LMFDB - Embedded newform 430.2.b.b.259.15

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 525x^{12} + 3518x^{10} + 12216x^{8} + 20990x^{6} + 15229x^{4} + 4754x^{2} + 529 $ x^16 + 38x^14 + 525x^12 + 3518x^10 + 12216x^8 + 20990x^6 + 15229x^4 + 4754*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.15
Root			$2.39034i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.b.259.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.39034i q^{3} -1.00000 q^{4} +(-1.86897 - 1.22758i) q^{5} -1.39034 q^{6} -4.65953i q^{7} -1.00000i q^{8} +1.06694 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.39034i q^{3} -1.00000 q^{4} +(-1.86897 - 1.22758i) q^{5} -1.39034 q^{6} -4.65953i q^{7} -1.00000i q^{8} +1.06694 q^{9} +(1.22758 - 1.86897i) q^{10} -1.52460 q^{11} -1.39034i q^{12} +0.137421i q^{13} +4.65953 q^{14} +(1.70676 - 2.59851i) q^{15} +1.00000 q^{16} -6.04088i q^{17} +1.06694i q^{18} -2.92160 q^{19} +(1.86897 + 1.22758i) q^{20} +6.47835 q^{21} -1.52460i q^{22} -7.26253i q^{23} +1.39034 q^{24} +(1.98607 + 4.58863i) q^{25} -0.137421 q^{26} +5.65445i q^{27} +4.65953i q^{28} -4.57775 q^{29} +(2.59851 + 1.70676i) q^{30} +10.0499 q^{31} +1.00000i q^{32} -2.11972i q^{33} +6.04088 q^{34} +(-5.71997 + 8.70851i) q^{35} -1.06694 q^{36} +4.34410i q^{37} -2.92160i q^{38} -0.191062 q^{39} +(-1.22758 + 1.86897i) q^{40} -1.53008 q^{41} +6.47835i q^{42} -1.00000i q^{43} +1.52460 q^{44} +(-1.99408 - 1.30976i) q^{45} +7.26253 q^{46} -5.65266i q^{47} +1.39034i q^{48} -14.7112 q^{49} +(-4.58863 + 1.98607i) q^{50} +8.39891 q^{51} -0.137421i q^{52} +1.32571i q^{53} -5.65445 q^{54} +(2.84942 + 1.87157i) q^{55} -4.65953 q^{56} -4.06203i q^{57} -4.57775i q^{58} -10.2566 q^{59} +(-1.70676 + 2.59851i) q^{60} +5.50689 q^{61} +10.0499i q^{62} -4.97146i q^{63} -1.00000 q^{64} +(0.168695 - 0.256835i) q^{65} +2.11972 q^{66} -11.2492i q^{67} +6.04088i q^{68} +10.0974 q^{69} +(-8.70851 - 5.71997i) q^{70} -4.33949 q^{71} -1.06694i q^{72} -1.66202i q^{73} -4.34410 q^{74} +(-6.37977 + 2.76133i) q^{75} +2.92160 q^{76} +7.10392i q^{77} -0.191062i q^{78} +8.24935 q^{79} +(-1.86897 - 1.22758i) q^{80} -4.66080 q^{81} -1.53008i q^{82} -15.2103i q^{83} -6.47835 q^{84} +(-7.41569 + 11.2902i) q^{85} +1.00000 q^{86} -6.36465i q^{87} +1.52460i q^{88} +11.3802 q^{89} +(1.30976 - 1.99408i) q^{90} +0.640316 q^{91} +7.26253i q^{92} +13.9728i q^{93} +5.65266 q^{94} +(5.46037 + 3.58651i) q^{95} -1.39034 q^{96} -0.210818i q^{97} -14.7112i q^{98} -1.62666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9	$ 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9} + 4 q^{11} - 6 q^{14} - 4 q^{15} + 16 q^{16} - 30 q^{19} - 2 q^{20} + 32 q^{21} - 8 q^{24} - 10 q^{25} - 6 q^{26} + 6 q^{29} - 12 q^{30} + 50 q^{31} - 36 q^{35} + 28 q^{36} - 4 q^{39} + 38 q^{41} - 4 q^{44} - 50 q^{45} + 24 q^{46} - 38 q^{49} - 8 q^{50} + 8 q^{51} - 20 q^{54} - 28 q^{55} + 6 q^{56} + 24 q^{59} + 4 q^{60} + 58 q^{61} - 16 q^{64} - 32 q^{65} + 36 q^{66} - 4 q^{69} - 22 q^{70} + 24 q^{71} + 4 q^{74} - 36 q^{75} + 30 q^{76} - 10 q^{79} + 2 q^{80} + 80 q^{81} - 32 q^{84} - 56 q^{85} + 16 q^{86} + 40 q^{89} - 22 q^{90} + 46 q^{91} - 12 q^{94} - 52 q^{95} + 8 q^{96} + 32 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9 + 4 * q^11 - 6 * q^14 - 4 * q^15 + 16 * q^16 - 30 * q^19 - 2 * q^20 + 32 * q^21 - 8 * q^24 - 10 * q^25 - 6 * q^26 + 6 * q^29 - 12 * q^30 + 50 * q^31 - 36 * q^35 + 28 * q^36 - 4 * q^39 + 38 * q^41 - 4 * q^44 - 50 * q^45 + 24 * q^46 - 38 * q^49 - 8 * q^50 + 8 * q^51 - 20 * q^54 - 28 * q^55 + 6 * q^56 + 24 * q^59 + 4 * q^60 + 58 * q^61 - 16 * q^64 - 32 * q^65 + 36 * q^66 - 4 * q^69 - 22 * q^70 + 24 * q^71 + 4 * q^74 - 36 * q^75 + 30 * q^76 - 10 * q^79 + 2 * q^80 + 80 * q^81 - 32 * q^84 - 56 * q^85 + 16 * q^86 + 40 * q^89 - 22 * q^90 + 46 * q^91 - 12 * q^94 - 52 * q^95 + 8 * q^96 + 32 * 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
$3$			1.39034i			0.802715i	0.915921	+	0.401358i	$0.131462\pi$
$3$			1.39034i			0.802715i	−0.915921	+	0.401358i	$0.868538\pi$
$4$	−1.00000			−0.500000
$5$	−1.86897	−	1.22758i	−0.835827	−	0.548992i
$5$	−1.86897	−	1.22758i	−0.835827	−	0.548992i
$6$	−1.39034			−0.567606
$7$		−	4.65953i		−	1.76114i	−0.473918	−	0.880569i	$-0.657161\pi$
$7$		−	4.65953i		−	1.76114i	0.473918	−	0.880569i	$-0.342839\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.06694			0.355648
$10$	1.22758	−	1.86897i	0.388196	−	0.591019i
$11$	−1.52460			−0.459684			−0.229842	−	0.973228i	$-0.573821\pi$
$11$	−1.52460			−0.459684			−0.229842	+	0.973228i	$0.573821\pi$
$12$		−	1.39034i		−	0.401358i
$13$			0.137421i			0.0381136i	0.999818	+	0.0190568i	$0.00606634\pi$
$13$			0.137421i			0.0381136i	−0.999818	+	0.0190568i	$0.993934\pi$
$14$	4.65953			1.24531
$15$	1.70676	−	2.59851i	0.440685	−	0.670932i
$16$	1.00000			0.250000
$17$		−	6.04088i		−	1.46513i	−0.680697	−	0.732565i	$-0.738323\pi$
$17$		−	6.04088i		−	1.46513i	0.680697	−	0.732565i	$-0.261677\pi$
$18$			1.06694i			0.251481i
$19$	−2.92160			−0.670261			−0.335130	−	0.942172i	$-0.608780\pi$
$19$	−2.92160			−0.670261			−0.335130	+	0.942172i	$0.608780\pi$
$20$	1.86897	+	1.22758i	0.417914	+	0.274496i
$21$	6.47835			1.41369
$22$		−	1.52460i		−	0.325045i
$23$		−	7.26253i		−	1.51434i	−0.653216	−	0.757171i	$-0.726581\pi$
$23$		−	7.26253i		−	1.51434i	0.653216	−	0.757171i	$-0.273419\pi$
$24$	1.39034			0.283803
$25$	1.98607	+	4.58863i	0.397215	+	0.917726i
$26$	−0.137421			−0.0269504
$27$			5.65445i			1.08820i
$28$			4.65953i			0.880569i
$29$	−4.57775			−0.850067			−0.425033	−	0.905178i	$-0.639738\pi$
$29$	−4.57775			−0.850067			−0.425033	+	0.905178i	$0.639738\pi$
$30$	2.59851	+	1.70676i	0.474420	+	0.311611i
$31$	10.0499			1.80501			0.902506	−	0.430678i	$-0.141726\pi$
$31$	10.0499			1.80501			0.902506	+	0.430678i	$0.141726\pi$
$32$			1.00000i			0.176777i
$33$		−	2.11972i		−	0.368995i
$34$	6.04088			1.03600
$35$	−5.71997	+	8.70851i	−0.966851	+	1.47201i
$36$	−1.06694			−0.177824
$37$			4.34410i			0.714165i	0.934073	+	0.357083i	$0.116229\pi$
$37$			4.34410i			0.714165i	−0.934073	+	0.357083i	$0.883771\pi$
$38$		−	2.92160i		−	0.473946i
$39$	−0.191062			−0.0305944
$40$	−1.22758	+	1.86897i	−0.194098	+	0.295510i
$41$	−1.53008			−0.238958			−0.119479	−	0.992837i	$-0.538122\pi$
$41$	−1.53008			−0.238958			−0.119479	+	0.992837i	$0.538122\pi$
$42$			6.47835i			0.999632i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	1.52460			0.229842
$45$	−1.99408	−	1.30976i	−0.297260	−	0.195248i
$46$	7.26253			1.07080
$47$		−	5.65266i		−	0.824525i	−0.911065	−	0.412262i	$-0.864739\pi$
$47$		−	5.65266i		−	0.824525i	0.911065	−	0.412262i	$-0.135261\pi$
$48$			1.39034i			0.200679i
$49$	−14.7112			−2.10161
$50$	−4.58863	+	1.98607i	−0.648930	+	0.280873i
$51$	8.39891			1.17608
$52$		−	0.137421i		−	0.0190568i
$53$			1.32571i			0.182101i	0.995846	+	0.0910504i	$0.0290224\pi$
$53$			1.32571i			0.182101i	−0.995846	+	0.0910504i	$0.970978\pi$
$54$	−5.65445			−0.769473
$55$	2.84942	+	1.87157i	0.384216	+	0.252363i
$56$	−4.65953			−0.622656
$57$		−	4.06203i		−	0.538029i
$58$		−	4.57775i		−	0.601088i
$59$	−10.2566			−1.33529			−0.667645	−	0.744480i	$-0.732698\pi$
