LMFDB - Embedded newform 177.3.c.a.58.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(58,177)]

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([0, 1]))

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 $ x^20 + 60x^18 + 1522x^16 + 21286x^14 + 179593x^12 + 941588x^10 + 3057025x^8 + 5962230x^6 + 6517782x^4 + 3428244*x^2 + 570861
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.1
Root			$-3.65759i$ of defining polynomial
Character	$\chi$	$=$	177.58
Dual form			177.3.c.a.58.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} -1.44793i q^{10} +8.54756i q^{11} +16.2431 q^{12} +0.0887419i q^{13} +22.7081i q^{14} -0.685665 q^{15} +34.4346 q^{16} -8.10940 q^{17} -10.9728i q^{18} +10.5067 q^{19} -3.71245 q^{20} +10.7534 q^{21} +31.2635 q^{22} +14.0307i q^{23} -34.0702i q^{24} -24.8433 q^{25} +0.324582 q^{26} -5.19615 q^{27} +58.2229 q^{28} -56.9344 q^{29} +2.50788i q^{30} -0.471045i q^{31} -47.2659i q^{32} -14.8048i q^{33} +29.6609i q^{34} -2.45774 q^{35} -28.1339 q^{36} -43.8322i q^{37} -38.4292i q^{38} -0.153705i q^{39} +7.78692i q^{40} +13.8735 q^{41} -39.3315i q^{42} +53.7675i q^{43} -80.1588i q^{44} +1.18761 q^{45} +51.3187 q^{46} +34.1786i q^{47} -59.6425 q^{48} -10.4549 q^{49} +90.8666i q^{50} +14.0459 q^{51} -0.832220i q^{52} -79.3757 q^{53} +19.0054i q^{54} +3.38371i q^{55} -122.123i q^{56} -18.1981 q^{57} +208.243i q^{58} +(-41.5316 + 41.9061i) q^{59} +6.43015 q^{60} +45.7782i q^{61} -1.72289 q^{62} -18.6254 q^{63} -35.1409 q^{64} +0.0351301i q^{65} -54.1499 q^{66} -104.453i q^{67} +76.0498 q^{68} -24.3019i q^{69} +8.98940i q^{70} +74.0325 q^{71} +59.0114i q^{72} -109.458i q^{73} -160.320 q^{74} +43.0298 q^{75} -98.5316 q^{76} -53.0673i q^{77} -0.562192 q^{78} -74.2528 q^{79} +13.6316 q^{80} +9.00000 q^{81} -50.7436i q^{82} -88.8936i q^{83} -100.845 q^{84} -3.21026 q^{85} +196.660 q^{86} +98.6133 q^{87} -168.134 q^{88} +142.879i q^{89} -4.34378i q^{90} -0.550951i q^{91} -131.580i q^{92} +0.815874i q^{93} +125.012 q^{94} +4.15927 q^{95} +81.8669i q^{96} -81.4737i q^{97} +38.2398i q^{98} +25.6427i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9}+O(q^{10}) $ 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9	$ 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 24 q^{12} + 24 q^{15} - 8 q^{16} + 16 q^{17} - 60 q^{19} - 164 q^{20} + 40 q^{22} + 100 q^{25} - 156 q^{26} + 200 q^{28} - 60 q^{29} - 32 q^{35} - 120 q^{36} + 28 q^{41} + 180 q^{46} - 96 q^{48} + 284 q^{49} - 24 q^{51} - 8 q^{53} + 24 q^{57} - 152 q^{59} - 72 q^{60} - 8 q^{62} - 24 q^{63} + 204 q^{64} - 120 q^{66} + 384 q^{68} + 92 q^{71} + 104 q^{74} + 240 q^{75} + 120 q^{76} - 468 q^{78} - 420 q^{79} + 376 q^{80} + 180 q^{81} + 168 q^{84} - 348 q^{85} + 232 q^{86} + 144 q^{87} - 212 q^{88} + 152 q^{94} + 788 q^{95}+O(q^{100}) $ 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9 - 24 * q^12 + 24 * q^15 - 8 * q^16 + 16 * q^17 - 60 * q^19 - 164 * q^20 + 40 * q^22 + 100 * q^25 - 156 * q^26 + 200 * q^28 - 60 * q^29 - 32 * q^35 - 120 * q^36 + 28 * q^41 + 180 * q^46 - 96 * q^48 + 284 * q^49 - 24 * q^51 - 8 * q^53 + 24 * q^57 - 152 * q^59 - 72 * q^60 - 8 * q^62 - 24 * q^63 + 204 * q^64 - 120 * q^66 + 384 * q^68 + 92 * q^71 + 104 * q^74 + 240 * q^75 + 120 * q^76 - 468 * q^78 - 420 * q^79 + 376 * q^80 + 180 * q^81 + 168 * q^84 - 348 * q^85 + 232 * q^86 + 144 * q^87 - 212 * q^88 + 152 * q^94 + 788 * q^95

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 $

$2$		−	3.65759i		−	1.82880i	−0.404816	−	0.914398i	$-0.632665\pi$
$2$		−	3.65759i		−	1.82880i	0.404816	−	0.914398i	$-0.367335\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−9.37798			−2.34450
$5$	0.395869			0.0791737			0.0395869	−	0.999216i	$-0.487396\pi$
$5$	0.395869			0.0791737			0.0395869	+	0.999216i	$0.487396\pi$
$6$			6.33514i			1.05586i
$7$	−6.20847			−0.886924			−0.443462	−	0.896293i	$-0.646250\pi$
$7$	−6.20847			−0.886924			−0.443462	+	0.896293i	$0.646250\pi$
$8$			19.6705i			2.45881i
$9$	3.00000			0.333333
$10$		−	1.44793i		−	0.144793i
$11$			8.54756i			0.777051i	0.921438	+	0.388525i	$0.127015\pi$
$11$			8.54756i			0.777051i	−0.921438	+	0.388525i	$0.872985\pi$
$12$	16.2431			1.35359
$13$			0.0887419i			0.00682630i	0.999994	+	0.00341315i	$0.00108644\pi$
$13$			0.0887419i			0.00682630i	−0.999994	+	0.00341315i	$0.998914\pi$
$14$			22.7081i			1.62200i
$15$	−0.685665			−0.0457110
$16$	34.4346			2.15216
$17$	−8.10940			−0.477023			−0.238512	−	0.971140i	$-0.576660\pi$
$17$	−8.10940			−0.477023			−0.238512	+	0.971140i	$0.576660\pi$
$18$		−	10.9728i		−	0.609599i
$19$	10.5067			0.552984			0.276492	−	0.961016i	$-0.410828\pi$
$19$	10.5067			0.552984			0.276492	+	0.961016i	$0.410828\pi$
$20$	−3.71245			−0.185622
$21$	10.7534			0.512066
$22$	31.2635			1.42107
$23$			14.0307i			0.610032i	0.952347	+	0.305016i	$0.0986618\pi$
$23$			14.0307i			0.610032i	−0.952347	+	0.305016i	$0.901338\pi$
$24$		−	34.0702i		−	1.41959i
$25$	−24.8433			−0.993732
$26$	0.324582			0.0124839
$27$	−5.19615			−0.192450
$28$	58.2229			2.07939
$29$	−56.9344			−1.96325			−0.981627	−	0.190808i	$-0.938889\pi$
$29$	−56.9344			−1.96325			−0.981627	+	0.190808i	$0.938889\pi$
$30$			2.50788i			0.0835960i
$31$		−	0.471045i		−	0.0151950i	−0.999971	−	0.00759751i	$-0.997582\pi$
$31$		−	0.471045i		−	0.0151950i	0.999971	−	0.00759751i	$-0.00241838\pi$
$32$		−	47.2659i		−	1.47706i
$33$		−	14.8048i		−	0.448631i
$34$			29.6609i			0.872378i
$35$	−2.45774			−0.0702211
$36$	−28.1339			−0.781498
$37$		−	43.8322i		−	1.18465i	−0.805698	−	0.592327i	$-0.798209\pi$
$37$		−	43.8322i		−	1.18465i	0.805698	−	0.592327i	$-0.201791\pi$
$38$		−	38.4292i		−	1.01129i
$39$		−	0.153705i		−	0.00394117i
$40$			7.78692i			0.194673i
$41$	13.8735			0.338378			0.169189	−	0.985584i	$-0.445885\pi$
$41$	13.8735			0.338378			0.169189	+	0.985584i	$0.445885\pi$
$42$		−	39.3315i		−	0.936464i
$43$			53.7675i			1.25041i	0.780462	+	0.625204i	$0.214984\pi$
$43$			53.7675i			1.25041i	−0.780462	+	0.625204i	$0.785016\pi$
$44$		−	80.1588i		−	1.82179i
$45$	1.18761			0.0263912
$46$	51.3187			1.11562
$47$			34.1786i			0.727205i	0.931554	+	0.363602i	$0.118453\pi$
$47$			34.1786i			0.727205i	−0.931554	+	0.363602i	$0.881547\pi$
$48$	−59.6425			−1.24255
$49$	−10.4549			−0.213365
$50$			90.8666i			1.81733i
$51$	14.0459			0.275410
$52$		−	0.832220i		−	0.0160042i
$53$	−79.3757			−1.49765			−0.748827	−	0.662765i	$-0.769383\pi$
$53$	−79.3757			−1.49765			−0.748827	+	0.662765i	$0.769383\pi$
$54$			19.0054i			0.351952i
$55$			3.38371i			0.0615220i
$56$		−	122.123i		−	2.18078i
$57$	−18.1981			−0.319265
$58$			208.243i			3.59039i
