LMFDB - Embedded newform 430.2.b.a.259.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(259,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("430.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.1
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.a.259.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.48119i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} -2.48119 q^{6} +0.193937i q^{7} +1.00000i q^{8} -3.15633 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.48119i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} -2.48119 q^{6} +0.193937i q^{7} +1.00000i q^{8} -3.15633 q^{9} +(-1.67513 + 1.48119i) q^{10} -3.67513 q^{11} +2.48119i q^{12} +2.35026i q^{13} +0.193937 q^{14} +(-4.15633 + 3.67513i) q^{15} +1.00000 q^{16} -5.44358i q^{17} +3.15633i q^{18} +5.80606 q^{19} +(1.48119 + 1.67513i) q^{20} +0.481194 q^{21} +3.67513i q^{22} -0.324869i q^{23} +2.48119 q^{24} +(-0.612127 + 4.96239i) q^{25} +2.35026 q^{26} +0.387873i q^{27} -0.193937i q^{28} -0.287258 q^{29} +(3.67513 + 4.15633i) q^{30} -8.02539 q^{31} -1.00000i q^{32} +9.11871i q^{33} -5.44358 q^{34} +(0.324869 - 0.287258i) q^{35} +3.15633 q^{36} -6.06300i q^{37} -5.80606i q^{38} +5.83146 q^{39} +(1.67513 - 1.48119i) q^{40} -2.22425 q^{41} -0.481194i q^{42} -1.00000i q^{43} +3.67513 q^{44} +(4.67513 + 5.28726i) q^{45} -0.324869 q^{46} +7.28726i q^{47} -2.48119i q^{48} +6.96239 q^{49} +(4.96239 + 0.612127i) q^{50} -13.5066 q^{51} -2.35026i q^{52} -8.46898i q^{53} +0.387873 q^{54} +(5.44358 + 6.15633i) q^{55} -0.193937 q^{56} -14.4060i q^{57} +0.287258i q^{58} -9.73813 q^{59} +(4.15633 - 3.67513i) q^{60} +1.79384 q^{61} +8.02539i q^{62} -0.612127i q^{63} -1.00000 q^{64} +(3.93700 - 3.48119i) q^{65} +9.11871 q^{66} -3.97461i q^{67} +5.44358i q^{68} -0.806063 q^{69} +(-0.287258 - 0.324869i) q^{70} -11.1817 q^{71} -3.15633i q^{72} -4.80114i q^{73} -6.06300 q^{74} +(12.3127 + 1.51881i) q^{75} -5.80606 q^{76} -0.712742i q^{77} -5.83146i q^{78} -2.44358 q^{79} +(-1.48119 - 1.67513i) q^{80} -8.50659 q^{81} +2.22425i q^{82} -17.2447i q^{83} -0.481194 q^{84} +(-9.11871 + 8.06300i) q^{85} -1.00000 q^{86} +0.712742i q^{87} -3.67513i q^{88} +14.4363 q^{89} +(5.28726 - 4.67513i) q^{90} -0.455802 q^{91} +0.324869i q^{92} +19.9126i q^{93} +7.28726 q^{94} +(-8.59991 - 9.72592i) q^{95} -2.48119 q^{96} +7.44358i q^{97} -6.96239i q^{98} +11.5999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.48119i		−	1.43252i	−0.697834	−	0.716259i	$-0.745853\pi$
$3$		−	2.48119i		−	1.43252i	0.697834	−	0.716259i	$-0.254147\pi$
$4$	−1.00000			−0.500000
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$	−2.48119			−1.01294
$7$			0.193937i			0.0733011i	0.999328	+	0.0366506i	$0.0116689\pi$
$7$			0.193937i			0.0733011i	−0.999328	+	0.0366506i	$0.988331\pi$
$8$			1.00000i			0.353553i
$9$	−3.15633			−1.05211
$10$	−1.67513	+	1.48119i	−0.529723	+	0.468395i
$11$	−3.67513			−1.10809			−0.554047	−	0.832486i	$-0.686917\pi$
$11$	−3.67513			−1.10809			−0.554047	+	0.832486i	$0.686917\pi$
$12$			2.48119i			0.716259i
$13$			2.35026i			0.651845i	0.945396	+	0.325923i	$0.105675\pi$
$13$			2.35026i			0.651845i	−0.945396	+	0.325923i	$0.894325\pi$
$14$	0.193937			0.0518317
$15$	−4.15633	+	3.67513i	−1.07316	+	0.948915i
$16$	1.00000			0.250000
$17$		−	5.44358i		−	1.32026i	−0.751150	−	0.660131i	$-0.770501\pi$
$17$		−	5.44358i		−	1.32026i	0.751150	−	0.660131i	$-0.229499\pi$
$18$			3.15633i			0.743953i
$19$	5.80606			1.33200			0.666001	−	0.745951i	$-0.268005\pi$
$19$	5.80606			1.33200			0.666001	+	0.745951i	$0.268005\pi$
$20$	1.48119	+	1.67513i	0.331205	+	0.374571i
$21$	0.481194			0.105005
$22$			3.67513i			0.783541i
$23$		−	0.324869i		−	0.0677399i	−0.999426	−	0.0338699i	$-0.989217\pi$
$23$		−	0.324869i		−	0.0677399i	0.999426	−	0.0338699i	$-0.0107832\pi$
$24$	2.48119			0.506472
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	2.35026			0.460924
$27$			0.387873i			0.0746462i
$28$		−	0.193937i		−	0.0366506i
$29$	−0.287258			−0.0533424			−0.0266712	−	0.999644i	$-0.508491\pi$
$29$	−0.287258			−0.0533424			−0.0266712	+	0.999644i	$0.508491\pi$
$30$	3.67513	+	4.15633i	0.670984	+	0.758838i
$31$	−8.02539			−1.44140			−0.720702	−	0.693245i	$-0.756180\pi$
$31$	−8.02539			−1.44140			−0.720702	+	0.693245i	$0.756180\pi$
$32$		−	1.00000i		−	0.176777i
$33$			9.11871i			1.58736i
$34$	−5.44358			−0.933567
$35$	0.324869	−	0.287258i	0.0549129	−	0.0485554i
$36$	3.15633			0.526054
$37$		−	6.06300i		−	0.996752i	−0.866961	−	0.498376i	$-0.833930\pi$
$37$		−	6.06300i		−	0.996752i	0.866961	−	0.498376i	$-0.166070\pi$
$38$		−	5.80606i		−	0.941868i
$39$	5.83146			0.933780
$40$	1.67513	−	1.48119i	0.264861	−	0.234197i
$41$	−2.22425			−0.347370			−0.173685	−	0.984801i	$-0.555567\pi$
$41$	−2.22425			−0.347370			−0.173685	+	0.984801i	$0.555567\pi$
$42$		−	0.481194i		−	0.0742499i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	3.67513			0.554047
$45$	4.67513	+	5.28726i	0.696927	+	0.788178i
$46$	−0.324869			−0.0478993
$47$			7.28726i			1.06296i	0.847072	+	0.531478i	$0.178363\pi$
$47$			7.28726i			1.06296i	−0.847072	+	0.531478i	$0.821637\pi$
$48$		−	2.48119i		−	0.358130i
$49$	6.96239			0.994627
$50$	4.96239	+	0.612127i	0.701788	+	0.0865678i
$51$	−13.5066			−1.89130
$52$		−	2.35026i		−	0.325923i
$53$		−	8.46898i		−	1.16330i	−0.813438	−	0.581652i	$-0.802407\pi$
$53$		−	8.46898i		−	1.16330i	0.813438	−	0.581652i	$-0.197593\pi$
$54$	0.387873			0.0527828
$55$	5.44358	+	6.15633i	0.734013	+	0.830119i
$56$	−0.193937			−0.0259159
$57$		−	14.4060i		−	1.90812i
$58$			0.287258i			0.0377188i
$59$	−9.73813			−1.26780			−0.633899	−	0.773416i	$-0.718546\pi$
$59$	−9.73813			−1.26780			−0.633899	+	0.773416i	$0.718546\pi$
$60$	4.15633	−	3.67513i	0.536579	−	0.474457i
$61$	1.79384			0.229678			0.114839	−	0.993384i	$-0.463365\pi$
$61$	1.79384			0.229678			0.114839	+	0.993384i	$0.463365\pi$
$62$			8.02539i			1.01923i
$63$		−	0.612127i		−	0.0771207i
$64$	−1.00000			−0.125000
$65$	3.93700	−	3.48119i	0.488324	−	0.431789i
$66$	9.11871			1.12244
$67$		−	3.97461i		−	0.485576i	−0.970079	−	0.242788i	$-0.921938\pi$
$67$		−	3.97461i		−	0.485576i	0.970079	−	0.242788i	$-0.0780619\pi$
$68$			5.44358i			0.660131i
$69$	−0.806063			−0.0970386
$70$	−0.287258	−	0.324869i	−0.0343339	−	0.0388293i
$71$	−11.1817			−1.32703			−0.663513	−	0.748165i	$-0.730935\pi$
$71$	−11.1817			−1.32703			−0.663513	+	0.748165i	$0.730935\pi$
$72$		−	3.15633i		−	0.371976i
$73$		−	4.80114i		−	0.561931i	−0.959718	−	0.280965i	$-0.909345\pi$
$73$		−	4.80114i		−	0.561931i	0.959718	−	0.280965i	$-0.0906546\pi$
$74$	−6.06300			−0.704810
$75$	12.3127	+	1.51881i	1.42174	+	0.175377i
$76$	−5.80606			−0.666001
$77$		−	0.712742i		−	0.0812245i
$78$		−	5.83146i		−	0.660282i
$79$	−2.44358			−0.274925			−0.137462	−	0.990507i	$-0.543895\pi$
