LMFDB - Embedded newform 555.2.g.a.184.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.15
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.818204 q^{2} -1.00000i q^{3} -1.33054 q^{4} +(0.157839 - 2.23049i) q^{5} +0.818204i q^{6} -3.66373i q^{7} +2.72506 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.818204 q^{2} -1.00000i q^{3} -1.33054 q^{4} +(0.157839 - 2.23049i) q^{5} +0.818204i q^{6} -3.66373i q^{7} +2.72506 q^{8} -1.00000 q^{9} +(-0.129144 + 1.82500i) q^{10} -5.24223 q^{11} +1.33054i q^{12} -1.85420 q^{13} +2.99768i q^{14} +(-2.23049 - 0.157839i) q^{15} +0.431428 q^{16} +3.75153 q^{17} +0.818204 q^{18} +1.89695i q^{19} +(-0.210011 + 2.96776i) q^{20} -3.66373 q^{21} +4.28921 q^{22} +6.57994 q^{23} -2.72506i q^{24} +(-4.95017 - 0.704115i) q^{25} +1.51711 q^{26} +1.00000i q^{27} +4.87475i q^{28} +7.35087i q^{29} +(1.82500 + 0.129144i) q^{30} -3.91539i q^{31} -5.80312 q^{32} +5.24223i q^{33} -3.06951 q^{34} +(-8.17191 - 0.578278i) q^{35} +1.33054 q^{36} +(-5.78358 - 1.88419i) q^{37} -1.55209i q^{38} +1.85420i q^{39} +(0.430120 - 6.07823i) q^{40} -10.8947 q^{41} +2.99768 q^{42} -5.06014 q^{43} +6.97500 q^{44} +(-0.157839 + 2.23049i) q^{45} -5.38373 q^{46} -2.73064i q^{47} -0.431428i q^{48} -6.42291 q^{49} +(4.05025 + 0.576109i) q^{50} -3.75153i q^{51} +2.46709 q^{52} +10.8230i q^{53} -0.818204i q^{54} +(-0.827425 + 11.6927i) q^{55} -9.98389i q^{56} +1.89695 q^{57} -6.01451i q^{58} +8.74598i q^{59} +(2.96776 + 0.210011i) q^{60} -11.7550i q^{61} +3.20359i q^{62} +3.66373i q^{63} +3.88528 q^{64} +(-0.292664 + 4.13578i) q^{65} -4.28921i q^{66} -12.0734i q^{67} -4.99157 q^{68} -6.57994i q^{69} +(6.68629 + 0.473149i) q^{70} +15.4705 q^{71} -2.72506 q^{72} -3.48304i q^{73} +(4.73215 + 1.54165i) q^{74} +(-0.704115 + 4.95017i) q^{75} -2.52397i q^{76} +19.2061i q^{77} -1.51711i q^{78} -3.56909i q^{79} +(0.0680960 - 0.962296i) q^{80} +1.00000 q^{81} +8.91405 q^{82} -1.57495i q^{83} +4.87475 q^{84} +(0.592136 - 8.36774i) q^{85} +4.14022 q^{86} +7.35087 q^{87} -14.2854 q^{88} -4.49583i q^{89} +(0.129144 - 1.82500i) q^{90} +6.79329i q^{91} -8.75489 q^{92} -3.91539 q^{93} +2.23422i q^{94} +(4.23113 + 0.299412i) q^{95} +5.80312i q^{96} +3.73519 q^{97} +5.25525 q^{98} +5.24223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.818204			−0.578557			−0.289279	−	0.957245i	$-0.593415\pi$
$2$	−0.818204			−0.578557			−0.289279	+	0.957245i	$0.593415\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.33054			−0.665271
$5$	0.157839	−	2.23049i	0.0705876	−	0.997506i
$5$	0.157839	−	2.23049i	0.0705876	−	0.997506i
$6$			0.818204i			0.334030i
$7$		−	3.66373i		−	1.38476i	−0.721533	−	0.692380i	$-0.756562\pi$
$7$		−	3.66373i		−	1.38476i	0.721533	−	0.692380i	$-0.243438\pi$
$8$	2.72506			0.963455
$9$	−1.00000			−0.333333
$10$	−0.129144	+	1.82500i	−0.0408390	+	0.577114i
$11$	−5.24223			−1.58059			−0.790295	−	0.612726i	$-0.790073\pi$
$11$	−5.24223			−1.58059			−0.790295	+	0.612726i	$0.790073\pi$
$12$			1.33054i			0.384095i
$13$	−1.85420			−0.514263			−0.257131	−	0.966376i	$-0.582777\pi$
$13$	−1.85420			−0.514263			−0.257131	+	0.966376i	$0.582777\pi$
$14$			2.99768i			0.801163i
$15$	−2.23049	−	0.157839i	−0.575910	−	0.0407537i
$16$	0.431428			0.107857
$17$	3.75153			0.909879			0.454939	−	0.890522i	$-0.349661\pi$
$17$	3.75153			0.909879			0.454939	+	0.890522i	$0.349661\pi$
$18$	0.818204			0.192852
$19$			1.89695i			0.435191i	0.976039	+	0.217595i	$0.0698213\pi$
$19$			1.89695i			0.435191i	−0.976039	+	0.217595i	$0.930179\pi$
$20$	−0.210011	+	2.96776i	−0.0469599	+	0.663612i
$21$	−3.66373			−0.799491
$22$	4.28921			0.914463
$23$	6.57994			1.37201			0.686006	−	0.727596i	$-0.259362\pi$
$23$	6.57994			1.37201			0.686006	+	0.727596i	$0.259362\pi$
$24$		−	2.72506i		−	0.556251i
$25$	−4.95017	−	0.704115i	−0.990035	−	0.140823i
$26$	1.51711			0.297531
$27$			1.00000i			0.192450i
$28$			4.87475i			0.921241i
$29$			7.35087i			1.36502i	0.730875	+	0.682511i	$0.239112\pi$
$29$			7.35087i			1.36502i	−0.730875	+	0.682511i	$0.760888\pi$
$30$	1.82500	+	0.129144i	0.333197	+	0.0235784i
$31$		−	3.91539i		−	0.703225i	−0.936146	−	0.351613i	$-0.885633\pi$
$31$		−	3.91539i		−	0.703225i	0.936146	−	0.351613i	$-0.114367\pi$
$32$	−5.80312			−1.02586
$33$			5.24223i			0.912554i
$34$	−3.06951			−0.526417
$35$	−8.17191	−	0.578278i	−1.38131	−	0.0977468i
$36$	1.33054			0.221757
$37$	−5.78358	−	1.88419i	−0.950815	−	0.309759i
$37$	−5.78358	−	1.88419i	−0.950815	−	0.309759i
$38$		−	1.55209i		−	0.251783i
$39$			1.85420i			0.296910i
$40$	0.430120	−	6.07823i	0.0680079	−	0.961052i
$41$	−10.8947			−1.70146			−0.850730	−	0.525603i	$-0.823840\pi$
$41$	−10.8947			−1.70146			−0.850730	+	0.525603i	$0.823840\pi$
$42$	2.99768			0.462552
$43$	−5.06014			−0.771664			−0.385832	−	0.922569i	$-0.626086\pi$
$43$	−5.06014			−0.771664			−0.385832	+	0.922569i	$0.626086\pi$
$44$	6.97500			1.05152
$45$	−0.157839	+	2.23049i	−0.0235292	+	0.332502i
$46$	−5.38373			−0.793788
$47$		−	2.73064i		−	0.398305i	−0.979969	−	0.199153i	$-0.936181\pi$
$47$		−	2.73064i		−	0.398305i	0.979969	−	0.199153i	$-0.0638189\pi$
$48$		−	0.431428i		−	0.0622713i
$49$	−6.42291			−0.917559
$50$	4.05025	+	0.576109i	0.572792	+	0.0814742i
$51$		−	3.75153i		−	0.525319i
$52$	2.46709			0.342124
$53$			10.8230i			1.48665i	0.668931	+	0.743324i	$0.266752\pi$
$53$			10.8230i			1.48665i	−0.668931	+	0.743324i	$0.733248\pi$
$54$		−	0.818204i		−	0.111343i
$55$	−0.827425	+	11.6927i	−0.111570	+	1.57665i
$56$		−	9.98389i		−	1.33415i
$57$	1.89695			0.251257
$58$		−	6.01451i		−	0.789743i
$59$			8.74598i			1.13863i	0.822120	+	0.569315i	$0.192791\pi$
$59$			8.74598i			1.13863i	−0.822120	+	0.569315i	$0.807209\pi$
$60$	2.96776	+	0.210011i	0.383136	+	0.0271123i
$61$		−	11.7550i		−	1.50507i	−0.658553	−	0.752535i	$-0.728831\pi$
$61$		−	11.7550i		−	1.50507i	0.658553	−	0.752535i	$-0.271169\pi$
$62$			3.20359i			0.406856i
$63$			3.66373i			0.461586i
$64$	3.88528			0.485660
$65$	−0.292664	+	4.13578i	−0.0363005	+	0.512980i
$66$		−	4.28921i		−	0.527965i
$67$		−	12.0734i		−	1.47500i	−0.675349	−	0.737498i	$-0.736007\pi$
$67$		−	12.0734i		−	1.47500i	0.675349	−	0.737498i	$-0.263993\pi$
$68$	−4.99157			−0.605316
$69$		−	6.57994i		−	0.792131i
$70$	6.68629	+	0.473149i	0.799165	+	0.0565521i
$71$	15.4705			1.83601			0.918006	−	0.396566i	$-0.129798\pi$
$71$	15.4705			1.83601			0.918006	+	0.396566i	$0.129798\pi$
$72$	−2.72506			−0.321152
$73$		−	3.48304i		−	0.407659i	−0.979006	−	0.203830i	$-0.934661\pi$
$73$		−	3.48304i		−	0.407659i	0.979006	−	0.203830i	$-0.0653389\pi$
$74$	4.73215	+	1.54165i	0.550101	+	0.179213i
$75$	−0.704115	+	4.95017i	−0.0813042	+	0.571597i
$76$		−	2.52397i		−	0.289520i
$77$			19.2061i			2.18874i
$78$		−	1.51711i		−	0.171779i
$79$		−	3.56909i		−	0.401554i	−0.979637	−	0.200777i	$-0.935653\pi$
$79$		−	3.56909i		−	0.401554i	0.979637	−	0.200777i	$-0.0643466\pi$
$80$	0.0680960	−	0.962296i	0.00761337	−	0.107588i