$59$	−41.5316	+	41.9061i	−0.703926	+	0.710273i
$59$	−41.5316	+	41.9061i	−0.703926	+	0.710273i
$60$	6.43015			0.107169
$61$			45.7782i			0.750462i	0.926931	+	0.375231i	$0.122437\pi$
$61$			45.7782i			0.750462i	−0.926931	+	0.375231i	$0.877563\pi$
$62$	−1.72289			−0.0277886
$63$	−18.6254			−0.295641
$64$	−35.1409			−0.549077
$65$			0.0351301i			0.000540463i
$66$	−54.1499			−0.820454
$67$		−	104.453i		−	1.55900i	−0.626403	−	0.779499i	$-0.715474\pi$
$67$		−	104.453i		−	1.55900i	0.626403	−	0.779499i	$-0.284526\pi$
$68$	76.0498			1.11838
$69$		−	24.3019i		−	0.352202i
$70$			8.98940i			0.128420i
$71$	74.0325			1.04271			0.521356	−	0.853340i	$-0.325427\pi$
$71$	74.0325			1.04271			0.521356	+	0.853340i	$0.325427\pi$
$72$			59.0114i			0.819602i
$73$		−	109.458i		−	1.49943i	−0.661761	−	0.749715i	$-0.730190\pi$
$73$		−	109.458i		−	1.49943i	0.661761	−	0.749715i	$-0.269810\pi$
$74$	−160.320			−2.16649
$75$	43.0298			0.573731
$76$	−98.5316			−1.29647
$77$		−	53.0673i		−	0.689185i
$78$	−0.562192			−0.00720759
$79$	−74.2528			−0.939909			−0.469954	−	0.882691i	$-0.655730\pi$
$79$	−74.2528			−0.939909			−0.469954	+	0.882691i	$0.655730\pi$
$80$	13.6316			0.170395
$81$	9.00000			0.111111
$82$		−	50.7436i		−	0.618825i
$83$		−	88.8936i		−	1.07101i	−0.844533	−	0.535503i	$-0.820122\pi$
$83$		−	88.8936i		−	1.07101i	0.844533	−	0.535503i	$-0.179878\pi$
$84$	−100.845			−1.20054
$85$	−3.21026			−0.0377677
$86$	196.660			2.28674
$87$	98.6133			1.13349
$88$	−168.134			−1.91062
$89$			142.879i			1.60538i	0.596394	+	0.802692i	$0.296600\pi$
$89$			142.879i			1.60538i	−0.596394	+	0.802692i	$0.703400\pi$
$90$		−	4.34378i		−	0.0482642i
$91$		−	0.550951i		−	0.00605441i
$92$		−	131.580i		−	1.43022i
$93$			0.815874i			0.00877284i
$94$	125.012			1.32991
$95$	4.15927			0.0437818
$96$			81.8669i			0.852780i
$97$		−	81.4737i		−	0.839935i	−0.907539	−	0.419968i	$-0.862041\pi$
$97$		−	81.4737i		−	0.839935i	0.907539	−	0.419968i	$-0.137959\pi$
$98$			38.2398i			0.390202i
$99$			25.6427i			0.259017i
$100$	232.980			2.32980
$101$		−	92.0885i		−	0.911768i	−0.890039	−	0.455884i	$-0.849323\pi$
$101$		−	92.0885i		−	0.911768i	0.890039	−	0.455884i	$-0.150677\pi$
$102$		−	51.3741i		−	0.503668i
$103$		−	147.520i		−	1.43223i	−0.697982	−	0.716115i	$-0.745918\pi$
$103$		−	147.520i		−	1.43223i	0.697982	−	0.716115i	$-0.254082\pi$
$104$	−1.74559			−0.0167846
$105$	4.25693			0.0405422
$106$			290.324i			2.73891i
$107$	68.9648			0.644530			0.322265	−	0.946649i	$-0.395556\pi$
$107$	68.9648			0.644530			0.322265	+	0.946649i	$0.395556\pi$
$108$	48.7294			0.451198
$109$		−	57.3299i		−	0.525963i	−0.964801	−	0.262981i	$-0.915294\pi$
$109$		−	57.3299i		−	0.525963i	0.964801	−	0.262981i	$-0.0847058\pi$
$110$	12.3762			0.112511
$111$			75.9196i			0.683961i
$112$	−213.786			−1.90881
$113$		−	19.6848i		−	0.174201i	−0.996200	−	0.0871007i	$-0.972240\pi$
$113$		−	19.6848i		−	0.174201i	0.996200	−	0.0871007i	$-0.0277602\pi$
$114$			66.5613i			0.583871i
$115$			5.55433i			0.0482985i
$116$	533.930			4.60284
$117$			0.266226i			0.00227543i
$118$	153.276	+	151.906i	1.29894	+	1.28734i
$119$	50.3469			0.423084
$120$		−	13.4873i		−	0.112394i
$121$	47.9392			0.396192
$122$	167.438			1.37244
$123$	−24.0296			−0.195363
$124$			4.41745i			0.0356246i
$125$	−19.7314			−0.157851
$126$			68.1242i			0.540668i
$127$	5.95404			0.0468822			0.0234411	−	0.999725i	$-0.492538\pi$
$127$	5.95404			0.0468822			0.0234411	+	0.999725i	$0.492538\pi$
$128$		−	60.5324i		−	0.472909i
$129$		−	93.1281i		−	0.721923i
$130$	0.128492			0.000988397
$131$			207.532i			1.58421i	0.610384	+	0.792106i	$0.291015\pi$
$131$			207.532i			1.58421i	−0.610384	+	0.792106i	$0.708985\pi$
$132$			138.839i			1.05181i
$133$	−65.2305			−0.490455
$134$	−382.046			−2.85109
$135$	−2.05699			−0.0152370
$136$		−	159.516i		−	1.17291i
$137$	−62.5295			−0.456419			−0.228210	−	0.973612i	$-0.573287\pi$
$137$	−62.5295			−0.456419			−0.228210	+	0.973612i	$0.573287\pi$
$138$	−88.8866			−0.644106
$139$	−101.500			−0.730217			−0.365108	−	0.930965i	$-0.618968\pi$
$139$	−101.500			−0.730217			−0.365108	+	0.930965i	$0.618968\pi$
$140$	23.0486			0.164633
$141$		−	59.1991i		−	0.419852i
$142$		−	270.781i		−	1.90691i
$143$	−0.758526			−0.00530438
$144$	103.304			0.717387
$145$	−22.5385			−0.155438
$146$	−400.354			−2.74215
$147$	18.1084			0.123187
$148$			411.058i			2.77742i
$149$		−	15.5533i		−	0.104385i	−0.998637	−	0.0521924i	$-0.983379\pi$
$149$		−	15.5533i		−	0.104385i	0.998637	−	0.0521924i	$-0.0166209\pi$
$150$		−	157.386i		−	1.04924i
$151$		−	48.2391i		−	0.319464i	−0.987160	−	0.159732i	$-0.948937\pi$
$151$		−	48.2391i		−	0.319464i	0.987160	−	0.159732i	$-0.0510631\pi$
$152$			206.671i			1.35968i
$153$	−24.3282			−0.159008
$154$	−194.098			−1.26038
$155$		−	0.186472i		−	0.00120305i
$156$			1.44145i			0.00924004i
$157$			218.253i			1.39014i	0.718940	+	0.695072i	$0.244628\pi$
$157$			218.253i			1.39014i	−0.718940	+	0.695072i	$0.755372\pi$
$158$			271.586i			1.71890i
$159$	137.483			0.864671
$160$		−	18.7111i		−	0.116944i
$161$		−	87.1094i		−	0.541052i
$162$		−	32.9183i		−	0.203200i
$163$	300.810			1.84546			0.922729	−	0.385449i	$-0.125953\pi$
$163$	300.810			1.84546			0.922729	+	0.385449i	$0.125953\pi$
$164$	−130.106			−0.793326
$165$		−	5.86076i		−	0.0355197i
$166$	−325.136			−1.95865
$167$	−285.372			−1.70881			−0.854407	−	0.519605i	$-0.826079\pi$
$167$	−285.372			−1.70881			−0.854407	+	0.519605i	$0.826079\pi$
$168$			211.524i			1.25907i
$169$	168.992			0.999953
$170$			11.7418i			0.0690694i
$171$	31.5201			0.184328
$172$		−	504.231i		−	2.93157i
$173$			115.450i			0.667344i	0.942689	+	0.333672i	$0.108288\pi$
$173$			115.450i			0.667344i	−0.942689	+	0.333672i	$0.891712\pi$
$174$		−	360.687i		−	2.07291i
$175$	154.239			0.881365
$176$			294.332i			1.67234i
$177$	71.9349	−	72.5835i	0.406412	−	0.410076i
$178$	522.594			2.93592
$179$			145.888i			0.815016i	0.913202	+	0.407508i	$0.133602\pi$
$179$			145.888i			0.815016i	−0.913202	+	0.407508i	$0.866398\pi$
$180$	−11.1373			−0.0618741
$181$	−40.9343			−0.226157			−0.113078	−	0.993586i	$-0.536071\pi$
$181$	−40.9343			−0.226157			−0.113078	+	0.993586i	$0.536071\pi$
$182$	−2.01516			−0.0110723
$183$		−	79.2901i		−	0.433280i
$184$	−275.991			−1.49995
$185$		−	17.3518i		−	0.0937935i
$186$	2.98414			0.0160437
$187$		−	69.3155i		−	0.370671i
$188$		−	320.527i		−	1.70493i
$189$	32.2602			0.170689
$190$		−	15.2129i		−	0.0800680i
$191$			281.121i			1.47184i	0.677070	+	0.735919i	$0.263249\pi$
$191$			281.121i			1.47184i	−0.677070	+	0.735919i	$0.736751\pi$
$192$	60.8658			0.317010