$79$	−2.44358			−0.274925			−0.137462	+	0.990507i	$0.543895\pi$
$80$	−1.48119	−	1.67513i	−0.165603	−	0.187285i
$81$	−8.50659			−0.945176
$82$			2.22425i			0.245628i
$83$		−	17.2447i		−	1.89285i	−0.322918	−	0.946427i	$-0.604664\pi$
$83$		−	17.2447i		−	1.89285i	0.322918	−	0.946427i	$-0.395336\pi$
$84$	−0.481194			−0.0525026
$85$	−9.11871	+	8.06300i	−0.989063	+	0.874556i
$86$	−1.00000			−0.107833
$87$			0.712742i			0.0764140i
$88$		−	3.67513i		−	0.391770i
$89$	14.4363			1.53024			0.765122	−	0.643886i	$-0.222679\pi$
$89$	14.4363			1.53024			0.765122	+	0.643886i	$0.222679\pi$
$90$	5.28726	−	4.67513i	0.557326	−	0.492802i
$91$	−0.455802			−0.0477810
$92$			0.324869i			0.0338699i
$93$			19.9126i			2.06484i
$94$	7.28726			0.751623
$95$	−8.59991	−	9.72592i	−0.882332	−	0.997858i
$96$	−2.48119			−0.253236
$97$			7.44358i			0.755781i	0.925850	+	0.377891i	$0.123350\pi$
$97$			7.44358i			0.755781i	−0.925850	+	0.377891i	$0.876650\pi$
$98$		−	6.96239i		−	0.703307i
$99$	11.5999			1.16583
$100$	0.612127	−	4.96239i	0.0612127	−	0.496239i
$101$	12.7186			1.26555			0.632775	−	0.774336i	$-0.281916\pi$
$101$	12.7186			1.26555			0.632775	+	0.774336i	$0.281916\pi$
$102$			13.5066i			1.33735i
$103$		−	4.57452i		−	0.450740i	−0.974273	−	0.225370i	$-0.927641\pi$
$103$		−	4.57452i		−	0.450740i	0.974273	−	0.225370i	$-0.0723592\pi$
$104$	−2.35026			−0.230462
$105$	−0.712742	−	0.806063i	−0.0695565	−	0.0786637i
$106$	−8.46898			−0.822580
$107$		−	4.56959i		−	0.441759i	−0.975301	−	0.220880i	$-0.929107\pi$
$107$		−	4.56959i		−	0.441759i	0.975301	−	0.220880i	$-0.0708928\pi$
$108$		−	0.387873i		−	0.0373231i
$109$	9.66291			0.925539			0.462770	−	0.886479i	$-0.346856\pi$
$109$	9.66291			0.925539			0.462770	+	0.886479i	$0.346856\pi$
$110$	6.15633	−	5.44358i	0.586983	−	0.519025i
$111$	−15.0435			−1.42786
$112$			0.193937i			0.0183253i
$113$		−	14.3684i		−	1.35166i	−0.737057	−	0.675831i	$-0.763785\pi$
$113$		−	14.3684i		−	1.35166i	0.737057	−	0.675831i	$-0.236215\pi$
$114$	−14.4060			−1.34924
$115$	−0.544198	+	0.481194i	−0.0507468	+	0.0448716i
$116$	0.287258			0.0266712
$117$		−	7.41819i		−	0.685812i
$118$			9.73813i			0.896468i
$119$	1.05571			0.0967768
$120$	−3.67513	−	4.15633i	−0.335492	−	0.379419i
$121$	2.50659			0.227872
$122$		−	1.79384i		−	0.162407i
$123$			5.51881i			0.497614i
$124$	8.02539			0.720702
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$	−0.612127			−0.0545326
$127$		−	8.70052i		−	0.772047i	−0.922489	−	0.386023i	$-0.873848\pi$
$127$		−	8.70052i		−	0.772047i	0.922489	−	0.386023i	$-0.126152\pi$
$128$			1.00000i			0.0883883i
$129$	−2.48119			−0.218457
$130$	−3.48119	−	3.93700i	−0.305321	−	0.345297i
$131$	15.4314			1.34824			0.674122	−	0.738620i	$-0.264522\pi$
$131$	15.4314			1.34824			0.674122	+	0.738620i	$0.264522\pi$
$132$		−	9.11871i		−	0.793682i
$133$			1.12601i			0.0976373i
$134$	−3.97461			−0.343354
$135$	0.649738	−	0.574515i	0.0559206	−	0.0494464i
$136$	5.44358			0.466783
$137$			6.70545i			0.572885i	0.958097	+	0.286443i	$0.0924728\pi$
$137$			6.70545i			0.572885i	−0.958097	+	0.286443i	$0.907527\pi$
$138$			0.806063i			0.0686167i
$139$	11.8011			1.00096			0.500480	−	0.865748i	$-0.333157\pi$
$139$	11.8011			1.00096			0.500480	+	0.865748i	$0.333157\pi$
$140$	−0.324869	+	0.287258i	−0.0274565	+	0.0242777i
$141$	18.0811			1.52270
$142$			11.1817i			0.938349i
$143$		−	8.63752i		−	0.722306i
$144$	−3.15633			−0.263027
$145$	0.425485	+	0.481194i	0.0353346	+	0.0399610i
$146$	−4.80114			−0.397345
$147$		−	17.2750i		−	1.42482i
$148$			6.06300i			0.498376i
$149$	4.25694			0.348742			0.174371	−	0.984680i	$-0.444211\pi$
$149$	4.25694			0.348742			0.174371	+	0.984680i	$0.444211\pi$
$150$	1.51881	−	12.3127i	0.124010	−	1.00532i
$151$	−14.5745			−1.18606			−0.593029	−	0.805181i	$-0.702068\pi$
$151$	−14.5745			−1.18606			−0.593029	+	0.805181i	$0.702068\pi$
$152$			5.80606i			0.470934i
$153$			17.1817i			1.38906i
$154$	−0.712742			−0.0574344
$155$	11.8872	+	13.4436i	0.954800	+	1.07981i
$156$	−5.83146			−0.466890
$157$			21.8373i			1.74281i	0.490565	+	0.871405i	$0.336790\pi$
$157$			21.8373i			1.74281i	−0.490565	+	0.871405i	$0.663210\pi$
$158$			2.44358i			0.194401i
$159$	−21.0132			−1.66645
$160$	−1.67513	+	1.48119i	−0.132431	+	0.117099i
$161$	0.0630040			0.00496541
$162$			8.50659i			0.668341i
$163$		−	0.312650i		−	0.0244887i	−0.999925	−	0.0122443i	$-0.996102\pi$
$163$		−	0.312650i		−	0.0244887i	0.999925	−	0.0122443i	$-0.00389759\pi$
$164$	2.22425			0.173685
$165$	15.2750	−	13.5066i	1.18916	−	1.05149i
$166$	−17.2447			−1.33845
$167$			15.9126i			1.23135i	0.788000	+	0.615675i	$0.211117\pi$
$167$			15.9126i			1.23135i	−0.788000	+	0.615675i	$0.788883\pi$
$168$			0.481194i			0.0371249i
$169$	7.47627			0.575098
$170$	8.06300	+	9.11871i	0.618404	+	0.699373i
$171$	−18.3258			−1.40141
$172$			1.00000i			0.0762493i
$173$			8.92478i			0.678538i	0.940689	+	0.339269i	$0.110180\pi$
$173$			8.92478i			0.678538i	−0.940689	+	0.339269i	$0.889820\pi$
$174$	0.712742			0.0540329
$175$	−0.962389	−	0.118714i	−0.0727497	−	0.00897392i
$176$	−3.67513			−0.277023
$177$			24.1622i			1.81614i
$178$		−	14.4363i		−	1.08205i
$179$	−8.69323			−0.649762			−0.324881	−	0.945755i	$-0.605324\pi$
$179$	−8.69323			−0.649762			−0.324881	+	0.945755i	$0.605324\pi$
$180$	−4.67513	−	5.28726i	−0.348464	−	0.394089i
$181$	6.21933			0.462279			0.231140	−	0.972921i	$-0.425755\pi$
$181$	6.21933			0.462279			0.231140	+	0.972921i	$0.425755\pi$
$182$			0.455802i			0.0337863i
$183$		−	4.45088i		−	0.329018i
$184$	0.324869			0.0239497
$185$	−10.1563	+	8.98049i	−0.746708	+	0.660259i
$186$	19.9126			1.46006
$187$			20.0059i			1.46297i
$188$		−	7.28726i		−	0.531478i
$189$	−0.0752228			−0.00547165
$190$	−9.72592	+	8.59991i	−0.705592	+	0.623903i
$191$	11.3684			0.822586			0.411293	−	0.911503i	$-0.365077\pi$
$191$	11.3684			0.822586			0.411293	+	0.911503i	$0.365077\pi$
$192$			2.48119i			0.179065i
$193$		−	3.73813i		−	0.269077i	−0.990908	−	0.134538i	$-0.957045\pi$
$193$		−	3.73813i		−	0.269077i	0.990908	−	0.134538i	$-0.0429552\pi$
$194$	7.44358			0.534418
$195$	−8.63752	−	9.76845i	−0.618546	−	0.699533i
$196$	−6.96239			−0.497313
$197$		−	24.8192i		−	1.76830i	−0.467206	−	0.884149i	$-0.654739\pi$
$197$		−	24.8192i		−	1.76830i	0.467206	−	0.884149i	$-0.345261\pi$
$198$		−	11.5999i		−	0.824370i
$199$	−6.91985			−0.490535			−0.245268	−	0.969455i	$-0.578876\pi$
$199$	−6.91985			−0.490535			−0.245268	+	0.969455i	$0.578876\pi$
$200$	−4.96239	−	0.612127i	−0.350894	−	0.0432839i
$201$	−9.86177			−0.695596
$202$		−	12.7186i		−	0.894879i
$203$		−	0.0557098i		−	0.00391006i
$204$	13.5066			0.945650
$205$	3.29455	+	3.72592i	0.230101	+	0.260229i
$206$	−4.57452			−0.318722
$207$			1.02539i			0.0712697i
$208$			2.35026i			0.162961i
$209$	−21.3380			−1.47598
$210$	−0.806063	+	0.712742i	−0.0556237	+	0.0491839i