$59$	−10.2566			−1.33529			−0.667645	+	0.744480i	$0.732698\pi$
$60$	−1.70676	+	2.59851i	−0.220342	+	0.335466i
$61$	5.50689			0.705085			0.352543	−	0.935796i	$-0.385317\pi$
$61$	5.50689			0.705085			0.352543	+	0.935796i	$0.385317\pi$
$62$			10.0499i			1.27634i
$63$		−	4.97146i		−	0.626345i
$64$	−1.00000			−0.125000
$65$	0.168695	−	0.256835i	0.0209241	−	0.0318564i
$66$	2.11972			0.260919
$67$		−	11.2492i		−	1.37430i	−0.726514	−	0.687152i	$-0.758861\pi$
$67$		−	11.2492i		−	1.37430i	0.726514	−	0.687152i	$-0.241139\pi$
$68$			6.04088i			0.732565i
$69$	10.0974			1.21559
$70$	−8.70851	−	5.71997i	−1.04087	−	0.683667i
$71$	−4.33949			−0.515003			−0.257502	−	0.966278i	$-0.582899\pi$
$71$	−4.33949			−0.515003			−0.257502	+	0.966278i	$0.582899\pi$
$72$		−	1.06694i		−	0.125741i
$73$		−	1.66202i		−	0.194525i	−0.995259	−	0.0972623i	$-0.968991\pi$
$73$		−	1.66202i		−	0.194525i	0.995259	−	0.0972623i	$-0.0310086\pi$
$74$	−4.34410			−0.504991
$75$	−6.37977	+	2.76133i	−0.736673	+	0.318850i
$76$	2.92160			0.335130
$77$			7.10392i			0.809566i
$78$		−	0.191062i		−	0.0216335i
$79$	8.24935			0.928125			0.464062	−	0.885803i	$-0.346391\pi$
$79$	8.24935			0.928125			0.464062	+	0.885803i	$0.346391\pi$
$80$	−1.86897	−	1.22758i	−0.208957	−	0.137248i
$81$	−4.66080			−0.517867
$82$		−	1.53008i		−	0.168969i
$83$		−	15.2103i		−	1.66955i	−0.550592	−	0.834774i	$-0.685598\pi$
$83$		−	15.2103i		−	1.66955i	0.550592	−	0.834774i	$-0.314402\pi$
$84$	−6.47835			−0.706846
$85$	−7.41569	+	11.2902i	−0.804345	+	1.22460i
$86$	1.00000			0.107833
$87$		−	6.36465i		−	0.682362i
$88$			1.52460i			0.162523i
$89$	11.3802			1.20630			0.603152	−	0.797626i	$-0.293911\pi$
$89$	11.3802			1.20630			0.603152	+	0.797626i	$0.293911\pi$
$90$	1.30976	−	1.99408i	0.138061	−	0.210195i
$91$	0.640316			0.0671233
$92$			7.26253i			0.757171i
$93$			13.9728i			1.44891i
$94$	5.65266			0.583027
$95$	5.46037	+	3.58651i	0.560222	+	0.367968i
$96$	−1.39034			−0.141901
$97$		−	0.210818i		−	0.0214054i	−0.999943	−	0.0107027i	$-0.996593\pi$
$97$		−	0.210818i		−	0.0214054i	0.999943	−	0.0107027i	$-0.00340683\pi$
$98$		−	14.7112i		−	1.48606i
$99$	−1.62666			−0.163486
$100$	−1.98607	−	4.58863i	−0.198607	−	0.458863i
$101$	0.0434258			0.00432103			0.00216051	−	0.999998i	$-0.499312\pi$
$101$	0.0434258			0.00432103			0.00216051	+	0.999998i	$0.499312\pi$
$102$			8.39891i			0.831616i
$103$			0.585287i			0.0576700i	0.999584	+	0.0288350i	$0.00917974\pi$
$103$			0.585287i			0.0576700i	−0.999584	+	0.0288350i	$0.990820\pi$
$104$	0.137421			0.0134752
$105$	−12.1078	−	7.95272i	−1.18160	−	0.776106i
$106$	−1.32571			−0.128765
$107$			3.09901i			0.299592i	0.988717	+	0.149796i	$0.0478617\pi$
$107$			3.09901i			0.299592i	−0.988717	+	0.149796i	$0.952138\pi$
$108$		−	5.65445i		−	0.544100i
$109$	−9.17143			−0.878464			−0.439232	−	0.898374i	$-0.644749\pi$
$109$	−9.17143			−0.878464			−0.439232	+	0.898374i	$0.644749\pi$
$110$	−1.87157	+	2.84942i	−0.178447	+	0.271682i
$111$	−6.03979			−0.573272
$112$		−	4.65953i		−	0.440284i
$113$			18.7092i			1.76001i	0.474962	+	0.880007i	$0.342462\pi$
$113$			18.7092i			1.76001i	−0.474962	+	0.880007i	$0.657538\pi$
$114$	4.06203			0.380444
$115$	−8.91537	+	13.5734i	−0.831363	+	1.26573i
$116$	4.57775			0.425033
$117$			0.146620i			0.0135550i
$118$		−	10.2566i		−	0.944192i
$119$	−28.1477			−2.58029
$120$	−2.59851	−	1.70676i	−0.237210	−	0.155806i
$121$	−8.67560			−0.788691
$122$			5.50689i			0.498571i
$123$		−	2.12734i		−	0.191815i
$124$	−10.0499			−0.902506
$125$	1.92102	−	11.0141i	0.171821	−	0.985128i
$126$	4.97146			0.442893
$127$			4.61173i			0.409225i	0.978843	+	0.204612i	$0.0655934\pi$
$127$			4.61173i			0.409225i	−0.978843	+	0.204612i	$0.934407\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.39034			0.122413
$130$	0.256835	+	0.168695i	0.0225259	+	0.0147956i
$131$	14.2491			1.24495			0.622473	−	0.782642i	$-0.286128\pi$
$131$	14.2491			1.24495			0.622473	+	0.782642i	$0.286128\pi$
$132$			2.11972i			0.184498i
$133$			13.6133i			1.18042i
$134$	11.2492			0.971779
$135$	6.94131	−	10.5680i	0.597413	−	0.909547i
$136$	−6.04088			−0.518001
$137$			20.2839i			1.73297i	0.499204	+	0.866485i	$0.333626\pi$
$137$			20.2839i			1.73297i	−0.499204	+	0.866485i	$0.666374\pi$
$138$			10.0974i			0.859549i
$139$	−2.43947			−0.206913			−0.103457	−	0.994634i	$-0.532990\pi$
$139$	−2.43947			−0.206913			−0.103457	+	0.994634i	$0.532990\pi$
$140$	5.71997	−	8.70851i	0.483426	−	0.736004i
$141$	7.85914			0.661859
$142$		−	4.33949i		−	0.364162i
$143$		−	0.209511i		−	0.0175202i
$144$	1.06694			0.0889120
$145$	8.55566	+	5.61957i	0.710509	+	0.466680i
$146$	1.66202			0.137550
$147$		−	20.4537i		−	1.68699i
$148$		−	4.34410i		−	0.357083i
$149$	18.7550			1.53647			0.768233	−	0.640170i	$-0.221136\pi$
$149$	18.7550			1.53647			0.768233	+	0.640170i	$0.221136\pi$
$150$	−2.76133	−	6.37977i	−0.225461	−	0.520906i
$151$	20.7527			1.68883			0.844414	−	0.535691i	$-0.179949\pi$
$151$	20.7527			1.68883			0.844414	+	0.535691i	$0.179949\pi$
$152$			2.92160i			0.236973i
$153$		−	6.44528i		−	0.521070i
$154$	−7.10392			−0.572450
$155$	−18.7829	−	12.3371i	−1.50868	−	0.990937i
$156$	0.191062			0.0152972
$157$			5.47157i			0.436679i	0.975873	+	0.218339i	$0.0700639\pi$
$157$			5.47157i			0.436679i	−0.975873	+	0.218339i	$0.929936\pi$
$158$			8.24935i			0.656283i
$159$	−1.84320			−0.146175
$160$	1.22758	−	1.86897i	0.0970491	−	0.147755i
$161$	−33.8400			−2.66697
$162$		−	4.66080i		−	0.366187i
$163$			7.30017i			0.571793i	0.958260	+	0.285897i	$0.0922914\pi$
$163$			7.30017i			0.571793i	−0.958260	+	0.285897i	$0.907709\pi$
$164$	1.53008			0.119479
$165$	−2.60213	+	3.96168i	−0.202576	+	0.308416i
$166$	15.2103			1.18055
$167$			15.2185i			1.17764i	0.808264	+	0.588820i	$0.200407\pi$
$167$			15.2185i			1.17764i	−0.808264	+	0.588820i	$0.799593\pi$
$168$		−	6.47835i		−	0.499816i
$169$	12.9811			0.998547
$170$	−11.2902	−	7.41569i	−0.865920	−	0.568758i
$171$	−3.11718			−0.238377
$172$			1.00000i			0.0762493i
$173$			4.14903i			0.315445i	0.987483	+	0.157722i	$0.0504151\pi$
$173$			4.14903i			0.315445i	−0.987483	+	0.157722i	$0.949585\pi$
$174$	6.36465			0.482502
$175$	21.3809	−	9.25418i	1.61624	−	0.699550i
$176$	−1.52460			−0.114921
$177$		−	14.2601i		−	1.07186i
$178$			11.3802i			0.852986i
$179$	−23.5902			−1.76321			−0.881606	−	0.471986i	$-0.843537\pi$
$179$	−23.5902			−1.76321			−0.881606	+	0.471986i	$0.843537\pi$
$180$	1.99408	+	1.30976i	0.148630	+	0.0976240i
$181$	24.5863			1.82749			0.913743	−	0.406292i	$-0.133178\pi$
$181$	24.5863			1.82749			0.913743	+	0.406292i	$0.133178\pi$
$182$			0.640316i			0.0474634i
$183$			7.65648i			0.565983i
$184$	−7.26253			−0.535401
$185$	5.33275	−	8.11898i	0.392071	−	0.596919i
$186$	−13.9728			−1.02453
$187$			9.20992i			0.673496i
$188$			5.65266i			0.412262i
$189$	26.3471			1.91647
$190$	−3.58651	+	5.46037i	−0.260193	+	0.396137i
$191$	1.81910			0.131626			0.0658128	−	0.997832i	$-0.479036\pi$
$191$	1.81910			0.131626			0.0658128	+	0.997832i	$0.479036\pi$
$192$		−	1.39034i		−	0.100339i
$193$			8.12745i			0.585026i	0.956261	+	0.292513i	$0.0944915\pi$
$193$			8.12745i			0.585026i	−0.956261	+	0.292513i	$0.905508\pi$