$81$	1.00000			0.111111
$82$	8.91405			0.984393
$83$		−	1.57495i		−	0.172873i	−0.996257	−	0.0864365i	$-0.972452\pi$
$83$		−	1.57495i		−	0.172873i	0.996257	−	0.0864365i	$-0.0275480\pi$
$84$	4.87475			0.531879
$85$	0.592136	−	8.36774i	0.0642261	−	0.907609i
$86$	4.14022			0.446452
$87$	7.35087			0.788096
$88$	−14.2854			−1.52283
$89$		−	4.49583i		−	0.476557i	−0.971197	−	0.238278i	$-0.923417\pi$
$89$		−	4.49583i		−	0.476557i	0.971197	−	0.238278i	$-0.0765830\pi$
$90$	0.129144	−	1.82500i	0.0136130	−	0.192371i
$91$			6.79329i			0.712130i
$92$	−8.75489			−0.912760
$93$	−3.91539			−0.406007
$94$			2.23422i			0.230442i
$95$	4.23113	+	0.299412i	0.434105	+	0.0307190i
$96$			5.80312i			0.592279i
$97$	3.73519			0.379251			0.189625	−	0.981856i	$-0.439273\pi$
$97$	3.73519			0.379251			0.189625	+	0.981856i	$0.439273\pi$
$98$	5.25525			0.530860
$99$	5.24223			0.526864
$100$	6.58642	+	0.936855i	0.658642	+	0.0936855i
$101$	−9.28549			−0.923941			−0.461970	−	0.886895i	$-0.652857\pi$
$101$	−9.28549			−0.923941			−0.461970	+	0.886895i	$0.652857\pi$
$102$			3.06951i			0.303927i
$103$	−9.37570			−0.923815			−0.461907	−	0.886928i	$-0.652835\pi$
$103$	−9.37570			−0.923815			−0.461907	+	0.886928i	$0.652835\pi$
$104$	−5.05281			−0.495469
$105$	−0.578278	+	8.17191i	−0.0564341	+	0.797497i
$106$		−	8.85539i		−	0.860112i
$107$		−	13.1610i		−	1.27232i	−0.771558	−	0.636159i	$-0.780522\pi$
$107$		−	13.1610i		−	1.27232i	0.771558	−	0.636159i	$-0.219478\pi$
$108$		−	1.33054i		−	0.128032i
$109$			7.59747i			0.727706i	0.931456	+	0.363853i	$0.118539\pi$
$109$			7.59747i			0.727706i	−0.931456	+	0.363853i	$0.881461\pi$
$110$	0.677003	−	9.56704i	0.0645497	−	0.912181i
$111$	−1.88419	+	5.78358i	−0.178839	+	0.548953i
$112$		−	1.58064i		−	0.149356i
$113$	2.20503			0.207432			0.103716	−	0.994607i	$-0.466927\pi$
$113$	2.20503			0.207432			0.103716	+	0.994607i	$0.466927\pi$
$114$	−1.55209			−0.145367
$115$	1.03857	−	14.6765i	0.0968470	−	1.36859i
$116$		−	9.78064i		−	0.908110i
$117$	1.85420			0.171421
$118$		−	7.15599i		−	0.658762i
$119$		−	13.7446i		−	1.25996i
$120$	−6.07823	−	0.430120i	−0.554864	−	0.0392644i
$121$	16.4809			1.49827
$122$			9.61796i			0.870769i
$123$			10.8947i			0.982339i
$124$			5.20959i			0.467835i
$125$	−2.35185	+	10.9302i	−0.210356	+	0.977625i
$126$		−	2.99768i		−	0.267054i
$127$		−	2.89381i		−	0.256784i	−0.991724	−	0.128392i	$-0.959018\pi$
$127$		−	2.89381i		−	0.256784i	0.991724	−	0.128392i	$-0.0409815\pi$
$128$	8.42729			0.744874
$129$			5.06014i			0.445520i
$130$	0.239459	−	3.38391i	0.0210020	−	0.296788i
$131$		−	5.52606i		−	0.482814i	−0.970424	−	0.241407i	$-0.922391\pi$
$131$		−	5.52606i		−	0.482814i	0.970424	−	0.241407i	$-0.0776088\pi$
$132$		−	6.97500i		−	0.607096i
$133$	6.94992			0.602634
$134$			9.87848i			0.853370i
$135$	2.23049	+	0.157839i	0.191970	+	0.0135846i
$136$	10.2231			0.876627
$137$		−	10.9709i		−	0.937303i	−0.883383	−	0.468652i	$-0.844740\pi$
$137$		−	10.9709i		−	0.937303i	0.883383	−	0.468652i	$-0.155260\pi$
$138$			5.38373i			0.458294i
$139$	−5.02182			−0.425945			−0.212972	−	0.977058i	$-0.568314\pi$
$139$	−5.02182			−0.425945			−0.212972	+	0.977058i	$0.568314\pi$
$140$	10.8731	+	0.769423i	0.918943	+	0.0650281i
$141$	−2.73064			−0.229962
$142$	−12.6580			−1.06224
$143$	9.72014			0.812839
$144$	−0.431428			−0.0359524
$145$	16.3960	+	1.16025i	1.36162	+	0.0963535i
$146$			2.84984i			0.235854i
$147$			6.42291i			0.529753i
$148$	7.69530	+	2.50699i	0.632550	+	0.206073i
$149$	3.05063			0.249917			0.124959	−	0.992162i	$-0.460120\pi$
$149$	3.05063			0.249917			0.124959	+	0.992162i	$0.460120\pi$
$150$	0.576109	−	4.05025i	0.0470391	−	0.330702i
$151$	0.608539			0.0495222			0.0247611	−	0.999693i	$-0.492117\pi$
$151$	0.608539			0.0495222			0.0247611	+	0.999693i	$0.492117\pi$
$152$			5.16931i			0.419287i
$153$	−3.75153			−0.303293
$154$		−	15.7145i		−	1.26631i
$155$	−8.73324	−	0.618000i	−0.701471	−	0.0496389i
$156$		−	2.46709i		−	0.197525i
$157$			4.76573i			0.380347i	0.981751	+	0.190173i	$0.0609050\pi$
$157$			4.76573i			0.380347i	−0.981751	+	0.190173i	$0.939095\pi$
$158$			2.92024i			0.232322i
$159$	10.8230			0.858317
$160$	−0.915956	+	12.9438i	−0.0724127	+	1.02330i
$161$		−	24.1071i		−	1.89991i
$162$	−0.818204			−0.0642842
$163$	13.9827			1.09521			0.547605	−	0.836737i	$-0.315540\pi$
$163$	13.9827			1.09521			0.547605	+	0.836737i	$0.315540\pi$
$164$	14.4958			1.13193
$165$	11.6927	+	0.827425i	0.910278	+	0.0644150i
$166$			1.28863i			0.100017i
$167$	−7.32793			−0.567052			−0.283526	−	0.958965i	$-0.591504\pi$
$167$	−7.32793			−0.567052			−0.283526	+	0.958965i	$0.591504\pi$
$168$	−9.98389			−0.770274
$169$	−9.56194			−0.735534
$170$	−0.484488	+	6.84652i	−0.0371585	+	0.525104i
$171$		−	1.89695i		−	0.145064i
$172$	6.73273			0.513366
$173$		−	10.7115i		−	0.814378i	−0.913344	−	0.407189i	$-0.866509\pi$
$173$		−	10.7115i		−	0.814378i	0.913344	−	0.407189i	$-0.133491\pi$
$174$	−6.01451			−0.455959
$175$	−2.57969	+	18.1361i	−0.195006	+	1.37096i
$176$	−2.26164			−0.170478
$177$	8.74598			0.657388
$178$			3.67850i			0.275715i
$179$		−	21.1329i		−	1.57955i	−0.613399	−	0.789773i	$-0.710198\pi$
$179$		−	21.1329i		−	1.57955i	0.613399	−	0.789773i	$-0.289802\pi$
$180$	0.210011	−	2.96776i	0.0156533	−	0.221204i
$181$	−21.7577			−1.61724			−0.808619	−	0.588333i	$-0.799785\pi$
$181$	−21.7577			−1.61724			−0.808619	+	0.588333i	$0.799785\pi$
$182$		−	5.55829i		−	0.412008i
$183$	−11.7550			−0.868952
$184$	17.9307			1.32187
$185$	−5.11553	+	12.6028i	−0.376102	+	0.926578i
$186$	3.20359			0.234898
$187$	−19.6663			−1.43815
$188$			3.63323i			0.264981i
$189$	3.66373			0.266497
$190$	−3.46193	−	0.244980i	−0.251155	−	0.0177727i
$191$			17.7457i			1.28404i	0.766689	+	0.642019i	$0.221903\pi$
$191$			17.7457i			1.28404i	−0.766689	+	0.642019i	$0.778097\pi$
$192$		−	3.88528i		−	0.280396i
$193$	16.1483			1.16238			0.581188	−	0.813769i	$-0.302588\pi$
$193$	16.1483			1.16238			0.581188	+	0.813769i	$0.302588\pi$
$194$	−3.05615			−0.219418
$195$	4.13578	+	0.292664i	0.296169	+	0.0209581i
$196$	8.54596			0.610425
$197$			7.50700i			0.534851i	0.963578	+	0.267426i	$0.0861730\pi$
$197$			7.50700i			0.534851i	−0.963578	+	0.267426i	$0.913827\pi$
$198$	−4.28921			−0.304821
$199$			4.43460i			0.314360i	0.987570	+	0.157180i	$0.0502403\pi$
$199$			4.43460i			0.314360i	−0.987570	+	0.157180i	$0.949760\pi$
$200$	−13.4895	−	1.91876i	−0.953854	−	0.135677i
$201$	−12.0734			−0.851590
$202$	7.59742			0.534553
$203$	26.9316			1.89023
$204$			4.99157i			0.349479i
$205$	−1.71960	+	24.3004i	−0.120102	+	1.69722i
$206$	7.67123			0.534480
$207$	−6.57994			−0.457337
$208$	−0.799954			−0.0554669
$209$		−	9.94425i		−	0.687858i
$210$	0.473149	−	6.68629i	0.0326504	−	0.461398i
$211$	−18.8857			−1.30014			−0.650071	−	0.759873i	$-0.725261\pi$
$211$	−18.8857			−1.30014			−0.650071	+	0.759873i	$0.725261\pi$
$212$		−	14.4004i		−	0.989025i