$211$	18.1768			1.25134			0.625671	−	0.780087i	$-0.284825\pi$
$211$	18.1768			1.25134			0.625671	+	0.780087i	$0.284825\pi$
$212$			8.46898i			0.581652i
$213$			27.7440i			1.90099i
$214$	−4.56959			−0.312371
$215$	−1.67513	+	1.48119i	−0.114243	+	0.101017i
$216$	−0.387873			−0.0263914
$217$		−	1.55642i		−	0.105656i
$218$		−	9.66291i		−	0.654455i
$219$	−11.9126			−0.804976
$220$	−5.44358	−	6.15633i	−0.367006	−	0.415059i
$221$	12.7938			0.860607
$222$			15.0435i			1.00965i
$223$		−	2.49341i		−	0.166971i	−0.996509	−	0.0834856i	$-0.973395\pi$
$223$		−	2.49341i		−	0.166971i	0.996509	−	0.0834856i	$-0.0266053\pi$
$224$	0.193937			0.0129579
$225$	1.93207	−	15.6629i	0.128805	−	1.04419i
$226$	−14.3684			−0.955769
$227$		−	18.1114i		−	1.20210i	−0.799212	−	0.601049i	$-0.794750\pi$
$227$		−	18.1114i		−	1.20210i	0.799212	−	0.601049i	$-0.205250\pi$
$228$			14.4060i			0.954059i
$229$	5.81336			0.384157			0.192079	−	0.981380i	$-0.438477\pi$
$229$	5.81336			0.384157			0.192079	+	0.981380i	$0.438477\pi$
$230$	0.481194	+	0.544198i	0.0317290	+	0.0358834i
$231$	−1.76845			−0.116356
$232$		−	0.287258i		−	0.0188594i
$233$			11.5818i			0.758750i	0.925243	+	0.379375i	$0.123861\pi$
$233$			11.5818i			0.758750i	−0.925243	+	0.379375i	$0.876139\pi$
$234$	−7.41819			−0.484942
$235$	12.2071	−	10.7938i	0.796304	−	0.704113i
$236$	9.73813			0.633899
$237$			6.06300i			0.393834i
$238$		−	1.05571i		−	0.0684315i
$239$	24.8822			1.60950			0.804749	−	0.593615i	$-0.202300\pi$
$239$	24.8822			1.60950			0.804749	+	0.593615i	$0.202300\pi$
$240$	−4.15633	+	3.67513i	−0.268290	+	0.237229i
$241$	−16.1138			−1.03798			−0.518990	−	0.854780i	$-0.673692\pi$
$241$	−16.1138			−1.03798			−0.518990	+	0.854780i	$0.673692\pi$
$242$		−	2.50659i		−	0.161130i
$243$			22.2701i			1.42863i
$244$	−1.79384			−0.114839
$245$	−10.3127	−	11.6629i	−0.658851	−	0.745116i
$246$	5.51881			0.351866
$247$			13.6458i			0.868259i
$248$		−	8.02539i		−	0.509613i
$249$	−42.7875			−2.71155
$250$	−6.32487	−	9.21933i	−0.400020	−	0.583082i
$251$	−24.4894			−1.54576			−0.772880	−	0.634552i	$-0.781185\pi$
$251$	−24.4894			−1.54576			−0.772880	+	0.634552i	$0.781185\pi$
$252$			0.612127i			0.0385604i
$253$			1.19394i			0.0750621i
$254$	−8.70052			−0.545919
$255$	20.0059	+	22.6253i	1.25282	+	1.41685i
$256$	1.00000			0.0625000
$257$			1.03269i			0.0644172i	0.999481	+	0.0322086i	$0.0102541\pi$
$257$			1.03269i			0.0644172i	−0.999481	+	0.0322086i	$0.989746\pi$
$258$			2.48119i			0.154472i
$259$	1.17584			0.0730630
$260$	−3.93700	+	3.48119i	−0.244162	+	0.215895i
$261$	0.906679			0.0561220
$262$		−	15.4314i		−	0.953353i
$263$			25.7367i			1.58699i	0.608574	+	0.793497i	$0.291742\pi$
$263$			25.7367i			1.58699i	−0.608574	+	0.793497i	$0.708258\pi$
$264$	−9.11871			−0.561218
$265$	−14.1866	+	12.5442i	−0.871479	+	0.770584i
$266$	1.12601			0.0690400
$267$		−	35.8192i		−	2.19210i
$268$			3.97461i			0.242788i
$269$	22.2130			1.35435			0.677175	−	0.735822i	$-0.263204\pi$
$269$	22.2130			1.35435			0.677175	+	0.735822i	$0.263204\pi$
$270$	−0.574515	−	0.649738i	−0.0349639	−	0.0395418i
$271$	−20.4739			−1.24370			−0.621850	−	0.783136i	$-0.713619\pi$
$271$	−20.4739			−1.24370			−0.621850	+	0.783136i	$0.713619\pi$
$272$		−	5.44358i		−	0.330066i
$273$			1.13093i			0.0684472i
$274$	6.70545			0.405091
$275$	2.24965	−	18.2374i	0.135659	−	1.09976i
$276$	0.806063			0.0485193
$277$		−	4.07522i		−	0.244856i	−0.992477	−	0.122428i	$-0.960932\pi$
$277$		−	4.07522i		−	0.244856i	0.992477	−	0.122428i	$-0.0390681\pi$
$278$		−	11.8011i		−	0.707785i
$279$	25.3307			1.51651
$280$	0.287258	+	0.324869i	0.0171669	+	0.0194146i
$281$	23.1114			1.37871			0.689356	−	0.724423i	$-0.257894\pi$
$281$	23.1114			1.37871			0.689356	+	0.724423i	$0.257894\pi$
$282$		−	18.0811i		−	1.07671i
$283$			16.3684i			0.972998i	0.873681	+	0.486499i	$0.161726\pi$
$283$			16.3684i			0.972998i	−0.873681	+	0.486499i	$0.838274\pi$
$284$	11.1817			0.663513
$285$	−24.1319	+	21.3380i	−1.42945	+	1.26396i
$286$	−8.63752			−0.510747
$287$		−	0.431364i		−	0.0254626i
$288$			3.15633i			0.185988i
$289$	−12.6326			−0.743094
$290$	0.481194	−	0.425485i	0.0282567	−	0.0249853i
$291$	18.4690			1.08267
$292$			4.80114i			0.280965i
$293$			30.4993i			1.78179i	0.454212	+	0.890894i	$0.349921\pi$
$293$			30.4993i			1.78179i	−0.454212	+	0.890894i	$0.650079\pi$
$294$	−17.2750			−1.00750
$295$	14.4241	+	16.3127i	0.839802	+	0.949759i
$296$	6.06300			0.352405
$297$		−	1.42548i		−	0.0827150i
$298$		−	4.25694i		−	0.246598i
$299$	0.763527			0.0441559
$300$	−12.3127	−	1.51881i	−0.710871	−	0.0876883i
$301$	0.193937			0.0111783
$302$			14.5745i			0.838669i
$303$		−	31.5574i		−	1.81292i
$304$	5.80606			0.333001
$305$	−2.65703	−	3.00492i	−0.152141	−	0.172061i
$306$	17.1817			0.982213
$307$			2.01951i			0.115260i	0.998338	+	0.0576298i	$0.0183543\pi$
$307$			2.01951i			0.115260i	−0.998338	+	0.0576298i	$0.981646\pi$
$308$			0.712742i			0.0406123i
$309$	−11.3503			−0.645694
$310$	13.4436	−	11.8872i	0.763544	−	0.675146i
$311$	13.7431			0.779297			0.389649	−	0.920964i	$-0.372596\pi$
$311$	13.7431			0.779297			0.389649	+	0.920964i	$0.372596\pi$
$312$			5.83146i			0.330141i
$313$			14.3127i			0.808999i	0.914538	+	0.404499i	$0.132554\pi$
$313$			14.3127i			0.808999i	−0.914538	+	0.404499i	$0.867446\pi$
$314$	21.8373			1.23235
$315$	−1.02539	+	0.906679i	−0.0577743	+	0.0510856i
$316$	2.44358			0.137462
$317$			8.89446i			0.499563i	0.968302	+	0.249781i	$0.0803587\pi$
$317$			8.89446i			0.499563i	−0.968302	+	0.249781i	$0.919641\pi$
$318$			21.0132i			1.17836i
$319$	1.05571			0.0591084
$320$	1.48119	+	1.67513i	0.0828013	+	0.0936427i
$321$	−11.3380			−0.632828
$322$		−	0.0630040i		−	0.00351108i
$323$		−	31.6058i		−	1.75859i
$324$	8.50659			0.472588
$325$	−11.6629	−	1.43866i	−0.646942	−	0.0798024i
$326$	−0.312650			−0.0173161
$327$		−	23.9756i		−	1.32585i
$328$		−	2.22425i		−	0.122814i
$329$	−1.41327			−0.0779159
$330$	−13.5066	−	15.2750i	−0.743513	−	0.840863i
$331$	4.88129			0.268300			0.134150	−	0.990961i	$-0.457170\pi$
$331$	4.88129			0.268300			0.134150	+	0.990961i	$0.457170\pi$
$332$			17.2447i			0.946427i
$333$			19.1368i			1.04869i
$334$	15.9126			0.870696
$335$	−6.65799	+	5.88717i	−0.363765	+	0.321650i
$336$	0.481194			0.0262513
$337$		−	21.2506i		−	1.15759i	−0.815472	−	0.578797i	$-0.803522\pi$
$337$		−	21.2506i		−	1.15759i	0.815472	−	0.578797i	$-0.196478\pi$
$338$		−	7.47627i		−	0.406655i
$339$	−35.6507			−1.93628
$340$	9.11871	−	8.06300i	0.494532	−	0.437278i
$341$	29.4944			1.59721
$342$			18.3258i			0.990947i
$343$			2.70782i			0.146208i
$344$	1.00000			0.0539164
$345$	1.19394	+	1.35026i	0.0642794	+	0.0726956i
$346$	8.92478			0.479799
$347$		−	27.9330i		−	1.49952i	−0.661708	−	0.749762i	$-0.730168\pi$
$347$		−	27.9330i		−	1.49952i	0.661708	−	0.749762i	$-0.269832\pi$