$194$	0.210818			0.0151359
$195$	0.357088	+	0.234545i	0.0255716	+	0.0167961i
$196$	14.7112			1.05080
$197$			4.64831i			0.331179i	0.986195	+	0.165589i	$0.0529526\pi$
$197$			4.64831i			0.331179i	−0.986195	+	0.165589i	$0.947047\pi$
$198$		−	1.62666i		−	0.115602i
$199$	−1.02467			−0.0726367			−0.0363183	−	0.999340i	$-0.511563\pi$
$199$	−1.02467			−0.0726367			−0.0363183	+	0.999340i	$0.511563\pi$
$200$	4.58863	−	1.98607i	0.324465	−	0.140437i
$201$	15.6402			1.10317
$202$			0.0434258i			0.00305543i
$203$			21.3302i			1.49708i
$204$	−8.39891			−0.588041
$205$	2.85967	+	1.87830i	0.199728	+	0.131186i
$206$	−0.585287			−0.0407788
$207$		−	7.74871i		−	0.538573i
$208$			0.137421i			0.00952840i
$209$	4.45427			0.308108
$210$	7.95272	−	12.1078i	0.548790	−	0.835519i
$211$	2.68263			0.184680			0.0923399	−	0.995728i	$-0.470565\pi$
$211$	2.68263			0.184680			0.0923399	+	0.995728i	$0.470565\pi$
$212$		−	1.32571i		−	0.0910504i
$213$		−	6.03339i		−	0.413401i
$214$	−3.09901			−0.211844
$215$	−1.22758	+	1.86897i	−0.0837206	+	0.127462i
$216$	5.65445			0.384737
$217$		−	46.8277i		−	3.17887i
$218$		−	9.17143i		−	0.621168i
$219$	2.31078			0.156148
$220$	−2.84942	−	1.87157i	−0.192108	−	0.126181i
$221$	0.830142			0.0558414
$222$		−	6.03979i		−	0.405364i
$223$		−	21.9396i		−	1.46918i	−0.678510	−	0.734591i	$-0.737374\pi$
$223$		−	21.9396i		−	1.46918i	0.678510	−	0.734591i	$-0.262626\pi$
$224$	4.65953			0.311328
$225$	2.11903	+	4.89581i	0.141269	+	0.326387i
$226$	−18.7092			−1.24452
$227$		−	16.7422i		−	1.11122i	−0.831444	−	0.555608i	$-0.812485\pi$
$227$		−	16.7422i		−	1.11122i	0.831444	−	0.555608i	$-0.187515\pi$
$228$			4.06203i			0.269014i
$229$	18.5097			1.22316			0.611578	−	0.791184i	$-0.290535\pi$
$229$	18.5097			1.22316			0.611578	+	0.791184i	$0.290535\pi$
$230$	−13.5734	−	8.91537i	−0.895006	−	0.587862i
$231$	−9.87689			−0.649851
$232$			4.57775i			0.300544i
$233$			3.07476i			0.201434i	0.994915	+	0.100717i	$0.0321137\pi$
$233$			3.07476i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$234$	−0.146620			−0.00958485
$235$	−6.93911	+	10.5646i	−0.452658	+	0.689161i
$236$	10.2566			0.667645
$237$			11.4694i			0.745020i
$238$		−	28.1477i		−	1.82454i
$239$	−17.7892			−1.15068			−0.575342	−	0.817913i	$-0.695131\pi$
$239$	−17.7892			−1.15068			−0.575342	+	0.817913i	$0.695131\pi$
$240$	1.70676	−	2.59851i	0.110171	−	0.167733i
$241$	1.07550			0.0692791			0.0346395	−	0.999400i	$-0.488972\pi$
$241$	1.07550			0.0692791			0.0346395	+	0.999400i	$0.488972\pi$
$242$		−	8.67560i		−	0.557689i
$243$			10.4832i			0.672500i
$244$	−5.50689			−0.352543
$245$	27.4948	+	18.0593i	1.75658	+	1.15377i
$246$	2.12734			0.135634
$247$		−	0.401488i		−	0.0255461i
$248$		−	10.0499i		−	0.638168i
$249$	21.1476			1.34017
$250$	11.0141	+	1.92102i	0.696591	+	0.121496i
$251$	−6.46992			−0.408378			−0.204189	−	0.978932i	$-0.565456\pi$
$251$	−6.46992			−0.408378			−0.204189	+	0.978932i	$0.565456\pi$
$252$			4.97146i			0.313173i
$253$			11.0724i			0.696119i
$254$	−4.61173			−0.289365
$255$	−15.6973	−	10.3104i	−0.983002	−	0.645660i
$256$	1.00000			0.0625000
$257$			11.5441i			0.720098i	0.932933	+	0.360049i	$0.117240\pi$
$257$			11.5441i			0.720098i	−0.932933	+	0.360049i	$0.882760\pi$
$258$			1.39034i			0.0865590i
$259$	20.2415			1.25774
$260$	−0.168695	+	0.256835i	−0.0104620	+	0.0159282i
$261$	−4.88420			−0.302324
$262$			14.2491i			0.880309i
$263$		−	11.3752i		−	0.701426i	−0.936483	−	0.350713i	$-0.885939\pi$
$263$		−	11.3752i		−	0.701426i	0.936483	−	0.350713i	$-0.114061\pi$
$264$	−2.11972			−0.130460
$265$	1.62743	−	2.47772i	0.0999720	−	0.152205i
$266$	−13.6133			−0.834684
$267$			15.8225i			0.968319i
$268$			11.2492i			0.687152i
$269$	4.54759			0.277271			0.138636	−	0.990343i	$-0.455728\pi$
$269$	4.54759			0.277271			0.138636	+	0.990343i	$0.455728\pi$
$270$	10.5680	+	6.94131i	0.643147	+	0.422435i
$271$	−14.7298			−0.894770			−0.447385	−	0.894342i	$-0.647645\pi$
$271$	−14.7298			−0.894770			−0.447385	+	0.894342i	$0.647645\pi$
$272$		−	6.04088i		−	0.366282i
$273$			0.890259i			0.0538809i
$274$	−20.2839			−1.22539
$275$	−3.02796	−	6.99582i	−0.182593	−	0.421864i
$276$	−10.0974			−0.607793
$277$			3.57527i			0.214817i	0.994215	+	0.107409i	$0.0342553\pi$
$277$			3.57527i			0.214817i	−0.994215	+	0.107409i	$0.965745\pi$
$278$		−	2.43947i		−	0.146310i
$279$	10.7227			0.641948
$280$	8.70851	+	5.71997i	0.520433	+	0.341834i
$281$	11.5753			0.690525			0.345263	−	0.938506i	$-0.387790\pi$
$281$	11.5753			0.690525			0.345263	+	0.938506i	$0.387790\pi$
$282$			7.85914i			0.468005i
$283$		−	29.7481i		−	1.76834i	−0.467164	−	0.884170i	$-0.654724\pi$
$283$		−	29.7481i		−	1.76834i	0.467164	−	0.884170i	$-0.345276\pi$
$284$	4.33949			0.257502
$285$	−4.98648	+	7.59180i	−0.295374	+	0.449699i
$286$	0.209511			0.0123887
$287$			7.12945i			0.420838i
$288$			1.06694i			0.0628703i
$289$	−19.4923			−1.14660
$290$	−5.61957	+	8.55566i	−0.329993	+	0.502406i
$291$	0.293110			0.0171824
$292$			1.66202i			0.0972623i
$293$		−	24.1297i		−	1.40967i	−0.709371	−	0.704835i	$-0.751021\pi$
$293$		−	24.1297i		−	1.40967i	0.709371	−	0.704835i	$-0.248979\pi$
$294$	20.4537			1.19288
$295$	19.1692	+	12.5908i	1.11607	+	0.733064i
$296$	4.34410			0.252496
$297$		−	8.62077i		−	0.500228i
$298$			18.7550i			1.08645i
$299$	0.998021			0.0577171
$300$	6.37977	−	2.76133i	0.368336	−	0.159425i
$301$	−4.65953			−0.268571
$302$			20.7527i			1.19418i
$303$			0.0603768i			0.00346855i
$304$	−2.92160			−0.167565
$305$	−10.2922	−	6.76018i	−0.589330	−	0.387087i
$306$	6.44528			0.368452
$307$		−	1.90051i		−	0.108468i	−0.998528	−	0.0542340i	$-0.982728\pi$
$307$		−	1.90051i		−	0.108468i	0.998528	−	0.0542340i	$-0.0172717\pi$
$308$		−	7.10392i		−	0.404783i
$309$	−0.813750			−0.0462926
$310$	12.3371	−	18.7829i	0.700699	−	1.06680i
$311$	17.2917			0.980525			0.490262	−	0.871575i	$-0.336901\pi$
$311$	17.2917			0.980525			0.490262	+	0.871575i	$0.336901\pi$
$312$			0.191062i			0.0108167i
$313$			20.8410i			1.17800i	0.808131	+	0.589002i	$0.200479\pi$
$313$			20.8410i			1.17800i	−0.808131	+	0.589002i	$0.799521\pi$
$314$	−5.47157			−0.308778
$315$	−6.10289	+	9.29149i	−0.343859	+	0.523516i
$316$	−8.24935			−0.464062
$317$		−	17.9510i		−	1.00823i	−0.863636	−	0.504115i	$-0.831819\pi$
$317$		−	17.9510i		−	1.00823i	0.863636	−	0.504115i	$-0.168181\pi$
$318$		−	1.84320i		−	0.103361i
$319$	6.97923			0.390762
$320$	1.86897	+	1.22758i	0.104478	+	0.0686240i
$321$	−4.30868			−0.240487
$322$		−	33.8400i		−	1.88583i
$323$			17.6490i			0.982019i
$324$	4.66080			0.258933
$325$	−0.630572	+	0.272927i	−0.0349778	+	0.0151393i
$326$	−7.30017			−0.404319
$327$		−	12.7514i		−	0.705156i
$328$			1.53008i			0.0844844i
$329$	−26.3387			−1.45210
$330$	−3.96168	−	2.60213i	−0.218083	−	0.143243i
$331$	30.7312			1.68914			0.844570	−	0.535445i	$-0.179856\pi$
$331$	30.7312			1.68914			0.844570	+	0.535445i	$0.179856\pi$
$332$			15.2103i			0.834774i
$333$			4.63491i			0.253991i
$334$	−15.2185			−0.832718
$335$	−13.8093	+	21.0243i	−0.754482	+	1.14868i
$336$	6.47835			0.353423
$337$			0.165564i			0.00901882i	0.999990	+	0.00450941i	$0.00143539\pi$
$337$			0.165564i			0.00901882i	−0.999990	+	0.00450941i	$0.998565\pi$
