LMFDB - Embedded newform 177.4.d.c.176.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(176,177)]

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, 1]))

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

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.12
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.85434 q^{2} +(-4.18856 + 3.07505i) q^{3} +6.85594 q^{4} +0.146910i q^{5} +(16.1441 - 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 - 25.7601i) q^{9} +O(q^{10})$	\(q-3.85434 q^{2} +(-4.18856 + 3.07505i) q^{3} +6.85594 q^{4} +0.146910i q^{5} +(16.1441 - 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 - 25.7601i) q^{9} -0.566243i q^{10} +16.8186 q^{11} +(-28.7165 + 21.0824i) q^{12} -51.2069i q^{13} +94.2076 q^{14} +(-0.451757 - 0.615343i) q^{15} -71.8436 q^{16} -61.9717i q^{17} +(-31.1743 + 99.2882i) q^{18} -98.2877 q^{19} +1.00721i q^{20} +(102.377 - 75.1603i) q^{21} -64.8246 q^{22} +40.4578 q^{23} +(-18.4699 + 13.5597i) q^{24} +124.978 q^{25} +197.369i q^{26} +(45.3362 + 132.769i) q^{27} -167.572 q^{28} +235.127i q^{29} +(1.74123 + 2.37174i) q^{30} +306.017i q^{31} +241.633 q^{32} +(-70.4458 + 51.7181i) q^{33} +238.860i q^{34} -3.59077i q^{35} +(55.4515 - 176.610i) q^{36} -353.773i q^{37} +378.834 q^{38} +(157.464 + 214.483i) q^{39} +0.647815i q^{40} +259.306i q^{41} +(-394.594 + 289.693i) q^{42} +58.9877i q^{43} +115.307 q^{44} +(3.78443 + 1.18822i) q^{45} -155.938 q^{46} +36.9696 q^{47} +(300.921 - 220.923i) q^{48} +254.408 q^{49} -481.709 q^{50} +(190.566 + 259.572i) q^{51} -351.072i q^{52} +105.746i q^{53} +(-174.741 - 511.737i) q^{54} +2.47083i q^{55} -107.779 q^{56} +(411.684 - 302.240i) q^{57} -906.258i q^{58} +(-384.876 + 239.268i) q^{59} +(-3.09722 - 4.21876i) q^{60} +270.462i q^{61} -1179.49i q^{62} +(-197.689 + 629.627i) q^{63} -356.587 q^{64} +7.52283 q^{65} +(271.522 - 199.339i) q^{66} -201.641i q^{67} -424.874i q^{68} +(-169.460 + 124.410i) q^{69} +13.8401i q^{70} -659.691i q^{71} +(35.6652 - 113.592i) q^{72} +604.150i q^{73} +1363.56i q^{74} +(-523.480 + 384.315i) q^{75} -673.855 q^{76} -411.079 q^{77} +(-606.920 - 826.692i) q^{78} +496.729 q^{79} -10.5546i q^{80} +(-598.166 - 416.700i) q^{81} -999.455i q^{82} +1456.75 q^{83} +(701.888 - 515.294i) q^{84} +9.10429 q^{85} -227.359i q^{86} +(-723.027 - 984.843i) q^{87} +74.1632 q^{88} +145.988 q^{89} +(-14.5865 - 4.57982i) q^{90} +1251.60i q^{91} +277.377 q^{92} +(-941.017 - 1281.77i) q^{93} -142.493 q^{94} -14.4395i q^{95} +(-1012.09 + 743.034i) q^{96} -1332.12i q^{97} -980.577 q^{98} +(136.030 - 433.249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

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 $

$2$	−3.85434			−1.36272			−0.681358	−	0.731951i	$-0.738610\pi$
$2$	−3.85434			−1.36272			−0.681358	+	0.731951i	$0.738610\pi$
$3$	−4.18856	+	3.07505i	−0.806089	+	0.591794i
$3$	−4.18856	+	3.07505i	−0.806089	+	0.591794i
$4$	6.85594			0.856993
$5$			0.146910i			0.0131401i	0.999978	+	0.00657003i	$0.00209132\pi$
$5$			0.146910i			0.0131401i	−0.999978	+	0.00657003i	$0.997909\pi$
$6$	16.1441	−	11.8523i	1.09847	−	0.806447i
$7$	−24.4419			−1.31974			−0.659870	−	0.751379i	$-0.729389\pi$
$7$	−24.4419			−1.31974			−0.659870	+	0.751379i	$0.729389\pi$
$8$	4.40959			0.194878
$9$	8.08809	−	25.7601i	0.299559	−	0.954078i
$10$		−	0.566243i		−	0.0179062i
$11$	16.8186			0.461000			0.230500	−	0.973072i	$-0.425964\pi$
$11$	16.8186			0.461000			0.230500	+	0.973072i	$0.425964\pi$
$12$	−28.7165	+	21.0824i	−0.690812	+	0.507163i
$13$		−	51.2069i		−	1.09248i	−0.837628	−	0.546240i	$-0.816058\pi$
$13$		−	51.2069i		−	1.09248i	0.837628	−	0.546240i	$-0.183942\pi$
$14$	94.2076			1.79843
$15$	−0.451757	−	0.615343i	−0.00777622	−	0.0105921i
$16$	−71.8436			−1.12256
$17$		−	61.9717i		−	0.884138i	−0.896981	−	0.442069i	$-0.854245\pi$
$17$		−	61.9717i		−	0.884138i	0.896981	−	0.442069i	$-0.145755\pi$
$18$	−31.1743	+	99.2882i	−0.408213	+	1.30014i
$19$	−98.2877			−1.18678			−0.593388	−	0.804916i	$-0.702210\pi$
$19$	−98.2877			−1.18678			−0.593388	+	0.804916i	$0.702210\pi$
$20$			1.00721i			0.0112609i
$21$	102.377	−	75.1603i	1.06383	−	0.781015i
$22$	−64.8246			−0.628212
$23$	40.4578			0.366785			0.183392	−	0.983040i	$-0.441292\pi$
$23$	40.4578			0.366785			0.183392	+	0.983040i	$0.441292\pi$
$24$	−18.4699	+	13.5597i	−0.157089	+	0.115328i
$25$	124.978			0.999827
$26$			197.369i			1.48874i
$27$	45.3362	+	132.769i	0.323147	+	0.946349i
$28$	−167.572			−1.13101
$29$			235.127i			1.50558i	0.658259	+	0.752792i	$0.271293\pi$
$29$			235.127i			1.50558i	−0.658259	+	0.752792i	$0.728707\pi$
$30$	1.74123	+	2.37174i	0.0105968	+	0.0144340i
$31$			306.017i			1.77297i	0.462753	+	0.886487i	$0.346862\pi$
$31$			306.017i			1.77297i	−0.462753	+	0.886487i	$0.653138\pi$
$32$	241.633			1.33485
$33$	−70.4458	+	51.7181i	−0.371607	+	0.272817i
$34$			238.860i			1.20483i
$35$		−	3.59077i		−	0.0173415i
$36$	55.4515	−	176.610i	0.256720	−	0.817638i
$37$		−	353.773i		−	1.57189i	−0.618298	−	0.785944i	$-0.712177\pi$
$37$		−	353.773i		−	1.57189i	0.618298	−	0.785944i	$-0.287823\pi$
$38$	378.834			1.61724
$39$	157.464	+	214.483i	0.646524	+	0.880637i
$40$			0.647815i			0.00256071i
$41$			259.306i			0.987728i	0.869539	+	0.493864i	$0.164416\pi$
$41$			259.306i			0.987728i	−0.869539	+	0.493864i	$0.835584\pi$
$42$	−394.594	+	289.693i	−1.44970	+	1.06430i
$43$			58.9877i			0.209199i	0.994514	+	0.104599i	$0.0333560\pi$
$43$			58.9877i			0.209199i	−0.994514	+	0.104599i	$0.966644\pi$
$44$	115.307			0.395074
$45$	3.78443	+	1.18822i	0.0125366	+	0.00393622i
$46$	−155.938			−0.499823
$47$	36.9696			0.114736			0.0573678	−	0.998353i	$-0.481729\pi$
$47$	36.9696			0.114736			0.0573678	+	0.998353i	$0.481729\pi$
$48$	300.921	−	220.923i	0.904880	−	0.664322i
$49$	254.408			0.741715
$50$	−481.709			−1.36248
$51$	190.566	+	259.572i	0.523228	+	0.712694i
$52$		−	351.072i		−	0.936248i
$53$			105.746i			0.274064i	0.990567	+	0.137032i	$0.0437563\pi$
$53$			105.746i			0.274064i	−0.990567	+	0.137032i	$0.956244\pi$
$54$	−174.741	−	511.737i	−0.440357	−	1.28960i
$55$			2.47083i			0.00605757i
$56$	−107.779			−0.257189
$57$	411.684	−	302.240i	0.956647	−	0.702328i
$58$		−	906.258i		−	2.05168i
$59$	−384.876	+	239.268i	−0.849265	+	0.527967i
$59$	−384.876	+	239.268i	−0.849265	+	0.527967i
$60$	−3.09722	−	4.21876i	−0.00666416	−	0.00907732i
$61$			270.462i			0.567690i	0.958870	+	0.283845i	$0.0916101\pi$
$61$			270.462i			0.567690i	−0.958870	+	0.283845i	$0.908390\pi$
$62$		−	1179.49i		−	2.41606i
$63$	−197.689	+	629.627i	−0.395340	+	1.25914i
$64$	−356.587			−0.696459
$65$	7.52283			0.0143553
$66$	271.522	−	199.339i	0.506395	−	0.371772i
$67$		−	201.641i		−	0.367678i	−0.982956	−	0.183839i	$-0.941147\pi$
$67$		−	201.641i		−	0.367678i	0.982956	−	0.183839i	$-0.0588525\pi$
$68$		−	424.874i		−	0.757700i
$69$	−169.460	+	124.410i	−0.295661	+	0.217061i
$70$			13.8401i			0.0236315i
$71$		−	659.691i		−	1.10269i	−0.834278	−	0.551345i	$-0.814115\pi$
$71$		−	659.691i		−	1.10269i	0.834278	−	0.551345i	$-0.185885\pi$
$72$	35.6652	−	113.592i	0.0583776	−	0.185929i
$73$			604.150i			0.968636i	0.874892	+	0.484318i	$0.160932\pi$
$73$			604.150i			0.968636i	−0.874892	+	0.484318i	$0.839068\pi$
$74$			1363.56i			2.14204i