$213$		−	15.4705i		−	1.06002i
$214$			10.7684i			0.736110i
$215$	−0.798685	+	11.2866i	−0.0544699	+	0.769739i
$216$			2.72506i			0.185417i
$217$	−14.3449			−0.973798
$218$		−	6.21628i		−	0.421020i
$219$	−3.48304			−0.235362
$220$	1.10092	−	15.5577i	0.0742243	−	1.04890i
$221$	−6.95608			−0.467917
$222$	1.54165	−	4.73215i	0.103469	−	0.317601i
$223$		−	11.9370i		−	0.799357i	−0.916655	−	0.399679i	$-0.869122\pi$
$223$		−	11.9370i		−	0.799357i	0.916655	−	0.399679i	$-0.130878\pi$
$224$			21.2611i			1.42056i
$225$	4.95017	+	0.704115i	0.330012	+	0.0469410i
$226$	−1.80417			−0.120011
$227$	5.87607			0.390008			0.195004	−	0.980802i	$-0.437528\pi$
$227$	5.87607			0.390008			0.195004	+	0.980802i	$0.437528\pi$
$228$	−2.52397			−0.167154
$229$	−11.4893			−0.759237			−0.379618	−	0.925143i	$-0.623945\pi$
$229$	−11.4893			−0.759237			−0.379618	+	0.925143i	$0.623945\pi$
$230$	−0.849760	+	12.0084i	−0.0560315	+	0.791808i
$231$	19.2061			1.26367
$232$			20.0316i			1.31514i
$233$		−	0.562989i		−	0.0368826i	−0.999830	−	0.0184413i	$-0.994130\pi$
$233$		−	0.562989i		−	0.0368826i	0.999830	−	0.0184413i	$-0.00587038\pi$
$234$	−1.51711			−0.0991768
$235$	−6.09067	−	0.431001i	−0.397311	−	0.0281154i
$236$		−	11.6369i		−	0.757497i
$237$	−3.56909			−0.231837
$238$			11.2459i			0.728961i
$239$		−	22.4997i		−	1.45539i	−0.685903	−	0.727693i	$-0.740592\pi$
$239$		−	22.4997i		−	1.45539i	0.685903	−	0.727693i	$-0.259408\pi$
$240$	−0.962296	−	0.0680960i	−0.0621160	−	0.00439558i
$241$		−	30.3380i		−	1.95424i	−0.212684	−	0.977121i	$-0.568221\pi$
$241$		−	30.3380i		−	1.95424i	0.212684	−	0.977121i	$-0.431779\pi$
$242$	−13.4848			−0.866833
$243$		−	1.00000i		−	0.0641500i
$244$			15.6405i			1.00128i
$245$	−1.01378	+	14.3262i	−0.0647682	+	0.915270i
$246$		−	8.91405i		−	0.568339i
$247$		−	3.51733i		−	0.223802i
$248$		−	10.6697i		−	0.677526i
$249$	−1.57495			−0.0998083
$250$	1.92429	−	8.94311i	0.121703	−	0.565612i
$251$			14.3133i			0.903445i	0.892159	+	0.451722i	$0.149190\pi$
$251$			14.3133i			0.903445i	−0.892159	+	0.451722i	$0.850810\pi$
$252$		−	4.87475i		−	0.307080i
$253$	−34.4935			−2.16859
$254$			2.36772i			0.148564i
$255$	−8.36774	−	0.592136i	−0.524008	−	0.0370810i
$256$	−14.6658			−0.916613
$257$	−24.0193			−1.49828			−0.749142	−	0.662409i	$-0.769534\pi$
$257$	−24.0193			−1.49828			−0.749142	+	0.662409i	$0.769534\pi$
$258$		−	4.14022i		−	0.257759i
$259$	−6.90315	+	21.1895i	−0.428941	+	1.31665i
$260$	0.389402	−	5.50283i	0.0241497	−	0.341271i
$261$		−	7.35087i		−	0.455007i
$262$			4.52144i			0.279336i
$263$		−	20.9132i		−	1.28956i	−0.764367	−	0.644781i	$-0.776948\pi$
$263$		−	20.9132i		−	1.28956i	0.764367	−	0.644781i	$-0.223052\pi$
$264$			14.2854i			0.879205i
$265$	24.1405	+	1.70828i	1.48294	+	0.104939i
$266$	−5.68645			−0.348659
$267$	−4.49583			−0.275140
$268$			16.0641i			0.981273i
$269$	−2.88231			−0.175737			−0.0878687	−	0.996132i	$-0.528006\pi$
$269$	−2.88231			−0.175737			−0.0878687	+	0.996132i	$0.528006\pi$
$270$	−1.82500	−	0.129144i	−0.111066	−	0.00785946i
$271$	−3.98436			−0.242033			−0.121016	−	0.992651i	$-0.538615\pi$
$271$	−3.98436			−0.242033			−0.121016	+	0.992651i	$0.538615\pi$
$272$	1.61851			0.0981368
$273$	6.79329			0.411149
$274$			8.97639i			0.542284i
$275$	25.9499	+	3.69113i	1.56484	+	0.222583i
$276$			8.75489i			0.526982i
$277$	32.5915			1.95823			0.979117	−	0.203299i	$-0.0651664\pi$
$277$	32.5915			1.95823			0.979117	+	0.203299i	$0.0651664\pi$
$278$	4.10887			0.246434
$279$			3.91539i			0.234408i
$280$	−22.2690	−	1.57584i	−1.33083	−	0.0941746i
$281$			6.23641i			0.372033i	0.982547	+	0.186016i	$0.0595578\pi$
$281$			6.23641i			0.372033i	−0.982547	+	0.186016i	$0.940442\pi$
$282$	2.23422			0.133046
$283$	24.7322			1.47018			0.735089	−	0.677971i	$-0.237140\pi$
$283$	24.7322			1.47018			0.735089	+	0.677971i	$0.237140\pi$
$284$	−20.5842			−1.22145
$285$	0.299412	−	4.23113i	0.0177356	−	0.250631i
$286$	−7.95305			−0.470274
$287$			39.9151i			2.35611i
$288$	5.80312			0.341952
$289$	−2.92605			−0.172121
$290$	−13.4153	−	0.949321i	−0.787774	−	0.0557461i
$291$		−	3.73519i		−	0.218961i
$292$			4.63434i			0.271204i
$293$			1.63321i			0.0954129i	0.998861	+	0.0477064i	$0.0151912\pi$
$293$			1.63321i			0.0954129i	−0.998861	+	0.0477064i	$0.984809\pi$
$294$		−	5.25525i		−	0.306492i
$295$	19.5078	+	1.38045i	1.13579	+	0.0803731i
$296$	−15.7606	−	5.13453i	−0.916068	−	0.298438i
$297$		−	5.24223i		−	0.304185i
$298$	−2.49604			−0.144591
$299$	−12.2005			−0.705575
$300$	0.936855	−	6.58642i	0.0540893	−	0.380267i
$301$			18.5390i			1.06857i
$302$	−0.497909			−0.0286514
$303$			9.28549i			0.533437i
$304$			0.818399i			0.0469384i
$305$	−26.2193	−	1.85539i	−1.50131	−	0.106239i
$306$	3.06951			0.175472
$307$			2.81468i			0.160642i	0.996769	+	0.0803211i	$0.0255946\pi$
$307$			2.81468i			0.160642i	−0.996769	+	0.0803211i	$0.974405\pi$
$308$		−	25.5545i		−	1.45610i
$309$			9.37570i			0.533365i
$310$	7.14557	+	0.505650i	0.405841	+	0.0287190i
$311$		−	10.5927i		−	0.600658i	−0.953836	−	0.300329i	$-0.902904\pi$
$311$		−	10.5927i		−	0.600658i	0.953836	−	0.300329i	$-0.0970964\pi$
$312$			5.05281i			0.286059i
$313$	−29.9308			−1.69179			−0.845895	−	0.533349i	$-0.820933\pi$
$313$	−29.9308			−1.69179			−0.845895	+	0.533349i	$0.820933\pi$
$314$		−	3.89934i		−	0.220052i
$315$	8.17191	+	0.578278i	0.460435	+	0.0325823i
$316$			4.74882i			0.267142i
$317$		−	25.7776i		−	1.44781i	−0.689897	−	0.723907i	$-0.742344\pi$
$317$		−	25.7776i		−	1.44781i	0.689897	−	0.723907i	$-0.257656\pi$
$318$	−8.85539			−0.496586
$319$		−	38.5349i		−	2.15754i
$320$	0.613247	−	8.66608i	0.0342816	−	0.484449i
$321$	−13.1610			−0.734574
$322$			19.7245i			1.09921i
$323$			7.11646i			0.395971i
$324$	−1.33054			−0.0739190
$325$	9.17862	+	1.30557i	0.509138	+	0.0724200i
$326$	−11.4407			−0.633642
$327$	7.59747			0.420141
$328$	−29.6886			−1.63928
$329$	−10.0043			−0.551557
$330$	−9.56704	−	0.677003i	−0.526648	−	0.0372678i
$331$			13.7042i			0.753251i	0.926366	+	0.376626i	$0.122916\pi$
$331$			13.7042i			0.753251i	−0.926366	+	0.376626i	$0.877084\pi$
$332$			2.09554i			0.115007i
$333$	5.78358	+	1.88419i	0.316938	+	0.103253i
$334$	5.99574			0.328072
$335$	−26.9295	−	1.90564i	−1.47132	−	0.104116i
$336$	−1.58064			−0.0862308
$337$			27.8327i			1.51614i	0.652172	+	0.758071i	$0.273858\pi$
$337$			27.8327i			1.51614i	−0.652172	+	0.758071i	$0.726142\pi$
$338$	7.82362			0.425549
$339$		−	2.20503i		−	0.119761i
$340$	−0.787862	+	11.1336i	−0.0427278	+	0.603806i
$341$			20.5254i			1.11151i
$342$			1.55209i			0.0839276i
$343$		−	2.11430i		−	0.114161i
$344$	−13.7892			−0.743463
$345$	−14.6765	−	1.03857i	−0.790156	−	0.0559146i
$346$			8.76417i			0.471165i
$347$	−4.29223			−0.230419			−0.115209	−	0.993341i	$-0.536754\pi$
$347$	−4.29223			−0.230419			−0.115209	+	0.993341i	$0.536754\pi$
$348$	−9.78064			−0.524297
$349$	0.278167			0.0148899			0.00744497	−	0.999972i	$-0.497630\pi$