$348$		−	0.712742i		−	0.0382070i
$349$	12.5745			0.673098			0.336549	−	0.941666i	$-0.390740\pi$
$349$	12.5745			0.673098			0.336549	+	0.941666i	$0.390740\pi$
$350$	−0.118714	+	0.962389i	−0.00634552	+	0.0514418i
$351$	−0.911603			−0.0486578
$352$			3.67513i			0.195885i
$353$		−	28.6190i		−	1.52323i	−0.648028	−	0.761617i	$-0.724406\pi$
$353$		−	28.6190i		−	1.52323i	0.648028	−	0.761617i	$-0.275594\pi$
$354$	24.1622			1.28421
$355$	16.5623	+	18.7308i	0.879035	+	0.994130i
$356$	−14.4363			−0.765122
$357$		−	2.61942i		−	0.138634i
$358$			8.69323i			0.459451i
$359$	−23.6678			−1.24914			−0.624570	−	0.780969i	$-0.714726\pi$
$359$	−23.6678			−1.24914			−0.624570	+	0.780969i	$0.714726\pi$
$360$	−5.28726	+	4.67513i	−0.278663	+	0.246401i
$361$	14.7104			0.774230
$362$		−	6.21933i		−	0.326881i
$363$		−	6.21933i		−	0.326430i
$364$	0.455802			0.0238905
$365$	−8.04254	+	7.11142i	−0.420966	+	0.372229i
$366$	−4.45088			−0.232651
$367$		−	23.0640i		−	1.20393i	−0.798523	−	0.601964i	$-0.794385\pi$
$367$		−	23.0640i		−	1.20393i	0.798523	−	0.601964i	$-0.205615\pi$
$368$		−	0.324869i		−	0.0169350i
$369$	7.02047			0.365471
$370$	8.98049	+	10.1563i	0.466873	+	0.528002i
$371$	1.64244			0.0852714
$372$		−	19.9126i		−	1.03242i
$373$		−	3.67513i		−	0.190291i	−0.995463	−	0.0951455i	$-0.969668\pi$
$373$		−	3.67513i		−	0.190291i	0.995463	−	0.0951455i	$-0.0303316\pi$
$374$	20.0059			1.03448
$375$	−15.6932	−	22.8749i	−0.810395	−	1.18126i
$376$	−7.28726			−0.375812
$377$		−	0.675131i		−	0.0347710i
$378$			0.0752228i			0.00386904i
$379$	17.7743			0.913006			0.456503	−	0.889722i	$-0.349102\pi$
$379$	17.7743			0.913006			0.456503	+	0.889722i	$0.349102\pi$
$380$	8.59991	+	9.72592i	0.441166	+	0.498929i
$381$	−21.5877			−1.10597
$382$		−	11.3684i		−	0.581656i
$383$		−	2.41090i		−	0.123191i	−0.998101	−	0.0615955i	$-0.980381\pi$
$383$		−	2.41090i		−	0.123191i	0.998101	−	0.0615955i	$-0.0196189\pi$
$384$	2.48119			0.126618
$385$	−1.19394	+	1.05571i	−0.0608486	+	0.0538040i
$386$	−3.73813			−0.190266
$387$			3.15633i			0.160445i
$388$		−	7.44358i		−	0.377891i
$389$	18.8773			0.957118			0.478559	−	0.878055i	$-0.341159\pi$
$389$	18.8773			0.957118			0.478559	+	0.878055i	$0.341159\pi$
$390$	−9.76845	+	8.63752i	−0.494645	+	0.437378i
$391$	−1.76845			−0.0894345
$392$			6.96239i			0.351654i
$393$		−	38.2882i		−	1.93138i
$394$	−24.8192			−1.25038
$395$	3.61942	+	4.09332i	0.182113	+	0.205957i
$396$	−11.5999			−0.582917
$397$		−	16.8061i		−	0.843472i	−0.906719	−	0.421736i	$-0.861421\pi$
$397$		−	16.8061i		−	0.843472i	0.906719	−	0.421736i	$-0.138579\pi$
$398$			6.91985i			0.346861i
$399$	2.79384			0.139867
$400$	−0.612127	+	4.96239i	−0.0306063	+	0.248119i
$401$	26.6385			1.33026			0.665131	−	0.746727i	$-0.268376\pi$
$401$	26.6385			1.33026			0.665131	+	0.746727i	$0.268376\pi$
$402$			9.86177i			0.491861i
$403$		−	18.8618i		−	0.939572i
$404$	−12.7186			−0.632775
$405$	12.5999	+	14.2496i	0.626094	+	0.708071i
$406$	−0.0557098			−0.00276483
$407$			22.2823i			1.10449i
$408$		−	13.5066i		−	0.668676i
$409$	−16.6131			−0.821464			−0.410732	−	0.911756i	$-0.634727\pi$
$409$	−16.6131			−0.821464			−0.410732	+	0.911756i	$0.634727\pi$
$410$	3.72592	−	3.29455i	0.184010	−	0.162706i
$411$	16.6375			0.820668
$412$			4.57452i			0.225370i
$413$		−	1.88858i		−	0.0929310i
$414$	1.02539			0.0503953
$415$	−28.8872	+	25.5428i	−1.41802	+	1.25385i
$416$	2.35026			0.115231
$417$		−	29.2809i		−	1.43389i
$418$			21.3380i			1.04368i
$419$	−11.9683			−0.584688			−0.292344	−	0.956313i	$-0.594435\pi$
$419$	−11.9683			−0.584688			−0.292344	+	0.956313i	$0.594435\pi$
$420$	0.712742	+	0.806063i	0.0347783	+	0.0393319i
$421$	10.2727			0.500659			0.250330	−	0.968161i	$-0.419461\pi$
$421$	10.2727			0.500659			0.250330	+	0.968161i	$0.419461\pi$
$422$		−	18.1768i		−	0.884832i
$423$		−	23.0010i		−	1.11834i
$424$	8.46898			0.411290
$425$	27.0132	+	3.33216i	1.31033	+	0.161634i
$426$	27.7440			1.34420
$427$			0.347892i			0.0168357i
$428$			4.56959i			0.220880i
$429$	−21.4314			−1.03472
$430$	1.48119	+	1.67513i	0.0714295	+	0.0807820i
$431$	−28.8423			−1.38928			−0.694641	−	0.719356i	$-0.744437\pi$
$431$	−28.8423			−1.38928			−0.694641	+	0.719356i	$0.744437\pi$
$432$			0.387873i			0.0186616i
$433$		−	37.2760i		−	1.79137i	−0.444689	−	0.895685i	$-0.646686\pi$
$433$		−	37.2760i		−	1.79137i	0.444689	−	0.895685i	$-0.353314\pi$
$434$	−1.55642			−0.0747104
$435$	1.19394	−	1.05571i	0.0572449	−	0.0506174i
$436$	−9.66291			−0.462770
$437$		−	1.88621i		−	0.0902297i
$438$			11.9126i			0.569204i
$439$	27.9102			1.33208			0.666040	−	0.745916i	$-0.267988\pi$
$439$	27.9102			1.33208			0.666040	+	0.745916i	$0.267988\pi$
$440$	−6.15633	+	5.44358i	−0.293491	+	0.259513i
$441$	−21.9756			−1.04646
$442$		−	12.7938i		−	0.608541i
$443$		−	7.29455i		−	0.346575i	−0.984871	−	0.173287i	$-0.944561\pi$
$443$		−	7.29455i		−	0.346575i	0.984871	−	0.173287i	$-0.0554389\pi$
$444$	15.0435			0.713932
$445$	−21.3829	−	24.1827i	−1.01365	−	1.14637i
$446$	−2.49341			−0.118067
$447$		−	10.5623i		−	0.499579i
$448$		−	0.193937i		−	0.00916264i
$449$	−31.9633			−1.50844			−0.754222	−	0.656620i	$-0.771986\pi$
$449$	−31.9633			−1.50844			−0.754222	+	0.656620i	$0.771986\pi$
$450$	−15.6629	−	1.93207i	−0.738357	−	0.0910787i
$451$	8.17442			0.384919
$452$			14.3684i			0.675831i
$453$			36.1622i			1.69905i
$454$	−18.1114			−0.850011
$455$	0.675131	+	0.763527i	0.0316506	+	0.0357947i
$456$	14.4060			0.674621
$457$		−	18.3733i		−	0.859466i	−0.902956	−	0.429733i	$-0.858608\pi$
$457$		−	18.3733i		−	0.859466i	0.902956	−	0.429733i	$-0.141392\pi$
$458$		−	5.81336i		−	0.271640i
$459$	2.11142			0.0985526
$460$	0.544198	−	0.481194i	0.0253734	−	0.0224358i
$461$	−40.6697			−1.89418			−0.947089	−	0.320970i	$-0.895991\pi$
$461$	−40.6697			−1.89418			−0.947089	+	0.320970i	$0.895991\pi$
$462$			1.76845i			0.0822758i
$463$			41.8178i			1.94344i	0.236138	+	0.971720i	$0.424118\pi$
$463$			41.8178i			1.94344i	−0.236138	+	0.971720i	$0.575882\pi$
$464$	−0.287258			−0.0133356
$465$	33.3561	−	29.4944i	1.54685	−	1.36777i
$466$	11.5818			0.536517
$467$		−	14.9805i		−	0.693214i	−0.938010	−	0.346607i	$-0.887334\pi$
$467$		−	14.9805i		−	0.693214i	0.938010	−	0.346607i	$-0.112666\pi$
$468$			7.41819i			0.342906i
$469$	0.770822			0.0355932
$470$	−10.7938	−	12.2071i	−0.497883	−	0.563072i
$471$	54.1827			2.49661
$472$		−	9.73813i		−	0.448234i
$473$			3.67513i			0.168983i
$474$	6.06300			0.278483
$475$	−3.55405	+	28.8119i	−0.163071	+	1.32198i
$476$	−1.05571			−0.0483884
$477$			26.7308i			1.22392i
$478$		−	24.8822i		−	1.13809i
$479$	−10.6399			−0.486149			−0.243074	−	0.970008i	$-0.578156\pi$
$479$	−10.6399			−0.486149			−0.243074	+	0.970008i	$0.578156\pi$
$480$	3.67513	+	4.15633i	0.167746	+	0.189709i
$481$	14.2496			0.649728
$482$			16.1138i			0.733963i
$483$		−	0.156325i		−	0.00711304i
