LMFDB - Embedded newform 177.3.c.a.58.13

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			58.13
Root			$1.39995i$ of defining polynomial
Character	$\chi$	$=$	177.58
Dual form			177.3.c.a.58.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} -2.42478i q^{6} -10.8938 q^{7} +8.45589i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} -2.42478i q^{6} -10.8938 q^{7} +8.45589i q^{8} +3.00000 q^{9} +0.382863i q^{10} +15.0527i q^{11} -3.53364 q^{12} +11.1132i q^{13} -15.2508i q^{14} -0.473689 q^{15} -3.67721 q^{16} -3.40920 q^{17} +4.19984i q^{18} -15.7121 q^{19} +0.557948 q^{20} +18.8687 q^{21} -21.0729 q^{22} -15.2765i q^{23} -14.6460i q^{24} -24.9252 q^{25} -15.5578 q^{26} -5.19615 q^{27} -22.2251 q^{28} +22.5689 q^{29} -0.663139i q^{30} +59.5188i q^{31} +28.6757i q^{32} -26.0720i q^{33} -4.77271i q^{34} -2.97929 q^{35} +6.12044 q^{36} -42.4500i q^{37} -21.9961i q^{38} -19.2485i q^{39} +2.31255i q^{40} +78.4822 q^{41} +26.4152i q^{42} -78.3986i q^{43} +30.7096i q^{44} +0.820453 q^{45} +21.3862 q^{46} +35.3465i q^{47} +6.36911 q^{48} +69.6759 q^{49} -34.8940i q^{50} +5.90491 q^{51} +22.6725i q^{52} +37.2779 q^{53} -7.27434i q^{54} +4.11666i q^{55} -92.1171i q^{56} +27.2142 q^{57} +31.5952i q^{58} +(52.6472 + 26.6321i) q^{59} -0.966395 q^{60} +44.2464i q^{61} -83.3232 q^{62} -32.6815 q^{63} -54.8532 q^{64} +3.03927i q^{65} +36.4994 q^{66} -17.3224i q^{67} -6.95528 q^{68} +26.4596i q^{69} -4.17086i q^{70} -59.0750 q^{71} +25.3677i q^{72} +85.3122i q^{73} +59.4278 q^{74} +43.1717 q^{75} -32.0550 q^{76} -163.981i q^{77} +26.9470 q^{78} +62.2163 q^{79} -1.00566 q^{80} +9.00000 q^{81} +109.871i q^{82} +98.9653i q^{83} +38.4949 q^{84} -0.932363 q^{85} +109.754 q^{86} -39.0904 q^{87} -127.284 q^{88} -35.9346i q^{89} +1.14859i q^{90} -121.065i q^{91} -31.1663i q^{92} -103.090i q^{93} -49.4833 q^{94} -4.29702 q^{95} -49.6677i q^{96} +11.0179i q^{97} +97.5426i q^{98} +45.1580i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.39995i			0.699974i	0.936755	+	0.349987i	$0.113814\pi$
$2$			1.39995i			0.699974i	−0.936755	+	0.349987i	$0.886186\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	2.04015			0.510037
$5$	0.273484			0.0546968			0.0273484	−	0.999626i	$-0.491294\pi$
$5$	0.273484			0.0546968			0.0273484	+	0.999626i	$0.491294\pi$
$6$		−	2.42478i		−	0.404130i
$7$	−10.8938			−1.55626			−0.778132	−	0.628101i	$-0.783832\pi$
$7$	−10.8938			−1.55626			−0.778132	+	0.628101i	$0.783832\pi$
$8$			8.45589i			1.05699i
$9$	3.00000			0.333333
$10$			0.382863i			0.0382863i
$11$			15.0527i			1.36842i	0.729284	+	0.684212i	$0.239854\pi$
$11$			15.0527i			1.36842i	−0.729284	+	0.684212i	$0.760146\pi$
$12$	−3.53364			−0.294470
$13$			11.1132i			0.854858i	0.904049	+	0.427429i	$0.140581\pi$
$13$			11.1132i			0.854858i	−0.904049	+	0.427429i	$0.859419\pi$
$14$		−	15.2508i		−	1.08934i
$15$	−0.473689			−0.0315792
$16$	−3.67721			−0.229825
$17$	−3.40920			−0.200541			−0.100271	−	0.994960i	$-0.531971\pi$
$17$	−3.40920			−0.200541			−0.100271	+	0.994960i	$0.531971\pi$
$18$			4.19984i			0.233325i
$19$	−15.7121			−0.826954			−0.413477	−	0.910515i	$-0.635686\pi$
$19$	−15.7121			−0.826954			−0.413477	+	0.910515i	$0.635686\pi$
$20$	0.557948			0.0278974
$21$	18.8687			0.898509
$22$	−21.0729			−0.957860
$23$		−	15.2765i		−	0.664194i	−0.943245	−	0.332097i	$-0.892244\pi$
$23$		−	15.2765i		−	0.664194i	0.943245	−	0.332097i	$-0.107756\pi$
$24$		−	14.6460i		−	0.610251i
$25$	−24.9252			−0.997008
$26$	−15.5578			−0.598378
$27$	−5.19615			−0.192450
$28$	−22.2251			−0.793752
$29$	22.5689			0.778237			0.389118	−	0.921188i	$-0.372780\pi$
$29$	22.5689			0.778237			0.389118	+	0.921188i	$0.372780\pi$
$30$		−	0.663139i		−	0.0221046i
$31$			59.5188i			1.91996i	0.280067	+	0.959981i	$0.409643\pi$
$31$			59.5188i			1.91996i	−0.280067	+	0.959981i	$0.590357\pi$
$32$			28.6757i			0.896114i
$33$		−	26.0720i		−	0.790060i
$34$		−	4.77271i		−	0.140374i
$35$	−2.97929			−0.0851227
$36$	6.12044			0.170012
$37$		−	42.4500i		−	1.14730i	−0.819101	−	0.573649i	$-0.805527\pi$
$37$		−	42.4500i		−	1.14730i	0.819101	−	0.573649i	$-0.194473\pi$
$38$		−	21.9961i		−	0.578846i
$39$		−	19.2485i		−	0.493553i
$40$			2.31255i			0.0578138i
$41$	78.4822			1.91420			0.957101	−	0.289756i	$-0.0935741\pi$
$41$	78.4822			1.91420			0.957101	+	0.289756i	$0.0935741\pi$
$42$			26.4152i			0.628933i
$43$		−	78.3986i		−	1.82322i	−0.411052	−	0.911612i	$-0.634838\pi$
$43$		−	78.3986i		−	1.82322i	0.411052	−	0.911612i	$-0.365162\pi$
$44$			30.7096i			0.697946i
$45$	0.820453			0.0182323
$46$	21.3862			0.464918
$47$			35.3465i			0.752054i	0.926609	+	0.376027i	$0.122710\pi$
$47$			35.3465i			0.752054i	−0.926609	+	0.376027i	$0.877290\pi$
$48$	6.36911			0.132690
$49$	69.6759			1.42196
$50$		−	34.8940i		−	0.697879i
$51$	5.90491			0.115783
$52$			22.6725i			0.436009i
$53$	37.2779			0.703357			0.351678	−	0.936121i	$-0.385611\pi$
$53$	37.2779			0.703357			0.351678	+	0.936121i	$0.385611\pi$
$54$		−	7.27434i		−	0.134710i
$55$			4.11666i			0.0748484i
$56$		−	92.1171i		−	1.64495i
$57$	27.2142			0.477442
$58$			31.5952i			0.544745i
$59$	52.6472	+	26.6321i	0.892326	+	0.451392i
$59$	52.6472	+	26.6321i	0.892326	+	0.451392i
$60$	−0.966395			−0.0161066
$61$			44.2464i			0.725350i	0.931916	+	0.362675i	$0.118136\pi$
$61$			44.2464i			0.725350i	−0.931916	+	0.362675i	$0.881864\pi$
$62$	−83.3232			−1.34392
$63$	−32.6815			−0.518755
$64$	−54.8532			−0.857082
$65$			3.03927i			0.0467580i
$66$	36.4994			0.553021
$67$		−	17.3224i		−	0.258544i	−0.991609	−	0.129272i	$-0.958736\pi$
$67$		−	17.3224i		−	0.258544i	0.991609	−	0.129272i	$-0.0412640\pi$
$68$	−6.95528			−0.102284
$69$			26.4596i			0.383473i
$70$		−	4.17086i		−	0.0595836i
$71$	−59.0750			−0.832043			−0.416021	−	0.909355i	$-0.636576\pi$
$71$	−59.0750			−0.832043			−0.416021	+	0.909355i	$0.636576\pi$
$72$			25.3677i			0.352329i
$73$			85.3122i			1.16866i	0.811516	+	0.584330i	$0.198643\pi$
$73$			85.3122i			1.16866i	−0.811516	+	0.584330i	$0.801357\pi$
$74$	59.4278			0.803079
$75$	43.1717			0.575623
$76$	−32.0550			−0.421777
$77$		−	163.981i		−	2.12963i
$78$	26.9470			0.345474
$79$	62.2163			0.787548			0.393774	−	0.919207i	$-0.371169\pi$
$79$	62.2163			0.787548			0.393774	+	0.919207i	$0.371169\pi$
$80$	−1.00566			−0.0125707
$81$	9.00000			0.111111