$75$	−523.480	+	384.315i	−0.805950	+	0.591692i
$76$	−673.855			−1.01706
$77$	−411.079			−0.608401
$78$	−606.920	−	826.692i	−0.881028	−	1.20006i
$79$	496.729			0.707422			0.353711	−	0.935355i	$-0.384920\pi$
$79$	496.729			0.707422			0.353711	+	0.935355i	$0.384920\pi$
$80$		−	10.5546i		−	0.0147505i
$81$	−598.166	−	416.700i	−0.820529	−	0.571605i
$82$		−	999.455i		−	1.34599i
$83$	1456.75			1.92649			0.963246	−	0.268620i	$-0.0865675\pi$
$83$	1456.75			1.92649			0.963246	+	0.268620i	$0.0865675\pi$
$84$	701.888	−	515.294i	0.911693	−	0.669324i
$85$	9.10429			0.0116176
$86$		−	227.359i		−	0.285078i
$87$	−723.027	−	984.843i	−0.890996	−	1.21363i
$88$	74.1632			0.0898389
$89$	145.988			0.173874			0.0869368	−	0.996214i	$-0.472292\pi$
$89$	145.988			0.173874			0.0869368	+	0.996214i	$0.472292\pi$
$90$	−14.5865	−	4.57982i	−0.0170839	−	0.00536395i
$91$			1251.60i			1.44179i
$92$	277.377			0.314332
$93$	−941.017	−	1281.77i	−1.04924	−	1.42918i
$94$	−142.493			−0.156352
$95$		−	14.4395i		−	0.0155943i
$96$	−1012.09	+	743.034i	−1.07600	+	0.789954i
$97$		−	1332.12i		−	1.39440i	−0.716878	−	0.697198i	$-0.754430\pi$
$97$		−	1332.12i		−	1.39440i	0.716878	−	0.697198i	$-0.245570\pi$
$98$	−980.577			−1.01075
$99$	136.030	−	433.249i	0.138097	−	0.439830i
$100$	856.845			0.856845
$101$	1810.79			1.78397			0.891984	−	0.452067i	$-0.149313\pi$
$101$	1810.79			1.78397			0.891984	+	0.452067i	$0.149313\pi$
$102$	−734.507	−	1000.48i	−0.713010	−	0.971199i
$103$			1377.13i			1.31740i	0.752405	+	0.658701i	$0.228894\pi$
$103$			1377.13i			1.31740i	−0.752405	+	0.658701i	$0.771106\pi$
$104$		−	225.802i		−	0.212901i
$105$	11.0418	+	15.0402i	0.0102626	+	0.0139788i
$106$		−	407.582i		−	0.373471i
$107$			1084.01i			0.979390i	0.871894	+	0.489695i	$0.162892\pi$
$107$			1084.01i			0.979390i	−0.871894	+	0.489695i	$0.837108\pi$
$108$	310.823	+	910.257i	0.276934	+	0.811014i
$109$			455.929i			0.400643i	0.979730	+	0.200322i	$0.0641987\pi$
$109$			455.929i			0.400643i	−0.979730	+	0.200322i	$0.935801\pi$
$110$		−	9.52341i		−	0.00825474i
$111$	1087.87	+	1481.80i	0.930235	+	1.26708i
$112$	1756.00			1.48148
$113$	−356.645			−0.296905			−0.148453	−	0.988920i	$-0.547429\pi$
$113$	−356.645			−0.296905			−0.148453	+	0.988920i	$0.547429\pi$
$114$	−1586.77	+	1164.94i	−1.30364	+	0.957073i
$115$			5.94368i			0.00481957i
$116$			1612.01i			1.29027i
$117$	−1319.10	−	414.166i	−1.04231	−	0.327262i
$118$	1483.44	−	922.220i	1.15731	−	0.719468i
$119$			1514.71i			1.16683i
$120$	−1.99207	−	2.71341i	−0.00151542	−	0.00206416i
$121$	−1048.13			−0.787479
$122$		−	1042.45i		−	0.773600i
$123$	−797.381	−	1086.12i	−0.584532	−	0.796197i
$124$			2098.03i			1.51943i
$125$			36.7244i			0.0262779i
$126$	761.959	−	2426.80i	0.538736	−	1.71584i
$127$	−467.771			−0.326834			−0.163417	−	0.986557i	$-0.552252\pi$
$127$	−467.771			−0.326834			−0.163417	+	0.986557i	$0.552252\pi$
$128$	−558.657			−0.385771
$129$	−181.390	−	247.074i	−0.123803	−	0.168633i
$130$	−28.9956			−0.0195621
$131$	2005.53			1.33759			0.668795	−	0.743447i	$-0.266811\pi$
$131$	2005.53			1.33759			0.668795	+	0.743447i	$0.266811\pi$
$132$	−482.972	+	354.576i	−0.318464	+	0.233802i
$133$	2402.34			1.56624
$134$			777.195i			0.501040i
$135$	−19.5052	+	6.66036i	−0.0124351	+	0.00424617i
$136$		−	273.270i		−	0.172299i
$137$			1176.51i			0.733695i	0.930281	+	0.366848i	$0.119563\pi$
$137$			1176.51i			0.733695i	−0.930281	+	0.366848i	$0.880437\pi$
$138$	653.157	−	479.519i	0.402902	−	0.295792i
$139$	1219.44			0.744111			0.372055	−	0.928210i	$-0.378653\pi$
$139$	1219.44			0.744111			0.372055	+	0.928210i	$0.378653\pi$
$140$		−	24.6181i		−	0.0148615i
$141$	−154.849	+	113.684i	−0.0924871	+	0.0678999i
$142$			2542.67i			1.50265i
$143$		−	861.229i		−	0.503634i
$144$	−581.078	+	1850.70i	−0.336272	+	1.07101i
$145$	−34.5426			−0.0197835
$146$		−	2328.60i		−	1.31998i
$147$	−1065.61	+	782.319i	−0.597889	+	0.438943i
$148$		−	2425.44i		−	1.34710i
$149$	2092.78			1.15065			0.575327	−	0.817924i	$-0.304875\pi$
$149$	2092.78			1.15065			0.575327	+	0.817924i	$0.304875\pi$
$150$	2017.67	−	1481.28i	1.09828	−	0.806308i
$151$			1352.06i			0.728668i	0.931268	+	0.364334i	$0.118703\pi$
$151$			1352.06i			0.728668i	−0.931268	+	0.364334i	$0.881297\pi$
$152$	−433.409			−0.231277
$153$	−1596.40	−	501.233i	−0.843536	−	0.264851i
$154$	1584.44			0.829077
$155$	−44.9570			−0.0232970
$156$	1079.56	+	1470.49i	0.554066	+	0.754699i
$157$			2269.35i			1.15359i	0.816888	+	0.576797i	$0.195698\pi$
$157$			2269.35i			1.15359i	−0.816888	+	0.576797i	$0.804302\pi$
$158$	−1914.56			−0.964015
$159$	−325.176	−	442.925i	−0.162189	−	0.220920i
$160$			35.4984i			0.0175400i
$161$	−988.868			−0.484060
$162$	2305.53	+	1606.10i	1.11815	+	0.778935i
$163$	−253.195			−0.121667			−0.0608336	−	0.998148i	$-0.519376\pi$
$163$	−253.195			−0.121667			−0.0608336	+	0.998148i	$0.519376\pi$
$164$			1777.79i			0.846476i
$165$	−7.59793	−	10.3492i	−0.00358484	−	0.00488294i
$166$	−5614.80			−2.62526
$167$			1565.36i			0.725335i	0.931919	+	0.362668i	$0.118134\pi$
$167$			1565.36i			0.725335i	−0.931919	+	0.362668i	$0.881866\pi$
$168$	451.439	−	331.426i	0.207317	−	0.152203i
$169$	−425.151			−0.193514
$170$	−35.0910			−0.0158315
$171$	−794.960	+	2531.90i	−0.355509	+	1.13228i
$172$			404.416i			0.179282i
$173$	2408.08			1.05828			0.529142	−	0.848534i	$-0.322514\pi$
$173$	2408.08			1.05828			0.529142	+	0.848534i	$0.322514\pi$
$174$	2786.79	+	3795.92i	1.21417	+	1.65384i
$175$	−3054.71			−1.31951
$176$	−1208.31			−0.517499
$177$	876.317	−	2185.70i	0.372136	−	0.928178i
$178$	−562.689			−0.236940
$179$	−254.566			−0.106297			−0.0531484	−	0.998587i	$-0.516926\pi$
$179$	−254.566			−0.106297			−0.0531484	+	0.998587i	$0.516926\pi$
$180$	25.9458	+	8.14640i	0.0107438	+	0.00337331i
$181$	−2916.59			−1.19773			−0.598864	−	0.800851i	$-0.704381\pi$
$181$	−2916.59			−1.19773			−0.598864	+	0.800851i	$0.704381\pi$
$182$		−	4824.08i		−	1.96475i
$183$	−831.685	−	1132.85i	−0.335956	−	0.457609i
$184$	178.403			0.0714784
$185$	51.9729			0.0206547
$186$	3627.00	+	4940.38i	1.42981	+	1.94756i
$187$		−	1042.28i		−	0.407588i
$188$	253.461			0.0983275
$189$	−1108.11	−	3245.13i	−0.426470	−	1.24894i
$190$			55.6547i			0.0212506i
$191$	821.031			0.311035			0.155518	−	0.987833i	$-0.450295\pi$
$191$	821.031			0.311035			0.155518	+	0.987833i	$0.450295\pi$
$192$	1493.59	−	1096.52i	0.561408	−	0.412160i
$193$	4097.34			1.52815			0.764074	−	0.645128i	$-0.223196\pi$
$193$	4097.34			1.52815			0.764074	+	0.645128i	$0.223196\pi$
$194$			5134.45i			1.90017i
$195$	−31.5098	+	23.1331i	−0.0115716	+	0.00849537i
$196$	1744.21			0.635645
$197$		−	770.845i		−	0.278784i	−0.990237	−	0.139392i	$-0.955485\pi$
$197$		−	770.845i		−	0.278784i	0.990237	−	0.139392i	$-0.0445148\pi$
$198$	−524.307	+	1669.89i	−0.188186	+	0.599363i
$199$	−732.811			−0.261043			−0.130522	−	0.991445i	$-0.541665\pi$
$199$	−732.811			−0.261043			−0.130522	+	0.991445i	$0.541665\pi$
$200$	551.104			0.194845
$201$	620.058	+	844.588i	0.217590	+	0.296381i
$202$	−6979.42			−2.43104
$203$		−	5746.95i		−	1.98698i
$204$	1306.51	+	1779.61i	0.448402	+	0.610773i
$205$	−38.0948			−0.0129788
$206$		−	5307.92i		−	1.79524i
$207$	327.227	−	1042.20i	0.109874	−	0.349941i
$208$			3678.89i			1.22637i