$484$	−2.50659			−0.113936
$485$	12.4690	−	11.0254i	0.566187	−	0.500637i
$486$	22.2701			1.01019
$487$			38.4119i			1.74061i	0.492516	+	0.870304i	$0.336077\pi$
$487$			38.4119i			1.74061i	−0.492516	+	0.870304i	$0.663923\pi$
$488$			1.79384i			0.0812035i
$489$	−0.775746			−0.0350805
$490$	−11.6629	+	10.3127i	−0.526877	+	0.465878i
$491$	7.11871			0.321263			0.160632	−	0.987014i	$-0.448647\pi$
$491$	7.11871			0.321263			0.160632	+	0.987014i	$0.448647\pi$
$492$		−	5.51881i		−	0.248807i
$493$			1.56371i			0.0704260i
$494$	13.6458			0.613952
$495$	−17.1817	−	19.4314i	−0.772261	−	0.873375i
$496$	−8.02539			−0.360351
$497$		−	2.16854i		−	0.0972725i
$498$			42.7875i			1.91735i
$499$	−22.5066			−1.00753			−0.503767	−	0.863840i	$-0.668053\pi$
$499$	−22.5066			−1.00753			−0.503767	+	0.863840i	$0.668053\pi$
$500$	−9.21933	+	6.32487i	−0.412301	+	0.282857i
$501$	39.4821			1.76393
$502$			24.4894i			1.09302i
$503$		−	23.3660i		−	1.04184i	−0.853606	−	0.520919i	$-0.825589\pi$
$503$		−	23.3660i		−	1.04184i	0.853606	−	0.520919i	$-0.174411\pi$
$504$	0.612127			0.0272663
$505$	−18.8388	−	21.3054i	−0.838313	−	0.948076i
$506$	1.19394			0.0530770
$507$		−	18.5501i		−	0.823838i
$508$			8.70052i			0.386023i
$509$	14.4993			0.642670			0.321335	−	0.946966i	$-0.395868\pi$
$509$	14.4993			0.642670			0.321335	+	0.946966i	$0.395868\pi$
$510$	22.6253	−	20.0059i	1.00187	−	0.885875i
$511$	0.931116			0.0411902
$512$		−	1.00000i		−	0.0441942i
$513$			2.25202i			0.0994289i
$514$	1.03269			0.0455499
$515$	−7.66291	+	6.77575i	−0.337668	+	0.298575i
$516$	2.48119			0.109228
$517$		−	26.7816i		−	1.17785i
$518$		−	1.17584i		−	0.0516634i
$519$	22.1441			0.972018
$520$	3.48119	+	3.93700i	0.152660	+	0.172649i
$521$	22.1744			0.971479			0.485740	−	0.874104i	$-0.338550\pi$
$521$	22.1744			0.971479			0.485740	+	0.874104i	$0.338550\pi$
$522$		−	0.906679i		−	0.0396843i
$523$		−	0.706863i		−	0.0309089i	−0.999881	−	0.0154545i	$-0.995080\pi$
$523$		−	0.706863i		−	0.0309089i	0.999881	−	0.0154545i	$-0.00491951\pi$
$524$	−15.4314			−0.674122
$525$	−0.294552	+	2.38787i	−0.0128553	+	0.104215i
$526$	25.7367			1.12217
$527$			43.6869i			1.90303i
$528$			9.11871i			0.396841i
$529$	22.8945			0.995411
$530$	12.5442	+	14.1866i	0.544885	+	0.616228i
$531$	30.7367			1.33386
$532$		−	1.12601i		−	0.0488186i
$533$		−	5.22758i		−	0.226432i
$534$	−35.8192			−1.55005
$535$	−7.65466	+	6.76845i	−0.330940	+	0.292626i
$536$	3.97461			0.171677
$537$			21.5696i			0.930797i
$538$		−	22.2130i		−	0.957670i
$539$	−25.5877			−1.10214
$540$	−0.649738	+	0.574515i	−0.0279603	+	0.0247232i
$541$	41.2262			1.77245			0.886226	−	0.463254i	$-0.153318\pi$
$541$	41.2262			1.77245			0.886226	+	0.463254i	$0.153318\pi$
$542$			20.4739i			0.879429i
$543$		−	15.4314i		−	0.662223i
$544$	−5.44358			−0.233392
$545$	−14.3127	−	16.1866i	−0.613087	−	0.693360i
$546$	1.13093			0.0483994
$547$			12.6497i			0.540864i	0.962739	+	0.270432i	$0.0871665\pi$
$547$			12.6497i			0.540864i	−0.962739	+	0.270432i	$0.912834\pi$
$548$		−	6.70545i		−	0.286443i
$549$	−5.66196			−0.241646
$550$	−18.2374	−	2.24965i	−0.777647	−	0.0959252i
$551$	−1.66784			−0.0710522
$552$		−	0.806063i		−	0.0343083i
$553$		−	0.473900i		−	0.0201523i
$554$	−4.07522			−0.173140
$555$	22.2823	+	25.1998i	0.945832	+	1.06967i
$556$	−11.8011			−0.500480
$557$		−	6.36485i		−	0.269687i	−0.990867	−	0.134844i	$-0.956947\pi$
$557$		−	6.36485i		−	0.269687i	0.990867	−	0.134844i	$-0.0430532\pi$
$558$		−	25.3307i		−	1.07234i
$559$	2.35026			0.0994055
$560$	0.324869	−	0.287258i	0.0137282	−	0.0121389i
$561$	49.6385			2.09574
$562$		−	23.1114i		−	0.974896i
$563$			11.4871i			0.484122i	0.970261	+	0.242061i	$0.0778235\pi$
$563$			11.4871i			0.484122i	−0.970261	+	0.242061i	$0.922177\pi$
$564$	−18.0811			−0.761352
$565$	−24.0689	+	21.2823i	−1.01259	+	0.895354i
$566$	16.3684			0.688013
$567$		−	1.64974i		−	0.0692825i
$568$		−	11.1817i		−	0.469174i
$569$	−43.9076			−1.84070			−0.920352	−	0.391091i	$-0.872098\pi$
$569$	−43.9076			−1.84070			−0.920352	+	0.391091i	$0.872098\pi$
$570$	21.3380	+	24.1319i	0.893752	+	1.01077i
$571$	−4.20967			−0.176169			−0.0880845	−	0.996113i	$-0.528075\pi$
$571$	−4.20967			−0.176169			−0.0880845	+	0.996113i	$0.528075\pi$
$572$			8.63752i			0.361153i
$573$		−	28.2071i		−	1.17837i
$574$	−0.431364			−0.0180048
$575$	1.61213	+	0.198861i	0.0672303	+	0.00829308i
$576$	3.15633			0.131514
$577$			3.47531i			0.144679i	0.997380	+	0.0723396i	$0.0230465\pi$
$577$			3.47531i			0.144679i	−0.997380	+	0.0723396i	$0.976953\pi$
$578$			12.6326i			0.525447i
$579$	−9.27504			−0.385457
$580$	−0.425485	−	0.481194i	−0.0176673	−	0.0199805i
$581$	3.34438			0.138748
$582$		−	18.4690i		−	0.765564i
$583$			31.1246i			1.28905i
$584$	4.80114			0.198673
$585$	−12.4264	+	10.9878i	−0.513770	+	0.454289i
$586$	30.4993			1.25991
$587$			41.0459i			1.69414i	0.531478	+	0.847072i	$0.321637\pi$
$587$			41.0459i			1.69414i	−0.531478	+	0.847072i	$0.678363\pi$
$588$			17.2750i			0.712411i
$589$	−46.5959			−1.91995
$590$	16.3127	−	14.4241i	0.671581	−	0.593830i
$591$	−61.5814			−2.53312
$592$		−	6.06300i		−	0.249188i
$593$			41.0287i			1.68485i	0.538816	+	0.842424i	$0.318872\pi$
$593$			41.0287i			1.68485i	−0.538816	+	0.842424i	$0.681128\pi$
$594$	−1.42548			−0.0584883
$595$	−1.56371	−	1.76845i	−0.0641059	−	0.0724995i
$596$	−4.25694			−0.174371
$597$			17.1695i			0.702701i
$598$		−	0.763527i		−	0.0312230i
$599$	13.7137			0.560326			0.280163	−	0.959952i	$-0.409611\pi$
$599$	13.7137			0.560326			0.280163	+	0.959952i	$0.409611\pi$
$600$	−1.51881	+	12.3127i	−0.0620050	+	0.502662i
$601$	−48.5764			−1.98147			−0.990737	−	0.135796i	$-0.956641\pi$
$601$	−48.5764			−1.98147			−0.990737	+	0.135796i	$0.956641\pi$
$602$		−	0.193937i		−	0.00790426i
$603$			12.5452i			0.510878i
$604$	14.5745			0.593029
$605$	−3.71274	−	4.19886i	−0.150944	−	0.170708i
$606$	−31.5574			−1.28193
$607$			10.2217i			0.414886i	0.978247	+	0.207443i	$0.0665141\pi$
$607$			10.2217i			0.414886i	−0.978247	+	0.207443i	$0.933486\pi$
$608$		−	5.80606i		−	0.235467i
$609$	−0.138227			−0.00560123
$610$	−3.00492	+	2.65703i	−0.121666	+	0.107580i
$611$	−17.1270			−0.692883
$612$		−	17.1817i		−	0.694530i
$613$		−	32.9756i		−	1.33187i	−0.746010	−	0.665935i	$-0.768033\pi$
$613$		−	32.9756i		−	1.33187i	0.746010	−	0.665935i	$-0.231967\pi$
$614$	2.01951			0.0815009
$615$	9.24472	−	8.17442i	0.372783	−	0.329625i
$616$	0.712742			0.0287172
$617$			5.01317i			0.201823i	0.994895	+	0.100911i	$0.0321759\pi$
$617$			5.01317i			0.201823i	−0.994895	+	0.100911i	$0.967824\pi$
$618$			11.3503i			0.456574i
$619$	4.96476			0.199550			0.0997752	−	0.995010i	$-0.468188\pi$
$619$	4.96476			0.199550			0.0997752	+	0.995010i	$0.468188\pi$
$620$	−11.8872	−	13.4436i	−0.477400	−	0.539907i
$621$	0.126008			0.00505653
$622$		−	13.7431i		−	0.551046i