$82$			109.871i			1.33989i
$83$			98.9653i			1.19235i	0.802853	+	0.596177i	$0.203314\pi$
$83$			98.9653i			1.19235i	−0.802853	+	0.596177i	$0.796686\pi$
$84$	38.4949			0.458273
$85$	−0.932363			−0.0109690
$86$	109.754			1.27621
$87$	−39.0904			−0.449315
$88$	−127.284			−1.44640
$89$		−	35.9346i		−	0.403759i	−0.979410	−	0.201880i	$-0.935295\pi$
$89$		−	35.9346i		−	0.403759i	0.979410	−	0.201880i	$-0.0647050\pi$
$90$			1.14859i			0.0127621i
$91$		−	121.065i		−	1.33038i
$92$		−	31.1663i		−	0.338764i
$93$		−	103.090i		−	1.10849i
$94$	−49.4833			−0.526418
$95$	−4.29702			−0.0452318
$96$		−	49.6677i		−	0.517372i
$97$			11.0179i			0.113587i	0.998386	+	0.0567935i	$0.0180877\pi$
$97$			11.0179i			0.113587i	−0.998386	+	0.0567935i	$0.981912\pi$
$98$			97.5426i			0.995332i
$99$			45.1580i			0.456141i
$100$	−50.8511			−0.508511
$101$		−	110.774i		−	1.09677i	−0.836227	−	0.548384i	$-0.815243\pi$
$101$		−	110.774i		−	1.09677i	0.836227	−	0.548384i	$-0.184757\pi$
$102$			8.26657i			0.0810448i
$103$		−	43.0668i		−	0.418125i	−0.977902	−	0.209062i	$-0.932959\pi$
$103$		−	43.0668i		−	0.418125i	0.977902	−	0.209062i	$-0.0670412\pi$
$104$	−93.9716			−0.903573
$105$	5.16029			0.0491456
$106$			52.1871i			0.492331i
$107$	−146.405			−1.36827			−0.684137	−	0.729353i	$-0.739821\pi$
$107$	−146.405			−1.36827			−0.684137	+	0.729353i	$0.739821\pi$
$108$	−10.6009			−0.0981567
$109$		−	141.124i		−	1.29472i	−0.762185	−	0.647359i	$-0.775873\pi$
$109$		−	141.124i		−	1.29472i	0.762185	−	0.647359i	$-0.224127\pi$
$110$	−5.76311			−0.0523919
$111$			73.5256i			0.662393i
$112$	40.0589			0.357669
$113$			21.1887i			0.187511i	0.995595	+	0.0937555i	$0.0298872\pi$
$113$			21.1887i			0.187511i	−0.995595	+	0.0937555i	$0.970113\pi$
$114$			38.0984i			0.334197i
$115$		−	4.17787i		−	0.0363293i
$116$	46.0438			0.396929
$117$			33.3395i			0.284953i
$118$	−37.2836	+	73.7033i	−0.315963	+	0.624604i
$119$	37.1393			0.312095
$120$		−	4.00546i		−	0.0333788i
$121$	−105.582			−0.872582
$122$	−61.9426			−0.507726
$123$	−135.935			−1.10516
$124$			121.427i			0.979251i
$125$	−13.6538			−0.109230
$126$		−	45.7524i		−	0.363115i
$127$	215.084			1.69358			0.846789	−	0.531929i	$-0.178533\pi$
$127$	215.084			1.69358			0.846789	+	0.531929i	$0.178533\pi$
$128$			37.9110i			0.296180i
$129$			135.790i			1.05264i
$130$	−4.25482			−0.0327294
$131$			79.8202i			0.609314i	0.952462	+	0.304657i	$0.0985419\pi$
$131$			79.8202i			0.609314i	−0.952462	+	0.304657i	$0.901458\pi$
$132$		−	53.1907i		−	0.402960i
$133$	171.165			1.28696
$134$	24.2505			0.180974
$135$	−1.42107			−0.0105264
$136$		−	28.8278i		−	0.211969i
$137$	−138.442			−1.01053			−0.505265	−	0.862965i	$-0.668605\pi$
$137$	−138.442			−1.01053			−0.505265	+	0.862965i	$0.668605\pi$
$138$	−37.0421			−0.268421
$139$	59.8615			0.430658			0.215329	−	0.976542i	$-0.430918\pi$
$139$	59.8615			0.430658			0.215329	+	0.976542i	$0.430918\pi$
$140$	−6.07820			−0.0434157
$141$		−	61.2220i		−	0.434198i
$142$		−	82.7019i		−	0.582408i
$143$	−167.282			−1.16981
$144$	−11.0316			−0.0766085
$145$	6.17223			0.0425671
$146$	−119.433			−0.818031
$147$	−120.682			−0.820967
$148$		−	86.6044i		−	0.585165i
$149$			218.369i			1.46556i	0.680464	+	0.732782i	$0.261778\pi$
$149$			218.369i			1.46556i	−0.680464	+	0.732782i	$0.738222\pi$
$150$			60.4381i			0.402921i
$151$		−	26.4104i		−	0.174904i	−0.996169	−	0.0874518i	$-0.972128\pi$
$151$		−	26.4104i		−	0.174904i	0.996169	−	0.0874518i	$-0.0278724\pi$
$152$		−	132.860i		−	0.874078i
$153$	−10.2276			−0.0668471
$154$	229.565			1.49068
$155$			16.2774i			0.105016i
$156$		−	39.2699i		−	0.251730i
$157$			18.4659i			0.117617i	0.998269	+	0.0588087i	$0.0187302\pi$
$157$			18.4659i			0.117617i	−0.998269	+	0.0588087i	$0.981270\pi$
$158$			87.0995i			0.551263i
$159$	−64.5672			−0.406083
$160$			7.84234i			0.0490146i
$161$			166.419i			1.03366i
$162$			12.5995i			0.0777748i
$163$	−247.452			−1.51811			−0.759055	−	0.651026i	$-0.774339\pi$
$163$	−247.452			−1.51811			−0.759055	+	0.651026i	$0.774339\pi$
$164$	160.115			0.976313
$165$		−	7.13027i		−	0.0432138i
$166$	−138.546			−0.834616
$167$	63.0046			0.377273			0.188637	−	0.982047i	$-0.439593\pi$
$167$	63.0046			0.377273			0.188637	+	0.982047i	$0.439593\pi$
$168$			159.552i			0.949712i
$169$	45.4978			0.269218
$170$		−	1.30526i		−	0.00767800i
$171$	−47.1364			−0.275651
$172$		−	159.945i		−	0.929912i
$173$			163.258i			0.943690i	0.881681	+	0.471845i	$0.156412\pi$
$173$			163.258i			0.943690i	−0.881681	+	0.471845i	$0.843588\pi$
$174$		−	54.7245i		−	0.314509i
$175$	271.531			1.55161
$176$		−	55.3517i		−	0.314498i
$177$	−91.1876	−	46.1282i	−0.515184	−	0.260611i
$178$	50.3065			0.282621
$179$			80.5355i			0.449919i	0.974368	+	0.224960i	$0.0722250\pi$
$179$			80.5355i			0.449919i	−0.974368	+	0.224960i	$0.927775\pi$
$180$	1.67384			0.00929914
$181$	−130.162			−0.719125			−0.359563	−	0.933121i	$-0.617074\pi$
$181$	−130.162			−0.719125			−0.359563	+	0.933121i	$0.617074\pi$
$182$	169.485			0.931234
$183$		−	76.6369i		−	0.418781i
$184$	129.176			0.702044
$185$		−	11.6094i		−	0.0627536i
$186$	144.320			0.775914
$187$		−	51.3176i		−	0.274426i
$188$			72.1121i			0.383575i
$189$	56.6061			0.299503
$190$		−	6.01560i		−	0.0316610i
$191$		−	206.275i		−	1.07997i	−0.841674	−	0.539987i	$-0.818429\pi$
$191$		−	206.275i		−	1.07997i	0.841674	−	0.539987i	$-0.181571\pi$
$192$	95.0086			0.494836
$193$	174.658			0.904964			0.452482	−	0.891773i	$-0.350539\pi$
$193$	174.658			0.904964			0.452482	+	0.891773i	$0.350539\pi$
$194$	−15.4245			−0.0795079
$195$		−	5.26417i		−	0.0269958i
$196$	142.149			0.725250
$197$	262.732			1.33367			0.666833	−	0.745207i	$-0.267649\pi$
$197$	262.732			1.33367			0.666833	+	0.745207i	$0.267649\pi$
$198$	−63.2188			−0.319287
$199$	−36.7705			−0.184776			−0.0923882	−	0.995723i	$-0.529450\pi$
$199$	−36.7705			−0.184776			−0.0923882	+	0.995723i	$0.529450\pi$
$200$		−	210.765i		−	1.05382i
$201$			30.0033i			0.149270i
$202$	155.077			0.767709
$203$	−245.862			−1.21114
$204$	12.0469			0.0590534
$205$	21.4637			0.104701
$206$	60.2913			0.292676
$207$		−	45.8294i		−	0.221398i
$208$		−	40.8654i		−	0.196468i
$209$		−	236.509i		−	1.13162i
$210$			7.22413i			0.0344006i
$211$			332.832i			1.57740i	0.614775	+	0.788702i	$0.289247\pi$
