e6i		−	1.22852i
$957$	−480910.	+	1.68793e6i	−0.525097	+	1.84302i
$958$	−446271.			−0.486259
$959$		−	1.44865e6i		−	1.57516i
$960$	38099.4	+	10854.9i	0.0413405	+	0.0117784i
$961$	−910252.			−0.985633
$962$			1799.95i			0.00194496i
$963$	−13698.4	+	22088.3i	−0.0147712	+	0.0238182i
$964$	−712244.			−0.766434
$965$			95099.6i			0.102123i
$966$	159290.	−	559087.i	0.170701	−	0.599136i
$967$	150053.			0.160469			0.0802347	−	0.996776i	$-0.474433\pi$
$967$	150053.			0.160469			0.0802347	+	0.996776i	$0.474433\pi$
$968$			1.16416e6i			1.24240i
$969$	213259.	+	60760.0i	0.227123	+	0.0647098i
$970$	13385.9			0.0142267
$971$			1.41303e6i			1.49869i	0.662180	+	0.749345i	$0.269631\pi$
$971$			1.41303e6i			1.49869i	−0.662180	+	0.749345i	$0.730369\pi$
$972$	−843232.	+	156066.i	−0.892513	+	0.165187i
$973$	−2.38229e6			−2.51634
$974$		−	145719.i		−	0.153602i
$975$	−98792.0	+	346747.i	−0.103923	+	0.364756i
$976$	−129564.			−0.136014
$977$		−	1.06266e6i		−	1.11328i	−0.830755	−	0.556639i	$-0.812091\pi$
$977$		−	1.06266e6i		−	1.11328i	0.830755	−	0.556639i	$-0.187909\pi$
$978$	2261.84	+	644.425i	0.00236475	+	0.000673744i
$979$	1.63075e6			1.70146
$980$		−	138392.i		−	0.144098i
$981$	−1.36158e6	−	844404.i	−1.41483	−	0.877430i
$982$	465963.			0.483201
$983$		−	267160.i		−	0.276481i	−0.990399	−	0.138240i	$-0.955855\pi$
$983$		−	267160.i		−	0.276481i	0.990399	−	0.138240i	$-0.0441446\pi$
$984$	−76024.0	+	266834.i	−0.0785164	+	0.275582i
$985$	64669.7			0.0666543
$986$			78500.1i			0.0807452i
$987$	−1.72089e6	−	490302.i	−1.76652	−	0.503302i
$988$	−325329.			−0.333280
$989$		−	1.07797e6i		−	1.10208i
$990$	24519.3	−	39536.7i	0.0250171	−	0.0403395i
$991$	91727.5			0.0934011			0.0467006	−	0.998909i	$-0.485129\pi$
$991$	91727.5			0.0934011			0.0467006	+	0.998909i	$0.485129\pi$
$992$		−	94592.6i		−	0.0961244i
$993$	70660.1	−	248007.i	0.0716598	−	0.251516i
$994$	298618.			0.302234
$995$		−	95862.7i		−	0.0968286i
$996$	−1.26433e6	−	360222.i	−1.27451	−	0.363121i
$997$	921517.			0.927071			0.463536	−	0.886078i	$-0.346581\pi$
$997$	921517.			0.927071			0.463536	+	0.886078i	$0.346581\pi$
$998$		−	386812.i		−	0.388364i
$999$	−12362.6	+	11245.7i	−0.0123874	+	0.0112682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.35	✓	78
3.2	odd	2	inner	177.5.b.a.119.44	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.35	✓	78	1.1	even	1	trivial
177.5.b.a.119.44	yes	78	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.21543i q^{2} +(-2.46606 + 8.65555i) q^{3} +14.5227 q^{4} -2.20277i q^{5} +(10.5202 + 2.99733i) q^{6} +82.0188 q^{7} -37.0983i q^{8} +(-68.8371 - 42.6903i) q^{9} +O(q^{10})\)	\(q-1.21543i q^{2} +(-2.46606 + 8.65555i) q^{3} +14.5227 q^{4} -2.20277i q^{5} +(10.5202 + 2.99733i) q^{6} +82.0188 q^{7} -37.0983i q^{8} +(-68.8371 - 42.6903i) q^{9} -2.67731 q^{10} -214.526i q^{11} +(-35.8140 + 125.702i) q^{12} +64.5985 q^{13} -99.6881i q^{14} +(19.0662 + 5.43216i) q^{15} +187.273 q^{16} +71.0494i q^{17} +(-51.8871 + 83.6667i) q^{18} -346.779 q^{19} -31.9902i q^{20} +(-202.264 + 709.917i) q^{21} -260.741 q^{22} -647.950i q^{23} +(321.106 + 91.4867i) q^{24} +620.148 q^{25} -78.5150i q^{26} +(539.264 - 490.546i) q^{27} +1191.14 q^{28} +909.033i q^{29} +(6.60242 - 23.1736i) q^{30} +115.190 q^{31} -821.190i q^{32} +(1856.84 + 529.035i) q^{33} +86.3557 q^{34} -180.668i q^{35} +(-999.702 - 619.979i) q^{36} -22.9249 q^{37} +421.486i q^{38} +(-159.304 + 559.135i) q^{39} -81.7188 q^{40} +830.984i q^{41} +(862.855 + 245.837i) q^{42} +1663.65 q^{43} -3115.50i q^{44} +(-94.0367 + 151.632i) q^{45} -787.539 q^{46} +2424.07i q^{47} +(-461.828 + 1620.95i) q^{48} +4326.08 q^{49} -753.747i q^{50} +(-614.972 - 175.212i) q^{51} +938.146 q^{52} -1372.64i q^{53} +(-596.224 - 655.439i) q^{54} -472.551 q^{55} -3042.75i q^{56} +(855.179 - 3001.56i) q^{57} +1104.87 q^{58} -453.188i q^{59} +(276.893 + 78.8899i) q^{60} -691.845 q^{61} -140.005i q^{62} +(-5645.93 - 3501.40i) q^{63} +1998.27 q^{64} -142.295i q^{65} +(643.005 - 2256.86i) q^{66} +6320.59 q^{67} +1031.83i q^{68} +(5608.37 + 1597.89i) q^{69} -219.590 q^{70} +2995.52i q^{71} +(-1583.74 + 2553.73i) q^{72} -9273.25 q^{73} +27.8637i q^{74} +(-1529.32 + 5367.72i) q^{75} -5036.17 q^{76} -17595.1i q^{77} +(679.590 + 193.623i) q^{78} -11789.5 q^{79} -412.519i q^{80} +(2916.08 + 5877.35i) q^{81} +1010.00 q^{82} +10058.1i q^{83} +(-2937.42 + 10309.9i) q^{84} +156.505 q^{85} -2022.06i q^{86} +(-7868.18 - 2241.73i) q^{87} -7958.54 q^{88} +7601.63i q^{89} +(184.298 + 114.295i) q^{90} +5298.29 q^{91} -9410.01i q^{92} +(-284.065 + 997.029i) q^{93} +2946.29 q^{94} +763.873i q^{95} +(7107.85 + 2025.11i) q^{96} -4999.76 q^{97} -5258.05i q^{98} +(-9158.17 + 14767.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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