$193$	46.9362			0.243193			0.121596	−	0.992580i	$-0.461199\pi$
$193$	46.9362			0.243193			0.121596	+	0.992580i	$0.461199\pi$
$194$	−297.998			−1.53607
$195$		−	0.0608472i		−	0.000312037i
$196$	98.0459			0.500234
$197$	20.8170			0.105670			0.0528350	−	0.998603i	$-0.483174\pi$
$197$	20.8170			0.105670			0.0528350	+	0.998603i	$0.483174\pi$
$198$	93.7905			0.473689
$199$	−206.378			−1.03707			−0.518537	−	0.855055i	$-0.673523\pi$
$199$	−206.378			−1.03707			−0.518537	+	0.855055i	$0.673523\pi$
$200$		−	488.679i		−	2.44339i
$201$			180.918i			0.900088i
$202$	−336.822			−1.66744
$203$	353.475			1.74126
$204$	−131.722			−0.645696
$205$	5.49209			0.0267907
$206$	−539.567			−2.61926
$207$			42.0922i			0.203344i
$208$			3.05579i			0.0146913i
$209$			89.8066i			0.429697i
$210$		−	15.5701i		−	0.0741434i
$211$			200.660i			0.950993i	0.879718	+	0.475497i	$0.157732\pi$
$211$			200.660i			0.950993i	−0.879718	+	0.475497i	$0.842268\pi$
$212$	744.384			3.51124
$213$	−128.228			−0.602010
$214$		−	252.245i		−	1.17871i
$215$			21.2849i			0.0989994i
$216$		−	102.211i		−	0.473198i
$217$			2.92447i			0.0134768i
$218$	−209.690			−0.961879
$219$			189.588i			0.865697i
$220$		−	31.7324i		−	0.144238i
$221$		−	0.719643i		−	0.00325630i
$222$	277.683			1.25082
$223$	−271.603			−1.21795			−0.608976	−	0.793189i	$-0.708419\pi$
$223$	−271.603			−1.21795			−0.608976	+	0.793189i	$0.708419\pi$
$224$			293.449i			1.31004i
$225$	−74.5299			−0.331244
$226$	−71.9989			−0.318579
$227$			124.072i			0.546571i	0.961933	+	0.273286i	$0.0881104\pi$
$227$			124.072i			0.546571i	−0.961933	+	0.273286i	$0.911890\pi$
$228$	170.662			0.748516
$229$		−	269.653i		−	1.17752i	−0.808307	−	0.588762i	$-0.799616\pi$
$229$		−	269.653i		−	1.17752i	0.808307	−	0.588762i	$-0.200384\pi$
$230$	20.3155			0.0883281
$231$			91.9152i			0.397901i
$232$		−	1119.93i		−	4.82727i
$233$		−	432.383i		−	1.85572i	−0.372928	−	0.927860i	$-0.621646\pi$
$233$		−	432.383i		−	1.85572i	0.372928	−	0.927860i	$-0.378354\pi$
$234$	0.973745			0.00416130
$235$			13.5302i			0.0575755i
$236$	389.483	−	392.995i	1.65035	−	1.66523i
$237$	128.610			0.542657
$238$		−	184.149i		−	0.773733i
$239$	345.014			1.44357			0.721787	−	0.692115i	$-0.243321\pi$
$239$	345.014			1.44357			0.721787	+	0.692115i	$0.243321\pi$
$240$	−23.6106			−0.0983774
$241$	−395.883			−1.64267			−0.821334	−	0.570447i	$-0.806770\pi$
$241$	−395.883			−1.64267			−0.821334	+	0.570447i	$0.806770\pi$
$242$		−	175.342i		−	0.724554i
$243$	−15.5885			−0.0641500
$244$		−	429.307i		−	1.75945i
$245$	−4.13877			−0.0168929
$246$			87.8906i			0.357279i
$247$			0.932384i			0.00377483i
$248$	9.26568			0.0373616
$249$			153.968i			0.618346i
$250$			72.1694i			0.288678i
$251$	98.2846			0.391572			0.195786	−	0.980647i	$-0.437274\pi$
$251$	98.2846			0.391572			0.195786	+	0.980647i	$0.437274\pi$
$252$	174.669			0.693130
$253$	−119.929			−0.474026
$254$		−	21.7774i		−	0.0857379i
$255$	5.56033			0.0218052
$256$	−361.966			−1.41393
$257$	−248.162			−0.965609			−0.482805	−	0.875728i	$-0.660382\pi$
$257$	−248.162			−0.965609			−0.482805	+	0.875728i	$0.660382\pi$
$258$	−340.625			−1.32025
$259$			272.131i			1.05070i
$260$		−	0.329450i		−	0.00126711i
$261$	−170.803			−0.654418
$262$	759.066			2.89720
$263$	194.073			0.737919			0.368959	−	0.929446i	$-0.379714\pi$
$263$	194.073			0.737919			0.368959	+	0.929446i	$0.379714\pi$
$264$	291.217			1.10310
$265$	−31.4224			−0.118575
$266$			238.587i			0.896942i
$267$		−	247.474i		−	0.926869i
$268$			979.557i			3.65506i
$269$			213.661i			0.794278i	0.917758	+	0.397139i	$0.129997\pi$
$269$			213.661i			0.794278i	−0.917758	+	0.397139i	$0.870003\pi$
$270$			7.52364i			0.0278653i
$271$	−56.3572			−0.207960			−0.103980	−	0.994579i	$-0.533158\pi$
$271$	−56.3572			−0.207960			−0.103980	+	0.994579i	$0.533158\pi$
$272$	−279.244			−1.02663
$273$			0.954276i			0.00349552i
$274$			228.707i			0.834698i
$275$		−	212.349i		−	0.772180i
$276$			227.903i			0.825736i
$277$	170.342			0.614953			0.307476	−	0.951556i	$-0.400515\pi$
$277$	170.342			0.614953			0.307476	+	0.951556i	$0.400515\pi$
$278$			371.246i			1.33542i
$279$		−	1.41314i		−	0.00506500i
$280$		−	48.3448i		−	0.172660i
$281$	−39.9961			−0.142335			−0.0711674	−	0.997464i	$-0.522672\pi$
$281$	−39.9961			−0.142335			−0.0711674	+	0.997464i	$0.522672\pi$
$282$	−216.526			−0.767824
$283$			357.475i			1.26316i	0.775309	+	0.631581i	$0.217594\pi$
$283$			357.475i			1.26316i	−0.775309	+	0.631581i	$0.782406\pi$
$284$	−694.275			−2.44463
$285$	−7.20407			−0.0252774
$286$			2.77438i			0.00970063i
$287$	−86.1333			−0.300116
$288$		−	141.798i		−	0.492353i
$289$	−223.238			−0.772449
$290$			82.4368i			0.284265i
$291$			141.117i			0.484937i
$292$			1026.50i			3.51541i
$293$	67.1472			0.229171			0.114586	−	0.993413i	$-0.463446\pi$
$293$	67.1472			0.229171			0.114586	+	0.993413i	$0.463446\pi$
$294$		−	66.2332i		−	0.225283i
$295$	−16.4411	+	16.5893i	−0.0557324	+	0.0562350i
$296$	862.200			2.91284
$297$		−	44.4144i		−	0.149544i
$298$	−56.8878			−0.190899
$299$	−1.24511			−0.00416426
$300$	−403.533			−1.34511
$301$		−	333.814i		−	1.10902i
$302$	−176.439			−0.584235
$303$			159.502i			0.526409i
$304$	361.794			1.19011
$305$			18.1221i			0.0594169i
$306$			88.9826i			0.290793i
$307$	123.299			0.401626			0.200813	−	0.979630i	$-0.435642\pi$
$307$	123.299			0.401626			0.200813	+	0.979630i	$0.435642\pi$
$308$			497.664i			1.61579i
$309$			255.512i			0.826899i
$310$	−0.682039			−0.00220013
$311$	−246.230			−0.791737			−0.395868	−	0.918307i	$-0.629556\pi$
$311$	−246.230			−0.791737			−0.395868	+	0.918307i	$0.629556\pi$
$312$	3.02346			0.00969057
$313$			489.577i			1.56414i	0.623189	+	0.782071i	$0.285837\pi$
$313$			489.577i			1.56414i	−0.623189	+	0.782071i	$0.714163\pi$
$314$	798.280			2.54229
$315$	−7.37322			−0.0234070
$316$	696.341			2.20361
$317$	319.318			1.00731			0.503656	−	0.863904i	$-0.331988\pi$
$317$	319.318			1.00731			0.503656	+	0.863904i	$0.331988\pi$
$318$		−	502.856i		−	1.58131i
$319$		−	486.650i		−	1.52555i
$320$	−13.9112			−0.0434725
$321$	−119.450			−0.372120
$322$	−318.611			−0.989474
$323$	−85.2029			−0.263786
$324$	−84.4018			−0.260499
$325$		−	2.20464i		−	0.00678351i
$326$		−	1100.24i		−	3.37497i
$327$			99.2984i			0.303665i
$328$			272.898i			0.832007i
$329$		−	212.197i		−	0.644976i
$330$	−21.4363			−0.0649584
$331$	−222.382			−0.671850			−0.335925	−	0.941889i	$-0.609049\pi$
$331$	−222.382			−0.671850			−0.335925	+	0.941889i	$0.609049\pi$
$332$			833.642i			2.51097i
$333$		−	131.497i		−	0.394885i
$334$			1043.77i			3.12507i
$335$		−	41.3496i		−	0.123432i