$209$	−1653.06			−0.547104
$210$	−42.5590	−	57.9700i	−0.0139850	−	0.0190491i
$211$		−	3592.04i		−	1.17197i	−0.810321	−	0.585986i	$-0.800707\pi$
$211$		−	3592.04i		−	1.17197i	0.810321	−	0.585986i	$-0.199293\pi$
$212$			724.990i			0.234870i
$213$	2028.59	+	2763.16i	0.652565	+	0.888865i
$214$		−	4178.12i		−	1.33463i
$215$	−8.66591			−0.00274888
$216$	199.914	+	585.458i	0.0629743	+	0.184423i
$217$		−	7479.64i		−	2.33987i
$218$		−	1757.31i		−	0.545963i
$219$	−1857.79	−	2530.52i	−0.573233	−	0.780807i
$220$			16.9398i			0.00519129i
$221$	−3173.38			−0.965904
$222$	−4193.02	−	5711.36i	−1.26764	−	1.72667i
$223$	3666.01			1.10087			0.550435	−	0.834878i	$-0.314462\pi$
$223$	3666.01			1.10087			0.550435	+	0.834878i	$0.314462\pi$
$224$	−5905.98			−1.76165
$225$	1010.84	−	3219.46i	0.299507	−	0.953913i
$226$	1374.63			0.404597
$227$	−3118.42			−0.911792			−0.455896	−	0.890033i	$-0.650681\pi$
$227$	−3118.42			−0.911792			−0.455896	+	0.890033i	$0.650681\pi$
$228$	2822.48	−	2072.14i	0.819840	−	0.601890i
$229$		−	2426.36i		−	0.700169i	−0.936718	−	0.350084i	$-0.886153\pi$
$229$		−	2426.36i		−	0.700169i	0.936718	−	0.350084i	$-0.113847\pi$
$230$		−	22.9090i		−	0.00656770i
$231$	1721.83	−	1264.09i	0.490425	−	0.360048i
$232$			1036.81i			0.293406i
$233$	−2575.90			−0.724262			−0.362131	−	0.932127i	$-0.617951\pi$
$233$	−2575.90			−0.724262			−0.362131	+	0.932127i	$0.617951\pi$
$234$	5084.25	+	1596.34i	1.42037	+	0.445965i
$235$			5.43122i			0.00150763i
$236$	−2638.69	+	1640.41i	−0.727814	+	0.452463i
$237$	−2080.58	+	1527.47i	−0.570245	+	0.418648i
$238$		−	5838.20i		−	1.59006i
$239$		−	4360.94i		−	1.18028i	−0.807303	−	0.590138i	$-0.799073\pi$
$239$		−	4360.94i		−	1.18028i	0.807303	−	0.590138i	$-0.200927\pi$
$240$	32.4559	+	44.2085i	0.00872924	+	0.0118902i
$241$	3041.06			0.812829			0.406415	−	0.913689i	$-0.366779\pi$
$241$	3041.06			0.812829			0.406415	+	0.913689i	$0.366779\pi$
$242$	4039.87			1.07311
$243$	3786.83	−	94.0177i	0.999692	−	0.0248199i
$244$			1854.27i			0.486506i
$245$			37.3752i			0.00974619i
$246$	3073.38	+	4186.28i	0.796550	+	1.08499i
$247$			5033.01i			1.29653i
$248$			1349.41i			0.345514i
$249$	−6101.68	+	4479.58i	−1.55292	+	1.14009i
$250$		−	141.548i		−	0.0358092i
$251$			6103.22i			1.53479i	0.641176	+	0.767394i	$0.278447\pi$
$251$			6103.22i			1.53479i	−0.641176	+	0.767394i	$0.721553\pi$
$252$	−1355.34	+	4316.68i	−0.338803	+	1.07907i
$253$	680.445			0.169088
$254$	1802.95			0.445382
$255$	−38.1339	+	27.9962i	−0.00936484	+	0.00687525i
$256$	5005.95			1.22216
$257$		−	1101.84i		−	0.267435i	−0.991019	−	0.133717i	$-0.957309\pi$
$257$		−	1101.84i		−	0.267435i	0.991019	−	0.133717i	$-0.0426915\pi$
$258$	699.140	+	952.306i	0.168708	+	0.229798i
$259$			8646.89i			2.07448i
$260$	51.5761			0.0123024
$261$	6056.89	+	1901.73i	1.43644	+	0.451011i
$262$	−7730.00			−1.82275
$263$			6790.33i			1.59205i	0.605262	+	0.796026i	$0.293068\pi$
$263$			6790.33i			1.59205i	−0.605262	+	0.796026i	$0.706932\pi$
$264$	−310.637	+	228.056i	−0.0724182	+	0.0531662i
$265$	−15.5352			−0.00360121
$266$	−9259.45			−2.13434
$267$	−611.482	+	448.922i	−0.140158	+	0.102897i
$268$		−	1382.44i		−	0.315097i
$269$	2014.39			0.456579			0.228290	−	0.973593i	$-0.426687\pi$
$269$	2014.39			0.456579			0.228290	+	0.973593i	$0.426687\pi$
$270$	75.1795	−	25.6713i	0.0169455	−	0.00578632i
$271$	−2969.59			−0.665646			−0.332823	−	0.942989i	$-0.608001\pi$
$271$	−2969.59			−0.665646			−0.332823	+	0.942989i	$0.608001\pi$
$272$			4452.27i			0.992494i
$273$	−3848.73	−	5242.39i	−0.853244	−	1.16221i
$274$		−	4534.68i		−	0.999818i
$275$	2101.96			0.460920
$276$	−1161.81	+	852.948i	−0.253379	+	0.186020i
$277$	3663.21			0.794589			0.397294	−	0.917691i	$-0.369949\pi$
$277$	3663.21			0.794589			0.397294	+	0.917691i	$0.369949\pi$
$278$	−4700.13			−1.01401
$279$	7883.02	+	2475.09i	1.69156	+	0.531110i
$280$		−	15.8339i		−	0.00337948i
$281$		−	4303.92i		−	0.913703i	−0.889543	−	0.456851i	$-0.848977\pi$
$281$		−	4303.92i		−	0.913703i	0.889543	−	0.456851i	$-0.151023\pi$
$282$	596.843	−	438.175i	0.126034	−	0.0925282i
$283$		−	5311.32i		−	1.11564i	−0.829963	−	0.557819i	$-0.811638\pi$
$283$		−	5311.32i		−	1.11564i	0.829963	−	0.557819i	$-0.188362\pi$
$284$		−	4522.80i		−	0.944996i
$285$	44.4022	+	60.4807i	0.00922863	+	0.0125704i
$286$			3319.47i			0.686309i
$287$		−	6337.95i		−	1.30354i
$288$	1954.35	−	6224.49i	0.399865	−	1.27355i
$289$	1072.51			0.218300
$290$	133.139			0.0269592
$291$	4096.35	+	5579.67i	0.825196	+	1.12401i
$292$			4142.02i			0.830114i
$293$			1647.73i			0.328538i	0.986416	+	0.164269i	$0.0525265\pi$
$293$			1647.73i			0.328538i	−0.986416	+	0.164269i	$0.947473\pi$
$294$	4107.21	−	3015.33i	0.814752	−	0.598154i
$295$	−35.1509	−	56.5423i	−0.00693752	−	0.0111594i
$296$		−	1559.99i		−	0.306327i
$297$	762.492	+	2232.99i	0.148971	+	0.436267i
$298$	−8066.29			−1.56801
$299$		−	2071.72i		−	0.400705i
$300$	−3588.95	+	2634.84i	−0.690693	+	0.507076i
$301$		−	1441.77i		−	0.276088i
$302$		−	5211.29i		−	0.992967i
$303$	−7584.62	+	5568.29i	−1.43804	+	1.05574i
$304$	7061.35			1.33222
$305$	−39.7337			−0.00745948
$306$	6153.06	+	1931.92i	1.14950	+	0.360917i
$307$	−9335.42			−1.73551			−0.867753	−	0.496995i	$-0.834437\pi$
$307$	−9335.42			−1.73551			−0.867753	+	0.496995i	$0.834437\pi$
$308$	−2818.34			−0.521395
$309$	−4234.74	−	5768.18i	−0.779631	−	1.06194i
$310$	173.280			0.0317472
$311$			2094.69i			0.381925i	0.981597	+	0.190963i	$0.0611610\pi$
$311$			2094.69i			0.381925i	−0.981597	+	0.190963i	$0.938839\pi$
$312$	694.353	+	945.785i	0.125994	+	0.171617i
$313$			2126.17i			0.383956i	0.981399	+	0.191978i	$0.0614903\pi$
$313$			2126.17i			0.383956i	−0.981399	+	0.191978i	$0.938510\pi$
$314$		−	8746.86i		−	1.57202i
$315$	−92.4987	−	29.0425i	−0.0165451	−	0.00519479i
$316$	3405.54			0.606255
$317$		−	310.556i		−	0.0550239i	−0.999621	−	0.0275119i	$-0.991242\pi$
$317$		−	310.556i		−	0.0550239i	0.999621	−	0.0275119i	$-0.00875842\pi$
$318$	1253.34	+	1707.18i	0.221018	+	0.301051i
$319$			3954.50i			0.694074i
$320$		−	52.3863i		−	0.00915151i
$321$	−3333.37	−	4540.42i	−0.579597	−	0.789476i
$322$	3811.43			0.659637
$323$			6091.06i			1.04927i
$324$	−4100.99	−	2856.87i	−0.703187	−	0.489861i
$325$		−	6399.76i		−	1.09229i
$326$	975.900			0.165798
$327$	−1402.01	−	1909.69i	−0.237098	−	0.322954i
$328$			1143.44i			0.192487i
$329$	−903.609			−0.151421
$330$	29.2850	+	39.8894i	0.00488511	+	0.00665406i
$331$	3520.17			0.584550			0.292275	−	0.956334i	$-0.405588\pi$
$331$	3520.17			0.584550			0.292275	+	0.956334i	$0.405588\pi$
$332$	9987.38			1.65099
$333$	−9113.22	−	2861.35i	−1.49970	−	0.470873i
$334$		−	6033.42i		−	0.988425i
$335$	29.6232			0.00483131
$336$	−7355.10	+	5399.79i	−1.19421	+	0.876733i
$337$		−	5562.60i		−	0.899152i	−0.893242	−	0.449576i	$-0.851575\pi$
$337$		−	5562.60i		−	0.899152i	0.893242	−	0.449576i	$-0.148425\pi$
$338$	1638.68			0.263705
$339$	1493.83	−	1096.70i	0.239332	−	0.175707i
$340$	62.4184			0.00995622
$341$			5146.77i			0.817341i
$342$	3064.05	−	9758.81i	0.484458	−	1.54297i
$343$	2165.35			0.340869
$344$			260.112i			0.0407683i
$345$	−18.2771	−	24.8955i	−0.00285220	−	0.00388500i
$346$	−9281.56			−1.44214
$347$	−679.142			−0.105067			−0.0525335	−	0.998619i	$-0.516730\pi$