$349$	0.278167			0.0148899			0.00744497	+	0.999972i	$0.497630\pi$
$350$	2.11071	−	14.8390i	0.112822	−	0.793179i
$351$		−	1.85420i		−	0.0989699i
$352$	30.4213			1.62146
$353$	−30.7454			−1.63641			−0.818206	−	0.574925i	$-0.805031\pi$
$353$	−30.7454			−1.63641			−0.818206	+	0.574925i	$0.805031\pi$
$354$	−7.15599			−0.380337
$355$	2.44184	−	34.5068i	0.129600	−	1.83143i
$356$			5.98189i			0.317039i
$357$	−13.7446			−0.727440
$358$			17.2910i			0.913859i
$359$	−2.17180			−0.114623			−0.0573116	−	0.998356i	$-0.518253\pi$
$359$	−2.17180			−0.114623			−0.0573116	+	0.998356i	$0.518253\pi$
$360$	−0.430120	+	6.07823i	−0.0226693	+	0.320351i
$361$	15.4016			0.810609
$362$	17.8022			0.935665
$363$		−	16.4809i		−	0.865025i
$364$		−	9.03876i		−	0.473760i
$365$	−7.76890	−	0.549759i	−0.406643	−	0.0287757i
$366$	9.61796			0.502739
$367$		−	28.8006i		−	1.50338i	−0.659518	−	0.751689i	$-0.729240\pi$
$367$		−	28.8006i		−	1.50338i	0.659518	−	0.751689i	$-0.270760\pi$
$368$	2.83877			0.147981
$369$	10.8947			0.567153
$370$	4.18555	−	10.3117i	0.217596	−	0.536079i
$371$	39.6524			2.05865
$372$	5.20959			0.270105
$373$			7.19672i			0.372632i	0.982490	+	0.186316i	$0.0596549\pi$
$373$			7.19672i			0.372632i	−0.982490	+	0.186316i	$0.940345\pi$
$374$	16.0911			0.832050
$375$	10.9302	+	2.35185i	0.564432	+	0.121449i
$376$		−	7.44117i		−	0.383749i
$377$		−	13.6300i		−	0.701980i
$378$	−2.99768			−0.154184
$379$	20.4579			1.05085			0.525427	−	0.850839i	$-0.323906\pi$
$379$	20.4579			1.05085			0.525427	+	0.850839i	$0.323906\pi$
$380$	−5.62970	−	0.398381i	−0.288798	−	0.0204365i
$381$	−2.89381			−0.148254
$382$		−	14.5196i		−	0.742889i
$383$	12.9964			0.664083			0.332042	−	0.943265i	$-0.392263\pi$
$383$	12.9964			0.664083			0.332042	+	0.943265i	$0.392263\pi$
$384$		−	8.42729i		−	0.430053i
$385$	42.8390	+	3.03146i	2.18328	+	0.154498i
$386$	−13.2126			−0.672502
$387$	5.06014			0.257221
$388$	−4.96983			−0.252305
$389$			31.5780i			1.60107i	0.599288	+	0.800533i	$0.295450\pi$
$389$			31.5780i			1.60107i	−0.599288	+	0.800533i	$0.704550\pi$
$390$	−3.38391	−	0.239459i	−0.171351	−	0.0121255i
$391$	24.6848			1.24836
$392$	−17.5028			−0.884027
$393$	−5.52606			−0.278753
$394$		−	6.14225i		−	0.309442i
$395$	−7.96082	−	0.563340i	−0.400552	−	0.0283447i
$396$	−6.97500			−0.350507
$397$		−	17.4007i		−	0.873314i	−0.899628	−	0.436657i	$-0.856162\pi$
$397$		−	17.4007i		−	0.873314i	0.899628	−	0.436657i	$-0.143838\pi$
$398$		−	3.62841i		−	0.181876i
$399$		−	6.94992i		−	0.347931i
$400$	−2.13564	−	0.303775i	−0.106782	−	0.0151887i
$401$			19.7708i			0.987304i	0.869659	+	0.493652i	$0.164338\pi$
$401$			19.7708i			0.987304i	−0.869659	+	0.493652i	$0.835662\pi$
$402$	9.87848			0.492694
$403$			7.25992i			0.361642i
$404$	12.3547			0.614671
$405$	0.157839	−	2.23049i	0.00784306	−	0.110834i
$406$	−22.0355			−1.09360
$407$	30.3189	+	9.87734i	1.50285	+	0.489601i
$408$		−	10.2231i		−	0.506121i
$409$			1.48321i			0.0733399i	0.999327	+	0.0366699i	$0.0116750\pi$
$409$			1.48321i			0.0733399i	−0.999327	+	0.0366699i	$0.988325\pi$
$410$	1.40698	−	19.8827i	0.0694859	−	0.981937i
$411$	−10.9709			−0.541152
$412$	12.4748			0.614587
$413$	32.0429			1.57673
$414$	5.38373			0.264596
$415$	−3.51291	−	0.248588i	−0.172442	−	0.0122027i
$416$	10.7602			0.527560
$417$			5.02182i			0.245919i
$418$			8.13642i			0.397965i
$419$	14.1957			0.693506			0.346753	−	0.937957i	$-0.387284\pi$
$419$	14.1957			0.693506			0.346753	+	0.937957i	$0.387284\pi$
$420$	0.769423	−	10.8731i	0.0375440	−	0.530552i
$421$			9.44452i			0.460298i	0.973155	+	0.230149i	$0.0739213\pi$
$421$			9.44452i			0.460298i	−0.973155	+	0.230149i	$0.926079\pi$
$422$	15.4523			0.752207
$423$			2.73064i			0.132768i
$424$			29.4933i			1.43232i
$425$	−18.5707	−	2.64151i	−0.900812	−	0.128132i
$426$			12.6580i			0.613284i
$427$	−43.0670			−2.08416
$428$			17.5112i			0.846437i
$429$		−	9.72014i		−	0.469293i
$430$	0.653487	−	9.23473i	0.0315139	−	0.445338i
$431$			19.7282i			0.950276i	0.879911	+	0.475138i	$0.157602\pi$
$431$			19.7282i			0.950276i	−0.879911	+	0.475138i	$0.842398\pi$
$432$			0.431428i			0.0207571i
$433$		−	11.5886i		−	0.556914i	−0.960449	−	0.278457i	$-0.910177\pi$
$433$		−	11.5886i		−	0.556914i	0.960449	−	0.278457i	$-0.0898230\pi$
$434$	11.7371			0.563398
$435$	1.16025	−	16.3960i	0.0556297	−	0.786130i
$436$		−	10.1088i		−	0.484122i
$437$			12.4818i			0.597087i
$438$	2.84984			0.136171
$439$			2.45871i			0.117348i	0.998277	+	0.0586739i	$0.0186872\pi$
$439$			2.45871i			0.117348i	−0.998277	+	0.0586739i	$0.981313\pi$
$440$	−2.25479	+	31.8634i	−0.107493	+	1.51903i
$441$	6.42291			0.305853
$442$	5.69149			0.270717
$443$		−	2.04162i		−	0.0970005i	−0.998823	−	0.0485002i	$-0.984556\pi$
$443$		−	2.04162i		−	0.0970005i	0.998823	−	0.0485002i	$-0.0154442\pi$
$444$	2.50699	−	7.69530i	0.118977	−	0.365203i
$445$	−10.0279	−	0.709615i	−0.475368	−	0.0336390i
$446$			9.76686i			0.462474i
$447$		−	3.05063i		−	0.144290i
$448$		−	14.2346i		−	0.672522i
$449$			2.38582i			0.112594i	0.998414	+	0.0562968i	$0.0179293\pi$
$449$			2.38582i			0.112594i	−0.998414	+	0.0562968i	$0.982071\pi$
$450$	−4.05025	−	0.576109i	−0.190931	−	0.0271581i
$451$	57.1123			2.68931
$452$	−2.93389			−0.137999
$453$		−	0.608539i		−	0.0285916i
$454$	−4.80782			−0.225642
$455$	15.1524	+	1.07224i	0.710354	+	0.0502675i
$456$	5.16931			0.242075
$457$	3.26990			0.152960			0.0764798	−	0.997071i	$-0.475632\pi$
$457$	3.26990			0.152960			0.0764798	+	0.997071i	$0.475632\pi$
$458$	9.40062			0.439262
$459$			3.75153i			0.175106i
$460$	−1.38186	+	19.5277i	−0.0644295	+	0.910483i
$461$		−	17.6963i		−	0.824198i	−0.911139	−	0.412099i	$-0.864796\pi$
$461$		−	17.6963i		−	0.824198i	0.911139	−	0.412099i	$-0.135204\pi$
$462$	−15.7145			−0.731105
$463$	−10.4819			−0.487134			−0.243567	−	0.969884i	$-0.578318\pi$
$463$	−10.4819			−0.487134			−0.243567	+	0.969884i	$0.578318\pi$
$464$			3.17137i			0.147227i
$465$	−0.618000	+	8.73324i	−0.0286591	+	0.404994i
$466$			0.460640i			0.0213387i
$467$	22.7143			1.05109			0.525547	−	0.850765i	$-0.323861\pi$
$467$	22.7143			1.05109			0.525547	+	0.850765i	$0.323861\pi$
$468$	−2.46709			−0.114041
$469$	−44.2335			−2.04252
$470$	4.98341	+	0.352646i	0.229868	+	0.0162664i
$471$	4.76573			0.219593
$472$			23.8333i			1.09702i
$473$	26.5264			1.21968
$474$	2.92024			0.134131
$475$	1.33567	−	9.39024i	0.0612848	−	0.430854i
$476$			18.2877i			0.838217i
$477$		−	10.8230i		−	0.495550i
$478$			18.4094i			0.842025i
$479$		−	25.2508i		−	1.15374i	−0.816836	−	0.576870i	$-0.804274\pi$
$479$		−	25.2508i		−	1.15374i	0.816836	−	0.576870i	$-0.195726\pi$
$480$	12.9438	+	0.915956i	0.590801	+	0.0418075i
$481$	10.7239	+	3.49366i	0.488969	+	0.159297i
$482$			24.8227i			1.13064i
$483$	−24.1071			−1.09691
$484$	−21.9286			−0.996754
$485$	0.589557	−	8.33130i	0.0267704	−	0.378305i
$486$			0.818204i			0.0371145i
$487$	26.5384			1.20257			0.601285	−	0.799034i	$-0.294655\pi$