$336$	370.288			1.10205
$337$			285.028i			0.845781i	0.906181	+	0.422890i	$0.138984\pi$
$337$			285.028i			0.845781i	−0.906181	+	0.422890i	$0.861016\pi$
$338$		−	618.104i		−	1.82871i
$339$			34.0950i			0.100575i
$340$	30.1057			0.0885462
$341$	4.02629			0.0118073
$342$		−	115.288i		−	0.337098i
$343$	369.124			1.07616
$344$	−1057.63			−3.07451
$345$		−	9.62037i		−	0.0278851i
$346$	422.271			1.22044
$347$		−	62.2130i		−	0.179288i	−0.995974	−	0.0896441i	$-0.971427\pi$
$347$		−	62.2130i		−	0.179288i	0.995974	−	0.0896441i	$-0.0285730\pi$
$348$	−924.793			−2.65745
$349$			291.454i			0.835112i	0.908651	+	0.417556i	$0.137113\pi$
$349$			291.454i			0.835112i	−0.908651	+	0.417556i	$0.862887\pi$
$350$		−	564.143i		−	1.61184i
$351$		−	0.461116i		−	0.00131372i
$352$	404.008			1.14775
$353$		−	306.106i		−	0.867156i	−0.901116	−	0.433578i	$-0.857251\pi$
$353$		−	306.106i		−	0.867156i	0.901116	−	0.433578i	$-0.142749\pi$
$354$	−265.481	−	263.109i	−0.749946	−	0.743245i
$355$	29.3071			0.0825553
$356$		−	1339.92i		−	3.76382i
$357$	−87.2035			−0.244267
$358$	533.598			1.49050
$359$	461.119			1.28445			0.642226	−	0.766515i	$-0.278011\pi$
$359$	461.119			1.28445			0.642226	+	0.766515i	$0.278011\pi$
$360$			23.3608i			0.0648910i
$361$	−250.609			−0.694209
$362$			149.721i			0.413594i
$363$	−83.0332			−0.228742
$364$			5.16681i			0.0141945i
$365$		−	43.3312i		−	0.118715i
$366$	−290.011			−0.792380
$367$		−	232.591i		−	0.633763i	−0.948465	−	0.316881i	$-0.897364\pi$
$367$		−	232.591i		−	0.633763i	0.948465	−	0.316881i	$-0.102636\pi$
$368$			483.143i			1.31289i
$369$	41.6205			0.112793
$370$	−63.4658			−0.171529
$371$	492.802			1.32831
$372$		−	7.65125i		−	0.0205679i
$373$	−36.2600			−0.0972117			−0.0486058	−	0.998818i	$-0.515478\pi$
$373$	−36.2600			−0.0972117			−0.0486058	+	0.998818i	$0.515478\pi$
$374$	−253.528			−0.677882
$375$	34.1758			0.0911354
$376$	−672.309			−1.78806
$377$		−	5.05246i		−	0.0134018i
$378$		−	117.994i		−	0.312155i
$379$	−37.4494			−0.0988110			−0.0494055	−	0.998779i	$-0.515733\pi$
$379$	−37.4494			−0.0988110			−0.0494055	+	0.998779i	$0.515733\pi$
$380$	−39.0056			−0.102646
$381$	−10.3127			−0.0270674
$382$	1028.23			2.69169
$383$	−487.151			−1.27193			−0.635967	−	0.771716i	$-0.719399\pi$
$383$	−487.151			−1.27193			−0.635967	+	0.771716i	$0.719399\pi$
$384$			104.845i			0.273034i
$385$		−	21.0077i		−	0.0545654i
$386$		−	171.673i		−	0.444750i
$387$			161.303i			0.416802i
$388$			764.059i			1.96922i
$389$	377.266			0.969834			0.484917	−	0.874560i	$-0.338850\pi$
$389$	377.266			0.969834			0.484917	+	0.874560i	$0.338850\pi$
$390$	−0.222554			−0.000570652
$391$		−	113.781i		−	0.290999i
$392$		−	205.653i		−	0.524624i
$393$		−	359.455i		−	0.914645i
$394$		−	76.1400i		−	0.193249i
$395$	−29.3944			−0.0744161
$396$		−	240.477i		−	0.607264i
$397$		−	457.106i		−	1.15140i	−0.817661	−	0.575700i	$-0.804730\pi$
$397$		−	457.106i		−	1.15140i	0.817661	−	0.575700i	$-0.195270\pi$
$398$			754.845i			1.89660i
$399$	112.983			0.283164
$400$	−855.469			−2.13867
$401$		−	242.627i		−	0.605056i	−0.953141	−	0.302528i	$-0.902169\pi$
$401$		−	242.627i		−	0.605056i	0.953141	−	0.302528i	$-0.0978305\pi$
$402$	661.723			1.64608
$403$	0.0418014			0.000103726
$404$			863.605i			2.13764i
$405$	3.56282			0.00879708
$406$		−	1292.87i		−	3.18441i
$407$	374.658			0.920537
$408$			276.289i			0.677179i
$409$		−	362.561i		−	0.886458i	−0.896408	−	0.443229i	$-0.853833\pi$
$409$		−	362.561i		−	0.886458i	0.896408	−	0.443229i	$-0.146167\pi$
$410$		−	20.0878i		−	0.0489947i
$411$	108.304			0.263514
$412$			1383.44i			3.35786i
$413$	257.848	−	260.173i	0.624329	−	0.629959i
$414$	153.956			0.371875
$415$		−	35.1902i		−	0.0847956i
$416$	4.19446			0.0100828
$417$	175.803			0.421591
$418$	328.476			0.785827
$419$		−	818.928i		−	1.95448i	−0.212133	−	0.977241i	$-0.568041\pi$
$419$		−	818.928i		−	1.95448i	0.212133	−	0.977241i	$-0.431959\pi$
$420$	−39.9214			−0.0950509
$421$		−	329.980i		−	0.783801i	−0.920008	−	0.391901i	$-0.871818\pi$
$421$		−	329.980i		−	0.783801i	0.920008	−	0.391901i	$-0.128182\pi$
$422$	733.931			1.73917
$423$			102.536i			0.242402i
$424$		−	1561.36i		−	3.68244i
$425$	201.464			0.474033
$426$			469.006i			1.10095i
$427$		−	284.213i		−	0.665603i
$428$	−646.750			−1.51110
$429$	1.31381			0.00306249
$430$	77.8514			0.181050
$431$			713.566i			1.65561i	0.561019	+	0.827803i	$0.310410\pi$
$431$			713.566i			1.65561i	−0.561019	+	0.827803i	$0.689590\pi$
$432$	−178.927			−0.414184
$433$	625.618			1.44485			0.722423	−	0.691452i	$-0.243029\pi$
$433$	625.618			1.44485			0.722423	+	0.691452i	$0.243029\pi$
$434$	10.6965			0.0246464
$435$	39.0379			0.0897423
$436$			537.639i			1.23312i
$437$			147.417i			0.337338i
$438$	693.434			1.58318
$439$	−461.737			−1.05179			−0.525897	−	0.850548i	$-0.676270\pi$
$439$	−461.737			−1.05179			−0.525897	+	0.850548i	$0.676270\pi$
$440$	−66.5591			−0.151271
$441$	−31.3647			−0.0711218
$442$	−2.63216			−0.00595511
$443$			255.246i			0.576175i	0.957604	+	0.288088i	$0.0930195\pi$
$443$			255.246i			0.576175i	−0.957604	+	0.288088i	$0.906981\pi$
$444$		−	711.973i		−	1.60354i
$445$			56.5614i			0.127104i
$446$			993.413i			2.22738i
$447$			26.9392i			0.0602666i
$448$	218.171			0.486989
$449$	−224.485			−0.499966			−0.249983	−	0.968250i	$-0.580425\pi$
$449$	−224.485			−0.499966			−0.249983	+	0.968250i	$0.580425\pi$
$450$			272.600i			0.605777i
$451$			118.585i			0.262937i
$452$			184.603i			0.408415i
$453$			83.5526i			0.184443i
$454$	453.804			0.999568
$455$		−	0.218104i		−	0.000479350i
$456$		−	357.966i		−	0.785012i
$457$		−	64.2869i		−	0.140671i	−0.997523	−	0.0703357i	$-0.977593\pi$
$457$		−	64.2869i		−	0.140671i	0.997523	−	0.0703357i	$-0.0224071\pi$
$458$	−986.281			−2.15345
$459$	42.1377			0.0918032
$460$		−	52.0884i		−	0.113236i
$461$	−212.758			−0.461513			−0.230757	−	0.973012i	$-0.574120\pi$
$461$	−212.758			−0.461513			−0.230757	+	0.973012i	$0.574120\pi$
$462$	336.188			0.727680
$463$		−	291.329i		−	0.629221i	−0.949221	−	0.314610i	$-0.898126\pi$
$463$		−	291.329i		−	0.629221i	0.949221	−	0.314610i	$-0.101874\pi$
$464$	−1960.51			−4.22524
$465$			0.322979i			0.000694579i
$466$	−1581.48			−3.39373
$467$			31.5294i			0.0675148i	0.999430	+	0.0337574i	$0.0107474\pi$
$467$			31.5294i			0.0675148i	−0.999430	+	0.0337574i	$0.989253\pi$
$468$		−	2.49666i		−	0.00533474i
$469$			648.493i			1.38271i
$470$	49.4881			0.105294
$471$		−	378.025i		−	0.802600i
$472$	−824.313	−	816.946i	−1.74643	−	1.73082i
$473$	−459.581			−0.971630
$474$		−	470.402i		−	0.992408i
$475$	−261.021			−0.549518