$347$	−679.142			−0.105067			−0.0525335	+	0.998619i	$0.516730\pi$
$348$	−4957.03	−	6752.02i	−0.763577	−	1.04008i
$349$			11855.2i			1.81832i	0.416452	+	0.909158i	$0.363273\pi$
$349$			11855.2i			1.81832i	−0.416452	+	0.909158i	$0.636727\pi$
$350$	11773.9			1.79812
$351$	6798.70	−	2321.53i	1.03387	−	0.353032i
$352$	4063.93			0.615364
$353$	−8993.79			−1.35607			−0.678033	−	0.735032i	$-0.737167\pi$
$353$	−8993.79			−1.35607			−0.678033	+	0.735032i	$0.737167\pi$
$354$	−3377.62	+	8424.45i	−0.507115	+	1.26484i
$355$	96.9155			0.0144894
$356$	1000.89			0.149008
$357$	−4657.81	−	6344.45i	−0.690525	−	0.940571i
$358$	981.183			0.144852
$359$			10648.2i			1.56543i	0.622383	+	0.782713i	$0.286165\pi$
$359$			10648.2i			1.56543i	−0.622383	+	0.782713i	$0.713835\pi$
$360$	16.6878	+	5.23959i	0.00244312	+	0.000767085i
$361$	2801.48			0.408439
$362$	11241.5			1.63216
$363$	4390.18	−	3223.07i	0.634778	−	0.466026i
$364$			8580.88i			1.23560i
$365$	−88.7559			−0.0127279
$366$	3205.60	+	4366.37i	0.457812	+	0.623590i
$367$			2110.22i			0.300144i	0.988675	+	0.150072i	$0.0479505\pi$
$367$			2110.22i			0.300144i	−0.988675	+	0.150072i	$0.952049\pi$
$368$	−2906.64			−0.411736
$369$	6679.76	+	2097.29i	0.942369	+	0.295883i
$370$	−200.321			−0.0281465
$371$		−	2584.64i		−	0.361693i
$372$	−6451.56	−	8787.73i	−0.899188	−	1.22479i
$373$	−5335.64			−0.740668			−0.370334	−	0.928899i	$-0.620757\pi$
$373$	−5335.64			−0.740668			−0.370334	+	0.928899i	$0.620757\pi$
$374$			4017.29i			0.555426i
$375$	−112.930	−	153.823i	−0.0155511	−	0.0211823i
$376$	163.021			0.0223595
$377$	12040.1			1.64482
$378$	4271.02	+	12507.8i	0.581157	+	1.70194i
$379$	4285.73			0.580853			0.290426	−	0.956897i	$-0.406203\pi$
$379$	4285.73			0.580853			0.290426	+	0.956897i	$0.406203\pi$
$380$		−	98.9963i		−	0.0133642i
$381$	1959.29	−	1438.42i	0.263458	−	0.193419i
$382$	−3164.53			−0.423853
$383$			5665.62i			0.755873i	0.925831	+	0.377937i	$0.123366\pi$
$383$			5665.62i			0.755873i	−0.925831	+	0.377937i	$0.876634\pi$
$384$	2339.97	−	1717.90i	0.310966	−	0.228297i
$385$		−	60.3918i		−	0.00799442i
$386$	−15792.5			−2.08243
$387$	1519.53	+	477.098i	0.199592	+	0.0626673i
$388$		−	9132.95i		−	1.19499i
$389$			522.623i			0.0681183i	0.999420	+	0.0340592i	$0.0108435\pi$
$389$			522.623i			0.0681183i	−0.999420	+	0.0340592i	$0.989157\pi$
$390$	121.450	−	89.1629i	0.0157688	−	0.0115768i
$391$		−	2507.24i		−	0.324288i
$392$	1121.84			0.144544
$393$	−8400.30	+	6167.12i	−1.07822	+	0.791578i
$394$			2971.10i			0.379903i
$395$			72.9746i			0.00929557i
$396$	932.616	−	2970.33i	0.118348	−	0.376931i
$397$		−	7111.99i		−	0.899094i	−0.893257	−	0.449547i	$-0.851585\pi$
$397$		−	7111.99i		−	0.899094i	0.893257	−	0.449547i	$-0.148415\pi$
$398$	2824.50			0.355727
$399$	−10062.4	+	7387.33i	−1.26253	+	0.926890i
$400$	−8978.90			−1.12236
$401$	−6816.87			−0.848923			−0.424461	−	0.905446i	$-0.639537\pi$
$401$	−6816.87			−0.848923			−0.424461	+	0.905446i	$0.639537\pi$
$402$	−2389.92	−	3255.33i	−0.296513	−	0.403883i
$403$	15670.2			1.93694
$404$	12414.7			1.52885
$405$	61.2176	−	87.8767i	0.00751093	−	0.0107818i
$406$			22150.7i			2.70769i
$407$		−	5949.96i		−	0.724641i
$408$	840.320	+	1144.61i	0.101966	+	0.138889i
$409$			15723.8i			1.90096i	0.310787	+	0.950480i	$0.399407\pi$
$409$			15723.8i			1.90096i	−0.310787	+	0.950480i	$0.600593\pi$
$410$	146.830			0.0176864
$411$	−3617.84	−	4927.90i	−0.434197	−	0.591424i
$412$			9441.50i			1.12900i
$413$	9407.13	−	5848.17i	1.12081	−	0.696779i
$414$	−1261.24	+	4016.99i	−0.149726	+	0.476870i
$415$			214.011i			0.0253142i
$416$		−	12373.3i		−	1.45829i
$417$	−5107.69	+	3749.84i	−0.599820	+	0.440361i
$418$	6371.47			0.745547
$419$	9134.66			1.06505			0.532526	−	0.846413i	$-0.321243\pi$
$419$	9134.66			1.06505			0.532526	+	0.846413i	$0.321243\pi$
$420$	75.7021	+	103.115i	0.00879496	+	0.0119797i
$421$		−	8009.90i		−	0.927265i	−0.886027	−	0.463633i	$-0.846546\pi$
$421$		−	8009.90i		−	0.927265i	0.886027	−	0.463633i	$-0.153454\pi$
$422$			13844.9i			1.59706i
$423$	299.013	−	952.341i	0.0343701	−	0.109467i
$424$			466.298i			0.0534091i
$425$		−	7745.12i		−	0.883985i
$426$	−7818.86	−	10650.1i	−0.889260	−	1.21127i
$427$		−	6610.61i		−	0.749204i
$428$			7431.87i			0.839330i
$429$	2648.33	+	3607.31i	0.298048	+	0.405974i
$430$	33.4014			0.00374595
$431$	11276.8			1.26028			0.630142	−	0.776480i	$-0.282997\pi$
$431$	11276.8			1.26028			0.630142	+	0.776480i	$0.282997\pi$
$432$	−3257.12	−	9538.61i	−0.362750	−	1.06233i
$433$	−733.247			−0.0813801			−0.0406901	−	0.999172i	$-0.512956\pi$
$433$	−733.247			−0.0813801			−0.0406901	+	0.999172i	$0.512956\pi$
$434$			28829.1i			3.18857i
$435$	144.684	−	106.220i	0.0159472	−	0.0117077i
$436$			3125.83i			0.343348i
$437$	−3976.51			−0.435291
$438$	7160.57	+	9753.49i	0.781154	+	1.06402i
$439$	−3985.01			−0.433244			−0.216622	−	0.976256i	$-0.569504\pi$
$439$	−3985.01			−0.433244			−0.216622	+	0.976256i	$0.569504\pi$
$440$			10.8953i			0.00118049i
$441$	2057.68	−	6553.59i	0.222187	−	0.707654i
$442$	12231.3			1.31625
$443$	−14314.5			−1.53522			−0.767609	−	0.640918i	$-0.778554\pi$
$443$	−14314.5			−1.53522			−0.767609	+	0.640918i	$0.778554\pi$
$444$	7458.37	+	10159.1i	0.797204	+	1.08588i
$445$			21.4472i			0.00228471i
$446$	−14130.0			−1.50017
$447$	−8765.74	+	6435.42i	−0.927529	+	0.680950i
$448$	8715.67			0.919145
$449$			3845.79i			0.404219i	0.979363	+	0.202109i	$0.0647796\pi$
$449$			3845.79i			0.404219i	−0.979363	+	0.202109i	$0.935220\pi$
$450$	−3896.11	+	12408.9i	−0.408143	+	1.29991i
$451$			4361.17i			0.455343i
$452$	−2445.13			−0.254446
$453$	−4157.65	−	5663.17i	−0.431222	−	0.587371i
$454$	12019.5			1.24251
$455$	−183.873			−0.0189452
$456$	1815.36	−	1332.76i	0.186430	−	0.136868i
$457$			1970.01i			0.201648i	0.994904	+	0.100824i	$0.0321479\pi$
$457$			1970.01i			0.201648i	−0.994904	+	0.100824i	$0.967852\pi$
$458$			9352.03i			0.954130i
$459$	8227.92	−	2809.56i	0.836703	−	0.285706i
$460$			40.7495i			0.00413034i
$461$		−	18528.1i		−	1.87188i	−0.352157	−	0.935941i	$-0.614552\pi$
$461$		−	18528.1i		−	1.87188i	0.352157	−	0.935941i	$-0.385448\pi$
$462$	−6636.52	+	4872.24i	−0.668310	+	0.490643i
$463$		−	16647.8i		−	1.67103i	−0.549465	−	0.835517i	$-0.685168\pi$
$463$		−	16647.8i		−	1.67103i	0.549465	−	0.835517i	$-0.314832\pi$
$464$		−	16892.3i		−	1.69010i
$465$	188.305	−	138.245i	0.0187795	−	0.0137870i
$466$	9928.41			0.986963
$467$	9292.78			0.920811			0.460405	−	0.887709i	$-0.347704\pi$
$467$	9292.78			0.920811			0.460405	+	0.887709i	$0.347704\pi$
$468$	−9043.64	−	2839.50i	−0.893253	−	0.280461i
$469$			4928.51i			0.485240i
$470$		−	20.9338i		−	0.00205447i
$471$	−6978.38	−	9505.33i	−0.682690	−	0.929899i
$472$	−1697.15	+	1055.07i	−0.165503	+	0.102889i
$473$			992.091i			0.0964406i
$474$	8019.26	−	5887.38i	0.777082	−	0.570498i
$475$	−12283.8			−1.18657
$476$			10384.8i			0.999967i
$477$	2724.04	+	855.286i	0.261478	+	0.0820982i
$478$			16808.5i			1.60838i
$479$			19464.5i			1.85670i	0.371712	+	0.928348i	$0.378771\pi$
$479$			19464.5i			1.85670i	−0.371712	+	0.928348i	$0.621229\pi$
$480$	−109.159	−	148.687i	−0.0103801	−	0.0141388i
$481$	−18115.6			−1.71726
$482$	−11721.3			−1.10765