$211$			332.832i			1.57740i	−0.614775	+	0.788702i	$0.710753\pi$
$212$	76.0525			0.358738
$213$	102.321			0.480380
$214$		−	204.960i		−	0.957756i
$215$		−	21.4408i		−	0.0997246i
$216$		−	43.9381i		−	0.203417i
$217$		−	648.389i		−	2.98797i
$218$	197.567			0.906269
$219$		−	147.765i		−	0.674726i
$220$			8.39860i			0.0381755i
$221$		−	37.8870i		−	0.171434i
$222$	−102.932			−0.463658
$223$	−68.0441			−0.305131			−0.152565	−	0.988293i	$-0.548753\pi$
$223$	−68.0441			−0.305131			−0.152565	+	0.988293i	$0.548753\pi$
$224$		−	312.388i		−	1.39459i
$225$	−74.7756			−0.332336
$226$	−29.6631			−0.131253
$227$			297.497i			1.31056i	0.755386	+	0.655280i	$0.227449\pi$
$227$			297.497i			1.31056i	−0.755386	+	0.655280i	$0.772551\pi$
$228$	55.5210			0.243513
$229$		−	27.5954i		−	0.120504i	−0.998183	−	0.0602519i	$-0.980810\pi$
$229$		−	27.5954i		−	0.120504i	0.998183	−	0.0602519i	$-0.0191904\pi$
$230$	5.84880			0.0254296
$231$			284.024i			1.22954i
$232$			190.840i			0.822585i
$233$			359.245i			1.54182i	0.636943	+	0.770911i	$0.280199\pi$
$233$			359.245i			1.54182i	−0.636943	+	0.770911i	$0.719801\pi$
$234$	−46.6735			−0.199459
$235$			9.66672i			0.0411350i
$236$	107.408	+	54.3335i	0.455119	+	0.230227i
$237$	−107.762			−0.454691
$238$			51.9931i			0.218458i
$239$	−265.127			−1.10932			−0.554659	−	0.832078i	$-0.687151\pi$
$239$	−265.127			−1.10932			−0.554659	+	0.832078i	$0.687151\pi$
$240$	1.74185			0.00725771
$241$	−58.8858			−0.244340			−0.122170	−	0.992509i	$-0.538985\pi$
$241$	−58.8858			−0.244340			−0.122170	+	0.992509i	$0.538985\pi$
$242$		−	147.810i		−	0.610784i
$243$	−15.5885			−0.0641500
$244$			90.2691i			0.369955i
$245$	19.0553			0.0777765
$246$		−	190.302i		−	0.773586i
$247$		−	174.611i		−	0.706928i
$248$	−503.284			−2.02937
$249$		−	171.413i		−	0.688406i
$250$		−	19.1145i		−	0.0764581i
$251$	1.34813			0.00537104			0.00268552	−	0.999996i	$-0.499145\pi$
$251$	1.34813			0.00537104			0.00268552	+	0.999996i	$0.499145\pi$
$252$	−66.6752			−0.264584
$253$	229.951			0.908899
$254$			301.107i			1.18546i
$255$	1.61490			0.00633294
$256$	−272.486			−1.06440
$257$	301.120			1.17167			0.585837	−	0.810429i	$-0.300766\pi$
$257$	301.120			1.17167			0.585837	+	0.810429i	$0.300766\pi$
$258$	−190.099			−0.736819
$259$			462.444i			1.78550i
$260$			6.20056i			0.0238483i
$261$	67.7066			0.259412
$262$	−111.744			−0.426504
$263$	82.6739			0.314350			0.157175	−	0.987571i	$-0.449761\pi$
$263$	82.6739			0.314350			0.157175	+	0.987571i	$0.449761\pi$
$264$	220.462			0.835082
$265$	10.1949			0.0384714
$266$			239.623i			0.900837i
$267$			62.2405i			0.233111i
$268$		−	35.3403i		−	0.131867i
$269$		−	208.155i		−	0.773810i	−0.922120	−	0.386905i	$-0.873544\pi$
$269$		−	208.155i		−	0.773810i	0.922120	−	0.386905i	$-0.126456\pi$
$270$		−	1.98942i		−	0.00736821i
$271$	38.7081			0.142834			0.0714171	−	0.997447i	$-0.477248\pi$
$271$	38.7081			0.142834			0.0714171	+	0.997447i	$0.477248\pi$
$272$	12.5363			0.0460895
$273$			209.691i			0.768098i
$274$		−	193.812i		−	0.707344i
$275$		−	375.191i		−	1.36433i
$276$			53.9815i			0.195585i
$277$	209.375			0.755866			0.377933	−	0.925833i	$-0.376635\pi$
$277$	209.375			0.755866			0.377933	+	0.925833i	$0.376635\pi$
$278$			83.8030i			0.301450i
$279$			178.556i			0.639987i
$280$		−	25.1926i		−	0.0899735i
$281$	307.082			1.09282			0.546409	−	0.837519i	$-0.315995\pi$
$281$	307.082			1.09282			0.546409	+	0.837519i	$0.315995\pi$
$282$	85.7075			0.303927
$283$		−	229.159i		−	0.809749i	−0.914372	−	0.404875i	$-0.867315\pi$
$283$		−	229.159i		−	0.809749i	0.914372	−	0.404875i	$-0.132685\pi$
$284$	−120.522			−0.424373
$285$	7.44265			0.0261146
$286$		−	234.187i		−	0.818834i
$287$	−854.974			−2.97900
$288$			86.0270i			0.298705i
$289$	−277.377			−0.959783
$290$			8.64079i			0.0297958i
$291$		−	19.0836i		−	0.0655795i
$292$			174.049i			0.596060i
$293$	56.5578			0.193030			0.0965150	−	0.995332i	$-0.469230\pi$
$293$	56.5578			0.193030			0.0965150	+	0.995332i	$0.469230\pi$
$294$		−	168.949i		−	0.574655i
$295$	14.3982	+	7.28347i	0.0488074	+	0.0246897i
$296$	358.953			1.21268
$297$		−	78.2159i		−	0.263353i
$298$	−305.705			−1.02586
$299$	169.770			0.567792
$300$	88.0767			0.293589
$301$			854.063i			2.83742i
$302$	36.9732			0.122428
$303$			191.865i			0.633219i
$304$	57.7767			0.190055
$305$			12.1007i			0.0396744i
$306$		−	14.3181i		−	0.0467912i
$307$	−38.1615			−0.124305			−0.0621523	−	0.998067i	$-0.519796\pi$
$307$	−38.1615			−0.124305			−0.0621523	+	0.998067i	$0.519796\pi$
$308$		−	334.546i		−	1.08619i
$309$			74.5940i			0.241404i
$310$	−22.7876			−0.0735083
$311$	−237.381			−0.763282			−0.381641	−	0.924311i	$-0.624641\pi$
$311$	−237.381			−0.763282			−0.381641	+	0.924311i	$0.624641\pi$
$312$	162.764			0.521678
$313$			468.363i			1.49637i	0.663491	+	0.748184i	$0.269074\pi$
$313$			468.363i			1.49637i	−0.663491	+	0.748184i	$0.730926\pi$
$314$	−25.8513			−0.0823291
$315$	−8.93788			−0.0283742
$316$	126.930			0.401679
$317$	−97.7779			−0.308447			−0.154224	−	0.988036i	$-0.549288\pi$
$317$	−97.7779			−0.308447			−0.154224	+	0.988036i	$0.549288\pi$
$318$		−	90.3907i		−	0.284248i
$319$			339.721i			1.06496i
$320$	−15.0015			−0.0468797
$321$	253.582			0.789974
$322$	−232.978			−0.723536
$323$	53.5658			0.165838
$324$	18.3613			0.0566708
$325$		−	276.998i		−	0.852300i
$326$		−	346.420i		−	1.06264i
$327$			244.434i			0.747506i
$328$			663.637i			2.02328i
$329$		−	385.060i		−	1.17039i
$330$	9.98200			0.0302485
$331$	−248.132			−0.749644			−0.374822	−	0.927097i	$-0.622296\pi$
$331$	−248.132			−0.749644			−0.374822	+	0.927097i	$0.622296\pi$
$332$			201.904i			0.608144i
$333$		−	127.350i		−	0.382433i
$334$			88.2032i			0.264081i
$335$		−	4.73741i		−	0.0141415i
$336$	−69.3841			−0.206500
$337$		−	84.1105i		−	0.249586i	−0.992183	−	0.124793i	$-0.960173\pi$
$337$		−	84.1105i		−	0.249586i	0.992183	−	0.124793i	$-0.0398267\pi$
$338$			63.6945i			0.188445i
$339$		−	36.7000i		−	0.108260i
$340$	−1.90216			−0.00559459
$341$	−895.916			−2.62732
$342$		−	65.9884i		−	0.192949i
$343$	−225.240			−0.656676
$344$	662.930			1.92712
$345$			7.23629i			0.0209747i
$346$	−228.553			−0.660558
$347$			521.687i			1.50342i	0.659493	+	0.751711i	$0.270771\pi$
$347$			521.687i			1.50342i	−0.659493	+	0.751711i	$0.729229\pi$
$348$	−79.7502			−0.229167