$476$	−472.153			−0.991917
$477$	−238.127			−0.499218
$478$		−	1261.92i		−	2.64000i
$479$	−172.294			−0.359695			−0.179848	−	0.983694i	$-0.557560\pi$
$479$	−172.294			−0.359695			−0.179848	+	0.983694i	$0.557560\pi$
$480$			32.4085i			0.0675178i
$481$	3.88975			0.00808680
$482$			1447.98i			3.00411i
$483$			150.878i			0.312376i
$484$	−449.573			−0.928870
$485$		−	32.2529i		−	0.0665008i
$486$			57.0162i			0.117317i
$487$	−403.087			−0.827694			−0.413847	−	0.910347i	$-0.635815\pi$
$487$	−403.087			−0.827694			−0.413847	+	0.910347i	$0.635815\pi$
$488$	−900.478			−1.84524
$489$	−521.018			−1.06548
$490$			15.1379i			0.0308937i
$491$	294.608			0.600017			0.300008	−	0.953937i	$-0.403011\pi$
$491$	294.608			0.600017			0.300008	+	0.953937i	$0.403011\pi$
$492$	225.349			0.458027
$493$	461.703			0.936518
$494$	3.41028			0.00690340
$495$			10.1511i			0.0205073i
$496$		−	16.2203i		−	0.0327021i
$497$	−459.628			−0.924806
$498$	563.153			1.13083
$499$	515.505			1.03308			0.516538	−	0.856264i	$-0.327220\pi$
$499$	515.505			1.03308			0.516538	+	0.856264i	$0.327220\pi$
$500$	185.041			0.370081
$501$	494.279			0.986584
$502$		−	359.485i		−	0.716105i
$503$		−	618.687i		−	1.22999i	−0.788529	−	0.614997i	$-0.789157\pi$
$503$		−	618.687i		−	1.22999i	0.788529	−	0.614997i	$-0.210843\pi$
$504$		−	366.370i		−	0.726925i
$505$		−	36.4550i		−	0.0721881i
$506$			438.650i			0.866896i
$507$	−292.703			−0.577323
$508$	−55.8368			−0.109915
$509$		−	597.596i		−	1.17406i	−0.809566	−	0.587029i	$-0.800297\pi$
$509$		−	597.596i		−	1.17406i	0.809566	−	0.587029i	$-0.199703\pi$
$510$		−	20.3374i		−	0.0398773i
$511$			679.569i			1.32988i
$512$			1081.80i			2.11288i
$513$	−54.5944			−0.106422
$514$			907.674i			1.76590i
$515$		−	58.3984i		−	0.113395i
$516$			873.353i			1.69255i
$517$	−292.144			−0.565075
$518$	995.344			1.92151
$519$		−	199.966i		−	0.385291i
$520$	−0.691026			−0.00132890
$521$	−190.298			−0.365256			−0.182628	−	0.983182i	$-0.558460\pi$
$521$	−190.298			−0.365256			−0.182628	+	0.983182i	$0.558460\pi$
$522$			624.728i			1.19680i
$523$	−579.438			−1.10791			−0.553956	−	0.832546i	$-0.686882\pi$
$523$	−579.438			−1.10791			−0.553956	+	0.832546i	$0.686882\pi$
$524$		−	1946.23i		−	3.71418i
$525$	−267.149			−0.508856
$526$		−	709.838i		−	1.34950i
$527$			3.81989i			0.00724837i
$528$		−	509.798i		−	0.965526i
$529$	332.139			0.627861
$530$			114.930i			0.216849i
$531$	−124.595	+	125.718i	−0.234642	+	0.236758i
$532$	611.730			1.14987
$533$			1.23116i			0.00230987i
$534$	−905.159			−1.69505
$535$	27.3010			0.0510299
$536$	2054.64			3.83328
$537$		−	252.685i		−	0.470550i
$538$	781.484			1.45257
$539$		−	89.3639i		−	0.165796i
$540$	19.2904			0.0357230
$541$			808.858i			1.49512i	0.664196	+	0.747558i	$0.268774\pi$
$541$			808.858i			1.49512i	−0.664196	+	0.747558i	$0.731226\pi$
$542$			206.132i			0.380317i
$543$	70.9004			0.130572
$544$			383.298i			0.704591i
$545$		−	22.6951i		−	0.0416424i
$546$	3.49035			0.00639258
$547$	270.832			0.495122			0.247561	−	0.968872i	$-0.420371\pi$
$547$	270.832			0.495122			0.247561	+	0.968872i	$0.420371\pi$
$548$	586.400			1.07007
$549$			137.335i			0.250154i
$550$	−776.688			−1.41216
$551$	−598.192			−1.08565
$552$	478.030			0.865997
$553$	460.996			0.833628
$554$		−	623.041i		−	1.12462i
$555$			30.0542i			0.0541517i
$556$	951.866			1.71199
$557$	−519.832			−0.933270			−0.466635	−	0.884450i	$-0.654534\pi$
$557$	−519.832			−0.933270			−0.466635	+	0.884450i	$0.654534\pi$
$558$	−5.16868			−0.00926286
$559$	−4.77143			−0.00853565
$560$	−84.6312			−0.151127
$561$			120.058i			0.214007i
$562$			146.289i			0.260301i
$563$			417.978i			0.742411i	0.928551	+	0.371206i	$0.121056\pi$
$563$			417.978i			0.742411i	−0.928551	+	0.371206i	$0.878944\pi$
$564$			555.168i			0.984341i
$565$		−	7.79258i		−	0.0137922i
$566$	1307.50			2.31007
$567$	−55.8762			−0.0985471
$568$			1456.25i			2.56383i
$569$		−	285.720i		−	0.502144i	−0.967968	−	0.251072i	$-0.919217\pi$
$569$		−	285.720i		−	0.502144i	0.967968	−	0.251072i	$-0.0807831\pi$
$570$			26.3495i			0.0462273i
$571$		−	69.7739i		−	0.122196i	−0.998132	−	0.0610980i	$-0.980540\pi$
$571$		−	69.7739i		−	0.122196i	0.998132	−	0.0610980i	$-0.0194602\pi$
$572$	7.11345			0.0124361
$573$		−	486.916i		−	0.849766i
$574$			315.040i			0.548851i
$575$		−	348.569i		−	0.606208i
$576$	−105.423			−0.183026
$577$	114.805			0.198968			0.0994840	−	0.995039i	$-0.468281\pi$
$577$	114.805			0.198968			0.0994840	+	0.995039i	$0.468281\pi$
$578$			816.512i			1.41265i
$579$	−81.2959			−0.140407
$580$	211.366			0.364424
$581$			551.893i			0.949902i
$582$	516.147			0.886850
$583$		−	678.469i		−	1.16375i
$584$	2153.10			3.68681
$585$			0.105390i			0.000180154i
$586$		−	245.597i		−	0.419108i
$587$			861.663i			1.46791i	0.679199	+	0.733954i	$0.262327\pi$
$587$			861.663i			1.46791i	−0.679199	+	0.733954i	$0.737673\pi$
$588$	−169.820			−0.288810
$589$		−	4.94913i		−	0.00840260i
$590$	60.6770	+	60.1347i	0.102842	+	0.101923i
$591$	−36.0561			−0.0610085
$592$		−	1509.34i		−	2.54957i
$593$	903.733			1.52400			0.762001	−	0.647576i	$-0.224217\pi$
$593$	903.733			1.52400			0.762001	+	0.647576i	$0.224217\pi$
$594$	−162.450			−0.273485
$595$	19.9308			0.0334971
$596$			145.859i			0.244730i
$597$	357.457			0.598755
$598$			4.55412i			0.00761558i
$599$	236.884			0.395466			0.197733	−	0.980256i	$-0.436642\pi$
$599$	236.884			0.395466			0.197733	+	0.980256i	$0.436642\pi$
$600$			846.417i			1.41069i
$601$			681.352i			1.13370i	0.823822	+	0.566848i	$0.191837\pi$
$601$			681.352i			1.13370i	−0.823822	+	0.566848i	$0.808163\pi$
$602$	−1220.96			−2.02817
$603$		−	313.359i		−	0.519666i
$604$			452.386i			0.748983i
$605$	18.9776			0.0313680
$606$	583.393			0.962695
$607$	−855.559			−1.40949			−0.704744	−	0.709462i	$-0.748938\pi$
$607$	−855.559			−1.40949			−0.704744	+	0.709462i	$0.748938\pi$
$608$		−	496.608i		−	0.816790i
$609$	−612.237			−1.00532
$610$	66.2834			0.108661
$611$	−3.03308			−0.00496412
$612$	228.149			0.372793
$613$			629.123i			1.02630i	0.858299	+	0.513151i	$0.171522\pi$
$613$			629.123i			1.02630i	−0.858299	+	0.513151i	$0.828478\pi$
$614$		−	450.978i		−	0.734492i
$615$	−9.51257			−0.0154676
$616$	1043.86			1.69457
$617$	−909.047			−1.47333			−0.736667	−	0.676256i	$-0.763602\pi$
$617$	−909.047			−1.47333			−0.736667	+	0.676256i	$0.763602\pi$
$618$	934.558			1.51223
$619$	437.303			0.706466			0.353233	−	0.935535i	$-0.385082\pi$
$619$	437.303			0.706466			0.353233	+	0.935535i	$0.385082\pi$
$620$			1.74873i			0.00282053i
$621$		−	72.9058i		−	0.117401i
$622$			900.609i			1.44792i