$483$	4141.93	−	3040.82i	0.390196	−	0.286464i
$484$	−7185.95			−0.674864
$485$	195.703			0.0183225
$486$	−14595.7	+	362.376i	−1.36230	+	0.0338225i
$487$	−3403.75			−0.316712			−0.158356	−	0.987382i	$-0.550619\pi$
$487$	−3403.75			−0.316712			−0.158356	+	0.987382i	$0.550619\pi$
$488$			1192.63i			0.110631i
$489$	1060.52	−	778.588i	0.0980746	−	0.0720020i
$490$		−	144.057i		−	0.0132813i
$491$		−	10503.8i		−	0.965436i	−0.875776	−	0.482718i	$-0.839650\pi$
$491$		−	10503.8i		−	0.965436i	0.875776	−	0.482718i	$-0.160350\pi$
$492$	−5466.80	−	7446.38i	−0.500939	−	0.682335i
$493$	14571.2			1.33114
$494$		−	19399.0i		−	1.76680i
$495$	63.6488	+	19.9843i	0.00577939	+	0.00181460i
$496$		−	21985.3i		−	1.99026i
$497$			16124.1i			1.45526i
$498$	23517.9	−	17265.8i	2.11619	−	1.55361i
$499$	−5259.11			−0.471804			−0.235902	−	0.971777i	$-0.575804\pi$
$499$	−5259.11			−0.471804			−0.235902	+	0.971777i	$0.575804\pi$
$500$			251.780i			0.0225199i
$501$	−4813.56	−	6556.59i	−0.429249	−	0.584685i
$502$		−	23523.9i		−	2.09148i
$503$	18638.3			1.65217			0.826086	−	0.563544i	$-0.190562\pi$
$503$	18638.3			1.65217			0.826086	+	0.563544i	$0.190562\pi$
$504$	−871.727	+	2776.40i	−0.0770432	+	0.245378i
$505$			266.024i			0.0234415i
$506$	−2622.66			−0.230418
$507$	1780.77	−	1307.36i	0.155990	−	0.114521i
$508$	−3207.01			−0.280095
$509$	−11732.0			−1.02163			−0.510817	−	0.859689i	$-0.670657\pi$
$509$	−11732.0			−1.02163			−0.510817	+	0.859689i	$0.670657\pi$
$510$	146.981	−	107.907i	0.0127616	−	0.00936900i
$511$		−	14766.6i		−	1.27835i
$512$	−14825.4			−1.27968
$513$	−4456.00	−	13049.6i	−0.383503	−	1.12310i
$514$			4246.86i			0.364438i
$515$	−202.314			−0.0173107
$516$	−1243.60	−	1693.92i	−0.106098	−	0.144517i
$517$	621.777			0.0528931
$518$		−	33328.1i		−	2.82693i
$519$	−10086.4	+	7404.98i	−0.853070	+	0.626286i
$520$	33.1726			0.00279753
$521$			13671.5i			1.14964i	0.818281	+	0.574818i	$0.194927\pi$
$521$			13671.5i			1.14964i	−0.818281	+	0.574818i	$0.805073\pi$
$522$	−23345.3	−	7329.90i	−1.95746	−	0.614600i
$523$	−19787.6			−1.65440			−0.827198	−	0.561910i	$-0.810067\pi$
$523$	−19787.6			−1.65440			−0.827198	+	0.561910i	$0.810067\pi$
$524$	13749.8			1.14630
$525$	12794.9	−	9393.41i	1.06364	−	0.780880i
$526$		−	26172.2i		−	2.16951i
$527$	18964.4			1.56755
$528$	5061.08	−	3715.62i	0.417150	−	0.306253i
$529$	−10530.2			−0.865469
$530$	59.8781			0.00490743
$531$	3050.65	+	11849.7i	0.249316	+	0.968422i
$532$	16470.3			1.34225
$533$	13278.3			1.07907
$534$	2356.86	−	1730.30i	0.190995	−	0.140220i
$535$	−159.252			−0.0128692
$536$		−	889.157i		−	0.0716525i
$537$	1066.26	−	782.803i	0.0856847	−	0.0629058i
$538$	−7764.16			−0.622187
$539$	4278.79			0.341931
$540$	−133.726	+	45.6631i	−0.0106568	+	0.00363894i
$541$		−	12188.6i		−	0.968630i	−0.874894	−	0.484315i	$-0.839069\pi$
$541$		−	12188.6i		−	0.968630i	0.874894	−	0.484315i	$-0.160931\pi$
$542$	11445.8			0.907086
$543$	12216.3	−	8968.68i	0.965475	−	0.708808i
$544$		−	14974.4i		−	1.18019i
$545$	−66.9808			−0.00526448
$546$	14834.3	+	20206.0i	1.16273	+	1.58376i
$547$	−10285.8			−0.804003			−0.402001	−	0.915639i	$-0.631685\pi$
$547$	−10285.8			−0.804003			−0.402001	+	0.915639i	$0.631685\pi$
$548$			8066.10i			0.628771i
$549$	6967.12	+	2187.52i	0.541620	+	0.170057i
$550$	−8101.68			−0.628103
$551$		−	23110.1i		−	1.78679i
$552$	−747.251	+	548.598i	−0.0576179	+	0.0423005i
$553$	−12141.0			−0.933614
$554$	−14119.3			−1.08280
$555$	−217.692	+	159.819i	−0.0166495	+	0.0122233i
$556$	8360.40			0.637698
$557$		−	2994.00i		−	0.227756i	−0.993495	−	0.113878i	$-0.963673\pi$
$557$		−	2994.00i		−	0.227756i	0.993495	−	0.113878i	$-0.0363272\pi$
$558$	−30383.8	−	9539.84i	−2.30511	−	0.723752i
$559$	3020.58			0.228546
$560$			257.974i			0.0194668i
$561$	3205.06	+	4365.64i	0.241208	+	0.328552i
$562$			16588.8i			1.24512i
$563$	3200.12			0.239554			0.119777	−	0.992801i	$-0.461782\pi$
$563$	3200.12			0.239554			0.119777	+	0.992801i	$0.461782\pi$
$564$	−1061.64	+	779.407i	−0.0792607	+	0.0581897i
$565$		−	52.3948i		−	0.00390135i
$566$			20471.6i			1.52030i
$567$	14620.3	+	10185.0i	1.08289	+	0.754370i
$568$		−	2908.97i		−	0.214890i
$569$	25341.0			1.86705			0.933524	−	0.358515i	$-0.116717\pi$
$569$	25341.0			1.86705			0.933524	+	0.358515i	$0.116717\pi$
$570$	−171.141	−	233.113i	−0.0125760	−	0.0171299i
$571$			2220.28i			0.162724i	0.996685	+	0.0813622i	$0.0259271\pi$
$571$			2220.28i			0.162724i	−0.996685	+	0.0813622i	$0.974073\pi$
$572$		−	5904.54i		−	0.431610i
$573$	−3438.94	+	2524.72i	−0.250722	+	0.184069i
$574$			24428.6i			1.77636i
$575$	5056.36			0.366721
$576$	−2884.11	+	9185.71i	−0.208630	+	0.664476i
$577$	−8017.59			−0.578469			−0.289234	−	0.957258i	$-0.593401\pi$
$577$	−8017.59			−0.578469			−0.289234	+	0.957258i	$0.593401\pi$
$578$	−4133.82			−0.297481
$579$	−17161.9	+	12599.5i	−1.23182	+	0.904350i
$580$	−236.822			−0.0169543
$581$	−35605.7			−2.54247
$582$	−15788.7	−	21506.0i	−1.12451	−	1.53170i
$583$			1778.51i			0.126343i
$584$			2664.06i			0.188766i
$585$	60.8453	−	193.789i	0.00430025	−	0.0136960i
$586$		−	6350.93i		−	0.447704i
$587$	−18610.1			−1.30856			−0.654278	−	0.756254i	$-0.727027\pi$
$587$	−18610.1			−1.30856			−0.654278	+	0.756254i	$0.727027\pi$
$588$	−7305.73	+	5363.54i	−0.512386	+	0.376171i
$589$		−	30077.7i		−	2.10412i
$590$	135.484	+	217.933i	0.00945386	+	0.0152071i
$591$	2370.39	+	3228.73i	0.164983	+	0.224725i
$592$			25416.3i			1.76453i
$593$			9313.64i			0.644967i	0.946575	+	0.322484i	$0.104518\pi$
$593$			9313.64i			0.644967i	−0.946575	+	0.322484i	$0.895482\pi$
$594$	−2938.90	−	8606.71i	−0.203005	−	0.594507i
$595$	−222.526			−0.0153323
$596$	14348.0			0.986101
$597$	3069.42	−	2253.43i	0.210424	−	0.154484i
$598$			7985.12i			0.546047i
$599$			17777.5i			1.21263i	0.795223	+	0.606317i	$0.207354\pi$
$599$			17777.5i			1.21263i	−0.795223	+	0.606317i	$0.792646\pi$
$600$	−2308.33	+	1694.67i	−0.157062	+	0.115308i
$601$			17209.0i			1.16800i	0.811753	+	0.584001i	$0.198514\pi$
$601$			17209.0i			1.16800i	−0.811753	+	0.584001i	$0.801486\pi$
$602$			5557.09i			0.376229i
$603$	−5194.31	−	1630.89i	−0.350793	−	0.110141i
$604$			9269.62i			0.624463i
$605$		−	153.982i		−	0.0103475i
$606$	29233.7	−	21462.1i	1.95963	−	1.43868i
$607$	7356.60			0.491920			0.245960	−	0.969280i	$-0.420897\pi$
$607$	7356.60			0.491920			0.245960	+	0.969280i	$0.420897\pi$
$608$	−23749.6			−1.58416
$609$	17672.2	+	24071.5i	1.17588	+	1.60168i
$610$	153.147			0.0101652
$611$		−	1893.10i		−	0.125346i
$612$	−10944.8	−	3436.42i	−0.722904	−	0.226976i
$613$		−	3287.75i		−	0.216625i	−0.994117	−	0.108312i	$-0.965455\pi$
$613$		−	3287.75i		−	0.216625i	0.994117	−	0.108312i	$-0.0345447\pi$
$614$	35981.9			2.36500
$615$	159.562	−	117.144i	0.0104621	−	0.00768079i
$616$	−1812.69			−0.118564
$617$		−	17552.0i		−	1.14524i	−0.819820	−	0.572622i	$-0.805926\pi$
$617$		−	17552.0i		−	1.14524i	0.819820	−	0.572622i	$-0.194074\pi$
$618$	16322.1	+	22232.5i	1.06241	+	1.44713i
$619$	24087.0			1.56404			0.782019	−	0.623254i	$-0.214190\pi$
$619$	24087.0			1.56404			0.782019	+	0.623254i	$0.214190\pi$
$620$	−308.223			−0.0199654
$621$	1834.21	+	5371.55i	0.118525	+	0.347106i
$622$		−	8073.64i		−	0.520456i
$623$	−3568.24			−0.229468
$624$	−11312.8	−	15409.3i	−0.725760	−	0.988564i