$338$			12.9811i			0.706080i
$339$	−26.0122			−1.41279
$340$	7.41569	−	11.2902i	0.402172	−	0.612298i
$341$	−15.3220			−0.829734
$342$		−	3.11718i		−	0.168558i
$343$			35.9308i			1.94008i
$344$	−1.00000			−0.0539164
$345$	−18.8717	−	12.3954i	−1.01602	−	0.667348i
$346$	−4.14903			−0.223053
$347$		−	5.39183i		−	0.289449i	−0.989472	−	0.144724i	$-0.953770\pi$
$347$		−	5.39183i		−	0.289449i	0.989472	−	0.144724i	$-0.0462295\pi$
$348$			6.36465i			0.341181i
$349$	−28.8503			−1.54432			−0.772160	−	0.635428i	$-0.780824\pi$
$349$	−28.8503			−1.54432			−0.772160	+	0.635428i	$0.780824\pi$
$350$	9.25418	+	21.3809i	0.494657	+	1.14286i
$351$	−0.777038			−0.0414752
$352$		−	1.52460i		−	0.0812614i
$353$		−	20.5726i		−	1.09497i	−0.836816	−	0.547485i	$-0.815585\pi$
$353$		−	20.5726i		−	1.09497i	0.836816	−	0.547485i	$-0.184415\pi$
$354$	14.2601			0.757918
$355$	8.11037	+	5.32709i	0.430454	+	0.282733i
$356$	−11.3802			−0.603152
$357$		−	39.1350i		−	2.07124i
$358$		−	23.5902i		−	1.24678i
$359$	33.4371			1.76474			0.882371	−	0.470555i	$-0.155946\pi$
$359$	33.4371			1.76474			0.882371	+	0.470555i	$0.155946\pi$
$360$	−1.30976	+	1.99408i	−0.0690306	+	0.105097i
$361$	−10.4643			−0.550750
$362$			24.5863i			1.29223i
$363$		−	12.0621i		−	0.633094i
$364$	−0.640316			−0.0335617
$365$	−2.04027	+	3.10626i	−0.106793	+	0.162589i
$366$	−7.65648			−0.400210
$367$			2.13208i			0.111294i	0.998451	+	0.0556468i	$0.0177221\pi$
$367$			2.13208i			0.111294i	−0.998451	+	0.0556468i	$0.982278\pi$
$368$		−	7.26253i		−	0.378586i
$369$	−1.63251			−0.0849850
$370$	8.11898	+	5.33275i	0.422085	+	0.277236i
$371$	6.17721			0.320705
$372$		−	13.9728i		−	0.724455i
$373$		−	21.3185i		−	1.10383i	−0.833901	−	0.551914i	$-0.813898\pi$
$373$		−	21.3185i		−	1.10383i	0.833901	−	0.551914i	$-0.186102\pi$
$374$	−9.20992			−0.476234
$375$	15.3133	+	2.67088i	0.790778	+	0.137924i
$376$	−5.65266			−0.291514
$377$		−	0.629077i		−	0.0323991i
$378$			26.3471i			1.35515i
$379$	−9.69017			−0.497751			−0.248875	−	0.968536i	$-0.580061\pi$
$379$	−9.69017			−0.497751			−0.248875	+	0.968536i	$0.580061\pi$
$380$	−5.46037	−	3.58651i	−0.280111	−	0.183984i
$381$	−6.41189			−0.328491
$382$			1.81910i			0.0930734i
$383$		−	21.8005i		−	1.11395i	−0.830528	−	0.556977i	$-0.811961\pi$
$383$		−	21.8005i		−	1.11395i	0.830528	−	0.556977i	$-0.188039\pi$
$384$	1.39034			0.0709507
$385$	8.72066	−	13.2770i	0.444446	−	0.676658i
$386$	−8.12745			−0.413676
$387$		−	1.06694i		−	0.0542358i
$388$			0.210818i			0.0107027i
$389$	−22.8863			−1.16038			−0.580192	−	0.814480i	$-0.697022\pi$
$389$	−22.8863			−1.16038			−0.580192	+	0.814480i	$0.697022\pi$
$390$	−0.234545	+	0.357088i	−0.0118766	+	0.0180819i
$391$	−43.8721			−2.21871
$392$			14.7112i			0.743030i
$393$			19.8111i			0.999337i
$394$	−4.64831			−0.234179
$395$	−15.4178	−	10.1268i	−0.775752	−	0.509533i
$396$	1.62666			0.0817428
$397$		−	12.0994i		−	0.607252i	−0.952791	−	0.303626i	$-0.901803\pi$
$397$		−	12.0994i		−	0.607252i	0.952791	−	0.303626i	$-0.0981974\pi$
$398$		−	1.02467i		−	0.0513619i
$399$	−18.9272			−0.947543
$400$	1.98607	+	4.58863i	0.0993037	+	0.229431i
$401$	0.487256			0.0243324			0.0121662	−	0.999926i	$-0.496127\pi$
$401$	0.487256			0.0243324			0.0121662	+	0.999926i	$0.496127\pi$
$402$			15.6402i			0.780062i
$403$			1.38106i			0.0687955i
$404$	−0.0434258			−0.00216051
$405$	8.71088	+	5.72152i	0.432847	+	0.284305i
$406$	−21.3302			−1.05860
$407$		−	6.62301i		−	0.328290i
$408$		−	8.39891i		−	0.415808i
$409$	17.6681			0.873631			0.436816	−	0.899551i	$-0.356106\pi$
$409$	17.6681			0.873631			0.436816	+	0.899551i	$0.356106\pi$
$410$	−1.87830	+	2.85967i	−0.0927626	+	0.141229i
$411$	−28.2016			−1.39108
$412$		−	0.585287i		−	0.0288350i
$413$			47.7908i			2.35163i
$414$	7.74871			0.380828
$415$	−18.6719	+	28.4276i	−0.916569	+	1.39545i
$416$	−0.137421			−0.00673760
$417$		−	3.39171i		−	0.166093i
$418$			4.45427i			0.217865i
$419$	34.3023			1.67578			0.837888	−	0.545842i	$-0.183790\pi$
$419$	34.3023			1.67578			0.837888	+	0.545842i	$0.183790\pi$
$420$	12.1078	+	7.95272i	0.590801	+	0.388053i
$421$	−15.0468			−0.733335			−0.366667	−	0.930352i	$-0.619501\pi$
$421$	−15.0468			−0.733335			−0.366667	+	0.930352i	$0.619501\pi$
$422$			2.68263i			0.130588i
$423$		−	6.03107i		−	0.293241i
$424$	1.32571			0.0643824
$425$	27.7194	−	11.9976i	1.34459	−	0.581971i
$426$	6.03339			0.292319
$427$		−	25.6596i		−	1.24175i
$428$		−	3.09901i		−	0.149796i
$429$	0.291293			0.0140637
$430$	−1.86897	−	1.22758i	−0.0901296	−	0.0591994i
$431$	−33.9744			−1.63649			−0.818244	−	0.574871i	$-0.805052\pi$
$431$	−33.9744			−1.63649			−0.818244	+	0.574871i	$0.805052\pi$
$432$			5.65445i			0.272050i
$433$			13.6203i			0.654548i	0.944930	+	0.327274i	$0.106130\pi$
$433$			13.6203i			0.654548i	−0.944930	+	0.327274i	$0.893870\pi$
$434$	46.8277			2.24780
$435$	−7.81314	+	11.8953i	−0.374611	+	0.570336i
$436$	9.17143			0.439232
$437$			21.2182i			1.01500i
$438$			2.31078i			0.110413i
$439$	20.6185			0.984067			0.492033	−	0.870576i	$-0.336254\pi$
$439$	20.6185			0.984067			0.492033	+	0.870576i	$0.336254\pi$
$440$	1.87157	−	2.84942i	0.0892237	−	0.135841i
$441$	−15.6961			−0.747432
$442$			0.830142i			0.0394858i
$443$			6.19619i			0.294390i	0.989107	+	0.147195i	$0.0470245\pi$
$443$			6.19619i			0.294390i	−0.989107	+	0.147195i	$0.952976\pi$
$444$	6.03979			0.286636
$445$	−21.2693	−	13.9702i	−1.00826	−	0.662252i
$446$	21.9396			1.03887
$447$			26.0758i			1.23334i
$448$			4.65953i			0.220142i
$449$	−9.88164			−0.466343			−0.233172	−	0.972436i	$-0.574910\pi$
$449$	−9.88164			−0.466343			−0.233172	+	0.972436i	$0.574910\pi$
$450$	−4.89581	+	2.11903i	−0.230791	+	0.0998920i
$451$	2.33275			0.109845
$452$		−	18.7092i		−	0.880007i
$453$			28.8534i			1.35565i
$454$	16.7422			0.785749
$455$	−1.19673	−	0.786042i	−0.0561035	−	0.0368502i
$456$	−4.06203			−0.190222
$457$			17.7613i			0.830837i	0.909630	+	0.415418i	$0.136365\pi$
$457$			17.7613i			0.830837i	−0.909630	+	0.415418i	$0.863635\pi$
$458$			18.5097i			0.864902i
$459$	34.1579			1.59435
$460$	8.91537	−	13.5734i	0.415681	−	0.632864i
$461$	13.5035			0.628922			0.314461	−	0.949270i	$-0.398176\pi$
$461$	13.5035			0.628922			0.314461	+	0.949270i	$0.398176\pi$
$462$		−	9.87689i		−	0.459514i
$463$		−	23.3264i		−	1.08407i	−0.840356	−	0.542035i	$-0.817654\pi$
$463$		−	23.3264i		−	1.08407i	0.840356	−	0.542035i	$-0.182346\pi$
$464$	−4.57775			−0.212517
$465$	17.1528	−	26.1147i	0.795441	−	1.21104i
$466$	−3.07476			−0.142435
$467$			27.6399i			1.27902i	0.768782	+	0.639511i	$0.220863\pi$
$467$			27.6399i			1.27902i	−0.768782	+	0.639511i	$0.779137\pi$
$468$		−	0.146620i		−	0.00677751i
$469$	−52.4158			−2.42034
$470$	−10.5646	−	6.93911i	−0.487310	−	0.320077i
$471$	−7.60736			−0.350529
$472$			10.2566i			0.472096i
$473$			1.52460i			0.0701011i
$474$	−11.4694			−0.526809
$475$	−5.80251	−	13.4061i	−0.266237	−	0.615116i
$476$	28.1477			1.29015
$477$			1.41446i			0.0647638i
$478$		−	17.7892i		−	0.813657i
$479$	3.48638			0.159297			0.0796483	−	0.996823i	$-0.474620\pi$
$479$	3.48638			0.159297			0.0796483	+	0.996823i	$0.474620\pi$
$480$	2.59851	+	1.70676i	0.118605	+	0.0779028i