$623$		−	887.061i		−	1.42385i
$624$		−	5.29279i		−	0.00848203i
$625$	613.271			0.981234
$626$	1790.67			2.86050
$627$		−	155.550i		−	0.248085i
$628$		−	2046.77i		−	3.25919i
$629$			355.453i			0.565108i
$630$			26.9682i			0.0428067i
$631$	−548.459			−0.869190			−0.434595	−	0.900626i	$-0.643108\pi$
$631$	−548.459			−0.869190			−0.434595	+	0.900626i	$0.643108\pi$
$632$		−	1460.59i		−	2.31106i
$633$		−	347.553i		−	0.549056i
$634$		−	1167.93i		−	1.84217i
$635$	2.35702			0.00371184
$636$	−1289.31			−2.02722
$637$		−	0.927788i		−	0.00145650i
$638$	−1779.97			−2.78992
$639$	222.097			0.347570
$640$		−	23.9629i		−	0.0374420i
$641$	−1064.88			−1.66128			−0.830640	−	0.556810i	$-0.812025\pi$
$641$	−1064.88			−1.66128			−0.830640	+	0.556810i	$0.812025\pi$
$642$			436.901i			0.680531i
$643$	1042.17			1.62079			0.810395	−	0.585884i	$-0.199252\pi$
$643$	1042.17			1.62079			0.810395	+	0.585884i	$0.199252\pi$
$644$			816.910i			1.26849i
$645$		−	36.8665i		−	0.0571573i
$646$			311.638i			0.482411i
$647$	−144.371			−0.223138			−0.111569	−	0.993757i	$-0.535588\pi$
$647$	−144.371			−0.223138			−0.111569	+	0.993757i	$0.535588\pi$
$648$			177.034i			0.273201i
$649$	−358.195	−	354.994i	−0.551918	−	0.546986i
$650$	−8.06367			−0.0124057
$651$		−	5.06533i		−	0.00778085i
$652$	−2820.99			−4.32667
$653$	−816.374			−1.25019			−0.625095	−	0.780549i	$-0.714940\pi$
$653$	−816.374			−1.25019			−0.625095	+	0.780549i	$0.714940\pi$
$654$	363.193			0.555341
$655$			82.1553i			0.125428i
$656$	477.729			0.728245
$657$		−	328.375i		−	0.499810i
$658$	−776.130			−1.17953
$659$			317.201i			0.481337i	0.970607	+	0.240669i	$0.0773667\pi$
$659$			317.201i			0.481337i	−0.970607	+	0.240669i	$0.922633\pi$
$660$			54.9621i			0.0832759i
$661$	307.730			0.465552			0.232776	−	0.972530i	$-0.425219\pi$
$661$	307.730			0.465552			0.232776	+	0.972530i	$0.425219\pi$
$662$			813.384i			1.22868i
$663$			1.24646i			0.00188003i
$664$	1748.58			2.63340
$665$	−25.8227			−0.0388311
$666$	−480.961			−0.722164
$667$		−	798.831i		−	1.19765i
$668$	2676.21			4.00631
$669$	470.430			0.703184
$670$	−151.240			−0.225731
$671$	−391.292			−0.583147
$672$		−	508.268i		−	0.756351i
$673$		−	1083.95i		−	1.61062i	−0.592853	−	0.805311i	$-0.701998\pi$
$673$		−	1083.95i		−	1.61062i	0.592853	−	0.805311i	$-0.298002\pi$
$674$	1042.52			1.54676
$675$	129.090			0.191244
$676$	−1584.80			−2.34439
$677$	−815.853			−1.20510			−0.602550	−	0.798081i	$-0.705849\pi$
$677$	−815.853			−1.20510			−0.602550	+	0.798081i	$0.705849\pi$
$678$	124.706			0.183932
$679$			505.827i			0.744959i
$680$		−	63.1472i		−	0.0928635i
$681$		−	214.899i		−	0.315563i
$682$		−	14.7265i		−	0.0215931i
$683$			1151.50i			1.68594i	0.537957	+	0.842972i	$0.319196\pi$
$683$			1151.50i			1.68594i	−0.537957	+	0.842972i	$0.680804\pi$
$684$	−295.595			−0.432156
$685$	−24.7534			−0.0361364
$686$		−	1350.10i		−	1.96808i
$687$			467.053i			0.679844i
$688$			1851.46i			2.69108i
$689$		−	7.04395i		−	0.0102234i
$690$	−35.1874			−0.0509962
$691$			939.727i			1.35995i	0.733234	+	0.679976i	$0.238010\pi$
$691$			939.727i			1.35995i	−0.733234	+	0.679976i	$0.761990\pi$
$692$		−	1082.69i		−	1.56458i
$693$		−	159.202i		−	0.229728i
$694$	−227.550			−0.327882
$695$	−40.1807			−0.0578140
$696$			1939.77i			2.78702i
$697$	−112.506			−0.161414
$698$	1066.02			1.52725
$699$			748.909i			1.07140i
$700$	−1446.45			−2.06636
$701$			782.026i			1.11559i	0.829980	+	0.557793i	$0.188352\pi$
$701$			782.026i			1.11559i	−0.829980	+	0.557793i	$0.811648\pi$
$702$	−1.68658			−0.00240253
$703$		−	460.532i		−	0.655095i
$704$		−	300.369i		−	0.426661i
$705$		−	23.4351i		−	0.0332412i
$706$	−1119.61			−1.58585
$707$			571.729i			0.808669i
$708$	−674.604	+	680.687i	−0.952831	+	0.961422i
$709$	−461.863			−0.651429			−0.325715	−	0.945468i	$-0.605605\pi$
$709$	−461.863			−0.651429			−0.325715	+	0.945468i	$0.605605\pi$
$710$		−	107.194i		−	0.150977i
$711$	−222.758			−0.313303
$712$	−2810.50			−3.94733
$713$	6.60911			0.00926944
$714$			318.955i			0.446715i
$715$	−0.300277			−0.000419968
$716$		−	1368.13i		−	1.91080i
$717$	−597.582			−0.833448
$718$		−	1686.58i		−	2.34900i
$719$		−	398.240i		−	0.553881i	−0.960887	−	0.276940i	$-0.910680\pi$
$719$		−	398.240i		−	0.553881i	0.960887	−	0.276940i	$-0.0893205\pi$
$720$	40.8947			0.0567982
$721$			915.872i			1.27028i
$722$			916.627i			1.26957i
$723$	685.690			0.948395
$724$	383.881			0.530223
$725$	1414.44			1.95095
$726$			303.701i			0.418322i
$727$	−402.797			−0.554053			−0.277027	−	0.960862i	$-0.589349\pi$
$727$	−402.797			−0.554053			−0.277027	+	0.960862i	$0.589349\pi$
$728$	10.8375			0.0148866
$729$	27.0000			0.0370370
$730$	−158.488			−0.217106
$731$		−	436.022i		−	0.596473i
$732$			743.581i			1.01582i
$733$	701.565			0.957114			0.478557	−	0.878056i	$-0.341160\pi$
$733$	701.565			0.957114			0.478557	+	0.878056i	$0.341160\pi$
$734$	−850.723			−1.15902
$735$	7.16856			0.00975314
$736$	663.175			0.901053
$737$	892.817			1.21142
$738$		−	152.231i		−	0.206275i
$739$			952.579i			1.28901i	0.764599	+	0.644506i	$0.222937\pi$
$739$			952.579i			1.28901i	−0.764599	+	0.644506i	$0.777063\pi$
$740$			162.725i			0.219898i
$741$		−	1.61494i		−	0.00217940i
$742$		−	1802.47i		−	2.42920i
$743$	−681.496			−0.917222			−0.458611	−	0.888637i	$-0.651653\pi$
$743$	−681.496			−0.917222			−0.458611	+	0.888637i	$0.651653\pi$
$744$	−16.0486			−0.0215707
$745$		−	6.15708i		−	0.00826454i
$746$			132.624i			0.177780i
$747$		−	266.681i		−	0.357002i
$748$			650.040i			0.869037i
$749$	−428.166			−0.571650
$750$		−	125.001i		−	0.166668i
$751$		−	1302.06i		−	1.73376i	−0.498514	−	0.866882i	$-0.666121\pi$
$751$		−	1302.06i		−	1.73376i	0.498514	−	0.866882i	$-0.333879\pi$
$752$			1176.93i			1.56506i
$753$	−170.234			−0.226074
$754$	−18.4799			−0.0245091
$755$		−	19.0964i		−	0.0252932i
$756$	−302.535			−0.400179
$757$	653.976			0.863904			0.431952	−	0.901896i	$-0.357825\pi$
$757$	653.976			0.863904			0.431952	+	0.901896i	$0.357825\pi$
$758$			136.975i			0.180705i
$759$	207.722			0.273679
$760$			81.8148i			0.107651i
$761$	638.164			0.838586			0.419293	−	0.907851i	$-0.362278\pi$
$761$	638.164			0.838586			0.419293	+	0.907851i	$0.362278\pi$
$762$			37.7196i			0.0495008i
$763$			355.931i			0.466489i
$764$		−	2636.35i		−	3.45072i
$765$	−9.63077			−0.0125892
$766$			1781.80i			2.32611i
$767$	−3.71883	−	3.68560i	−0.00484854	−	0.00480521i
$768$	626.944			0.816334
$769$			1305.23i			1.69730i	0.528951	+	0.848652i	$0.322586\pi$
$769$			1305.23i			1.69730i	−0.528951	+	0.848652i	$0.677414\pi$
$770$	−76.8375			−0.0997889
$771$	429.829			0.557495