$623$			2.79972i			0.112169i
$624$	5.83146			0.233445
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	14.3127			0.572049
$627$			52.9438i			2.11437i
$628$		−	21.8373i		−	0.871405i
$629$	−33.0045			−1.31597
$630$	0.906679	+	1.02539i	0.0361229	+	0.0408526i
$631$	41.6664			1.65871			0.829357	−	0.558719i	$-0.188707\pi$
$631$	41.6664			1.65871			0.829357	+	0.558719i	$0.188707\pi$
$632$		−	2.44358i		−	0.0972005i
$633$		−	45.1002i		−	1.79257i
$634$	8.89446			0.353244
$635$	−14.5745	+	12.8872i	−0.578372	+	0.511412i
$636$	21.0132			0.833227
$637$			16.3634i			0.648343i
$638$		−	1.05571i		−	0.0417960i
$639$	35.2931			1.39617
$640$	1.67513	−	1.48119i	0.0662154	−	0.0585493i
$641$	−26.0870			−1.03037			−0.515187	−	0.857078i	$-0.672277\pi$
$641$	−26.0870			−1.03037			−0.515187	+	0.857078i	$0.672277\pi$
$642$			11.3380i			0.447477i
$643$		−	24.9067i		−	0.982224i	−0.871097	−	0.491112i	$-0.836591\pi$
$643$		−	24.9067i		−	0.982224i	0.871097	−	0.491112i	$-0.163409\pi$
$644$	−0.0630040			−0.00248271
$645$	3.67513	+	4.15633i	0.144708	+	0.163655i
$646$	−31.6058			−1.24351
$647$			42.4617i			1.66934i	0.550750	+	0.834670i	$0.314342\pi$
$647$			42.4617i			1.66934i	−0.550750	+	0.834670i	$0.685658\pi$
$648$		−	8.50659i		−	0.334170i
$649$	35.7889			1.40484
$650$	−1.43866	+	11.6629i	−0.0564288	+	0.457457i
$651$	−3.86177			−0.151355
$652$			0.312650i			0.0122443i
$653$			28.4509i			1.11337i	0.830724	+	0.556684i	$0.187927\pi$
$653$			28.4509i			1.11337i	−0.830724	+	0.556684i	$0.812073\pi$
$654$	−23.9756			−0.937519
$655$	−22.8568	−	25.8496i	−0.893091	−	1.01003i
$656$	−2.22425			−0.0868425
$657$			15.1540i			0.591212i
$658$			1.41327i			0.0550948i
$659$	−27.7866			−1.08241			−0.541205	−	0.840891i	$-0.682032\pi$
$659$	−27.7866			−1.08241			−0.541205	+	0.840891i	$0.682032\pi$
$660$	−15.2750	+	13.5066i	−0.594580	+	0.525743i
$661$	−23.2424			−0.904023			−0.452011	−	0.892012i	$-0.649293\pi$
$661$	−23.2424			−0.904023			−0.452011	+	0.892012i	$0.649293\pi$
$662$		−	4.88129i		−	0.189717i
$663$		−	31.7440i		−	1.23284i
$664$	17.2447			0.669225
$665$	1.88621	−	1.66784i	0.0731441	−	0.0646759i
$666$	19.1368			0.741536
$667$			0.0933212i			0.00361341i
$668$		−	15.9126i		−	0.615675i
$669$	−6.18664			−0.239189
$670$	5.88717	+	6.65799i	0.227441	+	0.257220i
$671$	−6.59261			−0.254505
$672$		−	0.481194i		−	0.0185625i
$673$		−	25.9864i		−	1.00170i	−0.865534	−	0.500850i	$-0.833021\pi$
$673$		−	25.9864i		−	1.00170i	0.865534	−	0.500850i	$-0.166979\pi$
$674$	−21.2506			−0.818543
$675$	−1.92478	−	0.237428i	−0.0740847	−	0.00913859i
$676$	−7.47627			−0.287549
$677$			13.9854i			0.537503i	0.963210	+	0.268752i	$0.0866110\pi$
$677$			13.9854i			0.537503i	−0.963210	+	0.268752i	$0.913389\pi$
$678$			35.6507i			1.36916i
$679$	−1.44358			−0.0553996
$680$	−8.06300	−	9.11871i	−0.309202	−	0.349687i
$681$	−44.9380			−1.72203
$682$		−	29.4944i		−	1.12940i
$683$		−	26.0752i		−	0.997741i	−0.866677	−	0.498870i	$-0.833748\pi$
$683$		−	26.0752i		−	0.997741i	0.866677	−	0.498870i	$-0.166252\pi$
$684$	18.3258			0.700705
$685$	11.2325	−	9.93207i	0.429172	−	0.379485i
$686$	2.70782			0.103385
$687$		−	14.4241i		−	0.550313i
$688$		−	1.00000i		−	0.0381246i
$689$	19.9043			0.758294
$690$	1.35026	−	1.19394i	0.0514036	−	0.0454524i
$691$	−49.8192			−1.89521			−0.947607	−	0.319440i	$-0.896505\pi$
$691$	−49.8192			−1.89521			−0.947607	+	0.319440i	$0.896505\pi$
$692$		−	8.92478i		−	0.339269i
$693$			2.24965i			0.0854570i
$694$	−27.9330			−1.06032
$695$	−17.4798	−	19.7685i	−0.663046	−	0.749860i
$696$	−0.712742			−0.0270164
$697$			12.1079i			0.458620i
$698$		−	12.5745i		−	0.475952i
$699$	28.7367			1.08692
$700$	0.962389	+	0.118714i	0.0363749	+	0.00448696i
$701$	−33.9429			−1.28200			−0.641002	−	0.767539i	$-0.721481\pi$
$701$	−33.9429			−1.28200			−0.641002	+	0.767539i	$0.721481\pi$
$702$			0.911603i			0.0344063i
$703$		−	35.2022i		−	1.32768i
$704$	3.67513			0.138512
$705$	−26.7816	−	30.2882i	−1.00865	−	1.14072i
$706$	−28.6190			−1.07709
$707$			2.46661i			0.0927663i
$708$		−	24.1622i		−	0.908071i
$709$	23.3077			0.875340			0.437670	−	0.899136i	$-0.355804\pi$
$709$	23.3077			0.875340			0.437670	+	0.899136i	$0.355804\pi$
$710$	18.7308	−	16.5623i	0.702956	−	0.621572i
$711$	7.71274			0.289250
$712$			14.4363i			0.541023i
$713$			2.60720i			0.0976405i
$714$	−2.61942			−0.0980294
$715$	−14.4690	+	12.7938i	−0.541109	+	0.478463i
$716$	8.69323			0.324881
$717$		−	61.7377i		−	2.30564i
$718$			23.6678i			0.883276i
$719$	−43.4215			−1.61935			−0.809675	−	0.586879i	$-0.800356\pi$
$719$	−43.4215			−1.61935			−0.809675	+	0.586879i	$0.800356\pi$
$720$	4.67513	+	5.28726i	0.174232	+	0.197044i
$721$	0.887166			0.0330398
$722$		−	14.7104i		−	0.547463i
$723$			39.9814i			1.48693i
$724$	−6.21933			−0.231140
$725$	0.175838	−	1.42548i	0.00653047	−	0.0529412i
$726$	−6.21933			−0.230821
$727$			34.2941i			1.27190i	0.771731	+	0.635949i	$0.219391\pi$
$727$			34.2941i			1.27190i	−0.771731	+	0.635949i	$0.780609\pi$
$728$		−	0.455802i		−	0.0168931i
$729$	29.7367			1.10136
$730$	7.11142	+	8.04254i	0.263205	+	0.297668i
$731$	−5.44358			−0.201338
$732$			4.45088i			0.164509i
$733$			20.9765i			0.774785i	0.921915	+	0.387393i	$0.126624\pi$
$733$			20.9765i			0.774785i	−0.921915	+	0.387393i	$0.873376\pi$
$734$	−23.0640			−0.851306
$735$	−28.9380	+	25.5877i	−1.06739	+	0.943816i
$736$	−0.324869			−0.0119748
$737$			14.6072i			0.538063i
$738$		−	7.02047i		−	0.258427i
$739$	50.8251			1.86963			0.934816	−	0.355132i	$-0.115564\pi$
$739$	50.8251			1.86963			0.934816	+	0.355132i	$0.115564\pi$
$740$	10.1563	−	8.98049i	0.373354	−	0.330129i
$741$	33.8578			1.24380
$742$		−	1.64244i		−	0.0602960i
$743$			21.5902i			0.792069i	0.918236	+	0.396035i	$0.129614\pi$
$743$			21.5902i			0.792069i	−0.918236	+	0.396035i	$0.870386\pi$
$744$	−19.9126			−0.730030
$745$	−6.30536	−	7.13093i	−0.231010	−	0.261257i
$746$	−3.67513			−0.134556
$747$			54.4299i			1.99149i
$748$		−	20.0059i		−	0.731487i
$749$	0.886211			0.0323814
$750$	−22.8749	+	15.6932i	−0.835275	+	0.573036i
$751$	−8.01810			−0.292585			−0.146292	−	0.989241i	$-0.546734\pi$
$751$	−8.01810			−0.292585			−0.146292	+	0.989241i	$0.546734\pi$
$752$			7.28726i			0.265739i
$753$			60.7631i			2.21433i
$754$	−0.675131			−0.0245868
$755$	21.5877	+	24.4142i	0.785656	+	0.888524i
$756$	0.0752228			0.00273583
$757$		−	23.7499i		−	0.863205i	−0.902064	−	0.431602i	$-0.857948\pi$
$757$		−	23.7499i		−	0.863205i	0.902064	−	0.431602i	$-0.142052\pi$
$758$		−	17.7743i		−	0.645593i
$759$	2.96239			0.107528
$760$	9.72592	−	8.59991i	0.352796	−	0.311951i
$761$	40.7974			1.47890			0.739451	−	0.673210i	$-0.235085\pi$
$761$	40.7974			1.47890			0.739451	+	0.673210i	$0.235085\pi$
$762$			21.5877i			0.782039i
$763$			1.87399i			0.0678431i
$764$	−11.3684			−0.411293