$625$	15616.9			0.999482
$626$		−	8194.99i		−	0.523223i
$627$	6923.95	−	5083.26i	0.441015	−	0.323773i
$628$			15558.6i			0.988621i
$629$	−21923.9			−1.38977
$630$	356.522	+	111.940i	0.0225463	+	0.00707902i
$631$	−12126.1			−0.765026			−0.382513	−	0.923950i	$-0.624941\pi$
$631$	−12126.1			−0.765026			−0.382513	+	0.923950i	$0.624941\pi$
$632$	2190.37			0.137861
$633$	11045.7	+	15045.5i	0.693567	+	0.944714i
$634$			1196.99i			0.0749818i
$635$		−	68.7204i		−	0.00429462i
$636$	−2229.38	−	3036.67i	−0.138995	−	0.189326i
$637$		−	13027.5i		−	0.810310i
$638$		−	15242.0i		−	0.945825i
$639$	−16993.7	−	5335.64i	−1.05205	−	0.330320i
$640$		−	82.0724i		−	0.00506906i
$641$			15578.1i			0.959905i	0.877294	+	0.479952i	$0.159346\pi$
$641$			15578.1i			0.959905i	−0.877294	+	0.479952i	$0.840654\pi$
$642$	12848.0	+	17500.3i	0.789826	+	1.07583i
$643$	−12027.9			−0.737692			−0.368846	−	0.929491i	$-0.620247\pi$
$643$	−12027.9			−0.737692			−0.368846	+	0.929491i	$0.620247\pi$
$644$	−6779.62			−0.414836
$645$	36.2977	−	26.6481i	0.00221584	−	0.00162677i
$646$		−	23477.0i		−	1.42986i
$647$		−	11285.9i		−	0.685775i	−0.939376	−	0.342888i	$-0.888595\pi$
$647$		−	11285.9i		−	0.685775i	0.939376	−	0.342888i	$-0.111405\pi$
$648$	−2637.67	−	1837.48i	−0.159903	−	0.111393i
$649$	−6473.08	+	4024.15i	−0.391511	+	0.243393i
$650$			24666.9i			1.48848i
$651$	23000.3	+	31328.9i	1.38472	+	1.88614i
$652$	−1735.89			−0.104268
$653$			9149.02i			0.548283i	0.961689	+	0.274141i	$0.0883936\pi$
$653$			9149.02i			0.548283i	−0.961689	+	0.274141i	$0.911606\pi$
$654$	5403.81	+	7360.59i	0.323098	+	0.440095i
$655$			294.634i			0.0175760i
$656$		−	18629.5i		−	1.10878i
$657$	15563.0	+	4886.42i	0.924154	+	0.290164i
$658$	3482.82			0.206344
$659$	−4684.57			−0.276912			−0.138456	−	0.990369i	$-0.544214\pi$
$659$	−4684.57			−0.276912			−0.138456	+	0.990369i	$0.544214\pi$
$660$	−52.0909	−	70.9536i	−0.00307218	−	0.00418464i
$661$	−23736.6			−1.39675			−0.698373	−	0.715734i	$-0.746092\pi$
$661$	−23736.6			−1.39675			−0.698373	+	0.715734i	$0.746092\pi$
$662$	−13567.9			−0.796575
$663$	13291.9	−	9758.32i	0.778604	−	0.571616i
$664$	6423.67			0.375432
$665$			352.929i			0.0205805i
$666$	35125.4	+	11028.6i	2.04367	+	0.641666i
$667$			9512.72i			0.552225i
$668$			10732.0i			0.621607i
$669$	−15355.3	+	11273.2i	−0.887399	+	0.651489i
$670$	−114.178			−0.00658370
$671$			4548.79i			0.261705i
$672$	24737.6	−	18161.2i	1.42005	−	1.04253i
$673$			27614.0i			1.58164i	0.612052	+	0.790818i	$0.290344\pi$
$673$			27614.0i			1.58164i	−0.612052	+	0.790818i	$0.709656\pi$
$674$			21440.2i			1.22529i
$675$	5666.05	+	16593.3i	0.323091	+	0.946185i
$676$	−2914.81			−0.165840
$677$		−	13798.0i		−	0.783306i	−0.920113	−	0.391653i	$-0.871903\pi$
$677$		−	13798.0i		−	0.783306i	0.920113	−	0.391653i	$-0.128097\pi$
$678$	−5757.72	+	4227.06i	−0.326141	+	0.239438i
$679$			32559.6i			1.84024i
$680$	40.1462			0.00226402
$681$	13061.7	−	9589.31i	0.734986	−	0.539593i
$682$		−	19837.4i		−	1.11380i
$683$	−16270.4			−0.911522			−0.455761	−	0.890102i	$-0.650633\pi$
$683$	−16270.4			−0.911522			−0.455761	+	0.890102i	$0.650633\pi$
$684$	−5450.20	+	17358.6i	−0.304669	+	0.970353i
$685$	−172.842			−0.00964080
$686$	−8346.00			−0.464507
$687$	7461.20	+	10163.0i	0.414356	+	0.564398i
$688$		−	4237.89i		−	0.234837i
$689$	5414.94			0.299409
$690$	70.4463	+	95.9556i	0.00388673	+	0.00529415i
$691$			27102.8i			1.49210i	0.665891	+	0.746049i	$0.268052\pi$
$691$			27102.8i			1.49210i	−0.665891	+	0.746049i	$0.731948\pi$
$692$	16509.7			0.906941
$693$	−3324.85	+	10589.4i	−0.182252	+	0.580461i
$694$	2617.64			0.143176
$695$			179.148i			0.00977767i
$696$	−3188.26	−	4342.76i	−0.173636	−	0.236511i
$697$	16069.7			0.873288
$698$		−	45693.8i		−	2.47785i
$699$	10789.3	−	7921.04i	0.583820	−	0.428614i
$700$	−20942.9			−1.13081
$701$	30512.1			1.64398			0.821988	−	0.569505i	$-0.192865\pi$
$701$	30512.1			1.64398			0.821988	+	0.569505i	$0.192865\pi$
$702$	−26204.5	+	8947.97i	−1.40887	+	0.481082i
$703$			34771.5i			1.86548i
$704$	−5997.29			−0.321067
$705$	−16.7013	−	22.7490i	−0.000892208	−	0.00121529i
$706$	34665.1			1.84793
$707$	−44259.3			−2.35437
$708$	6007.98	−	14985.1i	0.318917	−	0.795442i
$709$	27019.6			1.43123			0.715615	−	0.698495i	$-0.246146\pi$
$709$	27019.6			1.43123			0.715615	+	0.698495i	$0.246146\pi$
$710$	−373.545			−0.0197449
$711$	4017.59	−	12795.8i	0.211915	−	0.674936i
$712$	643.750			0.0338842
$713$			12380.8i			0.650300i
$714$	17952.8	+	24453.7i	0.940989	+	1.28173i
$715$	126.524			0.00661778
$716$	−1745.29			−0.0910956
$717$	13410.1	+	18266.1i	0.698480	+	0.951407i
$718$		−	41041.6i		−	2.13323i
$719$	29232.7			1.51627			0.758135	−	0.652098i	$-0.226111\pi$
$719$	29232.7			1.51627			0.758135	+	0.652098i	$0.226111\pi$
$720$	−271.887	−	85.3663i	−0.0140731	−	0.00441863i
$721$		−	33659.7i		−	1.73863i
$722$	−10797.9			−0.556585
$723$	−12737.7	+	9351.42i	−0.655213	+	0.481028i
$724$	−19996.0			−1.02644
$725$			29385.8i			1.50532i
$726$	−16921.2	+	12422.8i	−0.865022	+	0.635060i
$727$	−2919.43			−0.148935			−0.0744676	−	0.997223i	$-0.523726\pi$
$727$	−2919.43			−0.148935			−0.0744676	+	0.997223i	$0.523726\pi$
$728$			5519.04i			0.280974i
$729$	−15572.3	+	12038.5i	−0.791152	+	0.611619i
$730$	342.096			0.0173446
$731$	3655.57			0.184960
$732$	−5701.98	−	7766.72i	−0.287912	−	0.392167i
$733$	21990.4			1.10809			0.554047	−	0.832485i	$-0.313083\pi$
$733$	21990.4			1.10809			0.554047	+	0.832485i	$0.313083\pi$
$734$		−	8133.52i		−	0.409010i
$735$	−114.931	−	156.548i	−0.00576774	−	0.00785630i
$736$	9775.95			0.489601
$737$		−	3391.33i		−	0.169500i
$738$	−25746.1	−	8083.68i	−1.28418	−	0.403204i
$739$		−	1784.00i		−	0.0888033i	−0.999014	−	0.0444017i	$-0.985862\pi$
$739$		−	1784.00i		−	0.0888033i	0.999014	−	0.0444017i	$-0.0141381\pi$
$740$	356.323			0.0177009
$741$	−15476.8	−	21081.1i	−0.767280	−	1.04512i
$742$			9962.10i			0.492884i
$743$		−	3104.70i		−	0.153298i	−0.997058	−	0.0766491i	$-0.975578\pi$
$743$		−	3104.70i		−	0.153298i	0.997058	−	0.0766491i	$-0.0244221\pi$
$744$	−4149.51	−	5652.08i	−0.204473	−	0.278515i
$745$			307.451i			0.0151197i
$746$	20565.4			1.00932
$747$	11782.3	−	37526.0i	0.577098	−	1.83802i
$748$		−	7145.79i		−	0.349300i
$749$		−	26495.2i		−	1.29254i
$750$	435.269	+	592.884i	0.0211917	+	0.0288654i
$751$			4396.17i			0.213607i	0.994280	+	0.106803i	$0.0340615\pi$
$751$			4396.17i			0.213607i	−0.994280	+	0.106803i	$0.965938\pi$
$752$	−2656.03			−0.128797
$753$	−18767.7	−	25563.7i	−0.908279	−	1.23718i
$754$	−46406.7			−2.24142
$755$	−198.631			−0.00957474
$756$	−7597.10	−	22248.4i	−0.365482	−	1.07033i
$757$	5977.58			0.287000			0.143500	−	0.989650i	$-0.454164\pi$
$757$	5977.58			0.287000			0.143500	+	0.989650i	$0.454164\pi$
$758$	−16518.7			−0.791537
$759$	−2850.08	+	2092.40i	−0.136300	+	0.100065i
$760$		−	63.6723i		−	0.00303900i
$761$		−	20959.5i		−	0.998400i	−0.866487	−	0.499200i	$-0.833627\pi$
$761$		−	20959.5i		−	0.998400i	0.866487	−	0.499200i	$-0.166373\pi$
$762$	−7551.76	+	5544.16i	−0.359018	+	0.263575i
$763$		−	11143.8i		−	0.528745i
$764$	5628.94			0.266555
$765$	73.6363	−	234.527i	0.00348016	−	0.0110841i
$766$		−	21837.2i		−	1.03004i
$767$	12252.2	+	19708.3i	0.576793	+	0.927806i