$772$	−440.167			−0.570164
$773$			155.891i			0.201671i	0.994903	+	0.100835i	$0.0321515\pi$
$773$			155.891i			0.201671i	−0.994903	+	0.100835i	$0.967848\pi$
$774$	589.979			0.762247
$775$			11.7023i			0.0150998i
$776$	1602.63			2.06524
$777$		−	471.345i		−	0.606621i
$778$		−	1379.88i		−	1.77363i
$779$	145.765			0.187118
$780$			0.570623i			0.000731569i
$781$			632.797i			0.810240i
$782$	−416.164			−0.532178
$783$	295.840			0.377829
$784$	−360.010			−0.459197
$785$			86.3994i			0.110063i
$786$	−1314.74			−1.67270
$787$	389.653			0.495111			0.247556	−	0.968874i	$-0.420373\pi$
$787$	389.653			0.495111			0.247556	+	0.968874i	$0.420373\pi$
$788$	−195.221			−0.247743
$789$	−336.144			−0.426037
$790$			107.513i			0.136092i
$791$			122.212i			0.154504i
$792$	−504.403			−0.636873
$793$	−4.06244			−0.00512288
$794$	−1671.91			−2.10568
$795$	54.4251			0.0684593
$796$	1935.41			2.43141
$797$			48.4897i			0.0608403i	0.999537	+	0.0304201i	$0.00968453\pi$
$797$			48.4897i			0.0608403i	−0.999537	+	0.0304201i	$0.990315\pi$
$798$		−	413.244i		−	0.517850i
$799$		−	277.168i		−	0.346894i
$800$			1174.24i			1.46780i
$801$			428.638i			0.535128i
$802$	−887.432			−1.10652
$803$	935.602			1.16513
$804$		−	1696.64i		−	2.11025i
$805$		−	34.4839i		−	0.0428371i
$806$		−	0.152893i		−	0.000189693i
$807$		−	370.071i		−	0.458577i
$808$	1811.42			2.24186
$809$			1140.26i			1.40947i	0.709472	+	0.704734i	$0.248934\pi$
$809$			1140.26i			1.40947i	−0.709472	+	0.704734i	$0.751066\pi$
$810$		−	13.0313i		−	0.0160881i
$811$		−	30.8005i		−	0.0379784i	−0.999820	−	0.0189892i	$-0.993955\pi$
$811$		−	30.8005i		−	0.0379784i	0.999820	−	0.0189892i	$-0.00604481\pi$
$812$	−3314.89			−4.08237
$813$	97.6135			0.120066
$814$		−	1370.35i		−	1.68347i
$815$	119.081			0.146112
$816$	483.664			0.592726
$817$			564.919i			0.691455i
$818$	−1326.10			−1.62115
$819$		−	1.65285i		−	0.00201814i
$820$	−51.5047			−0.0628106
$821$		−	892.226i		−	1.08675i	−0.839489	−	0.543377i	$-0.817145\pi$
$821$		−	892.226i		−	1.08675i	0.839489	−	0.543377i	$-0.182855\pi$
$822$		−	396.133i		−	0.481913i
$823$		−	1300.11i		−	1.57972i	−0.613290	−	0.789858i	$-0.710154\pi$
$823$		−	1300.11i		−	1.57972i	0.613290	−	0.789858i	$-0.289846\pi$
$824$	2901.78			3.52158
$825$			367.800i			0.445818i
$826$	−951.606	−	943.103i	−1.15207	−	1.14177i
$827$	−1617.28			−1.95559			−0.977797	−	0.209556i	$-0.932798\pi$
$827$	−1617.28			−1.95559			−0.977797	+	0.209556i	$0.932798\pi$
$828$		−	394.740i		−	0.476739i
$829$	353.866			0.426859			0.213430	−	0.976958i	$-0.431537\pi$
$829$	353.866			0.426859			0.213430	+	0.976958i	$0.431537\pi$
$830$	−128.711			−0.155074
$831$	−295.041			−0.355043
$832$		−	3.11847i		−	0.00374816i
$833$	84.7829			0.101780
$834$		−	643.017i		−	0.771003i
$835$	−112.970			−0.135293
$836$		−	842.204i		−	1.00742i
$837$			2.44762i			0.00292428i
$838$	−2995.30			−3.57435
$839$			968.406i			1.15424i	0.816660	+	0.577119i	$0.195823\pi$
$839$			968.406i			1.15424i	−0.816660	+	0.577119i	$0.804177\pi$
$840$			83.7357i			0.0996854i
$841$	2400.52			2.85437
$842$	−1206.93			−1.43341
$843$	69.2752			0.0821770
$844$		−	1881.78i		−	2.22960i
$845$	66.8987			0.0791700
$846$	375.035			0.443303
$847$	−297.629			−0.351392
$848$	−2733.27			−3.22320
$849$		−	619.165i		−	0.729287i
$850$		−	736.873i		−	0.866910i
$851$	614.998			0.722677
$852$	1202.52			1.41141
$853$	−303.366			−0.355646			−0.177823	−	0.984063i	$-0.556905\pi$
$853$	−303.366			−0.355646			−0.177823	+	0.984063i	$0.556905\pi$
$854$	−1039.53			−1.21725
$855$	12.4778			0.0145939
$856$			1356.57i			1.58478i
$857$		−	662.303i		−	0.772816i	−0.922328	−	0.386408i	$-0.873716\pi$
$857$		−	662.303i		−	0.772816i	0.922328	−	0.386408i	$-0.126284\pi$
$858$		−	4.80537i		−	0.00560066i
$859$		−	1317.31i		−	1.53354i	−0.641924	−	0.766769i	$-0.721863\pi$
$859$		−	1317.31i		−	1.53354i	0.641924	−	0.766769i	$-0.278137\pi$
$860$		−	199.609i		−	0.232104i
$861$	149.187			0.173272
$862$	2609.93			3.02777
$863$		−	248.154i		−	0.287548i	−0.989611	−	0.143774i	$-0.954076\pi$
$863$		−	248.154i		−	0.287548i	0.989611	−	0.143774i	$-0.0459238\pi$
$864$			245.601i			0.284260i
$865$			45.7032i			0.0528361i
$866$		−	2288.26i		−	2.64233i
$867$	386.659			0.445974
$868$		−	27.4256i		−	0.0315963i
$869$		−	634.680i		−	0.730357i
$870$		−	142.785i		−	0.164120i
$871$	9.26935			0.0106422
$872$	1127.71			1.29324
$873$		−	244.421i		−	0.279978i
$874$	539.190			0.616922
$875$	122.502			0.140002
$876$		−	1777.95i		−	2.02962i
$877$	1210.94			1.38078			0.690390	−	0.723437i	$-0.257439\pi$
$877$	1210.94			1.38078			0.690390	+	0.723437i	$0.257439\pi$
$878$			1688.85i			1.92352i
$879$	−116.302			−0.132312
$880$			116.517i			0.132405i
$881$			821.372i			0.932318i	0.884701	+	0.466159i	$0.154363\pi$
$881$			821.372i			0.932318i	−0.884701	+	0.466159i	$0.845637\pi$
$882$			114.719i			0.130067i
$883$	−121.125			−0.137175			−0.0685874	−	0.997645i	$-0.521849\pi$
$883$	−121.125			−0.137175			−0.0685874	+	0.997645i	$0.521849\pi$
$884$			6.74880i			0.00763439i
$885$	28.4768	−	28.7335i	0.0321771	−	0.0324673i
$886$	933.585			1.05371
$887$			385.806i			0.434956i	0.976065	+	0.217478i	$0.0697830\pi$
$887$			385.806i			0.434956i	−0.976065	+	0.217478i	$0.930217\pi$
$888$	−1493.37			−1.68173
$889$	−36.9655			−0.0415809
$890$	206.878			0.232448
$891$			76.9280i			0.0863390i
$892$	2547.09			2.85548
$893$			359.104i			0.402133i
$894$	98.5326			0.110215
$895$			57.7524i			0.0645278i
$896$			375.813i			0.419435i
$897$	2.15660			0.00240424
$898$			821.073i			0.914336i
$899$			26.8187i			0.0298317i
$900$	698.940			0.776600
$901$	643.689			0.714416
$902$	433.734			0.480858
$903$			578.183i			0.640291i
$904$	387.208			0.428328
$905$	−16.2046			−0.0179057
$906$	305.601			0.337308
$907$	−836.228			−0.921971			−0.460986	−	0.887408i	$-0.652504\pi$
$907$	−836.228			−0.921971			−0.460986	+	0.887408i	$0.652504\pi$
$908$		−	1163.54i		−	1.28143i
$909$		−	276.266i		−	0.303923i
$910$	−0.797737			−0.000876634
$911$	26.1105			0.0286614			0.0143307	−	0.999897i	$-0.495438\pi$
$911$	26.1105			0.0286614			0.0143307	+	0.999897i	$0.495438\pi$
$912$	−626.645			−0.687111
$913$	759.823			0.832227
$914$	−235.135			−0.257259
$915$		−	31.3885i		−	0.0343044i
$916$			2528.80i			2.76070i
$917$		−	1288.45i		−	1.40508i
$918$		−	154.122i		−	0.167889i
$919$		−	1116.36i		−	1.21476i	−0.794412	−	0.607380i	$-0.792221\pi$
$919$		−	1116.36i		−	1.21476i	0.794412	−	0.607380i	$-0.207779\pi$
$920$	−109.256			−0.118757
$921$	−213.560			−0.231879
$922$			778.180i			0.844013i
$923$			6.56978i			0.00711786i
$924$		−	861.979i		−	0.932878i