$349$		−	299.873i		−	0.859234i	−0.903011	−	0.429617i	$-0.858649\pi$
$349$		−	299.873i		−	0.859234i	0.903011	−	0.429617i	$-0.141351\pi$
$350$			380.130i			1.08608i
$351$		−	57.7456i		−	0.164518i
$352$	−431.645			−1.22626
$353$		−	633.470i		−	1.79453i	−0.441491	−	0.897266i	$-0.645550\pi$
$353$		−	633.470i		−	1.79453i	0.441491	−	0.897266i	$-0.354450\pi$
$354$	64.5771	−	127.658i	0.182421	−	0.360616i
$355$	−16.1561			−0.0455101
$356$		−	73.3119i		−	0.205932i
$357$	−64.3272			−0.180188
$358$	−112.745			−0.314932
$359$	456.186			1.27071			0.635356	−	0.772219i	$-0.280853\pi$
$359$	456.186			1.27071			0.635356	+	0.772219i	$0.280853\pi$
$360$			6.93765i			0.0192713i
$361$	−114.129			−0.316148
$362$		−	182.220i		−	0.503369i
$363$	182.874			0.503786
$364$		−	246.990i		−	0.678545i
$365$			23.3315i			0.0639220i
$366$	107.288			0.293136
$367$		−	505.395i		−	1.37710i	−0.725190	−	0.688549i	$-0.758248\pi$
$367$		−	505.395i		−	1.37710i	0.725190	−	0.688549i	$-0.241752\pi$
$368$			56.1747i			0.152649i
$369$	235.447			0.638067
$370$	16.2526			0.0439259
$371$	−406.100			−1.09461
$372$		−	210.318i		−	0.565371i
$373$	−262.292			−0.703195			−0.351598	−	0.936151i	$-0.614361\pi$
$373$	−262.292			−0.703195			−0.351598	+	0.936151i	$0.614361\pi$
$374$	71.8419			0.192091
$375$	23.6490			0.0630640
$376$	−298.886			−0.794910
$377$			250.811i			0.665282i
$378$			79.2455i			0.209644i
$379$	532.499			1.40501			0.702505	−	0.711679i	$-0.252065\pi$
$379$	532.499			1.40501			0.702505	+	0.711679i	$0.252065\pi$
$380$	−8.76655			−0.0230699
$381$	−372.537			−0.977787
$382$	288.774			0.755953
$383$	286.541			0.748150			0.374075	−	0.927398i	$-0.377960\pi$
$383$	286.541			0.748150			0.374075	+	0.927398i	$0.377960\pi$
$384$		−	65.6638i		−	0.170999i
$385$		−	44.8463i		−	0.116484i
$386$			244.512i			0.633451i
$387$		−	235.196i		−	0.607741i
$388$			22.4782i			0.0579336i
$389$	620.394			1.59484			0.797421	−	0.603423i	$-0.206197\pi$
$389$	620.394			1.59484			0.797421	+	0.603423i	$0.206197\pi$
$390$	7.36956			0.0188963
$391$			52.0806i			0.133198i
$392$			589.171i			1.50299i
$393$		−	138.253i		−	0.351788i
$394$			367.811i			0.933531i
$395$	17.0152			0.0430764
$396$			92.1289i			0.232649i
$397$			434.013i			1.09323i	0.837383	+	0.546616i	$0.184084\pi$
$397$			434.013i			1.09323i	−0.837383	+	0.546616i	$0.815916\pi$
$398$		−	51.4767i		−	0.129339i
$399$	−296.467			−0.743026
$400$	91.6551			0.229138
$401$		−	107.207i		−	0.267350i	−0.991025	−	0.133675i	$-0.957322\pi$
$401$		−	107.207i		−	0.267350i	0.991025	−	0.133675i	$-0.0426778\pi$
$402$	−42.0031			−0.104485
$403$	−661.442			−1.64129
$404$		−	225.994i		−	0.559392i
$405$	2.46136			0.00607743
$406$		−	344.193i		−	0.847767i
$407$	638.986			1.56999
$408$			49.9313i			0.122381i
$409$		−	550.503i		−	1.34597i	−0.739654	−	0.672987i	$-0.765011\pi$
$409$		−	550.503i		−	1.34597i	0.739654	−	0.672987i	$-0.234989\pi$
$410$			30.0480i			0.0732878i
$411$	239.789			0.583429
$412$		−	87.8627i		−	0.213259i
$413$	−573.531	−	290.126i	−1.38869	−	0.702485i
$414$	64.1587			0.154973
$415$			27.0655i			0.0652180i
$416$	−318.677			−0.766050
$417$	−103.683			−0.248641
$418$	331.100			0.792106
$419$		−	274.431i		−	0.654967i	−0.944857	−	0.327483i	$-0.893799\pi$
$419$		−	274.431i		−	0.654967i	0.944857	−	0.327483i	$-0.106201\pi$
$420$	10.5278			0.0250661
$421$		−	46.0928i		−	0.109484i	−0.998501	−	0.0547420i	$-0.982566\pi$
$421$		−	46.0928i		−	0.109484i	0.998501	−	0.0547420i	$-0.0174336\pi$
$422$	−465.948			−1.10414
$423$			106.040i			0.250685i
$424$			315.218i			0.743438i
$425$	84.9751			0.199941
$426$			143.244i			0.336253i
$427$		−	482.013i		−	1.12884i
$428$	−298.689			−0.697871
$429$	289.742			0.675389
$430$	30.0160			0.0698046
$431$		−	256.182i		−	0.594389i	−0.954817	−	0.297195i	$-0.903949\pi$
$431$		−	256.182i		−	0.594389i	0.954817	−	0.297195i	$-0.0960510\pi$
$432$	19.1073			0.0442299
$433$	76.7056			0.177149			0.0885746	−	0.996070i	$-0.471769\pi$
$433$	76.7056			0.177149			0.0885746	+	0.996070i	$0.471769\pi$
$434$	907.710			2.09150
$435$	−10.6906			−0.0245761
$436$		−	287.914i		−	0.660354i
$437$			240.026i			0.549258i
$438$	206.863			0.472291
$439$	622.390			1.41775			0.708873	−	0.705336i	$-0.249204\pi$
$439$	622.390			1.41775			0.708873	+	0.705336i	$0.249204\pi$
$440$	−34.8100			−0.0791137
$441$	209.028			0.473986
$442$	53.0398			0.120000
$443$		−	682.698i		−	1.54108i	−0.637392	−	0.770540i	$-0.719987\pi$
$443$		−	682.698i		−	1.54108i	0.637392	−	0.770540i	$-0.280013\pi$
$444$			150.003i			0.337845i
$445$		−	9.82754i		−	0.0220844i
$446$		−	95.2582i		−	0.213583i
$447$		−	378.226i		−	0.846144i
$448$	597.563			1.33385
$449$	−144.491			−0.321806			−0.160903	−	0.986970i	$-0.551441\pi$
$449$	−144.491			−0.321806			−0.160903	+	0.986970i	$0.551441\pi$
$450$		−	104.682i		−	0.232626i
$451$			1181.37i			2.61944i
$452$			43.2282i			0.0956375i
$453$			45.7442i			0.100981i
$454$	−416.480			−0.917358
$455$		−	33.1094i		−	0.0727678i
$456$			230.120i			0.504649i
$457$			293.853i			0.643004i	0.946909	+	0.321502i	$0.104188\pi$
$457$			293.853i			0.643004i	−0.946909	+	0.321502i	$0.895812\pi$
$458$	38.6321			0.0843495
$459$	17.7147			0.0385942
$460$		−	8.52348i		−	0.0185293i
$461$	457.634			0.992698			0.496349	−	0.868123i	$-0.334674\pi$
$461$	457.634			0.992698			0.496349	+	0.868123i	$0.334674\pi$
$462$	−397.619			−0.860646
$463$		−	671.285i		−	1.44986i	−0.688822	−	0.724930i	$-0.741872\pi$
$463$		−	671.285i		−	1.44986i	0.688822	−	0.724930i	$-0.258128\pi$
$464$	−82.9904			−0.178859
$465$		−	28.1934i		−	0.0606309i
$466$	−502.923			−1.07923
$467$			358.075i			0.766756i	0.923592	+	0.383378i	$0.125239\pi$
$467$			358.075i			0.766756i	−0.923592	+	0.383378i	$0.874761\pi$
$468$			68.0174i			0.145336i
$469$			188.708i			0.402362i
$470$	−13.5329			−0.0287934
$471$		−	31.9839i		−	0.0679065i
$472$	−225.198	+	445.179i	−0.477115	+	0.943176i
$473$	1180.11			2.49494
$474$		−	150.861i		−	0.318272i
$475$	391.628			0.824480
$476$	75.7697			0.159180
$477$	111.834			0.234452
$478$		−	371.164i		−	0.776493i
$479$	−23.3301			−0.0487059			−0.0243530	−	0.999703i	$-0.507753\pi$
$479$	−23.3301			−0.0487059			−0.0243530	+	0.999703i	$0.507753\pi$
$480$		−	13.5833i		−	0.0282986i
$481$	471.754			0.980777
$482$		−	82.4371i		−	0.171031i