$765$	28.7816	−	25.4495i	1.04060	−	0.920127i
$766$	−2.41090			−0.0871092
$767$		−	22.8872i		−	0.826408i
$768$		−	2.48119i		−	0.0895324i
$769$	19.9683			0.720074			0.360037	−	0.932938i	$-0.382764\pi$
$769$	19.9683			0.720074			0.360037	+	0.932938i	$0.382764\pi$
$770$	1.05571	+	1.19394i	0.0380451	+	0.0430265i
$771$	2.56230			0.0922789
$772$			3.73813i			0.134538i
$773$			10.8895i			0.391669i	0.980637	+	0.195835i	$0.0627416\pi$
$773$			10.8895i			0.391669i	−0.980637	+	0.195835i	$0.937258\pi$
$774$	3.15633			0.113452
$775$	4.91256	−	39.8251i	0.176464	−	1.43056i
$776$	−7.44358			−0.267209
$777$		−	2.91748i		−	0.104664i
$778$		−	18.8773i		−	0.676785i
$779$	−12.9142			−0.462698
$780$	8.63752	+	9.76845i	0.309273	+	0.349767i
$781$	41.0943			1.47047
$782$			1.76845i			0.0632397i
$783$		−	0.111420i		−	0.00398181i
$784$	6.96239			0.248657
$785$	36.5804	−	32.3453i	1.30561	−	1.15445i
$786$	−38.2882			−1.36570
$787$			24.2482i			0.864356i	0.901788	+	0.432178i	$0.142255\pi$
$787$			24.2482i			0.864356i	−0.901788	+	0.432178i	$0.857745\pi$
$788$			24.8192i			0.884149i
$789$	63.8578			2.27340
$790$	4.09332	−	3.61942i	0.145634	−	0.128773i
$791$	2.78655			0.0990783
$792$			11.5999i			0.412185i
$793$			4.21600i			0.149715i
$794$	−16.8061			−0.596425
$795$	31.1246	+	35.1998i	1.10388	+	1.24841i
$796$	6.91985			0.245268
$797$			12.1187i			0.429267i	0.976695	+	0.214633i	$0.0688557\pi$
$797$			12.1187i			0.429267i	−0.976695	+	0.214633i	$0.931144\pi$
$798$		−	2.79384i		−	0.0989010i
$799$	39.6688			1.40338
$800$	4.96239	+	0.612127i	0.175447	+	0.0216420i
$801$	−45.5656			−1.60998
$802$		−	26.6385i		−	0.940637i
$803$			17.6448i			0.622672i
$804$	9.86177			0.347798
$805$	−0.0933212	−	0.105540i	−0.00328914	−	0.00371979i
$806$	−18.8618			−0.664378
$807$		−	55.1147i		−	1.94013i
$808$			12.7186i			0.447440i
$809$	0.356141			0.0125213			0.00626063	−	0.999980i	$-0.498007\pi$
$809$	0.356141			0.0125213			0.00626063	+	0.999980i	$0.498007\pi$
$810$	14.2496	−	12.5999i	0.500682	−	0.442716i
$811$	23.4749			0.824314			0.412157	−	0.911113i	$-0.364776\pi$
$811$	23.4749			0.824314			0.412157	+	0.911113i	$0.364776\pi$
$812$			0.0557098i			0.00195503i
$813$			50.7997i			1.78162i
$814$	22.2823			0.780995
$815$	−0.523730	+	0.463096i	−0.0183455	+	0.0162215i
$816$	−13.5066			−0.472825
$817$		−	5.80606i		−	0.203128i
$818$			16.6131i			0.580863i
$819$	1.43866			0.0502708
$820$	−3.29455	−	3.72592i	−0.115051	−	0.130115i
$821$	−27.9610			−0.975845			−0.487922	−	0.872887i	$-0.662245\pi$
$821$	−27.9610			−0.975845			−0.487922	+	0.872887i	$0.662245\pi$
$822$		−	16.6375i		−	0.580300i
$823$		−	38.1260i		−	1.32899i	−0.747293	−	0.664495i	$-0.768647\pi$
$823$		−	38.1260i		−	1.32899i	0.747293	−	0.664495i	$-0.231353\pi$
$824$	4.57452			0.159361
$825$	−45.2506	−	5.58181i	−1.57542	−	0.194334i
$826$	−1.88858			−0.0657121
$827$			42.0372i			1.46177i	0.682498	+	0.730887i	$0.260894\pi$
$827$			42.0372i			1.46177i	−0.682498	+	0.730887i	$0.739106\pi$
$828$		−	1.02539i		−	0.0356349i
$829$	9.31028			0.323359			0.161680	−	0.986843i	$-0.448309\pi$
$829$	9.31028			0.323359			0.161680	+	0.986843i	$0.448309\pi$
$830$	25.5428	+	28.8872i	0.886603	+	1.00269i
$831$	−10.1114			−0.350761
$832$		−	2.35026i		−	0.0814807i
$833$		−	37.9003i		−	1.31317i
$834$	−29.2809			−1.01392
$835$	26.6556	−	23.5696i	0.922456	−	0.815659i
$836$	21.3380			0.737992
$837$		−	3.11283i		−	0.107595i
$838$			11.9683i			0.413437i
$839$	−3.19157			−0.110185			−0.0550926	−	0.998481i	$-0.517545\pi$
$839$	−3.19157			−0.110185			−0.0550926	+	0.998481i	$0.517545\pi$
$840$	0.806063	−	0.712742i	0.0278118	−	0.0245919i
$841$	−28.9175			−0.997155
$842$		−	10.2727i		−	0.354020i
$843$		−	57.3439i		−	1.97503i
$844$	−18.1768			−0.625671
$845$	−11.0738	−	12.5237i	−0.380951	−	0.430829i
$846$	−23.0010			−0.790789
$847$			0.486119i			0.0167032i
$848$		−	8.46898i		−	0.290826i
$849$	40.6131			1.39384
$850$	3.33216	−	27.0132i	0.114292	−	0.926544i
$851$	−1.96968			−0.0675199
$852$		−	27.7440i		−	0.950494i
$853$		−	0.0507852i		−	0.00173885i	−1.00000		0.000869426i	$-0.999723\pi$
$853$		−	0.0507852i		−	0.00173885i	1.00000		0.000869426i	$-0.000276747\pi$
$854$	0.347892			0.0119046
$855$	27.1441	+	30.6982i	0.928309	+	1.04985i
$856$	4.56959			0.156185
$857$			20.3453i			0.694983i	0.937683	+	0.347492i	$0.112967\pi$
$857$			20.3453i			0.694983i	−0.937683	+	0.347492i	$0.887033\pi$
$858$			21.4314i			0.731655i
$859$	−14.0494			−0.479358			−0.239679	−	0.970852i	$-0.577042\pi$
$859$	−14.0494			−0.479358			−0.239679	+	0.970852i	$0.577042\pi$
$860$	1.67513	−	1.48119i	0.0571215	−	0.0505083i
$861$	−1.07030			−0.0364757
$862$			28.8423i			0.982371i
$863$			24.0205i			0.817666i	0.912609	+	0.408833i	$0.134064\pi$
$863$			24.0205i			0.817666i	−0.912609	+	0.408833i	$0.865936\pi$
$864$	0.387873			0.0131957
$865$	14.9502	−	13.2193i	0.508321	−	0.449471i
$866$	−37.2760			−1.26669
$867$			31.3439i			1.06450i
$868$			1.55642i			0.0528282i
$869$	8.98049			0.304642
$870$	−1.05571	−	1.19394i	−0.0357919	−	0.0404782i
$871$	9.34137			0.316520
$872$			9.66291i			0.327227i
$873$		−	23.4944i		−	0.795164i
$874$	−1.88621			−0.0638020
$875$	1.22662	+	1.78797i	0.0414674	+	0.0604443i
$876$	11.9126			0.402488
$877$		−	15.4460i		−	0.521573i	−0.965397	−	0.260786i	$-0.916018\pi$
$877$		−	15.4460i		−	0.521573i	0.965397	−	0.260786i	$-0.0839818\pi$
$878$		−	27.9102i		−	0.941923i
$879$	75.6747			2.55244
$880$	5.44358	+	6.15633i	0.183503	+	0.207530i
$881$	50.4274			1.69894			0.849471	−	0.527635i	$-0.176921\pi$
$881$	50.4274			1.69894			0.849471	+	0.527635i	$0.176921\pi$
$882$			21.9756i			0.739956i
$883$		−	35.5682i		−	1.19696i	−0.801136	−	0.598482i	$-0.795771\pi$
$883$		−	35.5682i		−	1.19696i	0.801136	−	0.598482i	$-0.204229\pi$
$884$	−12.7938			−0.430304
$885$	40.4749	−	35.7889i	1.36055	−	1.20303i
$886$	−7.29455			−0.245065
$887$		−	16.8251i		−	0.564932i	−0.959277	−	0.282466i	$-0.908848\pi$
$887$		−	16.8251i		−	0.564932i	0.959277	−	0.282466i	$-0.0911525\pi$
$888$		−	15.0435i		−	0.504827i
$889$	1.68735			0.0565919
$890$	−24.1827	+	21.3829i	−0.810605	+	0.716758i
$891$	31.2628			1.04734
$892$			2.49341i			0.0834856i
$893$			42.3103i			1.41586i
$894$	−10.5623			−0.353256
$895$	12.8764	+	14.5623i	0.430409	+	0.486764i
$896$	−0.193937			−0.00647897
$897$		−	1.89446i		−	0.0632542i
$898$			31.9633i			1.06663i
$899$	2.30536			0.0768879
$900$	−1.93207	+	15.6629i	−0.0644024	+	0.522097i
$901$	−46.1016			−1.53587
$902$		−	8.17442i		−	0.272179i
$903$		−	0.481194i		−	0.0160131i
$904$	14.3684			0.477885
$905$	−9.21203	−	10.4182i	−0.306218	−	0.346312i
$906$	36.1622			1.20141
$907$		−	15.8096i		−	0.524948i	−0.964939	−	0.262474i	$-0.915462\pi$
$907$		−	15.8096i		−	0.524948i	0.964939	−	0.262474i	$-0.0845384\pi$
$908$			18.1114i			0.601049i
$909$	−40.1441			−1.33150
$910$	0.763527	−	0.675131i	0.0253107	−	0.0223804i