$487$	26.5384			1.20257			0.601285	+	0.799034i	$0.294655\pi$
$488$		−	32.0330i		−	1.45007i
$489$		−	13.9827i		−	0.632320i
$490$	0.829481	−	11.7218i	0.0374721	−	0.529536i
$491$	12.9859			0.586046			0.293023	−	0.956105i	$-0.405339\pi$
$491$	12.9859			0.586046			0.293023	+	0.956105i	$0.405339\pi$
$492$		−	14.4958i		−	0.653522i
$493$			27.5770i			1.24200i
$494$			2.87789i			0.129482i
$495$	0.827425	−	11.6927i	0.0371900	−	0.525549i
$496$		−	1.68921i		−	0.0758478i
$497$		−	56.6798i		−	2.54244i
$498$	1.28863			0.0577448
$499$		−	32.8019i		−	1.46841i	−0.678925	−	0.734207i	$-0.737554\pi$
$499$		−	32.8019i		−	1.46841i	0.678925	−	0.734207i	$-0.262446\pi$
$500$	3.12924	−	14.5431i	0.139944	−	0.650386i
$501$			7.32793i			0.327388i
$502$		−	11.7112i		−	0.522695i
$503$	−26.9304			−1.20077			−0.600385	−	0.799711i	$-0.704986\pi$
$503$	−26.9304			−1.20077			−0.600385	+	0.799711i	$0.704986\pi$
$504$			9.98389i			0.444718i
$505$	−1.46561	+	20.7112i	−0.0652187	+	0.921636i
$506$	28.2227			1.25465
$507$			9.56194i			0.424661i
$508$			3.85033i			0.170831i
$509$	36.5488			1.61999			0.809997	−	0.586433i	$-0.199468\pi$
$509$	36.5488			1.61999			0.809997	+	0.586433i	$0.199468\pi$
$510$	6.84652	+	0.484488i	0.303169	+	0.0214535i
$511$	−12.7609			−0.564510
$512$	−4.85497			−0.214561
$513$	−1.89695			−0.0837525
$514$	19.6527			0.866844
$515$	−1.47985	+	20.9124i	−0.0652098	+	0.921510i
$516$		−	6.73273i		−	0.296392i
$517$			14.3146i			0.629557i
$518$	5.64819	−	17.3373i	0.248167	−	0.761758i
$519$	−10.7115			−0.470181
$520$	−0.797529	+	11.2702i	−0.0349739	+	0.494233i
$521$	−16.4932			−0.722581			−0.361290	−	0.932453i	$-0.617664\pi$
$521$	−16.4932			−0.722581			−0.361290	+	0.932453i	$0.617664\pi$
$522$			6.01451i			0.263248i
$523$	−10.5221			−0.460100			−0.230050	−	0.973179i	$-0.573889\pi$
$523$	−10.5221			−0.460100			−0.230050	+	0.973179i	$0.573889\pi$
$524$			7.35265i			0.321202i
$525$	18.1361	+	2.57969i	0.791524	+	0.112587i
$526$			17.1113i			0.746086i
$527$		−	14.6887i		−	0.639850i
$528$			2.26164i			0.0984254i
$529$	20.2956			0.882417
$530$	−19.7519	−	1.39772i	−0.857966	−	0.0607132i
$531$		−	8.74598i		−	0.379543i
$532$	−9.24716			−0.400915
$533$	20.2009			0.874998
$534$	3.67850			0.159184
$535$	−29.3554	−	2.07731i	−1.26915	−	0.0898099i
$536$		−	32.9007i		−	1.42109i
$537$	−21.1329			−0.911952
$538$	2.35831			0.101674
$539$	33.6704			1.45028
$540$	−2.96776	−	0.210011i	−0.127712	−	0.00903743i
$541$		−	34.4663i		−	1.48182i	−0.671604	−	0.740910i	$-0.734394\pi$
$541$		−	34.4663i		−	1.48182i	0.671604	−	0.740910i	$-0.265606\pi$
$542$	3.26002			0.140030
$543$			21.7577i			0.933713i
$544$	−21.7706			−0.933405
$545$	16.9461	+	1.19917i	0.725891	+	0.0513670i
$546$	−5.55829			−0.237873
$547$	−17.2304			−0.736718			−0.368359	−	0.929684i	$-0.620080\pi$
$547$	−17.2304			−0.736718			−0.368359	+	0.929684i	$0.620080\pi$
$548$			14.5972i			0.623561i
$549$			11.7550i			0.501690i
$550$	−21.2323	−	3.02010i	−0.905350	−	0.128777i
$551$	−13.9442			−0.594045
$552$		−	17.9307i		−	0.763183i
$553$	−13.0762			−0.556055
$554$	−26.6665			−1.13295
$555$	12.6028	+	5.11553i	0.534960	+	0.217142i
$556$	6.68174			0.283369
$557$	−23.1512			−0.980948			−0.490474	−	0.871456i	$-0.663176\pi$
$557$	−23.1512			−0.980948			−0.490474	+	0.871456i	$0.663176\pi$
$558$		−	3.20359i		−	0.135619i
$559$	9.38251			0.396838
$560$	−3.52559	−	0.249485i	−0.148984	−	0.0105427i
$561$			19.6663i			0.830314i
$562$		−	5.10265i		−	0.215242i
$563$	7.63616			0.321826			0.160913	−	0.986969i	$-0.448556\pi$
$563$	7.63616			0.321826			0.160913	+	0.986969i	$0.448556\pi$
$564$	3.63323			0.152987
$565$	0.348039	−	4.91830i	0.0146421	−	0.206915i
$566$	−20.2360			−0.850582
$567$		−	3.66373i		−	0.153862i
$568$	42.1581			1.76892
$569$			11.1046i			0.465529i	0.972533	+	0.232764i	$0.0747771\pi$
$569$			11.1046i			0.465529i	−0.972533	+	0.232764i	$0.925223\pi$
$570$	−0.244980	+	3.46193i	−0.0102611	+	0.145004i
$571$	−1.91437			−0.0801137			−0.0400569	−	0.999197i	$-0.512754\pi$
$571$	−1.91437			−0.0801137			−0.0400569	+	0.999197i	$0.512754\pi$
$572$	−12.9331			−0.540758
$573$	17.7457			0.741339
$574$		−	32.6587i		−	1.36315i
$575$	−32.5718	−	4.63303i	−1.35834	−	0.193211i
$576$	−3.88528			−0.161887
$577$	0.389641			0.0162210			0.00811049	−	0.999967i	$-0.497418\pi$
$577$	0.389641			0.0162210			0.00811049	+	0.999967i	$0.497418\pi$
$578$	2.39410			0.0995816
$579$		−	16.1483i		−	0.671098i
$580$	−21.8156	−	1.54376i	−0.905844	−	0.0641012i
$581$	−5.77018			−0.239388
$582$			3.05615i			0.126681i
$583$		−	56.7364i		−	2.34978i
$584$		−	9.49151i		−	0.392762i
$585$	0.292664	−	4.13578i	0.0121002	−	0.170993i
$586$		−	1.33629i		−	0.0552018i
$587$	−18.6967			−0.771696			−0.385848	−	0.922562i	$-0.626091\pi$
$587$	−18.6967			−0.771696			−0.385848	+	0.922562i	$0.626091\pi$
$588$		−	8.54596i		−	0.352429i
$589$	7.42731			0.306037
$590$	−15.9614	−	1.12949i	−0.657119	−	0.0465004i
$591$	7.50700			0.308797
$592$	−2.49520	−	0.812892i	−0.102552	−	0.0334096i
$593$			9.42791i			0.387158i	0.981085	+	0.193579i	$0.0620095\pi$
$593$			9.42791i			0.387158i	−0.981085	+	0.193579i	$0.937990\pi$
$594$			4.28921i			0.175988i
$595$	−30.6571	−	2.16942i	−1.25682	−	0.0889377i
$596$	−4.05899			−0.166263
$597$	4.43460			0.181496
$598$	9.98252			0.408215
$599$	4.14724			0.169452			0.0847259	−	0.996404i	$-0.472999\pi$
$599$	4.14724			0.169452			0.0847259	+	0.996404i	$0.472999\pi$
$600$	−1.91876	+	13.4895i	−0.0783329	+	0.550708i
$601$	19.1275			0.780228			0.390114	−	0.920767i	$-0.372436\pi$
$601$	19.1275			0.780228			0.390114	+	0.920767i	$0.372436\pi$
$602$		−	15.1687i		−	0.618228i
$603$			12.0734i			0.491666i
$604$	−0.809687			−0.0329457
$605$	2.60133	−	36.7606i	0.105759	−	1.49453i
$606$		−	7.59742i		−	0.308624i
$607$	21.9651			0.891537			0.445768	−	0.895148i	$-0.352930\pi$
$607$	21.9651			0.891537			0.445768	+	0.895148i	$0.352930\pi$
$608$		−	11.0082i		−	0.446443i
$609$		−	26.9316i		−	1.09132i
$610$	21.4528	+	1.51808i	0.868597	+	0.0614655i
$611$			5.06316i			0.204833i
$612$	4.99157			0.201772
$613$			22.6523i			0.914917i	0.889231	+	0.457459i	$0.151240\pi$
$613$			22.6523i			0.914917i	−0.889231	+	0.457459i	$0.848760\pi$
$614$		−	2.30298i		−	0.0929407i
$615$	24.3004	+	1.71960i	0.979888	+	0.0693409i
$616$			52.3378i			2.10875i
$617$		−	27.8198i		−	1.11998i	−0.828498	−	0.559992i	$-0.810804\pi$
$617$		−	27.8198i		−	1.11998i	0.828498	−	0.559992i	$-0.189196\pi$
$618$		−	7.67123i		−	0.308582i
$619$	27.6493			1.11132			0.555660	−	0.831410i	$-0.312466\pi$
$619$	27.6493			1.11132			0.555660	+	0.831410i	$0.312466\pi$
$620$	11.6200	+	0.822275i	0.466668	+	0.0330234i
$621$			6.57994i			0.264044i
$622$			8.66700i			0.347515i
$623$	−16.4715			−0.659916
$624$			0.799954i			0.0320238i
$625$	24.0084	+	6.97098i	0.960338	+	0.278839i
$626$	24.4895			0.978798
$627$	−9.94425			−0.397135
$628$		−	6.34101i		−	0.253034i