$481$	−0.596969			−0.0272194
$482$			1.07550i			0.0489877i
$483$		−	47.0492i		−	2.14081i
$484$	8.67560			0.394345
$485$	−0.258797	+	0.394012i	−0.0117514	+	0.0178912i
$486$	−10.4832			−0.475529
$487$			8.24588i			0.373657i	0.982393	+	0.186828i	$0.0598208\pi$
$487$			8.24588i			0.373657i	−0.982393	+	0.186828i	$0.940179\pi$
$488$		−	5.50689i		−	0.249285i
$489$	−10.1497			−0.458987
$490$	−18.0593	+	27.4948i	−0.815836	+	1.24209i
$491$	−1.46133			−0.0659487			−0.0329744	−	0.999456i	$-0.510498\pi$
$491$	−1.46133			−0.0659487			−0.0329744	+	0.999456i	$0.510498\pi$
$492$			2.12734i			0.0959077i
$493$			27.6536i			1.24546i
$494$	0.401488			0.0180638
$495$	3.04017	+	1.99686i	0.136646	+	0.0897523i
$496$	10.0499			0.451253
$497$			20.2200i			0.906992i
$498$			21.1476i			0.947645i
$499$	41.5126			1.85836			0.929180	−	0.369629i	$-0.120515\pi$
$499$	41.5126			1.85836			0.929180	+	0.369629i	$0.120515\pi$
$500$	−1.92102	+	11.0141i	−0.0859107	+	0.492564i
$501$	−21.1589			−0.945310
$502$		−	6.46992i		−	0.288767i
$503$			17.5405i			0.782093i	0.920371	+	0.391046i	$0.127887\pi$
$503$			17.5405i			0.782093i	−0.920371	+	0.391046i	$0.872113\pi$
$504$	−4.97146			−0.221446
$505$	−0.0811613	−	0.0533088i	−0.00361163	−	0.00237221i
$506$	−11.0724			−0.492230
$507$			18.0482i			0.801549i
$508$		−	4.61173i		−	0.204612i
$509$	29.6036			1.31216			0.656078	−	0.754693i	$-0.272214\pi$
$509$	29.6036			1.31216			0.656078	+	0.754693i	$0.272214\pi$
$510$	10.3104	−	15.6973i	0.456551	−	0.695087i
$511$	−7.74423			−0.342585
$512$			1.00000i			0.0441942i
$513$		−	16.5200i		−	0.729378i
$514$	−11.5441			−0.509186
$515$	0.718489	−	1.09388i	0.0316604	−	0.0482022i
$516$	−1.39034			−0.0612065
$517$			8.61803i			0.379021i
$518$			20.2415i			0.889359i
$519$	−5.76858			−0.253213
$520$	−0.256835	−	0.168695i	−0.0112629	−	0.00739778i
$521$	−24.1098			−1.05627			−0.528134	−	0.849161i	$-0.677108\pi$
$521$	−24.1098			−1.05627			−0.528134	+	0.849161i	$0.677108\pi$
$522$		−	4.88420i		−	0.213776i
$523$		−	44.4248i		−	1.94256i	−0.237934	−	0.971281i	$-0.576470\pi$
$523$		−	44.4248i		−	1.94256i	0.237934	−	0.971281i	$-0.423530\pi$
$524$	−14.2491			−0.622473
$525$	12.8665	+	29.7268i	0.561540	+	1.29738i
$526$	11.3752			0.495983
$527$		−	60.7101i		−	2.64457i
$528$		−	2.11972i		−	0.0922488i
$529$	−29.7444			−1.29323
$530$	2.47772	+	1.62743i	0.107625	+	0.0706909i
$531$	−10.9432			−0.474893
$532$		−	13.6133i		−	0.590211i
$533$		−	0.210264i		−	0.00910756i
$534$	−15.8225			−0.684705
$535$	3.80429	−	5.79194i	0.164474	−	0.250407i
$536$	−11.2492			−0.485890
$537$		−	32.7984i		−	1.41536i
$538$			4.54759i			0.196060i
$539$	22.4287			0.966074
$540$	−6.94131	+	10.5680i	−0.298707	+	0.454773i
$541$	11.0923			0.476893			0.238447	−	0.971156i	$-0.423362\pi$
$541$	11.0923			0.476893			0.238447	+	0.971156i	$0.423362\pi$
$542$		−	14.7298i		−	0.632698i
$543$			34.1834i			1.46695i
$544$	6.04088			0.259001
$545$	17.1411	+	11.2587i	0.734244	+	0.482270i
$546$	−0.890259			−0.0380996
$547$			29.4211i			1.25796i	0.777423	+	0.628978i	$0.216526\pi$
$547$			29.4211i			1.25796i	−0.777423	+	0.628978i	$0.783474\pi$
$548$		−	20.2839i		−	0.866485i
$549$	5.87555			0.250762
$550$	6.99582	−	3.02796i	0.298303	−	0.129113i
$551$	13.3743			0.569766
$552$		−	10.0974i		−	0.429775i
$553$		−	38.4381i		−	1.63456i
$554$	−3.57527			−0.151899
$555$	11.2882	+	7.41435i	0.479156	+	0.314722i
$556$	2.43947			0.103457
$557$		−	19.8074i		−	0.839265i	−0.907694	−	0.419633i	$-0.862159\pi$
$557$		−	19.8074i		−	0.839265i	0.907694	−	0.419633i	$-0.137841\pi$
$558$			10.7227i			0.453926i
$559$	0.137421			0.00581227
$560$	−5.71997	+	8.70851i	−0.241713	+	0.368002i
$561$	−12.8050			−0.540626
$562$			11.5753i			0.488275i
$563$		−	16.1833i		−	0.682043i	−0.940056	−	0.341021i	$-0.889227\pi$
$563$		−	16.1833i		−	0.682043i	0.940056	−	0.341021i	$-0.110773\pi$
$564$	−7.85914			−0.330929
$565$	22.9671	−	34.9669i	0.966234	−	1.47107i
$566$	29.7481			1.25041
$567$			21.7171i			0.912035i
$568$			4.33949i			0.182081i
$569$	43.1750			1.80999			0.904995	−	0.425423i	$-0.139875\pi$
$569$	43.1750			1.80999			0.904995	+	0.425423i	$0.139875\pi$
$570$	−7.59180	−	4.98648i	−0.317985	−	0.208861i
$571$	3.66700			0.153459			0.0767295	−	0.997052i	$-0.475552\pi$
$571$	3.66700			0.153459			0.0767295	+	0.997052i	$0.475552\pi$
$572$			0.209511i			0.00876010i
$573$			2.52918i			0.105658i
$574$	−7.12945			−0.297578
$575$	33.3251	−	14.4239i	1.38975	−	0.601519i
$576$	−1.06694			−0.0444560
$577$			12.3714i			0.515027i	0.966275	+	0.257513i	$0.0829032\pi$
$577$			12.3714i			0.515027i	−0.966275	+	0.257513i	$0.917097\pi$
$578$		−	19.4923i		−	0.810772i
$579$	−11.2999			−0.469610
$580$	−8.55566	−	5.61957i	−0.355254	−	0.233340i
$581$	−70.8729			−2.94030
$582$			0.293110i			0.0121498i
$583$		−	2.02118i		−	0.0837088i
$584$	−1.66202			−0.0687748
$585$	0.179988	−	0.274028i	0.00744161	−	0.0113297i
$586$	24.1297			0.996787
$587$		−	6.82037i		−	0.281507i	−0.990045	−	0.140753i	$-0.955048\pi$
$587$		−	6.82037i		−	0.281507i	0.990045	−	0.140753i	$-0.0449525\pi$
$588$			20.4537i			0.843496i
$589$	−29.3617			−1.20983
$590$	−12.5908	+	19.1692i	−0.518354	+	0.789182i
$591$	−6.46275			−0.265842
$592$			4.34410i			0.178541i
$593$		−	19.9494i		−	0.819224i	−0.912260	−	0.409612i	$-0.865664\pi$
$593$		−	19.9494i		−	0.819224i	0.912260	−	0.409612i	$-0.134336\pi$
$594$	8.62077			0.353714
$595$	52.6071	+	34.5537i	2.15668	+	1.41656i
$596$	−18.7550			−0.768233
$597$		−	1.42464i		−	0.0583066i
$598$			0.998021i			0.0408121i
$599$	32.1465			1.31347			0.656736	−	0.754121i	$-0.271937\pi$
$599$	32.1465			1.31347			0.656736	+	0.754121i	$0.271937\pi$
$600$	2.76133	+	6.37977i	0.112731	+	0.260453i
$601$	9.96059			0.406301			0.203150	−	0.979148i	$-0.434882\pi$
$601$	9.96059			0.406301			0.203150	+	0.979148i	$0.434882\pi$
$602$		−	4.65953i		−	0.189908i
$603$		−	12.0022i		−	0.488768i
$604$	−20.7527			−0.844414
$605$	16.2144	+	10.6500i	0.659209	+	0.432985i
$606$	−0.0603768			−0.00245264
$607$			21.1567i			0.858723i	0.903133	+	0.429361i	$0.141261\pi$
$607$			21.1567i			0.858723i	−0.903133	+	0.429361i	$0.858739\pi$
$608$		−	2.92160i		−	0.118486i
$609$	−29.6563			−1.20173
$610$	6.76018	−	10.2922i	0.273712	−	0.416719i
$611$	0.776792			0.0314256
$612$			6.44528i			0.260535i
$613$			3.09375i			0.124956i	0.998046	+	0.0624778i	$0.0199002\pi$
$613$			3.09375i			0.124956i	−0.998046	+	0.0624778i	$0.980100\pi$
$614$	1.90051			0.0766985
$615$	−2.61148	+	3.97592i	−0.105305	+	0.160325i
$616$	7.10392			0.286225
$617$		−	10.6440i		−	0.428513i	−0.976777	−	0.214256i	$-0.931267\pi$
$617$		−	10.6440i		−	0.428513i	0.976777	−	0.214256i	$-0.0687328\pi$
$618$		−	0.813750i		−	0.0327338i
$619$	12.7177			0.511167			0.255584	−	0.966787i	$-0.417732\pi$
$619$	12.7177			0.511167			0.255584	+	0.966787i	$0.417732\pi$
$620$	18.7829	+	12.3371i	0.754339	+	0.495469i
$621$	41.0656			1.64791
$622$			17.2917i			0.693336i
$623$		−	53.0266i		−	2.12447i
$624$	−0.191062			−0.00764860
$625$	−17.1110	+	18.2267i	−0.684441	+	0.729068i
$626$	−20.8410			−0.832975
$627$			6.19296i			0.247323i
$628$		−	5.47157i		−	0.218339i
$629$	26.2422			1.04634