$925$			1088.94i			1.17723i
$926$	−1065.56			−1.15072
$927$		−	442.559i		−	0.477410i
$928$			2691.05i			2.89984i
$929$		−	1393.02i		−	1.49949i	−0.661730	−	0.749743i	$-0.730177\pi$
$929$		−	1393.02i		−	1.49949i	0.661730	−	0.749743i	$-0.269823\pi$
$930$	1.18133			0.00127024
$931$	−109.846			−0.117988
$932$			4054.88i			4.35073i
$933$	426.483			0.457109
$934$	115.322			0.123471
$935$		−	27.4398i		−	0.0293474i
$936$	−5.23678			−0.00559485
$937$			1420.84i			1.51637i	0.652041	+	0.758184i	$0.273913\pi$
$937$			1420.84i			1.51637i	−0.652041	+	0.758184i	$0.726087\pi$
$938$	2371.92			2.52870
$939$		−	847.972i		−	0.903058i
$940$		−	126.886i		−	0.134986i
$941$			968.807i			1.02955i	0.857325	+	0.514775i	$0.172125\pi$
$941$			968.807i			1.02955i	−0.857325	+	0.514775i	$0.827875\pi$
$942$	−1382.66			−1.46779
$943$			194.655i			0.206422i
$944$	−1430.13	+	1443.02i	−1.51496	+	1.52862i
$945$	12.7708			0.0135141
$946$			1680.96i			1.77691i
$947$	−573.028			−0.605098			−0.302549	−	0.953134i	$-0.597838\pi$
$947$	−573.028			−0.605098			−0.302549	+	0.953134i	$0.597838\pi$
$948$	−1206.10			−1.27226
$949$	9.71355			0.0102356
$950$			954.708i			1.00496i
$951$	−553.075			−0.581572
$952$			990.347i			1.04028i
$953$	834.685			0.875850			0.437925	−	0.899011i	$-0.355713\pi$
$953$	834.685			0.875850			0.437925	+	0.899011i	$0.355713\pi$
$954$			870.972i			0.912968i
$955$			111.287i			0.116531i
$956$	−3235.54			−3.38445
$957$			842.903i			0.880776i
$958$			630.182i			0.657810i
$959$	388.212			0.404809
$960$	24.0949			0.0250988
$961$	960.778			0.999769
$962$		−	14.2271i		−	0.0147891i
$963$	206.894			0.214843
$964$	3712.58			3.85123
$965$	18.5806			0.0192545
$966$	551.850			0.571273
$967$			128.620i			0.133009i	0.997786	+	0.0665046i	$0.0211847\pi$
$967$			128.620i			0.133009i	−0.997786	+	0.0665046i	$0.978815\pi$
$968$			942.987i			0.974160i
$969$	147.576			0.152297
$970$	−117.968			−0.121616
$971$	1485.57			1.52994			0.764969	−	0.644067i	$-0.222754\pi$
$971$	1485.57			1.52994			0.764969	+	0.644067i	$0.222754\pi$
$972$	146.188			0.150399
$973$	630.160			0.647647
$974$			1474.33i			1.51368i
$975$			3.81855i			0.00391646i
$976$			1576.35i			1.61512i
$977$			1.03419i			0.00105854i	1.00000		0.000529271i	$0.000168472\pi$
$977$			1.03419i			0.00105854i	−1.00000		0.000529271i	$0.999832\pi$
$978$			1905.67i			1.94854i
$979$	−1221.27			−1.24747
$980$	38.8133			0.0396054
$981$		−	171.990i		−	0.175321i
$982$		−	1077.56i		−	1.09731i
$983$		−	941.272i		−	0.957550i	−0.877938	−	0.478775i	$-0.841081\pi$
$983$		−	941.272i		−	0.957550i	0.877938	−	0.478775i	$-0.158919\pi$
$984$		−	472.674i		−	0.480360i
$985$	8.24079			0.00836628
$986$		−	1688.72i		−	1.71270i
$987$			367.536i			0.372377i
$988$		−	8.74388i		−	0.00885008i
$989$	−754.398			−0.762788
$990$	37.1287			0.0375037
$991$		−	1077.04i		−	1.08682i	−0.839467	−	0.543410i	$-0.817133\pi$
$991$		−	1077.04i		−	1.08682i	0.839467	−	0.543410i	$-0.182867\pi$
$992$	−22.2644			−0.0224439
$993$	385.178			0.387893
$994$			1681.13i			1.69128i
$995$	−81.6984			−0.0821090
$996$		−	1443.91i		−	1.44971i
$997$	−1366.02			−1.37013			−0.685063	−	0.728484i	$-0.740225\pi$
$997$	−1366.02			−1.37013			−0.685063	+	0.728484i	$0.740225\pi$
$998$		−	1885.51i		−	1.88929i
$999$			227.759i			0.227987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.c.a.58.1	✓	20
3.2	odd	2		531.3.c.c.235.20		20
59.58	odd	2	inner	177.3.c.a.58.20	yes	20
177.176	even	2		531.3.c.c.235.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.c.a.58.1	✓	20	1.1	even	1	trivial
177.3.c.a.58.20	yes	20	59.58	odd	2	inner
531.3.c.c.235.1		20	177.176	even	2
531.3.c.c.235.20		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} -1.44793i q^{10} +8.54756i q^{11} +16.2431 q^{12} +0.0887419i q^{13} +22.7081i q^{14} -0.685665 q^{15} +34.4346 q^{16} -8.10940 q^{17} -10.9728i q^{18} +10.5067 q^{19} -3.71245 q^{20} +10.7534 q^{21} +31.2635 q^{22} +14.0307i q^{23} -34.0702i q^{24} -24.8433 q^{25} +0.324582 q^{26} -5.19615 q^{27} +58.2229 q^{28} -56.9344 q^{29} +2.50788i q^{30} -0.471045i q^{31} -47.2659i q^{32} -14.8048i q^{33} +29.6609i q^{34} -2.45774 q^{35} -28.1339 q^{36} -43.8322i q^{37} -38.4292i q^{38} -0.153705i q^{39} +7.78692i q^{40} +13.8735 q^{41} -39.3315i q^{42} +53.7675i q^{43} -80.1588i q^{44} +1.18761 q^{45} +51.3187 q^{46} +34.1786i q^{47} -59.6425 q^{48} -10.4549 q^{49} +90.8666i q^{50} +14.0459 q^{51} -0.832220i q^{52} -79.3757 q^{53} +19.0054i q^{54} +3.38371i q^{55} -122.123i q^{56} -18.1981 q^{57} +208.243i q^{58} +(-41.5316 + 41.9061i) q^{59} +6.43015 q^{60} +45.7782i q^{61} -1.72289 q^{62} -18.6254 q^{63} -35.1409 q^{64} +0.0351301i q^{65} -54.1499 q^{66} -104.453i q^{67} +76.0498 q^{68} -24.3019i q^{69} +8.98940i q^{70} +74.0325 q^{71} +59.0114i q^{72} -109.458i q^{73} -160.320 q^{74} +43.0298 q^{75} -98.5316 q^{76} -53.0673i q^{77} -0.562192 q^{78} -74.2528 q^{79} +13.6316 q^{80} +9.00000 q^{81} -50.7436i q^{82} -88.8936i q^{83} -100.845 q^{84} -3.21026 q^{85} +196.660 q^{86} +98.6133 q^{87} -168.134 q^{88} +142.879i q^{89} -4.34378i q^{90} -0.550951i q^{91} -131.580i q^{92} +0.815874i q^{93} +125.012 q^{94} +4.15927 q^{95} +81.8669i q^{96} -81.4737i q^{97} +38.2398i q^{98} +25.6427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9}+O(q^{10}) \) 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9	\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 24 q^{12} + 24 q^{15} - 8 q^{16} + 16 q^{17} - 60 q^{19} - 164 q^{20} + 40 q^{22} + 100 q^{25} - 156 q^{26} + 200 q^{28} - 60 q^{29} - 32 q^{35} - 120 q^{36} + 28 q^{41} + 180 q^{46} - 96 q^{48} + 284 q^{49} - 24 q^{51} - 8 q^{53} + 24 q^{57} - 152 q^{59} - 72 q^{60} - 8 q^{62} - 24 q^{63} + 204 q^{64} - 120 q^{66} + 384 q^{68} + 92 q^{71} + 104 q^{74} + 240 q^{75} + 120 q^{76} - 468 q^{78} - 420 q^{79} + 376 q^{80} + 180 q^{81} + 168 q^{84} - 348 q^{85} + 232 q^{86} + 144 q^{87} - 212 q^{88} + 152 q^{94} + 788 q^{95}+O(q^{100}) \) 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9 - 24 * q^12 + 24 * q^15 - 8 * q^16 + 16 * q^17 - 60 * q^19 - 164 * q^20 + 40 * q^22 + 100 * q^25 - 156 * q^26 + 200 * q^28 - 60 * q^29 - 32 * q^35 - 120 * q^36 + 28 * q^41 + 180 * q^46 - 96 * q^48 + 284 * q^49 - 24 * q^51 - 8 * q^53 + 24 * q^57 - 152 * q^59 - 72 * q^60 - 8 * q^62 - 24 * q^63 + 204 * q^64 - 120 * q^66 + 384 * q^68 + 92 * q^71 + 104 * q^74 + 240 * q^75 + 120 * q^76 - 468 * q^78 - 420 * q^79 + 376 * q^80 + 180 * q^81 + 168 * q^84 - 348 * q^85 + 232 * q^86 + 144 * q^87 - 212 * q^88 + 152 * q^94 + 788 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more