$483$		−	288.247i		−	0.596785i
$484$	−215.404			−0.445049
$485$			3.01323i			0.00621285i
$486$		−	21.8230i		−	0.0449033i
$487$	718.517			1.47539			0.737697	−	0.675132i	$-0.235913\pi$
$487$	718.517			1.47539			0.737697	+	0.675132i	$0.235913\pi$
$488$	−374.142			−0.766685
$489$	428.600			0.876482
$490$			26.6763i			0.0544415i
$491$	406.760			0.828431			0.414215	−	0.910179i	$-0.364056\pi$
$491$	406.760			0.828431			0.414215	+	0.910179i	$0.364056\pi$
$492$	−277.328			−0.563675
$493$	−76.9419			−0.156069
$494$	244.446			0.494831
$495$			12.3500i			0.0249495i
$496$		−	218.863i		−	0.441256i
$497$	643.554			1.29488
$498$	239.969			0.481866
$499$	−828.694			−1.66071			−0.830355	−	0.557235i	$-0.811862\pi$
$499$	−828.694			−1.66071			−0.830355	+	0.557235i	$0.811862\pi$
$500$	−27.8557			−0.0557114
$501$	−109.127			−0.217819
$502$			1.88731i			0.00375959i
$503$			491.016i			0.976175i	0.872795	+	0.488088i	$0.162305\pi$
$503$			491.016i			0.976175i	−0.872795	+	0.488088i	$0.837695\pi$
$504$		−	276.351i		−	0.548316i
$505$		−	30.2948i		−	0.0599897i
$506$			321.920i			0.636205i
$507$	−78.8045			−0.155433
$508$	438.804			0.863787
$509$			299.875i			0.589146i	0.955629	+	0.294573i	$0.0951774\pi$
$509$			299.875i			0.589146i	−0.955629	+	0.294573i	$0.904823\pi$
$510$			2.26078i			0.00443289i
$511$		−	929.378i		−	1.81874i
$512$		−	229.822i		−	0.448872i
$513$	81.6426			0.159147
$514$			421.553i			0.820141i
$515$		−	11.7781i		−	0.0228701i
$516$			277.033i			0.536885i
$517$	−532.059			−1.02913
$518$	−647.398			−1.24980
$519$		−	282.772i		−	0.544840i
$520$	−25.6997			−0.0494226
$521$	−793.658			−1.52334			−0.761668	−	0.647967i	$-0.775619\pi$
$521$	−793.658			−1.52334			−0.761668	+	0.647967i	$0.775619\pi$
$522$			94.7857i			0.181582i
$523$	−991.881			−1.89652			−0.948261	−	0.317493i	$-0.897159\pi$
$523$	−991.881			−1.89652			−0.948261	+	0.317493i	$0.897159\pi$
$524$			162.845i			0.310773i
$525$	−470.306			−0.895821
$526$			115.739i			0.220036i
$527$		−	202.912i		−	0.385032i
$528$			95.8720i			0.181576i
$529$	295.630			0.558846
$530$			14.2723i			0.0269290i
$531$	157.942	+	79.8964i	0.297442	+	0.150464i
$532$	349.203			0.656396
$533$			872.185i			1.63637i
$534$	−87.1335			−0.163171
$535$	−40.0396			−0.0748403
$536$	146.477			0.273277
$537$		−	139.492i		−	0.259761i
$538$	291.406			0.541646
$539$			1048.81i			1.94584i
$540$	−2.89918			−0.00536886
$541$			200.875i			0.371303i	0.982616	+	0.185652i	$0.0594396\pi$
$541$			200.875i			0.371303i	−0.982616	+	0.185652i	$0.940560\pi$
$542$			54.1893i			0.0999802i
$543$	225.447			0.415187
$544$		−	97.7612i		−	0.179708i
$545$		−	38.5953i		−	0.0708170i
$546$	−293.556			−0.537648
$547$	−412.389			−0.753911			−0.376955	−	0.926231i	$-0.623029\pi$
$547$	−412.389			−0.753911			−0.376955	+	0.926231i	$0.623029\pi$
$548$	−282.443			−0.515407
$549$			132.739i			0.241783i
$550$	525.247			0.954994
$551$	−354.605			−0.643566
$552$	−223.740			−0.405325
$553$	−677.775			−1.22563
$554$			293.114i			0.529086i
$555$			20.1081i			0.0362308i
$556$	122.126			0.219652
$557$	−214.797			−0.385632			−0.192816	−	0.981235i	$-0.561762\pi$
$557$	−214.797			−0.385632			−0.192816	+	0.981235i	$0.561762\pi$
$558$	−249.970			−0.447974
$559$	871.256			1.55860
$560$	10.9555			0.0195634
$561$			88.8846i			0.158440i
$562$			429.898i			0.764943i
$563$			104.763i			0.186079i	0.995662	+	0.0930396i	$0.0296583\pi$
$563$			104.763i			0.186079i	−0.995662	+	0.0930396i	$0.970342\pi$
$564$		−	124.902i		−	0.221457i
$565$			5.79479i			0.0102563i
$566$	320.810			0.566803
$567$	−98.0446			−0.172918
$568$		−	499.532i		−	0.879458i
$569$		−	765.436i		−	1.34523i	−0.739992	−	0.672615i	$-0.765171\pi$
$569$		−	765.436i		−	1.34523i	0.739992	−	0.672615i	$-0.234829\pi$
$570$			10.4193i			0.0182795i
$571$		−	249.624i		−	0.437170i	−0.975818	−	0.218585i	$-0.929856\pi$
$571$		−	249.624i		−	0.437170i	0.975818	−	0.218585i	$-0.0701441\pi$
$572$	−341.281			−0.596645
$573$			357.279i			0.623523i
$574$		−	1196.92i		−	2.08522i
$575$			380.769i			0.662207i
$576$	−164.560			−0.285694
$577$	−268.842			−0.465930			−0.232965	−	0.972485i	$-0.574843\pi$
$577$	−268.842			−0.465930			−0.232965	+	0.972485i	$0.574843\pi$
$578$		−	388.314i		−	0.671823i
$579$	−302.517			−0.522481
$580$	12.5923			0.0217108
$581$		−	1078.11i		−	1.85562i
$582$	26.7161			0.0459039
$583$			561.132i			0.962490i
$584$	−721.390			−1.23526
$585$			9.11782i			0.0155860i
$586$			79.1779i			0.135116i
$587$		−	793.085i		−	1.35108i	−0.737322	−	0.675541i	$-0.763910\pi$
$587$		−	793.085i		−	1.35108i	0.737322	−	0.675541i	$-0.236090\pi$
$588$	−246.209			−0.418724
$589$		−	935.166i		−	1.58772i
$590$	−10.1965	+	20.1567i	−0.0172822	+	0.0341639i
$591$	−455.066			−0.769993
$592$			156.098i			0.263678i
$593$	−108.147			−0.182373			−0.0911866	−	0.995834i	$-0.529066\pi$
$593$	−108.147			−0.182373			−0.0911866	+	0.995834i	$0.529066\pi$
$594$	109.498			0.184340
$595$	10.1570			0.0170706
$596$			445.505i			0.747492i
$597$	63.6884			0.106681
$598$			237.669i			0.397439i
$599$	21.0152			0.0350837			0.0175419	−	0.999846i	$-0.494416\pi$
$599$	21.0152			0.0350837			0.0175419	+	0.999846i	$0.494416\pi$
$600$			365.055i			0.608425i
$601$			792.854i			1.31922i	0.751606	+	0.659612i	$0.229279\pi$
$601$			792.854i			1.31922i	−0.751606	+	0.659612i	$0.770721\pi$
$602$	−1195.64			−1.98612
$603$		−	51.9673i		−	0.0861813i
$604$		−	53.8812i		−	0.0892073i
$605$	−28.8751			−0.0477275
$606$	−268.602			−0.443237
$607$	848.008			1.39705			0.698524	−	0.715587i	$-0.253841\pi$
$607$	848.008			1.39705			0.698524	+	0.715587i	$0.253841\pi$
$608$		−	450.555i		−	0.741045i
$609$	425.845			0.699253
$610$	−16.9403			−0.0277710
$611$	−392.811			−0.642899
$612$	−20.8658			−0.0340945
$613$		−	355.689i		−	0.580243i	−0.956990	−	0.290121i	$-0.906304\pi$
$613$		−	355.689i		−	0.580243i	0.956990	−	0.290121i	$-0.0936957\pi$
$614$		−	53.4241i		−	0.0870100i
$615$	−37.1761			−0.0604490
$616$	1386.61			2.25099
$617$	120.858			0.195880			0.0979402	−	0.995192i	$-0.468775\pi$
$617$	120.858			0.195880			0.0979402	+	0.995192i	$0.468775\pi$
$618$	−104.428			−0.168977
$619$	−112.377			−0.181546			−0.0907732	−	0.995872i	$-0.528934\pi$
$619$	−112.377			−0.181546			−0.0907732	+	0.995872i	$0.528934\pi$
$620$			33.2084i			0.0535619i
$621$			79.3789i			0.127824i