$630$	−9.29149	−	6.10289i	−0.370182	−	0.243145i
$631$	−18.9965			−0.756240			−0.378120	−	0.925757i	$-0.623429\pi$
$631$	−18.9965			−0.756240			−0.378120	+	0.925757i	$0.623429\pi$
$632$		−	8.24935i		−	0.328142i
$633$			3.72978i			0.148245i
$634$	17.9510			0.712927
$635$	5.66128	−	8.61916i	0.224661	−	0.342041i
$636$	1.84320			0.0730876
$637$		−	2.02163i		−	0.0800998i
$638$			6.97923i			0.276310i
$639$	−4.63000			−0.183160
$640$	−1.22758	+	1.86897i	−0.0485245	+	0.0738774i
$641$	−10.8240			−0.427523			−0.213761	−	0.976886i	$-0.568571\pi$
$641$	−10.8240			−0.427523			−0.213761	+	0.976886i	$0.568571\pi$
$642$		−	4.30868i		−	0.170050i
$643$		−	17.2682i		−	0.680990i	−0.940246	−	0.340495i	$-0.889405\pi$
$643$		−	17.2682i		−	0.680990i	0.940246	−	0.340495i	$-0.110595\pi$
$644$	33.8400			1.33348
$645$	−2.59851	−	1.70676i	−0.102316	−	0.0672038i
$646$	−17.6490			−0.694392
$647$		−	18.4350i		−	0.724753i	−0.932032	−	0.362377i	$-0.881965\pi$
$647$		−	18.4350i		−	0.724753i	0.932032	−	0.362377i	$-0.118035\pi$
$648$			4.66080i			0.183094i
$649$	15.6371			0.613811
$650$	−0.272927	−	0.630572i	−0.0107051	−	0.0247331i
$651$	65.1067			2.55173
$652$		−	7.30017i		−	0.285897i
$653$			34.9216i			1.36659i	0.730144	+	0.683294i	$0.239453\pi$
$653$			34.9216i			1.36659i	−0.730144	+	0.683294i	$0.760547\pi$
$654$	12.7514			0.498621
$655$	−26.6310	−	17.4919i	−1.04056	−	0.683466i
$656$	−1.53008			−0.0597395
$657$		−	1.77328i		−	0.0691823i
$658$		−	26.3387i		−	1.02679i
$659$	−3.93087			−0.153125			−0.0765624	−	0.997065i	$-0.524394\pi$
$659$	−3.93087			−0.153125			−0.0765624	+	0.997065i	$0.524394\pi$
$660$	2.60213	−	3.96168i	0.101288	−	0.154208i
$661$	7.11460			0.276726			0.138363	−	0.990382i	$-0.455816\pi$
$661$	7.11460			0.276726			0.138363	+	0.990382i	$0.455816\pi$
$662$			30.7312i			1.19440i
$663$			1.15418i			0.0448247i
$664$	−15.2103			−0.590275
$665$	16.7115	−	25.4428i	0.648043	−	0.986629i
$666$	−4.63491			−0.179599
$667$			33.2460i			1.28729i
$668$		−	15.2185i		−	0.588820i
$669$	30.5035			1.17934
$670$	−21.0243	−	13.8093i	−0.812240	−	0.533499i
$671$	−8.39580			−0.324116
$672$			6.47835i			0.249908i
$673$		−	49.3577i		−	1.90260i	−0.308269	−	0.951299i	$-0.599750\pi$
$673$		−	49.3577i		−	1.90260i	0.308269	−	0.951299i	$-0.400250\pi$
$674$	−0.165564			−0.00637727
$675$	−25.9462	+	11.2302i	−0.998669	+	0.432249i
$676$	−12.9811			−0.499274
$677$			3.65475i			0.140463i	0.997531	+	0.0702317i	$0.0223739\pi$
$677$			3.65475i			0.140463i	−0.997531	+	0.0702317i	$0.977626\pi$
$678$		−	26.0122i		−	0.998993i
$679$	−0.982315			−0.0376978
$680$	11.2902	+	7.41569i	0.432960	+	0.284379i
$681$	23.2774			0.891990
$682$		−	15.3220i		−	0.586711i
$683$			21.5452i			0.824404i	0.911093	+	0.412202i	$0.135240\pi$
$683$			21.5452i			0.824404i	−0.911093	+	0.412202i	$0.864760\pi$
$684$	3.11718			0.119188
$685$	24.9002	−	37.9099i	0.951387	−	1.44846i
$686$	−35.9308			−1.37184
$687$			25.7349i			0.981846i
$688$		−	1.00000i		−	0.0381246i
$689$	−0.182180			−0.00694052
$690$	12.3954	−	18.8717i	0.471886	−	0.718435i
$691$	−11.2256			−0.427041			−0.213521	−	0.976939i	$-0.568493\pi$
$691$	−11.2256			−0.427041			−0.213521	+	0.976939i	$0.568493\pi$
$692$		−	4.14903i		−	0.157722i
$693$			7.57948i			0.287921i
$694$	5.39183			0.204671
$695$	4.55929	+	2.99466i	0.172944	+	0.113594i
$696$	−6.36465			−0.241251
$697$			9.24303i			0.350105i
$698$		−	28.8503i		−	1.09200i
$699$	−4.27497			−0.161694
$700$	−21.3809	+	9.25418i	−0.808121	+	0.349775i
$701$	−7.23643			−0.273316			−0.136658	−	0.990618i	$-0.543636\pi$
$701$	−7.23643			−0.273316			−0.136658	+	0.990618i	$0.543636\pi$
$702$		−	0.777038i		−	0.0293274i
$703$		−	12.6917i		−	0.478677i
$704$	1.52460			0.0574605
$705$	−14.6885	−	9.64776i	−0.553200	−	0.363356i
$706$	20.5726			0.774261
$707$		−	0.202344i		−	0.00760992i
$708$			14.2601i			0.535929i
$709$	3.81372			0.143227			0.0716137	−	0.997432i	$-0.477185\pi$
$709$	3.81372			0.143227			0.0716137	+	0.997432i	$0.477185\pi$
$710$	−5.32709	+	8.11037i	−0.199922	+	0.304377i
$711$	8.80160			0.330086
$712$		−	11.3802i		−	0.426493i
$713$		−	72.9876i		−	2.73341i
$714$	39.1350			1.46459
$715$	−0.257193	+	0.391569i	−0.00961846	+	0.0146439i
$716$	23.5902			0.881606
$717$		−	24.7330i		−	0.923673i
$718$			33.4371i			1.24786i
$719$	−26.7466			−0.997480			−0.498740	−	0.866752i	$-0.666204\pi$
$719$	−26.7466			−0.997480			−0.498740	+	0.866752i	$0.666204\pi$
$720$	−1.99408	−	1.30976i	−0.0743151	−	0.0488120i
$721$	2.72716			0.101565
$722$		−	10.4643i		−	0.389439i
$723$			1.49532i			0.0556114i
$724$	−24.5863			−0.913743
$725$	−9.09175	−	21.0056i	−0.337659	−	0.780128i
$726$	12.0621			0.447665
$727$			24.5102i			0.909032i	0.890738	+	0.454516i	$0.150188\pi$
$727$			24.5102i			0.909032i	−0.890738	+	0.454516i	$0.849812\pi$
$728$		−	0.640316i		−	0.0237317i
$729$	−28.5577			−1.05769
$730$	−3.10626	−	2.04027i	−0.114968	−	0.0755137i
$731$	−6.04088			−0.223430
$732$		−	7.65648i		−	0.282992i
$733$		−	22.2929i		−	0.823406i	−0.911318	−	0.411703i	$-0.864934\pi$
$733$		−	22.2929i		−	0.823406i	0.911318	−	0.411703i	$-0.135066\pi$
$734$	−2.13208			−0.0786965
$735$	−25.1086	+	38.2273i	−0.926146	+	1.41003i
$736$	7.26253			0.267700
$737$			17.1504i			0.631745i
$738$		−	1.63251i		−	0.0600934i
$739$	−33.2845			−1.22439			−0.612195	−	0.790706i	$-0.709713\pi$
$739$	−33.2845			−1.22439			−0.612195	+	0.790706i	$0.709713\pi$
$740$	−5.33275	+	8.11898i	−0.196036	+	0.298460i
$741$	0.558206			0.0205062
$742$			6.17721i			0.226772i
$743$		−	12.2565i		−	0.449649i	−0.974399	−	0.224824i	$-0.927819\pi$
$743$		−	12.2565i		−	0.449649i	0.974399	−	0.224824i	$-0.0721808\pi$
$744$	13.9728			0.512267
$745$	−35.0524	−	23.0233i	−1.28422	−	0.843508i
$746$	21.3185			0.780525
$747$		−	16.2285i		−	0.593771i
$748$		−	9.20992i		−	0.336748i
$749$	14.4399			0.527623
$750$	−2.67088	+	15.3133i	−0.0975268	+	0.559164i
$751$	−4.32484			−0.157816			−0.0789078	−	0.996882i	$-0.525143\pi$
$751$	−4.32484			−0.157816			−0.0789078	+	0.996882i	$0.525143\pi$
$752$		−	5.65266i		−	0.206131i
$753$		−	8.99541i		−	0.327811i
$754$	0.629077			0.0229096
$755$	−38.7861	−	25.4757i	−1.41157	−	0.927154i
$756$	−26.3471			−0.958235
$757$			31.2894i			1.13723i	0.822602	+	0.568617i	$0.192521\pi$
$757$			31.2894i			1.13723i	−0.822602	+	0.568617i	$0.807479\pi$
$758$		−	9.69017i		−	0.351963i
$759$	−15.3945			−0.558785
$760$	3.58651	−	5.46037i	0.130096	−	0.198069i
$761$	46.6799			1.69214			0.846072	−	0.533069i	$-0.178961\pi$
$761$	46.6799			1.69214			0.846072	+	0.533069i	$0.178961\pi$
$762$		−	6.41189i		−	0.232278i
$763$			42.7346i			1.54710i
$764$	−1.81910			−0.0658128
$765$	−7.91213	+	12.0460i	−0.286064	+	0.435525i
$766$	21.8005			0.787685
$767$		−	1.40946i		−	0.0508927i
$768$			1.39034i			0.0501697i
$769$	−43.0989			−1.55418			−0.777092	−	0.629386i	$-0.783306\pi$
$769$	−43.0989			−1.55418			−0.777092	+	0.629386i	$0.783306\pi$
$770$	13.2770	+	8.72066i	0.478469	+	0.314271i
$771$	−16.0502			−0.578034
$772$		−	8.12745i		−	0.292513i
$773$			29.7091i			1.06856i	0.845307	+	0.534282i	$0.179418\pi$
$773$			29.7091i			1.06856i	−0.845307	+	0.534282i	$0.820582\pi$
$774$	1.06694			0.0383505
$775$	19.9598	+	46.1152i	0.716977	+	1.65651i