$768$	−20967.7	+	15393.6i	−0.985166	+	0.723264i
$769$			37081.2i			1.73886i	0.494056	+	0.869430i	$0.335514\pi$
$769$			37081.2i			1.73886i	−0.494056	+	0.869430i	$0.664486\pi$
$770$			232.771i			0.0108941i
$771$	3388.21	+	4615.12i	0.158266	+	0.215576i
$772$	28091.1			1.30961
$773$	3721.27			0.173150			0.0865749	−	0.996245i	$-0.472408\pi$
$773$	3721.27			0.173150			0.0865749	+	0.996245i	$0.472408\pi$
$774$	−5856.78	−	1838.90i	−0.271987	−	0.0853977i
$775$			38245.5i			1.77267i
$776$		−	5874.12i		−	0.271738i
$777$	−26589.6	−	36218.0i	−1.22767	−	1.67222i
$778$		−	2014.37i		−	0.0928259i
$779$		−	25486.6i		−	1.17221i
$780$	−216.030	+	158.599i	−0.00991680	+	0.00728047i
$781$		−	11095.1i		−	0.508340i
$782$			9663.76i			0.441912i
$783$	−31217.6	+	10659.8i	−1.42481	+	0.486525i
$784$	−18277.6			−0.832617
$785$	−333.392			−0.0151583
$786$	32377.6	−	23770.2i	1.46930	−	1.07869i
$787$	19741.9			0.894184			0.447092	−	0.894488i	$-0.352460\pi$
$787$	19741.9			0.894184			0.447092	+	0.894488i	$0.352460\pi$
$788$		−	5284.87i		−	0.238916i
$789$	−20880.6	−	28441.7i	−0.942168	−	1.28334i
$790$		−	281.269i		−	0.0126672i
$791$	8717.08			0.391838
$792$	599.839	−	1910.45i	0.0269121	−	0.0857133i
$793$	13849.5			0.620190
$794$			27412.0i			1.22521i
$795$	65.0703	−	47.7717i	0.00290290	−	0.00213118i
$796$	−5024.11			−0.223712
$797$	−16127.4			−0.716766			−0.358383	−	0.933575i	$-0.616672\pi$
$797$	−16127.4			−0.716766			−0.358383	+	0.933575i	$0.616672\pi$
$798$	38783.8	−	28473.3i	1.72046	−	1.26309i
$799$		−	2291.07i		−	0.101442i
$800$	30198.9			1.33462
$801$	1180.77	−	3760.68i	0.0520854	−	0.165889i
$802$	26274.5			1.15684
$803$			10161.0i			0.446541i
$804$	4251.08	+	5790.44i	0.186473	+	0.253997i
$805$		−	145.275i		−	0.00636059i
$806$	−60398.2			−2.63950
$807$	−8437.41	+	6194.37i	−0.368043	+	0.270201i
$808$	7984.87			0.347657
$809$	1411.49			0.0613417			0.0306708	−	0.999530i	$-0.490236\pi$
$809$	1411.49			0.0613417			0.0306708	+	0.999530i	$0.490236\pi$
$810$	−235.953	+	338.707i	−0.0102353	+	0.0146925i
$811$		−	36185.1i		−	1.56675i	−0.621551	−	0.783374i	$-0.713497\pi$
$811$		−	36185.1i		−	1.56675i	0.621551	−	0.783374i	$-0.286503\pi$
$812$		−	39400.8i		−	1.70283i
$813$	12438.3	−	9131.66i	0.536570	−	0.393925i
$814$			22933.2i			0.987479i
$815$		−	37.1970i		−	0.00159872i
$816$	−13691.0	−	18648.6i	−0.587353	−	0.800039i
$817$		−	5797.77i		−	0.248272i
$818$		−	60604.9i		−	2.59047i
$819$	32241.3	+	10123.0i	1.37558	+	0.431901i
$820$	−261.176			−0.0111227
$821$	8784.58			0.373428			0.186714	−	0.982414i	$-0.440216\pi$
$821$	8784.58			0.373428			0.186714	+	0.982414i	$0.440216\pi$
$822$	13944.4	+	18993.8i	0.591686	+	0.805942i
$823$			1228.55i			0.0520348i	0.999661	+	0.0260174i	$0.00828254\pi$
$823$			1228.55i			0.0520348i	−0.999661	+	0.0260174i	$0.991717\pi$
$824$			6072.57i			0.256733i
$825$	−8804.20	+	6463.65i	−0.371543	+	0.272770i
$826$	−36258.3	+	22540.8i	−1.52734	+	0.949511i
$827$			19099.1i			0.803073i	0.915843	+	0.401537i	$0.131524\pi$
$827$			19099.1i			0.803073i	−0.915843	+	0.401537i	$0.868476\pi$
$828$	2243.45	−	7145.25i	0.0941608	−	0.299897i
$829$	−5765.28			−0.241540			−0.120770	−	0.992681i	$-0.538536\pi$
$829$	−5765.28			−0.241540			−0.120770	+	0.992681i	$0.538536\pi$
$830$		−	824.873i		−	0.0344961i
$831$	−15343.6	+	11264.6i	−0.640509	+	0.470233i
$832$			18259.7i			0.760868i
$833$		−	15766.1i		−	0.655779i
$834$	19686.8	−	14453.2i	0.817383	−	0.600086i
$835$	−229.967			−0.00953095
$836$	−11333.3			−0.468864
$837$	−40629.5	+	13873.6i	−1.67785	+	0.572931i
$838$	−35208.1			−1.45136
$839$	−37576.8			−1.54624			−0.773121	−	0.634259i	$-0.781305\pi$
$839$	−37576.8			−1.54624			−0.773121	+	0.634259i	$0.781305\pi$
$840$	48.6900	+	66.3211i	0.00199996	+	0.00272416i
$841$	−30895.6			−1.26678
$842$			30872.9i			1.26360i
$843$	13234.8	+	18027.2i	0.540724	+	0.736526i
$844$		−	24626.8i		−	1.00437i
$845$		−	62.4591i		−	0.00254279i
$846$	−1152.50	+	3670.65i	−0.0468366	+	0.149172i
$847$	25618.4			1.03927
$848$		−	7597.19i		−	0.307652i
$849$	16332.6	+	22246.8i	0.660228	+	0.899303i
$850$			29852.3i			1.20462i
$851$		−	14312.9i		−	0.576544i
$852$	13907.9	+	18944.0i	0.559243	+	0.761751i
$853$	21853.4			0.877193			0.438596	−	0.898684i	$-0.355476\pi$
$853$	21853.4			0.877193			0.438596	+	0.898684i	$0.355476\pi$
$854$			25479.5i			1.02095i
$855$	−371.963	−	116.788i	−0.0148782	−	0.00467142i
$856$			4780.02i			0.190862i
$857$	−343.264			−0.0136822			−0.00684111	−	0.999977i	$-0.502178\pi$
$857$	−343.264			−0.0136822			−0.00684111	+	0.999977i	$0.502178\pi$
$858$	−10207.6	−	13903.8i	−0.406154	−	0.553226i
$859$		−	37138.8i		−	1.47516i	−0.675261	−	0.737579i	$-0.735969\pi$
$859$		−	37138.8i		−	1.47516i	0.675261	−	0.737579i	$-0.264031\pi$
$860$	−59.4129			−0.00235577
$861$	19489.5	+	26546.9i	0.771430	+	1.05077i
$862$	−43464.5			−1.71741
$863$	−5382.33			−0.212302			−0.106151	−	0.994350i	$-0.533853\pi$
$863$	−5382.33			−0.212302			−0.106151	+	0.994350i	$0.533853\pi$
$864$	10954.7	+	32081.4i	0.431351	+	1.26323i
$865$			353.772i			0.0139059i
$866$	2826.18			0.110898
$867$	−4492.27	+	3298.02i	−0.175969	+	0.129189i
$868$		−	51280.0i		−	2.00525i
$869$	8354.28			0.326122
$870$	−557.660	+	409.409i	−0.0217315	+	0.0159543i
$871$	−10325.4			−0.401681
$872$			2010.46i			0.0780767i
$873$	−34315.6	−	10774.3i	−1.33036	−	0.417704i
$874$	15326.8			0.593178
$875$		−	897.616i		−	0.0346800i
$876$	−12736.9	−	17349.1i	−0.491257	−	0.669146i
$877$	33387.1			1.28552			0.642761	−	0.766066i	$-0.277789\pi$
$877$	33387.1			1.28552			0.642761	+	0.766066i	$0.277789\pi$
$878$	15359.6			0.590388
$879$	−5066.87	−	6901.63i	−0.194427	−	0.264831i
$880$		−	177.513i		−	0.00679996i
$881$	6166.90			0.235832			0.117916	−	0.993024i	$-0.462379\pi$
$881$	6166.90			0.235832			0.117916	+	0.993024i	$0.462379\pi$
$882$	−7930.99	+	25259.8i	−0.302778	+	0.964331i
$883$	2447.98			0.0932966			0.0466483	−	0.998911i	$-0.485146\pi$
$883$	2447.98			0.0932966			0.0466483	+	0.998911i	$0.485146\pi$
$884$	−21756.5			−0.827772
$885$	321.103	+	128.740i	0.0121963	+	0.00488989i
$886$	55172.9			2.09207
$887$	20830.1			0.788506			0.394253	−	0.919002i	$-0.371003\pi$
$887$	20830.1			0.788506			0.394253	+	0.919002i	$0.371003\pi$
$888$	4797.07	+	6534.13i	0.181283	+	0.246927i
$889$	11433.2			0.431337
$890$		−	82.6649i		−	0.00311341i
$891$	−10060.3	−	7008.31i	−0.378264	−	0.263510i
$892$	25133.9			0.943438
$893$	−3633.66			−0.136165
$894$	33786.2	−	24804.3i	1.26396	−	0.927941i
$895$		−	37.3983i		−	0.00139675i
$896$	13654.6			0.509118
$897$	6370.66	+	8677.54i	0.237135	+	0.323004i
$898$		−	14823.0i		−	0.550835i
$899$	−71952.7			−2.66936
$900$	6930.24	−	22072.4i	0.256675	−	0.817496i
$901$	6553.28			0.242310
$902$		−	16809.4i		−	0.620502i
$903$	4433.53	+	6038.96i	0.163387	+	0.222551i
$904$	−1572.66			−0.0578604
$905$		−	428.478i		−	0.0157382i
$906$	16025.0	+	21827.8i	0.587632	+	0.800420i
$907$	36944.9			1.35252			0.676261	−	0.736663i	$-0.263599\pi$
$907$	36944.9			1.35252			0.676261	+	0.736663i	$0.263599\pi$
$908$	−21379.7			−0.781399
$909$	14645.9	−	46646.2i	0.534403	−	1.70204i
$910$	708.708			0.0258170
$911$			48490.3i			1.76351i	0.471708	+	0.881755i	$0.343638\pi$
$911$			48490.3i			1.76351i	−0.471708	+	0.881755i	$0.656362\pi$