$622$		−	332.320i		−	0.534277i
$623$			391.466i			0.628356i
$624$			70.7809i			0.113431i
$625$	619.396			0.991034
$626$	−655.684			−1.04742
$627$			409.646i			0.653343i
$628$			37.6732i			0.0599892i
$629$			144.721i			0.230081i
$630$		−	12.5126i		−	0.0198612i
$631$	467.803			0.741368			0.370684	−	0.928759i	$-0.379123\pi$
$631$	467.803			0.741368			0.370684	+	0.928759i	$0.379123\pi$
$632$			526.094i			0.832427i
$633$		−	576.483i		−	0.910715i
$634$		−	136.884i		−	0.215905i
$635$	58.8222			0.0926333
$636$	−131.727			−0.207117
$637$			774.319i			1.21557i
$638$	−475.592			−0.745442
$639$	−177.225			−0.277348
$640$			10.3681i			0.0162001i
$641$	−1006.77			−1.57062			−0.785311	−	0.619102i	$-0.787497\pi$
$641$	−1006.77			−1.57062			−0.785311	+	0.619102i	$0.787497\pi$
$642$			355.001i			0.552961i
$643$	65.4231			0.101747			0.0508734	−	0.998705i	$-0.483800\pi$
$643$	65.4231			0.101747			0.0508734	+	0.998705i	$0.483800\pi$
$644$			339.520i			0.527205i
$645$			37.1365i			0.0575760i
$646$			74.9893i			0.116083i
$647$	1000.16			1.54584			0.772920	−	0.634503i	$-0.218795\pi$
$647$	1000.16			1.54584			0.772920	+	0.634503i	$0.218795\pi$
$648$			76.1030i			0.117443i
$649$	−400.884	+	792.480i	−0.617696	+	1.22108i
$650$	387.782			0.596588
$651$			1123.04i			1.72510i
$652$	−504.839			−0.774293
$653$	−635.037			−0.972492			−0.486246	−	0.873822i	$-0.661634\pi$
$653$	−635.037			−0.972492			−0.486246	+	0.873822i	$0.661634\pi$
$654$	−342.195			−0.523234
$655$			21.8296i			0.0333276i
$656$	−288.595			−0.439932
$657$			255.937i			0.389553i
$658$	539.063			0.819245
$659$		−	445.774i		−	0.676440i	−0.941067	−	0.338220i	$-0.890175\pi$
$659$		−	445.774i		−	0.676440i	0.941067	−	0.338220i	$-0.109825\pi$
$660$		−	14.5468i		−	0.0220406i
$661$	4.13501			0.00625568			0.00312784	−	0.999995i	$-0.499004\pi$
$661$	4.13501			0.00625568			0.00312784	+	0.999995i	$0.499004\pi$
$662$		−	347.372i		−	0.524731i
$663$			65.6222i			0.0989777i
$664$	−836.840			−1.26030
$665$	46.8110			0.0703925
$666$	178.283			0.267693
$667$		−	344.773i		−	0.516900i
$668$	128.539			0.192423
$669$	117.856			0.176167
$670$	6.63213			0.00989870
$671$	−666.025			−0.992586
$672$			541.072i			0.805167i
$673$			144.454i			0.214641i	0.994224	+	0.107321i	$0.0342271\pi$
$673$			144.454i			0.214641i	−0.994224	+	0.107321i	$0.965773\pi$
$674$	117.750			0.174704
$675$	129.515			0.191874
$676$	92.8222			0.137311
$677$	567.757			0.838637			0.419318	−	0.907839i	$-0.362269\pi$
$677$	567.757			0.838637			0.419318	+	0.907839i	$0.362269\pi$
$678$	51.3780			0.0757788
$679$		−	120.028i		−	0.176771i
$680$		−	7.88396i		−	0.0115941i
$681$		−	515.280i		−	0.756652i
$682$		−	1254.24i		−	1.83905i
$683$		−	505.717i		−	0.740435i	−0.928945	−	0.370218i	$-0.879283\pi$
$683$		−	505.717i		−	0.740435i	0.928945	−	0.370218i	$-0.120717\pi$
$684$	−96.1651			−0.140592
$685$	−37.8618			−0.0552727
$686$		−	315.324i		−	0.459656i
$687$			47.7966i			0.0695729i
$688$			288.288i			0.419023i
$689$			414.275i			0.601270i
$690$	−10.1304			−0.0146818
$691$		−	843.080i		−	1.22009i	−0.792368	−	0.610044i	$-0.791152\pi$
$691$		−	843.080i		−	1.22009i	0.792368	−	0.610044i	$-0.208848\pi$
$692$			333.071i			0.481317i
$693$		−	491.944i		−	0.709876i
$694$	−730.334			−1.05236
$695$	16.3712			0.0235557
$696$		−	330.544i		−	0.474920i
$697$	−267.562			−0.383877
$698$	419.806			0.601441
$699$		−	622.230i		−	0.890171i
$700$	553.964			0.791377
$701$		−	873.826i		−	1.24654i	−0.782006	−	0.623271i	$-0.785803\pi$
$701$		−	873.826i		−	1.24654i	0.782006	−	0.623271i	$-0.214197\pi$
$702$	80.8409			0.115158
$703$			666.980i			0.948763i
$704$		−	825.687i		−	1.17285i
$705$		−	16.7432i		−	0.0237493i
$706$	886.824			1.25612
$707$			1206.75i			1.70686i
$708$	−186.036	−	94.1084i	−0.262763	−	0.132921i
$709$	159.514			0.224985			0.112492	−	0.993653i	$-0.464117\pi$
$709$	159.514			0.224985			0.112492	+	0.993653i	$0.464117\pi$
$710$		−	22.6177i		−	0.0318559i
$711$	186.649			0.262516
$712$	303.859			0.426768
$713$	909.237			1.27523
$714$		−	90.0547i		−	0.126127i
$715$	−45.7491			−0.0639848
$716$			164.304i			0.229475i
$717$	459.213			0.640465
$718$			638.636i			0.889465i
$719$			35.0202i			0.0487068i	0.999703	+	0.0243534i	$0.00775270\pi$
$719$			35.0202i			0.0487068i	−0.999703	+	0.0243534i	$0.992247\pi$
$720$	−3.01697			−0.00419024
$721$			469.164i			0.650712i
$722$		−	159.775i		−	0.221295i
$723$	101.993			0.141070
$724$	−265.549			−0.366781
$725$	−562.534			−0.775908
$726$			256.014i			0.352637i
$727$	1123.28			1.54509			0.772544	−	0.634961i	$-0.218984\pi$
$727$	1123.28			1.54509			0.772544	+	0.634961i	$0.218984\pi$
$728$	1023.71			1.40620
$729$	27.0000			0.0370370
$730$	−32.6629			−0.0447437
$731$			267.277i			0.365632i
$732$		−	156.351i		−	0.213594i
$733$	−1337.07			−1.82411			−0.912053	−	0.410073i	$-0.865503\pi$
$733$	−1337.07			−1.82411			−0.912053	+	0.410073i	$0.865503\pi$
$734$	707.526			0.963932
$735$	−33.0047			−0.0449043
$736$	438.063			0.595194
$737$	260.749			0.353797
$738$			329.613i			0.446630i
$739$		−	393.835i		−	0.532930i	−0.963845	−	0.266465i	$-0.914144\pi$
$739$		−	393.835i		−	0.532930i	0.963845	−	0.266465i	$-0.0858556\pi$
$740$		−	23.6849i		−	0.0320067i
$741$			302.435i			0.408145i
$742$		−	568.518i		−	0.766197i
$743$	−42.0432			−0.0565857			−0.0282929	−	0.999600i	$-0.509007\pi$
$743$	−42.0432			−0.0565857			−0.0282929	+	0.999600i	$0.509007\pi$
$744$	871.714			1.17166
$745$			59.7205i			0.0801617i
$746$		−	367.195i		−	0.492218i
$747$			296.896i			0.397451i
$748$		−	104.695i		−	0.139967i
$749$	1594.92			2.12940
$750$			33.1073i			0.0441431i
$751$			1078.71i			1.43636i	0.695858	+	0.718180i	$0.255025\pi$
$751$			1078.71i			1.43636i	−0.695858	+	0.718180i	$0.744975\pi$
$752$		−	129.976i		−	0.172841i
$753$	−2.33503			−0.00310097
$754$	−351.123			−0.465680
$755$		−	7.22284i		−	0.00956667i
$756$	115.485			0.152758
$757$	−247.277			−0.326654			−0.163327	−	0.986572i	$-0.552223\pi$
$757$	−247.277			−0.326654			−0.163327	+	0.986572i	$0.552223\pi$
$758$			745.470i			0.983470i
$759$	−398.288			−0.524753
$760$		−	36.3351i		−	0.0478093i
$761$	681.030			0.894914			0.447457	−	0.894305i	$-0.352330\pi$
$761$	681.030			0.894914			0.447457	+	0.894305i	$0.352330\pi$
$762$		−	521.532i		−	0.684425i
$763$			1537.39i			2.01492i