$776$	−0.210818			−0.00756794
$777$			28.1426i			1.00961i
$778$		−	22.8863i		−	0.820515i
$779$	4.47028			0.160164
$780$	−0.357088	−	0.234545i	−0.0127858	−	0.00839804i
$781$	6.61598			0.236739
$782$		−	43.8721i		−	1.56886i
$783$		−	25.8847i		−	0.925042i
$784$	−14.7112			−0.525402
$785$	6.71681	−	10.2262i	0.239733	−	0.364988i
$786$	−19.8111			−0.706638
$787$			52.9244i			1.88655i	0.332011	+	0.943276i	$0.392273\pi$
$787$			52.9244i			1.88655i	−0.332011	+	0.943276i	$0.607727\pi$
$788$		−	4.64831i		−	0.165589i
$789$	15.8155			0.563045
$790$	10.1268	−	15.4178i	0.360295	−	0.548540i
$791$	87.1761			3.09963
$792$			1.62666i			0.0578009i
$793$			0.756761i			0.0268734i
$794$	12.0994			0.429392
$795$	3.44488	+	2.26268i	0.122177	+	0.0802490i
$796$	1.02467			0.0363183
$797$		−	36.3706i		−	1.28831i	−0.764894	−	0.644157i	$-0.777208\pi$
$797$		−	36.3706i		−	1.28831i	0.764894	−	0.644157i	$-0.222792\pi$
$798$		−	18.9272i		−	0.670014i
$799$	−34.1471			−1.20804
$800$	−4.58863	+	1.98607i	−0.162233	+	0.0702183i
$801$	12.1421			0.429019
$802$			0.487256i			0.0172056i
$803$			2.53391i			0.0894198i
$804$	−15.6402			−0.551587
$805$	63.2458	+	41.5415i	2.22912	+	1.46414i
$806$	−1.38106			−0.0486458
$807$			6.32271i			0.222570i
$808$		−	0.0434258i		−	0.00152771i
$809$	−27.6021			−0.970437			−0.485219	−	0.874393i	$-0.661260\pi$
$809$	−27.6021			−0.970437			−0.485219	+	0.874393i	$0.661260\pi$
$810$	−5.72152	+	8.71088i	−0.201034	+	0.306069i
$811$	−17.9831			−0.631474			−0.315737	−	0.948847i	$-0.602252\pi$
$811$	−17.9831			−0.631474			−0.315737	+	0.948847i	$0.602252\pi$
$812$		−	21.3302i		−	0.748542i
$813$		−	20.4794i		−	0.718246i
$814$	6.62301			0.232136
$815$	8.96157	−	13.6438i	0.313910	−	0.477920i
$816$	8.39891			0.294021
$817$			2.92160i			0.102214i
$818$			17.6681i			0.617751i
$819$	0.683181			0.0238723
$820$	−2.85967	−	1.87830i	−0.0998639	−	0.0655931i
$821$	41.1142			1.43489			0.717447	−	0.696613i	$-0.245310\pi$
$821$	41.1142			1.43489			0.717447	+	0.696613i	$0.245310\pi$
$822$		−	28.2016i		−	0.983643i
$823$			54.2464i			1.89091i	0.325753	+	0.945455i	$0.394382\pi$
$823$			54.2464i			1.89091i	−0.325753	+	0.945455i	$0.605618\pi$
$824$	0.585287			0.0203894
$825$	9.72659	−	4.20991i	0.338636	−	0.146570i
$826$	−47.7908			−1.66285
$827$			23.3176i			0.810833i	0.914132	+	0.405417i	$0.132874\pi$
$827$			23.3176i			0.810833i	−0.914132	+	0.405417i	$0.867126\pi$
$828$			7.74871i			0.269286i
$829$	−25.1455			−0.873338			−0.436669	−	0.899622i	$-0.643842\pi$
$829$	−25.1455			−0.873338			−0.436669	+	0.899622i	$0.643842\pi$
$830$	−28.4276	−	18.6719i	−0.986735	−	0.648112i
$831$	−4.97085			−0.172437
$832$		−	0.137421i		−	0.00476420i
$833$			88.8689i			3.07913i
$834$	3.39171			0.117445
$835$	18.6820	−	28.4428i	0.646516	−	0.984304i
$836$	−4.45427			−0.154054
$837$			56.8265i			1.96421i
$838$			34.3023i			1.18495i
$839$	9.99310			0.345000			0.172500	−	0.985010i	$-0.444816\pi$
$839$	9.99310			0.345000			0.172500	+	0.985010i	$0.444816\pi$
$840$	−7.95272	+	12.1078i	−0.274395	+	0.417760i
$841$	−8.04422			−0.277387
$842$		−	15.0468i		−	0.518546i
$843$			16.0937i			0.554295i
$844$	−2.68263			−0.0923399
$845$	−24.2613	−	15.9354i	−0.834613	−	0.548195i
$846$	6.03107			0.207352
$847$			40.4242i			1.38899i
$848$			1.32571i			0.0455252i
$849$	41.3601			1.41947
$850$	11.9976	+	27.7194i	0.411516	+	0.950767i
$851$	31.5492			1.08149
$852$			6.03339i			0.206700i
$853$			11.4042i			0.390472i	0.980756	+	0.195236i	$0.0625473\pi$
$853$			11.4042i			0.390472i	−0.980756	+	0.195236i	$0.937453\pi$
$854$	25.6596			0.878052
$855$	5.82591	+	3.82660i	0.199242	+	0.130867i
$856$	3.09901			0.105922
$857$			23.5880i			0.805751i	0.915255	+	0.402875i	$0.131989\pi$
$857$			23.5880i			0.805751i	−0.915255	+	0.402875i	$0.868011\pi$
$858$			0.291293i			0.00994457i
$859$	43.5874			1.48718			0.743591	−	0.668635i	$-0.233121\pi$
$859$	43.5874			1.48718			0.743591	+	0.668635i	$0.233121\pi$
$860$	1.22758	−	1.86897i	0.0418603	−	0.0637312i
$861$	−9.91239			−0.337813
$862$		−	33.9744i		−	1.15717i
$863$			2.51230i			0.0855196i	0.999085	+	0.0427598i	$0.0136150\pi$
$863$			2.51230i			0.0855196i	−0.999085	+	0.0427598i	$0.986385\pi$
$864$	−5.65445			−0.192368
$865$	5.09328	−	7.75440i	0.173177	−	0.263657i
$866$	−13.6203			−0.462835
$867$		−	27.1010i		−	0.920397i
$868$			46.8277i			1.58944i
$869$	−12.5770			−0.426644
$870$	−11.8953	−	7.81314i	−0.403289	−	0.264890i
$871$	1.54587			0.0523797
$872$			9.17143i			0.310584i
$873$		−	0.224931i		−	0.00761277i
$874$	−21.2182			−0.717717
$875$	−51.3204	−	8.95107i	−1.73495	−	0.302601i
$876$	−2.31078			−0.0780739
$877$		−	39.5018i		−	1.33388i	−0.745111	−	0.666940i	$-0.767604\pi$
$877$		−	39.5018i		−	1.33388i	0.745111	−	0.666940i	$-0.232396\pi$
$878$			20.6185i			0.695840i
$879$	33.5485			1.13156
$880$	2.84942	+	1.87157i	0.0960541	+	0.0630907i
$881$	−55.6111			−1.87359			−0.936793	−	0.349884i	$-0.886221\pi$
$881$	−55.6111			−1.87359			−0.936793	+	0.349884i	$0.886221\pi$
$882$		−	15.6961i		−	0.528514i
$883$			41.0618i			1.38184i	0.722932	+	0.690919i	$0.242794\pi$
$883$			41.0618i			1.38184i	−0.722932	+	0.690919i	$0.757206\pi$
$884$	−0.830142			−0.0279207
$885$	−17.5055	+	26.6517i	−0.588442	+	0.895888i
$886$	−6.19619			−0.208165
$887$			41.8173i			1.40409i	0.712134	+	0.702044i	$0.247729\pi$
$887$			41.8173i			1.40409i	−0.712134	+	0.702044i	$0.752271\pi$
$888$			6.03979i			0.202682i
$889$	21.4885			0.720701
$890$	13.9702	−	21.2693i	0.468283	−	0.712949i
$891$	7.10585			0.238055
$892$			21.9396i			0.734591i
$893$			16.5148i			0.552647i
$894$	−26.0758			−0.872107
$895$	44.0892	+	28.9589i	1.47374	+	0.967990i
$896$	−4.65953			−0.155664
$897$			1.38759i			0.0463304i
$898$		−	9.88164i		−	0.329755i
$899$	−46.0058			−1.53438
$900$	−2.11903	−	4.89581i	−0.0706343	−	0.163194i
$901$	8.00848			0.266801
$902$			2.33275i			0.0776722i
$903$		−	6.47835i		−	0.215586i
$904$	18.7092			0.622259
$905$	−45.9510	−	30.1818i	−1.52746	−	1.00328i
$906$	−28.8534			−0.958588
$907$		−	11.9953i		−	0.398298i	−0.979969	−	0.199149i	$-0.936182\pi$
$907$		−	11.9953i		−	0.398298i	0.979969	−	0.199149i	$-0.0638178\pi$
$908$			16.7422i			0.555608i
$909$	0.0463329			0.00153676
$910$	0.786042	−	1.19673i	0.0260570	−	0.0396712i
$911$	−23.6432			−0.783334			−0.391667	−	0.920107i	$-0.628101\pi$
$911$	−23.6432			−0.783334			−0.391667	+	0.920107i	$0.628101\pi$
$912$		−	4.06203i		−	0.134507i
$913$			23.1896i			0.767464i
$914$	−17.7613			−0.587490
$915$	9.39897	−	14.3097i	0.310720	−	0.473064i
$916$	−18.5097			−0.611578
$917$		−	66.3939i		−	2.19252i
$918$			34.1579i			1.12738i
$919$	−47.1098			−1.55401			−0.777004	−	0.629495i	$-0.783262\pi$
$919$	−47.1098			−1.55401			−0.777004	+	0.629495i	$0.783262\pi$
$920$	13.5734	+	8.91537i	0.447503	+	0.293931i
$921$	2.64237			0.0870690
$922$			13.5035i			0.444715i
$923$		−	0.596336i		−	0.0196286i
$924$	9.87689			0.324926
$925$	−19.9335	+	8.62770i	−0.655408	+	0.283677i
$926$	23.3264			0.766554
$927$			0.624468i			0.0205102i
$928$		−	4.57775i		−	0.150272i
$929$	−38.9434			−1.27769			−0.638845	−	0.769335i	$-0.720588\pi$
$929$	−38.9434			−1.27769			−0.638845	+	0.769335i	$0.720588\pi$