$629$	−21.6973	−	7.06858i	−0.865127	−	0.281843i
$630$	−6.68629	−	0.473149i	−0.266388	−	0.0188507i
$631$			15.4856i			0.616474i	0.951310	+	0.308237i	$0.0997390\pi$
$631$			15.4856i			0.616474i	−0.951310	+	0.308237i	$0.900261\pi$
$632$		−	9.72599i		−	0.386879i
$633$			18.8857i			0.750638i
$634$			21.0913i			0.837644i
$635$	−6.45461	−	0.456754i	−0.256143	−	0.0181257i
$636$	−14.4004			−0.571014
$637$	11.9094			0.471866
$638$			31.5294i			1.24826i
$639$	−15.4705			−0.612004
$640$	1.33015	−	18.7970i	0.0525789	−	0.743016i
$641$	33.5314			1.32441			0.662205	−	0.749323i	$-0.269621\pi$
$641$	33.5314			1.32441			0.662205	+	0.749323i	$0.269621\pi$
$642$	10.7684			0.424993
$643$	−20.3502			−0.802533			−0.401267	−	0.915961i	$-0.631430\pi$
$643$	−20.3502			−0.802533			−0.401267	+	0.915961i	$0.631430\pi$
$644$			32.0755i			1.26395i
$645$	11.2866	+	0.798685i	0.444409	+	0.0314482i
$646$		−	5.82272i		−	0.229092i
$647$	17.0824			0.671579			0.335790	−	0.941937i	$-0.390997\pi$
$647$	17.0824			0.671579			0.335790	+	0.941937i	$0.390997\pi$
$648$	2.72506			0.107051
$649$		−	45.8484i		−	1.79971i
$650$	−7.50998	−	1.06822i	−0.294566	−	0.0418991i
$651$			14.3449i			0.562222i
$652$	−18.6046			−0.728612
$653$	−14.4797			−0.566634			−0.283317	−	0.959026i	$-0.591435\pi$
$653$	−14.4797			−0.566634			−0.283317	+	0.959026i	$0.591435\pi$
$654$	−6.21628			−0.243076
$655$	−12.3258	−	0.872225i	−0.481609	−	0.0340806i
$656$	−4.70027			−0.183515
$657$			3.48304i			0.135886i
$658$	8.18558			0.319107
$659$	−31.8100			−1.23914			−0.619570	−	0.784942i	$-0.712693\pi$
$659$	−31.8100			−1.23914			−0.619570	+	0.784942i	$0.712693\pi$
$660$	−15.5577	−	1.10092i	−0.605582	−	0.0428534i
$661$			39.8604i			1.55039i	0.631721	+	0.775196i	$0.282349\pi$
$661$			39.8604i			1.55039i	−0.631721	+	0.775196i	$0.717651\pi$
$662$		−	11.2128i		−	0.435799i
$663$			6.95608i			0.270152i
$664$		−	4.29183i		−	0.166555i
$665$	1.09697	−	15.5017i	0.0425385	−	0.601131i
$666$	−4.73215	−	1.54165i	−0.183367	−	0.0597377i
$667$			48.3682i			1.87283i
$668$	9.75012			0.377244
$669$	−11.9370			−0.461509
$670$	22.0338	+	1.55920i	0.851242	+	0.0602373i
$671$			61.6222i			2.37890i
$672$	21.2611			0.820163
$673$			45.2044i			1.74250i	0.490838	+	0.871251i	$0.336691\pi$
$673$			45.2044i			1.74250i	−0.490838	+	0.871251i	$0.663309\pi$
$674$		−	22.7728i		−	0.877176i
$675$	0.704115	−	4.95017i	0.0271014	−	0.190532i
$676$	12.7226			0.489330
$677$			33.0435i			1.26996i	0.772527	+	0.634982i	$0.218993\pi$
$677$			33.0435i			1.26996i	−0.772527	+	0.634982i	$0.781007\pi$
$678$			1.80417i			0.0692886i
$679$		−	13.6847i		−	0.525171i
$680$	1.61361	−	22.8026i	0.0618790	−	0.874441i
$681$		−	5.87607i		−	0.225171i
$682$		−	16.7939i		−	0.643073i
$683$	35.9212			1.37449			0.687244	−	0.726427i	$-0.258821\pi$
$683$	35.9212			1.37449			0.687244	+	0.726427i	$0.258821\pi$
$684$			2.52397i			0.0965066i
$685$	−24.4704	−	1.73162i	−0.934965	−	0.0661619i
$686$			1.72993i			0.0660489i
$687$			11.4893i			0.438346i
$688$	−2.18309			−0.0832294
$689$		−	20.0680i		−	0.764528i
$690$	12.0084	+	0.849760i	0.457150	+	0.0323498i
$691$	33.5150			1.27497			0.637485	−	0.770463i	$-0.279975\pi$
$691$	33.5150			1.27497			0.637485	+	0.770463i	$0.279975\pi$
$692$			14.2521i			0.541782i
$693$		−	19.2061i		−	0.729579i
$694$	3.51192			0.133311
$695$	−0.792636	+	11.2011i	−0.0300664	+	0.424882i
$696$	20.0316			0.759295
$697$	−40.8716			−1.54812
$698$	−0.227597			−0.00861469
$699$	−0.562989			−0.0212942
$700$	3.43238	−	24.1308i	0.129732	−	0.912060i
$701$		−	14.8049i		−	0.559175i	−0.960120	−	0.279587i	$-0.909802\pi$
$701$		−	14.8049i		−	0.559175i	0.960120	−	0.279587i	$-0.0901977\pi$
$702$			1.51711i			0.0572598i
$703$	3.57421	−	10.9712i	0.134804	−	0.413786i
$704$	−20.3675			−0.767630
$705$	−0.431001	+	6.09067i	−0.0162324	+	0.229388i
$706$	25.1560			0.946759
$707$			34.0195i			1.27944i
$708$	−11.6369			−0.437341
$709$			3.70273i			0.139059i	0.997580	+	0.0695295i	$0.0221498\pi$
$709$			3.70273i			0.139059i	−0.997580	+	0.0695295i	$0.977850\pi$
$710$	−1.99793	+	28.2336i	−0.0749808	+	1.05959i
$711$			3.56909i			0.133851i
$712$		−	12.2514i		−	0.459141i
$713$		−	25.7630i		−	0.964833i
$714$	11.2459			0.420866
$715$	1.53421	−	21.6807i	0.0573763	−	0.810811i
$716$			28.1182i			1.05083i
$717$	−22.4997			−0.840268
$718$	1.77697			0.0663161
$719$	24.7645			0.923561			0.461781	−	0.886994i	$-0.347211\pi$
$719$	24.7645			0.923561			0.461781	+	0.886994i	$0.347211\pi$
$720$	−0.0680960	+	0.962296i	−0.00253779	+	0.0358627i
$721$			34.3500i			1.27926i
$722$	−12.6016			−0.468984
$723$	−30.3380			−1.12828
$724$	28.9496			1.07590
$725$	5.17585	−	36.3881i	0.192226	−	1.35142i
$726$			13.4848i			0.500466i
$727$	43.9667			1.63064			0.815318	−	0.579014i	$-0.196562\pi$
$727$	43.9667			1.63064			0.815318	+	0.579014i	$0.196562\pi$
$728$			18.5121i			0.686105i
$729$	−1.00000			−0.0370370
$730$	6.35654	+	0.449815i	0.235266	+	0.0166484i
$731$	−18.9832			−0.702121
$732$	15.6405			0.578089
$733$		−	34.7074i		−	1.28195i	−0.767563	−	0.640973i	$-0.778531\pi$
$733$		−	34.7074i		−	1.28195i	0.767563	−	0.640973i	$-0.221469\pi$
$734$			23.5647i			0.869790i
$735$	14.3262	+	1.01378i	0.528431	+	0.0373940i
$736$	−38.1842			−1.40749
$737$			63.2913i			2.33137i
$738$	−8.91405			−0.328131
$739$	−5.23596			−0.192608			−0.0963039	−	0.995352i	$-0.530702\pi$
$739$	−5.23596			−0.192608			−0.0963039	+	0.995352i	$0.530702\pi$
$740$	6.80644	−	16.7686i	0.250210	−	0.616426i
$741$	−3.51733			−0.129212
$742$	−32.4438			−1.19105
$743$			52.3225i			1.91953i	0.280809	+	0.959764i	$0.409397\pi$
$743$			52.3225i			1.91953i	−0.280809	+	0.959764i	$0.590603\pi$
$744$	−10.6697			−0.391170
$745$	0.481507	−	6.80440i	0.0176410	−	0.249294i
$746$		−	5.88839i		−	0.215589i
$747$			1.57495i			0.0576244i
$748$	26.1669			0.956757
$749$	−48.2182			−1.76186
$750$	−8.94311	−	1.92429i	−0.326556	−	0.0702652i
$751$	2.60180			0.0949412			0.0474706	−	0.998873i	$-0.484884\pi$
$751$	2.60180			0.0949412			0.0474706	+	0.998873i	$0.484884\pi$
$752$		−	1.17808i		−	0.0429600i
$753$	14.3133			0.521604
$754$			11.1521i			0.406136i
$755$	0.0960509	−	1.35734i	0.00349565	−	0.0493987i
$756$	−4.87475			−0.177293
$757$	17.6345			0.640936			0.320468	−	0.947259i	$-0.396160\pi$
$757$	17.6345			0.640936			0.320468	+	0.947259i	$0.396160\pi$
$758$	−16.7388			−0.607979
$759$			34.4935i			1.25204i
$760$	11.5301	+	0.815917i	0.418241	+	0.0295964i
$761$	9.03086			0.327368			0.163684	−	0.986513i	$-0.447662\pi$
$761$	9.03086			0.327368			0.163684	+	0.986513i	$0.447662\pi$
$762$	2.36772			0.0857736
$763$	27.8351			1.00770
$764$		−	23.6115i		−	0.854233i
$765$	−0.592136	+	8.36774i	−0.0214087	+	0.302536i
$766$	−10.6337			−0.384210
$767$		−	16.2168i		−	0.585555i
$768$			14.6658i			0.529207i
$769$		−	45.1158i		−	1.62692i	−0.581622	−	0.813459i	$-0.697582\pi$
$769$		−	45.1158i		−	1.62692i	0.581622	−	0.813459i	$-0.302418\pi$