$912$	−29576.9	+	21714.0i	−1.07389	+	0.788402i
$913$	24500.5			0.888113
$914$		−	7593.09i		−	0.274789i
$915$	166.427	−	122.183i	0.00601301	−	0.00441448i
$916$		−	16635.0i		−	0.600039i
$917$	−49019.1			−1.76527
$918$	−31713.2	+	10829.0i	−1.14019	+	0.389336i
$919$		−	6130.82i		−	0.220062i	−0.993928	−	0.110031i	$-0.964905\pi$
$919$		−	6130.82i		−	0.220062i	0.993928	−	0.110031i	$-0.0350950\pi$
$920$			26.2092i			0.000939230i
$921$	39102.0	−	28706.9i	1.39897	−	1.02706i
$922$			71413.4i			2.55084i
$923$	−33780.8			−1.20467
$924$	11804.8	−	8666.53i	0.420291	−	0.308558i
$925$		−	44213.9i		−	1.57162i
$926$			64166.3i			2.27714i
$927$	35474.9	+	11138.3i	1.25690	+	0.394639i
$928$			56814.4i			2.00972i
$929$	−13881.4			−0.490243			−0.245121	−	0.969492i	$-0.578828\pi$
$929$	−13881.4			−0.490243			−0.245121	+	0.969492i	$0.578828\pi$
$930$	−725.792	+	532.844i	−0.0255910	+	0.0187878i
$931$	−25005.2			−0.880251
$932$	−17660.2			−0.620687
$933$	−6441.28	−	8773.72i	−0.226021	−	0.307866i
$934$	−35817.6			−1.25480
$935$	153.121			0.00535573
$936$	−5816.68	−	1826.31i	−0.203124	−	0.0637764i
$937$			6800.40i			0.237097i	0.992948	+	0.118548i	$0.0378240\pi$
$937$			6800.40i			0.237097i	−0.992948	+	0.118548i	$0.962176\pi$
$938$		−	18996.2i		−	0.661243i
$939$	−6538.09	−	8905.60i	−0.227223	−	0.309503i
$940$			37.2361i			0.00129203i
$941$	18823.1			0.652088			0.326044	−	0.945355i	$-0.394284\pi$
$941$	18823.1			0.652088			0.326044	+	0.945355i	$0.394284\pi$
$942$	26897.1	+	36636.8i	0.930312	+	1.26719i
$943$			10491.0i			0.362283i
$944$	27650.9	−	17189.9i	0.953348	−	0.592672i
$945$	476.744	−	162.792i	0.0164111	−	0.00560384i
$946$		−	3823.86i		−	0.131421i
$947$		−	49064.3i		−	1.68361i	−0.539784	−	0.841804i	$-0.681494\pi$
$947$		−	49064.3i		−	1.68361i	0.539784	−	0.841804i	$-0.318506\pi$
$948$	−14264.3	+	10472.2i	−0.488696	+	0.358779i
$949$	30936.7			1.05822
$950$	47346.1			1.61696
$951$	954.976	+	1300.78i	0.0325628	+	0.0443541i
$952$			6679.25i			0.227390i
$953$		−	5325.52i		−	0.181018i	−0.995896	−	0.0905092i	$-0.971151\pi$
$953$		−	5325.52i		−	0.181018i	0.995896	−	0.0905092i	$-0.0288495\pi$
$954$	−10499.4	−	3296.56i	−0.356320	−	0.111876i
$955$			120.618i			0.00408702i
$956$		−	29898.3i		−	1.01149i
$957$	−12160.3	−	16563.7i	−0.410749	−	0.559486i
$958$		−	75023.0i		−	2.53015i
$959$		−	28756.3i		−	0.968288i
$960$	161.091	+	219.423i	0.00541581	+	0.00737693i
$961$	−63855.2			−2.14344
$962$	69823.8			2.34013
$963$	27924.1	+	8767.53i	0.934414	+	0.293385i
$964$	20849.3			0.696588
$965$			601.941i			0.0200800i
$966$	−15964.4	+	11720.4i	−0.531726	+	0.390369i
$967$			1226.78i			0.0407970i	0.999792	+	0.0203985i	$0.00649349\pi$
$967$			1226.78i			0.0407970i	−0.999792	+	0.0203985i	$0.993507\pi$
$968$	−4621.85			−0.153463
$969$	−18730.3	−	25512.8i	−0.620954	−	0.845808i
$970$	−754.304			−0.0249683
$971$		−	46347.0i		−	1.53177i	−0.642979	−	0.765883i	$-0.722302\pi$
$971$		−	46347.0i		−	1.53177i	0.642979	−	0.765883i	$-0.277698\pi$
$972$	25962.3	−	644.580i	0.856729	−	0.0212705i
$973$	−29805.4			−0.982034
$974$	13119.2			0.431588
$975$	19679.6	+	26805.8i	0.646412	+	0.880485i
$976$		−	19431.0i		−	0.637264i
$977$	−16323.1			−0.534517			−0.267259	−	0.963625i	$-0.586118\pi$
$977$	−16323.1			−0.534517			−0.267259	+	0.963625i	$0.586118\pi$
$978$	−4087.62	+	3000.94i	−0.133648	+	0.0981182i
$979$	2455.32			0.0801557
$980$			256.242i			0.00835241i
$981$	11744.8	+	3687.60i	0.382245	+	0.120016i
$982$			40485.1i			1.31561i
$983$	−26029.3			−0.844563			−0.422282	−	0.906465i	$-0.638771\pi$
$983$	−26029.3			−0.844563			−0.422282	+	0.906465i	$0.638771\pi$
$984$	−3516.13	−	4789.35i	−0.113913	−	0.155162i
$985$	113.245			0.00366324
$986$	−56162.4			−1.81397
$987$	3784.82	−	2778.65i	0.122059	−	0.0896102i
$988$			34506.1i			1.11112i
$989$			2386.52i			0.0767308i
$990$	−245.324	−	77.0262i	−0.00787567	−	0.00247278i
$991$		−	46331.2i		−	1.48513i	−0.669776	−	0.742563i	$-0.733610\pi$
$991$		−	46331.2i		−	1.48513i	0.669776	−	0.742563i	$-0.266390\pi$
$992$			73943.7i			2.36665i
$993$	−14744.4	+	10824.7i	−0.471199	+	0.345933i
$994$		−	62147.9i		−	1.98311i
$995$		−	107.657i		−	0.00343012i
$996$	−41832.7	+	30711.7i	−1.33084	+	0.977046i
$997$	−38528.8			−1.22389			−0.611945	−	0.790900i	$-0.709613\pi$
$997$	−38528.8			−1.22389			−0.611945	+	0.790900i	$0.709613\pi$
$998$	20270.4			0.642935
$999$	46970.1	−	16038.7i	1.48755	−	0.507951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.12	yes	52
3.2	odd	2	inner	177.4.d.c.176.41	yes	52
59.58	odd	2	inner	177.4.d.c.176.42	yes	52
177.176	even	2	inner	177.4.d.c.176.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.11	✓	52	177.176	even	2	inner
177.4.d.c.176.12	yes	52	1.1	even	1	trivial
177.4.d.c.176.41	yes	52	3.2	odd	2	inner
177.4.d.c.176.42	yes	52	59.58	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.85434 q^{2} +(-4.18856 + 3.07505i) q^{3} +6.85594 q^{4} +0.146910i q^{5} +(16.1441 - 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 - 25.7601i) q^{9} +O(q^{10})\)	\(q-3.85434 q^{2} +(-4.18856 + 3.07505i) q^{3} +6.85594 q^{4} +0.146910i q^{5} +(16.1441 - 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 - 25.7601i) q^{9} -0.566243i q^{10} +16.8186 q^{11} +(-28.7165 + 21.0824i) q^{12} -51.2069i q^{13} +94.2076 q^{14} +(-0.451757 - 0.615343i) q^{15} -71.8436 q^{16} -61.9717i q^{17} +(-31.1743 + 99.2882i) q^{18} -98.2877 q^{19} +1.00721i q^{20} +(102.377 - 75.1603i) q^{21} -64.8246 q^{22} +40.4578 q^{23} +(-18.4699 + 13.5597i) q^{24} +124.978 q^{25} +197.369i q^{26} +(45.3362 + 132.769i) q^{27} -167.572 q^{28} +235.127i q^{29} +(1.74123 + 2.37174i) q^{30} +306.017i q^{31} +241.633 q^{32} +(-70.4458 + 51.7181i) q^{33} +238.860i q^{34} -3.59077i q^{35} +(55.4515 - 176.610i) q^{36} -353.773i q^{37} +378.834 q^{38} +(157.464 + 214.483i) q^{39} +0.647815i q^{40} +259.306i q^{41} +(-394.594 + 289.693i) q^{42} +58.9877i q^{43} +115.307 q^{44} +(3.78443 + 1.18822i) q^{45} -155.938 q^{46} +36.9696 q^{47} +(300.921 - 220.923i) q^{48} +254.408 q^{49} -481.709 q^{50} +(190.566 + 259.572i) q^{51} -351.072i q^{52} +105.746i q^{53} +(-174.741 - 511.737i) q^{54} +2.47083i q^{55} -107.779 q^{56} +(411.684 - 302.240i) q^{57} -906.258i q^{58} +(-384.876 + 239.268i) q^{59} +(-3.09722 - 4.21876i) q^{60} +270.462i q^{61} -1179.49i q^{62} +(-197.689 + 629.627i) q^{63} -356.587 q^{64} +7.52283 q^{65} +(271.522 - 199.339i) q^{66} -201.641i q^{67} -424.874i q^{68} +(-169.460 + 124.410i) q^{69} +13.8401i q^{70} -659.691i q^{71} +(35.6652 - 113.592i) q^{72} +604.150i q^{73} +1363.56i q^{74} +(-523.480 + 384.315i) q^{75} -673.855 q^{76} -411.079 q^{77} +(-606.920 - 826.692i) q^{78} +496.729 q^{79} -10.5546i q^{80} +(-598.166 - 416.700i) q^{81} -999.455i q^{82} +1456.75 q^{83} +(701.888 - 515.294i) q^{84} +9.10429 q^{85} -227.359i q^{86} +(-723.027 - 984.843i) q^{87} +74.1632 q^{88} +145.988 q^{89} +(-14.5865 - 4.57982i) q^{90} +1251.60i q^{91} +277.377 q^{92} +(-941.017 - 1281.77i) q^{93} -142.493 q^{94} -14.4395i q^{95} +(-1012.09 + 743.034i) q^{96} -1332.12i q^{97} -980.577 q^{98} +(136.030 - 433.249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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