$930$	26.1147	+	17.1528i	0.856334	+	0.562462i
$931$	42.9804			1.40862
$932$		−	3.07476i		−	0.100717i
$933$			24.0415i			0.787083i
$934$	−27.6399			−0.904406
$935$	11.3060	−	17.2130i	0.369744	−	0.562926i
$936$	0.146620			0.00479243
$937$			14.3838i			0.469898i	0.972008	+	0.234949i	$0.0754923\pi$
$937$			14.3838i			0.469898i	−0.972008	+	0.234949i	$0.924508\pi$
$938$		−	52.4158i		−	1.71144i
$939$	−28.9762			−0.945603
$940$	6.93911	−	10.5646i	0.226329	−	0.344580i
$941$	7.40689			0.241458			0.120729	−	0.992686i	$-0.461477\pi$
$941$	7.40689			0.241458			0.120729	+	0.992686i	$0.461477\pi$
$942$		−	7.60736i		−	0.247861i
$943$			11.1122i			0.361864i
$944$	−10.2566			−0.333822
$945$	−49.2419	−	32.3433i	−1.60184	−	1.05213i
$946$	−1.52460			−0.0495690
$947$			6.43943i			0.209253i	0.994512	+	0.104627i	$0.0333648\pi$
$947$			6.43943i			0.209253i	−0.994512	+	0.104627i	$0.966635\pi$
$948$		−	11.4694i		−	0.372510i
$949$	0.228396			0.00741404
$950$	13.4061	−	5.80251i	0.434952	−	0.188258i
$951$	24.9581			0.809322
$952$			28.1477i			0.912272i
$953$		−	7.19908i		−	0.233201i	−0.993179	−	0.116600i	$-0.962800\pi$
$953$		−	7.19908i		−	0.233201i	0.993179	−	0.116600i	$-0.0371997\pi$
$954$	−1.41446			−0.0457949
$955$	−3.39984	−	2.23310i	−0.110016	−	0.0722615i
$956$	17.7892			0.575342
$957$			9.70353i			0.313670i
$958$			3.48638i			0.112640i
$959$	94.5134			3.05200
$960$	−1.70676	+	2.59851i	−0.0550856	+	0.0838664i
$961$	70.0000			2.25807
$962$		−	0.596969i		−	0.0192470i
$963$			3.30646i			0.106549i
$964$	−1.07550			−0.0346395
$965$	9.97712	−	15.1899i	0.321175	−	0.488981i
$966$	47.0492			1.51378
$967$		−	12.8320i		−	0.412648i	−0.978484	−	0.206324i	$-0.933850\pi$
$967$		−	12.8320i		−	0.412648i	0.978484	−	0.206324i	$-0.0661501\pi$
$968$			8.67560i			0.278844i
$969$	−24.5382			−0.788282
$970$	−0.394012	−	0.258797i	−0.0126510	−	0.00830948i
$971$	−13.4063			−0.430229			−0.215114	−	0.976589i	$-0.569012\pi$
$971$	−13.4063			−0.430229			−0.215114	+	0.976589i	$0.569012\pi$
$972$		−	10.4832i		−	0.336250i
$973$			11.3668i			0.364403i
$974$	−8.24588			−0.264215
$975$	−0.379463	−	0.876712i	−0.0121525	−	0.0280773i
$976$	5.50689			0.176271
$977$			43.6828i			1.39754i	0.715347	+	0.698769i	$0.246268\pi$
$977$			43.6828i			1.39754i	−0.715347	+	0.698769i	$0.753732\pi$
$978$		−	10.1497i		−	0.324553i
$979$	−17.3503			−0.554518
$980$	−27.4948	−	18.0593i	−0.878290	−	0.576883i
$981$	−9.78540			−0.312424
$982$		−	1.46133i		−	0.0466328i
$983$			13.2637i			0.423047i	0.977373	+	0.211524i	$0.0678425\pi$
$983$			13.2637i			0.423047i	−0.977373	+	0.211524i	$0.932157\pi$
$984$	−2.12734			−0.0678170
$985$	5.70620	−	8.68754i	0.181815	−	0.276808i
$986$	−27.6536			−0.880671
$987$		−	36.6199i		−	1.16562i
$988$			0.401488i			0.0127730i
$989$	−7.26253			−0.230935
$990$	−1.99686	+	3.04017i	−0.0634645	+	0.0966231i
$991$	−12.0362			−0.382343			−0.191171	−	0.981557i	$-0.561229\pi$
$991$	−12.0362			−0.382343			−0.191171	+	0.981557i	$0.561229\pi$
$992$			10.0499i			0.319084i
$993$			42.7270i			1.35590i
$994$	−20.2200			−0.641340
$995$	1.91507	+	1.25786i	0.0607117	+	0.0398770i
$996$	−21.1476			−0.670086
$997$		−	56.3550i		−	1.78478i	−0.451264	−	0.892391i	$-0.649027\pi$
$997$		−	56.3550i		−	1.78478i	0.451264	−	0.892391i	$-0.350973\pi$
$998$			41.5126i			1.31406i
$999$	−24.5635			−0.777155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.b.259.15	yes	16
5.2	odd	4		2150.2.a.bg.1.7		8
5.3	odd	4		2150.2.a.bh.1.2		8
5.4	even	2	inner	430.2.b.b.259.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.b.259.2	✓	16	5.4	even	2	inner
430.2.b.b.259.15	yes	16	1.1	even	1	trivial
2150.2.a.bg.1.7		8	5.2	odd	4
2150.2.a.bh.1.2		8	5.3	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.39034i q^{3} -1.00000 q^{4} +(-1.86897 - 1.22758i) q^{5} -1.39034 q^{6} -4.65953i q^{7} -1.00000i q^{8} +1.06694 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.39034i q^{3} -1.00000 q^{4} +(-1.86897 - 1.22758i) q^{5} -1.39034 q^{6} -4.65953i q^{7} -1.00000i q^{8} +1.06694 q^{9} +(1.22758 - 1.86897i) q^{10} -1.52460 q^{11} -1.39034i q^{12} +0.137421i q^{13} +4.65953 q^{14} +(1.70676 - 2.59851i) q^{15} +1.00000 q^{16} -6.04088i q^{17} +1.06694i q^{18} -2.92160 q^{19} +(1.86897 + 1.22758i) q^{20} +6.47835 q^{21} -1.52460i q^{22} -7.26253i q^{23} +1.39034 q^{24} +(1.98607 + 4.58863i) q^{25} -0.137421 q^{26} +5.65445i q^{27} +4.65953i q^{28} -4.57775 q^{29} +(2.59851 + 1.70676i) q^{30} +10.0499 q^{31} +1.00000i q^{32} -2.11972i q^{33} +6.04088 q^{34} +(-5.71997 + 8.70851i) q^{35} -1.06694 q^{36} +4.34410i q^{37} -2.92160i q^{38} -0.191062 q^{39} +(-1.22758 + 1.86897i) q^{40} -1.53008 q^{41} +6.47835i q^{42} -1.00000i q^{43} +1.52460 q^{44} +(-1.99408 - 1.30976i) q^{45} +7.26253 q^{46} -5.65266i q^{47} +1.39034i q^{48} -14.7112 q^{49} +(-4.58863 + 1.98607i) q^{50} +8.39891 q^{51} -0.137421i q^{52} +1.32571i q^{53} -5.65445 q^{54} +(2.84942 + 1.87157i) q^{55} -4.65953 q^{56} -4.06203i q^{57} -4.57775i q^{58} -10.2566 q^{59} +(-1.70676 + 2.59851i) q^{60} +5.50689 q^{61} +10.0499i q^{62} -4.97146i q^{63} -1.00000 q^{64} +(0.168695 - 0.256835i) q^{65} +2.11972 q^{66} -11.2492i q^{67} +6.04088i q^{68} +10.0974 q^{69} +(-8.70851 - 5.71997i) q^{70} -4.33949 q^{71} -1.06694i q^{72} -1.66202i q^{73} -4.34410 q^{74} +(-6.37977 + 2.76133i) q^{75} +2.92160 q^{76} +7.10392i q^{77} -0.191062i q^{78} +8.24935 q^{79} +(-1.86897 - 1.22758i) q^{80} -4.66080 q^{81} -1.53008i q^{82} -15.2103i q^{83} -6.47835 q^{84} +(-7.41569 + 11.2902i) q^{85} +1.00000 q^{86} -6.36465i q^{87} +1.52460i q^{88} +11.3802 q^{89} +(1.30976 - 1.99408i) q^{90} +0.640316 q^{91} +7.26253i q^{92} +13.9728i q^{93} +5.65266 q^{94} +(5.46037 + 3.58651i) q^{95} -1.39034 q^{96} -0.210818i q^{97} -14.7112i q^{98} -1.62666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9} + 4 q^{11} - 6 q^{14} - 4 q^{15} + 16 q^{16} - 30 q^{19} - 2 q^{20} + 32 q^{21} - 8 q^{24} - 10 q^{25} - 6 q^{26} + 6 q^{29} - 12 q^{30} + 50 q^{31} - 36 q^{35} + 28 q^{36} - 4 q^{39} + 38 q^{41} - 4 q^{44} - 50 q^{45} + 24 q^{46} - 38 q^{49} - 8 q^{50} + 8 q^{51} - 20 q^{54} - 28 q^{55} + 6 q^{56} + 24 q^{59} + 4 q^{60} + 58 q^{61} - 16 q^{64} - 32 q^{65} + 36 q^{66} - 4 q^{69} - 22 q^{70} + 24 q^{71} + 4 q^{74} - 36 q^{75} + 30 q^{76} - 10 q^{79} + 2 q^{80} + 80 q^{81} - 32 q^{84} - 56 q^{85} + 16 q^{86} + 40 q^{89} - 22 q^{90} + 46 q^{91} - 12 q^{94} - 52 q^{95} + 8 q^{96} + 32 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9 + 4 * q^11 - 6 * q^14 - 4 * q^15 + 16 * q^16 - 30 * q^19 - 2 * q^20 + 32 * q^21 - 8 * q^24 - 10 * q^25 - 6 * q^26 + 6 * q^29 - 12 * q^30 + 50 * q^31 - 36 * q^35 + 28 * q^36 - 4 * q^39 + 38 * q^41 - 4 * q^44 - 50 * q^45 + 24 * q^46 - 38 * q^49 - 8 * q^50 + 8 * q^51 - 20 * q^54 - 28 * q^55 + 6 * q^56 + 24 * q^59 + 4 * q^60 + 58 * q^61 - 16 * q^64 - 32 * q^65 + 36 * q^66 - 4 * q^69 - 22 * q^70 + 24 * q^71 + 4 * q^74 - 36 * q^75 + 30 * q^76 - 10 * q^79 + 2 * q^80 + 80 * q^81 - 32 * q^84 - 56 * q^85 + 16 * q^86 + 40 * q^89 - 22 * q^90 + 46 * q^91 - 12 * q^94 - 52 * q^95 + 8 * q^96 + 32 * q^99

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