$764$		−	420.831i		−	0.550826i
$765$	−2.79709			−0.00365633
$766$			401.143i			0.523685i
$767$	−295.967	+	585.077i	−0.385876	+	0.762812i
$768$	471.960			0.614531
$769$		−	1018.02i		−	1.32382i	−0.749582	−	0.661912i	$-0.769745\pi$
$769$		−	1018.02i		−	1.32382i	0.749582	−	0.661912i	$-0.230255\pi$
$770$	62.7824			0.0815356
$771$	−521.556			−0.676466
$772$	356.328			0.461565
$773$			1082.79i			1.40076i	0.713770	+	0.700380i	$0.246986\pi$
$773$			1082.79i			1.40076i	−0.713770	+	0.700380i	$0.753014\pi$
$774$	329.262			0.425403
$775$		−	1483.52i		−	1.91422i
$776$	−93.1664			−0.120060
$777$		−	800.977i		−	1.03086i
$778$			868.518i			1.11635i
$779$	−1233.12			−1.58296
$780$		−	10.7397i		−	0.0137688i
$781$		−	889.236i		−	1.13859i
$782$	−72.9101			−0.0932354
$783$	−117.271			−0.149772
$784$	−256.213			−0.326802
$785$			5.05014i			0.00643330i
$786$	193.546			0.246242
$787$	302.623			0.384527			0.192263	−	0.981343i	$-0.438417\pi$
$787$	302.623			0.384527			0.192263	+	0.981343i	$0.438417\pi$
$788$	536.013			0.680219
$789$	−143.195			−0.181490
$790$			23.8203i			0.0301523i
$791$		−	230.827i		−	0.291817i
$792$	−381.851			−0.482135
$793$	−491.717			−0.620071
$794$	−607.596			−0.765234
$795$	−17.6581			−0.0222115
$796$	−75.0172			−0.0942428
$797$		−	319.419i		−	0.400776i	−0.979717	−	0.200388i	$-0.935780\pi$
$797$		−	319.419i		−	0.400776i	0.979717	−	0.200388i	$-0.0642204\pi$
$798$		−	415.038i		−	0.520098i
$799$		−	120.504i		−	0.150818i
$800$		−	714.747i		−	0.893433i
$801$		−	107.804i		−	0.134586i
$802$	150.085			0.187138
$803$	−1284.18			−1.59922
$804$			61.2112i			0.0761334i
$805$			45.5131i			0.0565380i
$806$		−	925.983i		−	1.14886i
$807$			360.535i			0.446759i
$808$	936.689			1.15927
$809$		−	474.757i		−	0.586844i	−0.955983	−	0.293422i	$-0.905206\pi$
$809$		−	474.757i		−	0.586844i	0.955983	−	0.293422i	$-0.0947941\pi$
$810$			3.44577i			0.00425404i
$811$		−	48.5354i		−	0.0598464i	−0.999552	−	0.0299232i	$-0.990474\pi$
$811$		−	48.5354i		−	0.0598464i	0.999552	−	0.0299232i	$-0.00952627\pi$
$812$	−501.594			−0.617727
$813$	−67.0443			−0.0824654
$814$			894.547i			1.09895i
$815$	−67.6742			−0.0830359
$816$	−21.7136			−0.0266098
$817$			1231.81i			1.50772i
$818$	770.675			0.942146
$819$		−	363.195i		−	0.443461i
$820$	43.7890			0.0534012
$821$		−	60.2763i		−	0.0734182i	−0.999326	−	0.0367091i	$-0.988313\pi$
$821$		−	60.2763i		−	0.0734182i	0.999326	−	0.0367091i	$-0.0116875\pi$
$822$			335.693i			0.408385i
$823$		−	1276.52i		−	1.55105i	−0.631316	−	0.775526i	$-0.717485\pi$
$823$		−	1276.52i		−	1.55105i	0.631316	−	0.775526i	$-0.282515\pi$
$824$	364.168			0.441952
$825$			649.849i			0.787696i
$826$	406.162	−	802.913i	0.491721	−	0.972049i
$827$	692.996			0.837964			0.418982	−	0.907995i	$-0.362387\pi$
$827$	692.996			0.837964			0.418982	+	0.907995i	$0.362387\pi$
$828$		−	93.4988i		−	0.112921i
$829$	−1079.49			−1.30215			−0.651077	−	0.759012i	$-0.725682\pi$
$829$	−1079.49			−1.30215			−0.651077	+	0.759012i	$0.725682\pi$
$830$	−37.8902			−0.0456509
$831$	−362.648			−0.436400
$832$		−	609.592i		−	0.732683i
$833$	−237.539			−0.285161
$834$		−	145.151i		−	0.174042i
$835$	17.2308			0.0206357
$836$		−	482.514i		−	0.577169i
$837$		−	309.269i		−	0.369497i
$838$	384.189			0.458459
$839$		−	974.349i		−	1.16132i	−0.814145	−	0.580661i	$-0.802794\pi$
$839$		−	974.349i		−	1.16132i	0.814145	−	0.580661i	$-0.197206\pi$
$840$			43.6348i			0.0519462i
$841$	−331.646			−0.394348
$842$	64.5275			0.0766360
$843$	−531.881			−0.630938
$844$			679.027i			0.804535i
$845$	12.4429			0.0147254
$846$	−148.450			−0.175473
$847$	1150.20			1.35797
$848$	−137.079			−0.161649
$849$			396.915i			0.467509i
$850$			118.961i			0.139954i
$851$	−648.487			−0.762029
$852$	208.750			0.245012
$853$	−966.592			−1.13317			−0.566584	−	0.824004i	$-0.691735\pi$
$853$	−966.592			−1.13317			−0.566584	+	0.824004i	$0.691735\pi$
$854$	674.793			0.790155
$855$	−12.8910			−0.0150773
$856$		−	1237.99i		−	1.44625i
$857$			1521.97i			1.77593i	0.459912	+	0.887965i	$0.347881\pi$
$857$			1521.97i			1.77593i	−0.459912	+	0.887965i	$0.652119\pi$
$858$			405.623i			0.472754i
$859$		−	110.413i		−	0.128536i	−0.997933	−	0.0642681i	$-0.979529\pi$
$859$		−	110.413i		−	0.128536i	0.997933	−	0.0642681i	$-0.0204713\pi$
$860$		−	43.7424i		−	0.0508632i
$861$	1480.86			1.71993
$862$	358.641			0.416057
$863$		−	499.067i		−	0.578293i	−0.957285	−	0.289146i	$-0.906629\pi$
$863$		−	499.067i		−	0.578293i	0.957285	−	0.289146i	$-0.0933714\pi$
$864$		−	149.003i		−	0.172457i
$865$			44.6486i			0.0516169i
$866$			107.384i			0.124000i
$867$	480.432			0.554131
$868$		−	1322.81i		−	1.52397i
$869$			936.521i			1.07770i
$870$		−	14.9663i		−	0.0172026i
$871$	192.507			0.221018
$872$	1193.33			1.36850
$873$			33.0538i			0.0378623i
$874$	−336.023			−0.384466
$875$	148.742			0.169991
$876$		−	301.463i		−	0.344135i
$877$	−91.5133			−0.104348			−0.0521741	−	0.998638i	$-0.516615\pi$
$877$	−91.5133			−0.104348			−0.0521741	+	0.998638i	$0.516615\pi$
$878$			871.314i			0.992385i
$879$	−97.9610			−0.111446
$880$		−	15.1378i		−	0.0172021i
$881$			711.614i			0.807734i	0.914818	+	0.403867i	$0.132334\pi$
$881$			711.614i			0.807734i	−0.914818	+	0.403867i	$0.867666\pi$
$882$			292.628i			0.331777i
$883$	919.400			1.04122			0.520612	−	0.853794i	$-0.325704\pi$
$883$	919.400			1.04122			0.520612	+	0.853794i	$0.325704\pi$
$884$		−	77.2951i		−	0.0874379i
$885$	−24.9384	−	12.6153i	−0.0281790	−	0.0142546i
$886$	955.741			1.07871
$887$		−	1322.56i		−	1.49105i	−0.666479	−	0.745523i	$-0.732200\pi$
$887$		−	1322.56i		−	1.49105i	0.666479	−	0.745523i	$-0.267800\pi$
$888$	−621.725			−0.700140
$889$	−2343.10			−2.63565
$890$	13.7580			0.0154585
$891$			135.474i			0.152047i
$892$	−138.820			−0.155628
$893$		−	555.369i		−	0.621914i
$894$	529.497			0.592278
$895$			22.0252i			0.0246092i
$896$		−	412.997i		−	0.460934i
$897$	−294.050			−0.327815
$898$		−	202.280i		−	0.225256i
$899$			1343.27i			1.49418i
$900$	−152.553			−0.169504
$901$	−127.088			−0.141052
$902$	−1653.85			−1.83354
$903$		−	1479.28i		−	1.63818i
$904$	−179.170			−0.198196
$905$	−35.5972			−0.0393339
$906$	−64.0395			−0.0706838
$907$	735.997			0.811464			0.405732	−	0.913992i	$-0.367017\pi$
$907$	735.997			0.811464			0.405732	+	0.913992i	$0.367017\pi$