$911$	26.3815			0.874059			0.437030	−	0.899447i	$-0.356030\pi$
$911$	26.3815			0.874059			0.437030	+	0.899447i	$0.356030\pi$
$912$		−	14.4060i		−	0.477029i
$913$			63.3766i			2.09746i
$914$	−18.3733			−0.607734
$915$	−7.45580	+	6.59261i	−0.246481	+	0.217945i
$916$	−5.81336			−0.192079
$917$			2.99271i			0.0988279i
$918$		−	2.11142i		−	0.0696872i
$919$	7.05315			0.232662			0.116331	−	0.993210i	$-0.462887\pi$
$919$	7.05315			0.232662			0.116331	+	0.993210i	$0.462887\pi$
$920$	−0.481194	−	0.544198i	−0.0158645	−	0.0179417i
$921$	5.01080			0.165112
$922$			40.6697i			1.33939i
$923$		−	26.2800i		−	0.865016i
$924$	1.76845			0.0581778
$925$	30.0870	+	3.71133i	0.989254	+	0.122028i
$926$	41.8178			1.37422
$927$			14.4387i			0.474228i
$928$			0.287258i			0.00942970i
$929$	−3.64832			−0.119698			−0.0598488	−	0.998207i	$-0.519062\pi$
$929$	−3.64832			−0.119698			−0.0598488	+	0.998207i	$0.519062\pi$
$930$	−29.4944	−	33.3561i	−0.967158	−	1.09379i
$931$	40.4241			1.32485
$932$		−	11.5818i		−	0.379375i
$933$		−	34.0992i		−	1.11636i
$934$	−14.9805			−0.490177
$935$	33.5125	−	29.6326i	1.09597	−	0.969089i
$936$	7.41819			0.242471
$937$			4.62927i			0.151232i	0.997137	+	0.0756158i	$0.0240923\pi$
$937$			4.62927i			0.151232i	−0.997137	+	0.0756158i	$0.975908\pi$
$938$		−	0.770822i		−	0.0251682i
$939$	35.5125			1.15891
$940$	−12.2071	+	10.7938i	−0.398152	+	0.352056i
$941$	−41.6156			−1.35663			−0.678315	−	0.734771i	$-0.737290\pi$
$941$	−41.6156			−1.35663			−0.678315	+	0.734771i	$0.737290\pi$
$942$		−	54.1827i		−	1.76537i
$943$			0.722591i			0.0235308i
$944$	−9.73813			−0.316949
$945$	0.111420	+	0.126008i	0.00362448	+	0.00409904i
$946$	3.67513			0.119489
$947$		−	25.7344i		−	0.836254i	−0.908389	−	0.418127i	$-0.862687\pi$
$947$		−	25.7344i		−	0.836254i	0.908389	−	0.418127i	$-0.137313\pi$
$948$		−	6.06300i		−	0.196917i
$949$	11.2839			0.366292
$950$	28.8119	+	3.55405i	0.934783	+	0.115309i
$951$	22.0689			0.715633
$952$			1.05571i			0.0342158i
$953$			14.2062i			0.460183i	0.973169	+	0.230091i	$0.0739025\pi$
$953$			14.2062i			0.460183i	−0.973169	+	0.230091i	$0.926098\pi$
$954$	26.7308			0.865443
$955$	−16.8388	−	19.0435i	−0.544889	−	0.616233i
$956$	−24.8822			−0.804749
$957$		−	2.61942i		−	0.0846739i
$958$			10.6399i			0.343759i
$959$	−1.30043			−0.0419931
$960$	4.15633	−	3.67513i	0.134145	−	0.118614i
$961$	33.4069			1.07764
$962$		−	14.2496i		−	0.459427i
$963$			14.4231i			0.464778i
$964$	16.1138			0.518990
$965$	−6.26187	+	5.53690i	−0.201577	+	0.178239i
$966$	−0.156325			−0.00502968
$967$		−	24.2642i		−	0.780285i	−0.920754	−	0.390143i	$-0.872426\pi$
$967$		−	24.2642i		−	0.780285i	0.920754	−	0.390143i	$-0.127574\pi$
$968$			2.50659i			0.0805648i
$969$	−78.4201			−2.51922
$970$	−11.0254	−	12.4690i	−0.354004	−	0.400355i
$971$	−5.36248			−0.172090			−0.0860451	−	0.996291i	$-0.527423\pi$
$971$	−5.36248			−0.172090			−0.0860451	+	0.996291i	$0.527423\pi$
$972$		−	22.2701i		−	0.714314i
$973$			2.28867i			0.0733715i
$974$	38.4119			1.23080
$975$	−3.56959	+	28.9380i	−0.114318	+	0.926756i
$976$	1.79384			0.0574196
$977$		−	46.1314i		−	1.47588i	−0.674869	−	0.737938i	$-0.735800\pi$
$977$		−	46.1314i		−	1.47588i	0.674869	−	0.737938i	$-0.264200\pi$
$978$			0.775746i			0.0248056i
$979$	−53.0553			−1.69565
$980$	10.3127	+	11.6629i	0.329426	+	0.372558i
$981$	−30.4993			−0.973767
$982$		−	7.11871i		−	0.227167i
$983$			27.1465i			0.865838i	0.901433	+	0.432919i	$0.142516\pi$
$983$			27.1465i			0.865838i	−0.901433	+	0.432919i	$0.857484\pi$
$984$	−5.51881			−0.175933
$985$	−41.5755	+	36.7621i	−1.32470	+	1.17134i
$986$	1.56371			0.0497987
$987$			3.50659i			0.111616i
$988$		−	13.6458i		−	0.434130i
$989$	−0.324869			−0.0103302
$990$	−19.4314	+	17.1817i	−0.617569	+	0.546071i
$991$	50.8745			1.61608			0.808041	−	0.589127i	$-0.200528\pi$
$991$	50.8745			1.61608			0.808041	+	0.589127i	$0.200528\pi$
$992$			8.02539i			0.254806i
$993$		−	12.1114i		−	0.384344i
$994$	−2.16854			−0.0687820
$995$	10.2496	+	11.5917i	0.324936	+	0.367480i
$996$	42.7875			1.35577
$997$		−	48.3488i		−	1.53122i	−0.643303	−	0.765612i	$-0.722436\pi$
$997$		−	48.3488i		−	1.53122i	0.643303	−	0.765612i	$-0.277564\pi$
$998$			22.5066i			0.712434i
$999$	2.35168			0.0744037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.a.259.1	✓	6
5.2	odd	4		2150.2.a.bd.1.1		3
5.3	odd	4		2150.2.a.bc.1.3		3
5.4	even	2	inner	430.2.b.a.259.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.a.259.1	✓	6	1.1	even	1	trivial
430.2.b.a.259.6	yes	6	5.4	even	2	inner
2150.2.a.bc.1.3		3	5.3	odd	4
2150.2.a.bd.1.1		3	5.2	odd	4

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.48119i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} -2.48119 q^{6} +0.193937i q^{7} +1.00000i q^{8} -3.15633 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.48119i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} -2.48119 q^{6} +0.193937i q^{7} +1.00000i q^{8} -3.15633 q^{9} +(-1.67513 + 1.48119i) q^{10} -3.67513 q^{11} +2.48119i q^{12} +2.35026i q^{13} +0.193937 q^{14} +(-4.15633 + 3.67513i) q^{15} +1.00000 q^{16} -5.44358i q^{17} +3.15633i q^{18} +5.80606 q^{19} +(1.48119 + 1.67513i) q^{20} +0.481194 q^{21} +3.67513i q^{22} -0.324869i q^{23} +2.48119 q^{24} +(-0.612127 + 4.96239i) q^{25} +2.35026 q^{26} +0.387873i q^{27} -0.193937i q^{28} -0.287258 q^{29} +(3.67513 + 4.15633i) q^{30} -8.02539 q^{31} -1.00000i q^{32} +9.11871i q^{33} -5.44358 q^{34} +(0.324869 - 0.287258i) q^{35} +3.15633 q^{36} -6.06300i q^{37} -5.80606i q^{38} +5.83146 q^{39} +(1.67513 - 1.48119i) q^{40} -2.22425 q^{41} -0.481194i q^{42} -1.00000i q^{43} +3.67513 q^{44} +(4.67513 + 5.28726i) q^{45} -0.324869 q^{46} +7.28726i q^{47} -2.48119i q^{48} +6.96239 q^{49} +(4.96239 + 0.612127i) q^{50} -13.5066 q^{51} -2.35026i q^{52} -8.46898i q^{53} +0.387873 q^{54} +(5.44358 + 6.15633i) q^{55} -0.193937 q^{56} -14.4060i q^{57} +0.287258i q^{58} -9.73813 q^{59} +(4.15633 - 3.67513i) q^{60} +1.79384 q^{61} +8.02539i q^{62} -0.612127i q^{63} -1.00000 q^{64} +(3.93700 - 3.48119i) q^{65} +9.11871 q^{66} -3.97461i q^{67} +5.44358i q^{68} -0.806063 q^{69} +(-0.287258 - 0.324869i) q^{70} -11.1817 q^{71} -3.15633i q^{72} -4.80114i q^{73} -6.06300 q^{74} +(12.3127 + 1.51881i) q^{75} -5.80606 q^{76} -0.712742i q^{77} -5.83146i q^{78} -2.44358 q^{79} +(-1.48119 - 1.67513i) q^{80} -8.50659 q^{81} +2.22425i q^{82} -17.2447i q^{83} -0.481194 q^{84} +(-9.11871 + 8.06300i) q^{85} -1.00000 q^{86} +0.712742i q^{87} -3.67513i q^{88} +14.4363 q^{89} +(5.28726 - 4.67513i) q^{90} -0.455802 q^{91} +0.324869i q^{92} +19.9126i q^{93} +7.28726 q^{94} +(-8.59991 - 9.72592i) q^{95} -2.48119 q^{96} +7.44358i q^{97} -6.96239i q^{98} +11.5999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

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