$770$	−35.0510	−	2.48035i	−1.26315	−	0.0893858i
$771$			24.0193i			0.865035i
$772$	−21.4859			−0.773296
$773$			22.9270i			0.824625i	0.911042	+	0.412313i	$0.135279\pi$
$773$			22.9270i			0.824625i	−0.911042	+	0.412313i	$0.864721\pi$
$774$	−4.14022			−0.148817
$775$	−2.75688	+	19.3819i	−0.0990302	+	0.696217i
$776$	10.1786			0.365391
$777$	21.1895	+	6.90315i	0.760168	+	0.247649i
$778$		−	25.8372i		−	0.926309i
$779$		−	20.6666i		−	0.740460i
$780$	−5.50283	−	0.389402i	−0.197033	−	0.0139428i
$781$	−81.0999			−2.90198
$782$	−20.1972			−0.722251
$783$	−7.35087			−0.262699
$784$	−2.77103			−0.0989652
$785$	10.6299	+	0.752216i	0.379398	+	0.0268477i
$786$	4.52144			0.161274
$787$		−	43.0672i		−	1.53518i	−0.640940	−	0.767591i	$-0.721455\pi$
$787$		−	43.0672i		−	1.53518i	0.640940	−	0.767591i	$-0.278545\pi$
$788$		−	9.98838i		−	0.355821i
$789$	−20.9132			−0.744529
$790$	6.51357	+	0.460927i	0.231742	+	0.0163990i
$791$		−	8.07864i		−	0.287243i
$792$	14.2854			0.507609
$793$			21.7961i			0.774001i
$794$			14.2373i			0.505263i
$795$	1.70828	−	24.1405i	0.0605865	−	0.856176i
$796$		−	5.90042i		−	0.209135i
$797$	34.2266			1.21237			0.606183	−	0.795325i	$-0.292700\pi$
$797$	34.2266			1.21237			0.606183	+	0.795325i	$0.292700\pi$
$798$			5.68645i			0.201298i
$799$		−	10.2441i		−	0.362409i
$800$	28.7265	+	4.08606i	1.01563	+	0.144464i
$801$			4.49583i			0.158852i
$802$		−	16.1765i		−	0.571212i
$803$			18.2589i			0.644343i
$804$	16.0641			0.566538
$805$	−53.7707	−	3.80503i	−1.89517	−	0.134110i
$806$		−	5.94010i		−	0.209231i
$807$			2.88231i			0.101462i
$808$	−25.3035			−0.890175
$809$			10.5158i			0.369715i	0.982765	+	0.184857i	$0.0591823\pi$
$809$			10.5158i			0.369715i	−0.982765	+	0.184857i	$0.940818\pi$
$810$	−0.129144	+	1.82500i	−0.00453766	+	0.0641238i
$811$	−20.9219			−0.734666			−0.367333	−	0.930089i	$-0.619729\pi$
$811$	−20.9219			−0.734666			−0.367333	+	0.930089i	$0.619729\pi$
$812$	−35.8336			−1.25751
$813$			3.98436i			0.139738i
$814$	−24.8070	−	8.08168i	−0.869485	−	0.283263i
$815$	2.20701	−	31.1883i	0.0773082	−	1.09248i
$816$		−	1.61851i		−	0.0566593i
$817$		−	9.59884i		−	0.335821i
$818$		−	1.21357i		−	0.0424313i
$819$		−	6.79329i		−	0.237377i
$820$	2.28800	−	32.3328i	0.0799004	−	1.12911i
$821$	−5.95894			−0.207968			−0.103984	−	0.994579i	$-0.533159\pi$
$821$	−5.95894			−0.207968			−0.103984	+	0.994579i	$0.533159\pi$
$822$	8.97639			0.313088
$823$		−	42.5840i		−	1.48438i	−0.670187	−	0.742192i	$-0.733786\pi$
$823$		−	42.5840i		−	1.48438i	0.670187	−	0.742192i	$-0.266214\pi$
$824$	−25.5494			−0.890054
$825$	3.69113	−	25.9499i	0.128509	−	0.903461i
$826$	−26.2176			−0.912228
$827$	45.8353			1.59385			0.796925	−	0.604079i	$-0.206459\pi$
$827$	45.8353			1.59385			0.796925	+	0.604079i	$0.206459\pi$
$828$	8.75489			0.304253
$829$			44.0267i			1.52911i	0.644558	+	0.764555i	$0.277041\pi$
$829$			44.0267i			1.52911i	−0.644558	+	0.764555i	$0.722959\pi$
$830$	2.87427	+	0.203395i	0.0997675	+	0.00705996i
$831$		−	32.5915i		−	1.13059i
$832$	−7.20409			−0.249757
$833$	−24.0957			−0.834867
$834$		−	4.10887i		−	0.142278i
$835$	−1.15663	+	16.3449i	−0.0400268	+	0.565638i
$836$			13.2312i			0.457612i
$837$	3.91539			0.135336
$838$	−11.6150			−0.401233
$839$	−34.9093			−1.20520			−0.602602	−	0.798042i	$-0.705869\pi$
$839$	−34.9093			−1.20520			−0.602602	+	0.798042i	$0.705869\pi$
$840$	−1.57584	+	22.2690i	−0.0543718	+	0.768353i
$841$	−25.0352			−0.863284
$842$		−	7.72754i		−	0.266309i
$843$	6.23641			0.214793
$844$	25.1282			0.864948
$845$	−1.50924	+	21.3278i	−0.0519195	+	0.733699i
$846$		−	2.23422i		−	0.0768141i
$847$		−	60.3817i		−	2.07474i
$848$			4.66933i			0.160346i
$849$		−	24.7322i		−	0.848808i
$850$	15.1946	+	2.16129i	0.521171	+	0.0741316i
$851$	−38.0556	−	12.3978i	−1.30453	−	0.424992i
$852$			20.5842i			0.705202i
$853$	−5.00844			−0.171486			−0.0857429	−	0.996317i	$-0.527326\pi$
$853$	−5.00844			−0.171486			−0.0857429	+	0.996317i	$0.527326\pi$
$854$	35.2376			1.20581
$855$	−4.23113	−	0.299412i	−0.144702	−	0.0102397i
$856$		−	35.8645i		−	1.22582i
$857$	−3.77478			−0.128944			−0.0644720	−	0.997920i	$-0.520536\pi$
$857$	−3.77478			−0.128944			−0.0644720	+	0.997920i	$0.520536\pi$
$858$			7.95305i			0.271513i
$859$			26.8612i			0.916494i	0.888825	+	0.458247i	$0.151522\pi$
$859$			26.8612i			0.916494i	−0.888825	+	0.458247i	$0.848478\pi$
$860$	1.06268	−	15.0173i	0.0362372	−	0.512085i
$861$	39.9151			1.36030
$862$		−	16.1417i		−	0.549789i
$863$		−	29.1622i		−	0.992691i	−0.868125	−	0.496346i	$-0.834675\pi$
$863$		−	29.1622i		−	0.992691i	0.868125	−	0.496346i	$-0.165325\pi$
$864$		−	5.80312i		−	0.197426i
$865$	−23.8918	−	1.69068i	−0.812347	−	0.0574850i
$866$			9.48186i			0.322207i
$867$			2.92605i			0.0993738i
$868$	19.0865			0.647839
$869$			18.7100i			0.634692i
$870$	−0.949321	+	13.4153i	−0.0321850	+	0.454821i
$871$			22.3864i			0.758536i
$872$			20.7036i			0.701112i
$873$	−3.73519			−0.126417
$874$		−	10.2127i		−	0.345449i
$875$	40.0452	+	8.61654i	1.35378	+	0.291292i
$876$	4.63434			0.156580
$877$		−	10.0730i		−	0.340142i	−0.985432	−	0.170071i	$-0.945600\pi$
$877$		−	10.0730i		−	0.340142i	0.985432	−	0.170071i	$-0.0543997\pi$
$878$		−	2.01173i		−	0.0678925i
$879$	1.63321			0.0550866
$880$	−0.356975	+	5.04458i	−0.0120336	+	0.170053i
$881$	20.8499			0.702453			0.351226	−	0.936291i	$-0.385765\pi$
$881$	20.8499			0.702453			0.351226	+	0.936291i	$0.385765\pi$
$882$	−5.25525			−0.176953
$883$	21.5835			0.726344			0.363172	−	0.931722i	$-0.381694\pi$
$883$	21.5835			0.726344			0.363172	+	0.931722i	$0.381694\pi$
$884$	9.25536			0.311292
$885$	1.38045	−	19.5078i	0.0464034	−	0.655748i
$886$			1.67046i			0.0561204i
$887$		−	13.9998i		−	0.470069i	−0.971987	−	0.235034i	$-0.924480\pi$
$887$		−	13.9998i		−	0.470069i	0.971987	−	0.235034i	$-0.0755202\pi$
$888$	−5.13453	+	15.7606i	−0.172304	+	0.528892i
$889$	−10.6021			−0.355584
$890$	8.20486	+	0.580609i	0.275028	+	0.0194621i
$891$	−5.24223			−0.175621
$892$			15.8826i			0.531789i
$893$	5.17990			0.173339
$894$			2.49604i			0.0834799i
$895$	−47.1367	−	3.33559i	−1.57561	−	0.111496i
$896$		−	30.8753i		−	1.03147i
$897$			12.2005i			0.407364i
$898$		−	1.95208i		−	0.0651419i
$899$	28.7815			0.959917
$900$	−6.58642	−	0.936855i	−0.219547	−	0.0312285i
$901$			40.6026i			1.35267i
$902$	−46.7295			−1.55592
$903$	18.5390			0.616938
$904$	6.00885			0.199851
$905$	−3.43421	+	48.5304i	−0.114157	+	1.61320i
$906$			0.497909i			0.0165419i
$907$	5.72485			0.190091			0.0950453	−	0.995473i	$-0.469700\pi$
$907$	5.72485			0.190091			0.0950453	+	0.995473i	$0.469700\pi$
$908$	−7.81836			−0.259461
$909$	9.28549			0.307980
$910$	−12.3977	−	0.877313i	−0.410981	−	0.0290827i
$911$		−	12.0636i		−	0.399685i	−0.979828	−	0.199843i	$-0.935957\pi$
$911$		−	12.0636i		−	0.399685i	0.979828	−	0.199843i	$-0.0640431\pi$
$912$	0.818399			0.0270999
$913$			8.25624i			0.273242i
$914$	−2.67545			−0.0884960