$908$			606.938i			0.668434i
$909$		−	332.321i		−	0.365589i
$910$	46.3514			0.0509356
$911$	1461.31			1.60407			0.802036	−	0.597276i	$-0.203750\pi$
$911$	1461.31			1.60407			0.802036	+	0.597276i	$0.203750\pi$
$912$	−100.072			−0.109728
$913$	−1489.69			−1.63164
$914$	−411.378			−0.450086
$915$		−	20.9590i		−	0.0229060i
$916$		−	56.2986i		−	0.0614614i
$917$		−	869.549i		−	0.948254i
$918$			24.7997i			0.0270149i
$919$			1461.36i			1.59016i	0.606506	+	0.795079i	$0.292571\pi$
$919$			1461.36i			1.59016i	−0.606506	+	0.795079i	$0.707429\pi$
$920$	35.3276			0.0383996
$921$	66.0977			0.0717673
$922$			640.663i			0.694862i
$923$		−	656.510i		−	0.711278i
$924$			579.451i			0.627111i
$925$			1058.08i			1.14387i
$926$	939.764			1.01486
$927$		−	129.201i		−	0.139375i
$928$			647.177i			0.697389i
$929$		−	467.354i		−	0.503072i	−0.967848	−	0.251536i	$-0.919064\pi$
$929$		−	467.354i		−	0.503072i	0.967848	−	0.251536i	$-0.0809357\pi$
$930$	39.4692			0.0424400
$931$	−1094.76			−1.17589
$932$			732.912i			0.786386i
$933$	411.155			0.440681
$934$	−501.286			−0.536709
$935$		−	14.0345i		−	0.0150102i
$936$	−281.915			−0.301191
$937$			939.907i			1.00310i	0.865128	+	0.501551i	$0.167237\pi$
$937$			939.907i			1.00310i	−0.865128	+	0.501551i	$0.832763\pi$
$938$	−264.181			−0.281643
$939$		−	811.229i		−	0.863928i
$940$			19.7215i			0.0209804i
$941$			1495.70i			1.58948i	0.606948	+	0.794741i	$0.292394\pi$
$941$			1495.70i			1.58948i	−0.606948	+	0.794741i	$0.707606\pi$
$942$	44.7758			0.0475327
$943$		−	1198.93i		−	1.27140i
$944$	−193.595	−	97.9319i	−0.205079	−	0.103741i
$945$	15.4809			0.0163819
$946$			1652.09i			1.74639i
$947$	−999.461			−1.05540			−0.527699	−	0.849432i	$-0.676945\pi$
$947$	−999.461			−1.05540			−0.527699	+	0.849432i	$0.676945\pi$
$948$	−219.850			−0.231909
$949$	−948.088			−0.999039
$950$			548.258i			0.577114i
$951$	169.356			0.178082
$952$			314.046i			0.329880i
$953$	−87.5531			−0.0918710			−0.0459355	−	0.998944i	$-0.514627\pi$
$953$	−87.5531			−0.0918710			−0.0459355	+	0.998944i	$0.514627\pi$
$954$			156.561i			0.164110i
$955$		−	56.4129i		−	0.0590711i
$956$	−540.898			−0.565793
$957$		−	588.415i		−	0.614853i
$958$		−	32.6610i		−	0.0340929i
$959$	1508.17			1.57265
$960$	25.9833			0.0270660
$961$	−2581.49			−2.68625
$962$			660.431i			0.686518i
$963$	−439.216			−0.456092
$964$	−120.136			−0.124622
$965$	47.7662			0.0494987
$966$	403.531			0.417734
$967$		−	1799.89i		−	1.86132i	−0.365887	−	0.930659i	$-0.619234\pi$
$967$		−	1799.89i		−	1.86132i	0.365887	−	0.930659i	$-0.380766\pi$
$968$		−	892.793i		−	0.922307i
$969$	−92.7787			−0.0957469
$970$	−4.21836			−0.00434883
$971$	1423.88			1.46641			0.733205	−	0.680008i	$-0.238024\pi$
$971$	1423.88			1.46641			0.733205	+	0.680008i	$0.238024\pi$
$972$	−31.8028			−0.0327189
$973$	−652.122			−0.670218
$974$			1005.89i			1.03274i
$975$			479.774i			0.492076i
$976$		−	162.703i		−	0.166704i
$977$			535.083i			0.547679i	0.961775	+	0.273840i	$0.0882938\pi$
$977$			535.083i			0.547679i	−0.961775	+	0.273840i	$0.911706\pi$
$978$			600.017i			0.613514i
$979$	540.911			0.552514
$980$	38.8755			0.0396689
$981$		−	423.373i		−	0.431573i
$982$			569.442i			0.579880i
$983$			1248.96i			1.27056i	0.772282	+	0.635280i	$0.219115\pi$
$983$			1248.96i			1.27056i	−0.772282	+	0.635280i	$0.780885\pi$
$984$		−	1149.45i		−	1.16814i
$985$	71.8531			0.0729473
$986$		−	107.715i		−	0.109244i
$987$			666.943i			0.675727i
$988$		−	356.233i		−	0.360559i
$989$	−1197.65			−1.21097
$990$	−17.2893			−0.0174640
$991$		−	431.674i		−	0.435595i	−0.975994	−	0.217797i	$-0.930113\pi$
$991$		−	431.674i		−	0.435595i	0.975994	−	0.217797i	$-0.0698872\pi$
$992$	−1706.74			−1.72050
$993$	429.777			0.432807
$994$			900.942i			0.906380i
$995$	−10.0561			−0.0101067
$996$		−	349.708i		−	0.351112i
$997$	−133.711			−0.134113			−0.0670565	−	0.997749i	$-0.521361\pi$
$997$	−133.711			−0.134113			−0.0670565	+	0.997749i	$0.521361\pi$
$998$		−	1160.13i		−	1.16245i
$999$			220.577i			0.220798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.c.a.58.13	yes	20
3.2	odd	2		531.3.c.c.235.8		20
59.58	odd	2	inner	177.3.c.a.58.8	✓	20
177.176	even	2		531.3.c.c.235.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.c.a.58.8	✓	20	59.58	odd	2	inner
177.3.c.a.58.13	yes	20	1.1	even	1	trivial
531.3.c.c.235.8		20	3.2	odd	2
531.3.c.c.235.13		20	177.176	even	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)

\(f(q)\)	\(=\)	\(q+1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} -2.42478i q^{6} -10.8938 q^{7} +8.45589i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} -2.42478i q^{6} -10.8938 q^{7} +8.45589i q^{8} +3.00000 q^{9} +0.382863i q^{10} +15.0527i q^{11} -3.53364 q^{12} +11.1132i q^{13} -15.2508i q^{14} -0.473689 q^{15} -3.67721 q^{16} -3.40920 q^{17} +4.19984i q^{18} -15.7121 q^{19} +0.557948 q^{20} +18.8687 q^{21} -21.0729 q^{22} -15.2765i q^{23} -14.6460i q^{24} -24.9252 q^{25} -15.5578 q^{26} -5.19615 q^{27} -22.2251 q^{28} +22.5689 q^{29} -0.663139i q^{30} +59.5188i q^{31} +28.6757i q^{32} -26.0720i q^{33} -4.77271i q^{34} -2.97929 q^{35} +6.12044 q^{36} -42.4500i q^{37} -21.9961i q^{38} -19.2485i q^{39} +2.31255i q^{40} +78.4822 q^{41} +26.4152i q^{42} -78.3986i q^{43} +30.7096i q^{44} +0.820453 q^{45} +21.3862 q^{46} +35.3465i q^{47} +6.36911 q^{48} +69.6759 q^{49} -34.8940i q^{50} +5.90491 q^{51} +22.6725i q^{52} +37.2779 q^{53} -7.27434i q^{54} +4.11666i q^{55} -92.1171i q^{56} +27.2142 q^{57} +31.5952i q^{58} +(52.6472 + 26.6321i) q^{59} -0.966395 q^{60} +44.2464i q^{61} -83.3232 q^{62} -32.6815 q^{63} -54.8532 q^{64} +3.03927i q^{65} +36.4994 q^{66} -17.3224i q^{67} -6.95528 q^{68} +26.4596i q^{69} -4.17086i q^{70} -59.0750 q^{71} +25.3677i q^{72} +85.3122i q^{73} +59.4278 q^{74} +43.1717 q^{75} -32.0550 q^{76} -163.981i q^{77} +26.9470 q^{78} +62.2163 q^{79} -1.00566 q^{80} +9.00000 q^{81} +109.871i q^{82} +98.9653i q^{83} +38.4949 q^{84} -0.932363 q^{85} +109.754 q^{86} -39.0904 q^{87} -127.284 q^{88} -35.9346i q^{89} +1.14859i q^{90} -121.065i q^{91} -31.1663i q^{92} -103.090i q^{93} -49.4833 q^{94} -4.29702 q^{95} -49.6677i q^{96} +11.0179i q^{97} +97.5426i q^{98} +45.1580i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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