$915$	−1.85539	+	26.2193i	−0.0613372	+	0.866785i
$916$	15.2871			0.505099
$917$	−20.2460			−0.668581
$918$		−	3.06951i		−	0.101309i
$919$		−	22.3692i		−	0.737893i	−0.929451	−	0.368946i	$-0.879719\pi$
$919$		−	22.3692i		−	0.737893i	0.929451	−	0.368946i	$-0.120281\pi$
$920$	2.83016	−	39.9944i	0.0933077	−	1.31857i
$921$	2.81468			0.0927468
$922$			14.4792i			0.476846i
$923$	−28.6854			−0.944193
$924$	−25.5545			−0.840682
$925$	27.3031	+	13.3994i	0.897719	+	0.440568i
$926$	8.57631			0.281835
$927$	9.37570			0.307938
$928$		−	42.6580i		−	1.40032i
$929$	24.7800			0.813007			0.406504	−	0.913649i	$-0.366748\pi$
$929$	24.7800			0.813007			0.406504	+	0.913649i	$0.366748\pi$
$930$	0.505650	−	7.14557i	0.0165809	−	0.234313i
$931$		−	12.1840i		−	0.399313i
$932$			0.749080i			0.0245369i
$933$	−10.5927			−0.346790
$934$	−18.5849			−0.608118
$935$	−3.10411	+	43.8656i	−0.101515	+	1.43456i
$936$	5.05281			0.165156
$937$			0.500418i			0.0163479i	0.999967	+	0.00817397i	$0.00260188\pi$
$937$			0.500418i			0.0163479i	−0.999967	+	0.00817397i	$0.997398\pi$
$938$	36.1921			1.18171
$939$			29.9308i			0.976756i
$940$	8.10389	+	0.573465i	0.264320	+	0.0187044i
$941$	−21.2713			−0.693426			−0.346713	−	0.937971i	$-0.612702\pi$
$941$	−21.2713			−0.693426			−0.346713	+	0.937971i	$0.612702\pi$
$942$	−3.89934			−0.127047
$943$	−71.6862			−2.33442
$944$			3.77326i			0.122809i
$945$	0.578278	−	8.17191i	0.0188114	−	0.265832i
$946$	−21.7040			−0.705658
$947$	17.4680			0.567632			0.283816	−	0.958879i	$-0.408399\pi$
$947$	17.4680			0.567632			0.283816	+	0.958879i	$0.408399\pi$
$948$	4.74882			0.154235
$949$			6.45826i			0.209644i
$950$	−1.09285	+	7.68313i	−0.0354568	+	0.249274i
$951$	−25.7776			−0.835896
$952$		−	37.4548i		−	1.21392i
$953$		−	37.7854i		−	1.22399i	−0.790862	−	0.611994i	$-0.790368\pi$
$953$		−	37.7854i		−	1.22399i	0.790862	−	0.611994i	$-0.209632\pi$
$954$			8.85539i			0.286704i
$955$	39.5817	+	2.80096i	1.28083	+	0.0906370i
$956$			29.9368i			0.968227i
$957$	−38.5349			−1.24566
$958$			20.6603i			0.667505i
$959$	−40.1942			−1.29794
$960$	−8.66608	−	0.613247i	−0.279696	−	0.0197925i
$961$	15.6697			0.505475
$962$	−8.77436	−	2.85853i	−0.282897	−	0.0921626i
$963$			13.1610i			0.424106i
$964$			40.3660i			1.30010i
$965$	2.54882	−	36.0185i	0.0820493	−	1.15948i
$966$	19.7245			0.634626
$967$	−44.4805			−1.43040			−0.715198	−	0.698922i	$-0.753664\pi$
$967$	−44.4805			−1.43040			−0.715198	+	0.698922i	$0.753664\pi$
$968$	44.9116			1.44351
$969$	7.11646			0.228614
$970$	−0.482378	+	6.81670i	−0.0154882	+	0.218871i
$971$	11.8119			0.379062			0.189531	−	0.981875i	$-0.439303\pi$
$971$	11.8119			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$972$			1.33054i			0.0426772i
$973$			18.3986i			0.589831i
$974$	−21.7138			−0.695756
$975$	1.30557	−	9.17862i	0.0418117	−	0.293951i
$976$		−	5.07142i		−	0.162332i
$977$	57.4122			1.83678			0.918390	−	0.395677i	$-0.129490\pi$
$977$	57.4122			1.83678			0.918390	+	0.395677i	$0.129490\pi$
$978$			11.4407i			0.365833i
$979$			23.5681i			0.753241i
$980$	1.34888	−	19.0617i	0.0430884	−	0.608903i
$981$		−	7.59747i		−	0.242569i
$982$	−10.6251			−0.339061
$983$			41.0662i			1.30981i	0.755711	+	0.654905i	$0.227291\pi$
$983$			41.0662i			1.30981i	−0.755711	+	0.654905i	$0.772709\pi$
$984$			29.6886i			0.946439i
$985$	16.7443	+	1.18489i	0.533517	+	0.0377538i
$986$		−	22.5636i		−	0.718571i
$987$			10.0043i			0.318441i
$988$			4.67996i			0.148889i
$989$	−33.2954			−1.05873
$990$	−0.677003	+	9.56704i	−0.0215166	+	0.304060i
$991$			53.4124i			1.69670i	0.529434	+	0.848351i	$0.322404\pi$
$991$			53.4124i			1.69670i	−0.529434	+	0.848351i	$0.677596\pi$
$992$			22.7215i			0.721408i
$993$	13.7042			0.434890
$994$			46.3756i			1.47095i
$995$	9.89133	+	0.699951i	0.313576	+	0.0221899i
$996$	2.09554			0.0663996
$997$	−17.7903			−0.563424			−0.281712	−	0.959499i	$-0.590902\pi$
$997$	−17.7903			−0.563424			−0.281712	+	0.959499i	$0.590902\pi$
$998$			26.8386i			0.849562i
$999$	1.88419	−	5.78358i	0.0596131	−	0.182984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.15	✓	40
3.2	odd	2		1665.2.g.e.739.25		40
5.4	even	2	inner	555.2.g.a.184.26	yes	40
15.14	odd	2		1665.2.g.e.739.16		40
37.36	even	2	inner	555.2.g.a.184.25	yes	40
111.110	odd	2		1665.2.g.e.739.15		40
185.184	even	2	inner	555.2.g.a.184.16	yes	40
555.554	odd	2		1665.2.g.e.739.26		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.15	✓	40	1.1	even	1	trivial
555.2.g.a.184.16	yes	40	185.184	even	2	inner
555.2.g.a.184.25	yes	40	37.36	even	2	inner
555.2.g.a.184.26	yes	40	5.4	even	2	inner
1665.2.g.e.739.15		40	111.110	odd	2
1665.2.g.e.739.16		40	15.14	odd	2
1665.2.g.e.739.25		40	3.2	odd	2
1665.2.g.e.739.26		40	555.554	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.818204 q^{2} -1.00000i q^{3} -1.33054 q^{4} +(0.157839 - 2.23049i) q^{5} +0.818204i q^{6} -3.66373i q^{7} +2.72506 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.818204 q^{2} -1.00000i q^{3} -1.33054 q^{4} +(0.157839 - 2.23049i) q^{5} +0.818204i q^{6} -3.66373i q^{7} +2.72506 q^{8} -1.00000 q^{9} +(-0.129144 + 1.82500i) q^{10} -5.24223 q^{11} +1.33054i q^{12} -1.85420 q^{13} +2.99768i q^{14} +(-2.23049 - 0.157839i) q^{15} +0.431428 q^{16} +3.75153 q^{17} +0.818204 q^{18} +1.89695i q^{19} +(-0.210011 + 2.96776i) q^{20} -3.66373 q^{21} +4.28921 q^{22} +6.57994 q^{23} -2.72506i q^{24} +(-4.95017 - 0.704115i) q^{25} +1.51711 q^{26} +1.00000i q^{27} +4.87475i q^{28} +7.35087i q^{29} +(1.82500 + 0.129144i) q^{30} -3.91539i q^{31} -5.80312 q^{32} +5.24223i q^{33} -3.06951 q^{34} +(-8.17191 - 0.578278i) q^{35} +1.33054 q^{36} +(-5.78358 - 1.88419i) q^{37} -1.55209i q^{38} +1.85420i q^{39} +(0.430120 - 6.07823i) q^{40} -10.8947 q^{41} +2.99768 q^{42} -5.06014 q^{43} +6.97500 q^{44} +(-0.157839 + 2.23049i) q^{45} -5.38373 q^{46} -2.73064i q^{47} -0.431428i q^{48} -6.42291 q^{49} +(4.05025 + 0.576109i) q^{50} -3.75153i q^{51} +2.46709 q^{52} +10.8230i q^{53} -0.818204i q^{54} +(-0.827425 + 11.6927i) q^{55} -9.98389i q^{56} +1.89695 q^{57} -6.01451i q^{58} +8.74598i q^{59} +(2.96776 + 0.210011i) q^{60} -11.7550i q^{61} +3.20359i q^{62} +3.66373i q^{63} +3.88528 q^{64} +(-0.292664 + 4.13578i) q^{65} -4.28921i q^{66} -12.0734i q^{67} -4.99157 q^{68} -6.57994i q^{69} +(6.68629 + 0.473149i) q^{70} +15.4705 q^{71} -2.72506 q^{72} -3.48304i q^{73} +(4.73215 + 1.54165i) q^{74} +(-0.704115 + 4.95017i) q^{75} -2.52397i q^{76} +19.2061i q^{77} -1.51711i q^{78} -3.56909i q^{79} +(0.0680960 - 0.962296i) q^{80} +1.00000 q^{81} +8.91405 q^{82} -1.57495i q^{83} +4.87475 q^{84} +(0.592136 - 8.36774i) q^{85} +4.14022 q^{86} +7.35087 q^{87} -14.2854 q^{88} -4.49583i q^{89} +(0.129144 - 1.82500i) q^{90} +6.79329i q^{91} -8.75489 q^{92} -3.91539 q^{93} +2.23422i q^{94} +(4.23113 + 0.299412i) q^{95} +5.80312i q^{96} +3.73519 q^{97} +5.25525 q^{98} +5.24223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more