LMFDB - Embedded newform 430.2.b.b.259.13

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			259.13
Root			$0.689100i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.b.259.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.310900i q^{3} -1.00000 q^{4} +(-0.205955 + 2.22656i) q^{5} +0.310900 q^{6} -2.43727i q^{7} -1.00000i q^{8} +2.90334 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.310900i q^{3} -1.00000 q^{4} +(-0.205955 + 2.22656i) q^{5} +0.310900 q^{6} -2.43727i q^{7} -1.00000i q^{8} +2.90334 q^{9} +(-2.22656 - 0.205955i) q^{10} +4.13135 q^{11} +0.310900i q^{12} +2.98705i q^{13} +2.43727 q^{14} +(0.692239 + 0.0640316i) q^{15} +1.00000 q^{16} +8.05940i q^{17} +2.90334i q^{18} -4.02536 q^{19} +(0.205955 - 2.22656i) q^{20} -0.757747 q^{21} +4.13135i q^{22} +1.71944i q^{23} -0.310900 q^{24} +(-4.91516 - 0.917145i) q^{25} -2.98705 q^{26} -1.83535i q^{27} +2.43727i q^{28} -1.98253 q^{29} +(-0.0640316 + 0.692239i) q^{30} +6.12637 q^{31} +1.00000i q^{32} -1.28444i q^{33} -8.05940 q^{34} +(5.42673 + 0.501968i) q^{35} -2.90334 q^{36} +1.06271i q^{37} -4.02536i q^{38} +0.928676 q^{39} +(2.22656 + 0.205955i) q^{40} +8.13859 q^{41} -0.757747i q^{42} -1.00000i q^{43} -4.13135 q^{44} +(-0.597958 + 6.46447i) q^{45} -1.71944 q^{46} -0.297064i q^{47} -0.310900i q^{48} +1.05973 q^{49} +(0.917145 - 4.91516i) q^{50} +2.50567 q^{51} -2.98705i q^{52} -13.0290i q^{53} +1.83535 q^{54} +(-0.850874 + 9.19872i) q^{55} -2.43727 q^{56} +1.25148i q^{57} -1.98253i q^{58} -0.202020 q^{59} +(-0.692239 - 0.0640316i) q^{60} -3.83397 q^{61} +6.12637i q^{62} -7.07622i q^{63} -1.00000 q^{64} +(-6.65086 - 0.615199i) q^{65} +1.28444 q^{66} -6.74414i q^{67} -8.05940i q^{68} +0.534575 q^{69} +(-0.501968 + 5.42673i) q^{70} +5.40129 q^{71} -2.90334i q^{72} +1.14430i q^{73} -1.06271 q^{74} +(-0.285141 + 1.52813i) q^{75} +4.02536 q^{76} -10.0692i q^{77} +0.928676i q^{78} -14.1162 q^{79} +(-0.205955 + 2.22656i) q^{80} +8.13941 q^{81} +8.13859i q^{82} -3.57563i q^{83} +0.757747 q^{84} +(-17.9448 - 1.65988i) q^{85} +1.00000 q^{86} +0.616368i q^{87} -4.13135i q^{88} -3.88382 q^{89} +(-6.46447 - 0.597958i) q^{90} +7.28025 q^{91} -1.71944i q^{92} -1.90469i q^{93} +0.297064 q^{94} +(0.829044 - 8.96271i) q^{95} +0.310900 q^{96} -4.77755i q^{97} +1.05973i q^{98} +11.9947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	0.310900i		−	0.179498i	−0.995964	−	0.0897492i	$-0.971393\pi$
$3$		−	0.310900i		−	0.179498i	0.995964	−	0.0897492i	$-0.0286065\pi$
$4$	−1.00000			−0.500000
$5$	−0.205955	+	2.22656i	−0.0921060	+	0.995749i
$5$	−0.205955	+	2.22656i	−0.0921060	+	0.995749i
$6$	0.310900			0.126925
$7$		−	2.43727i		−	0.921201i	−0.887608	−	0.460600i	$-0.847634\pi$
$7$		−	2.43727i		−	0.921201i	0.887608	−	0.460600i	$-0.152366\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.90334			0.967780
$10$	−2.22656	−	0.205955i	−0.704101	−	0.0651288i
$11$	4.13135			1.24565			0.622825	−	0.782361i	$-0.285985\pi$
$11$	4.13135			1.24565			0.622825	+	0.782361i	$0.285985\pi$
$12$			0.310900i			0.0897492i
$13$			2.98705i			0.828459i	0.910172	+	0.414230i	$0.135949\pi$
$13$			2.98705i			0.828459i	−0.910172	+	0.414230i	$0.864051\pi$
$14$	2.43727			0.651387
$15$	0.692239	+	0.0640316i	0.178735	+	0.0165329i
$16$	1.00000			0.250000
$17$			8.05940i			1.95469i	0.211647	+	0.977346i	$0.432117\pi$
$17$			8.05940i			1.95469i	−0.211647	+	0.977346i	$0.567883\pi$
$18$			2.90334i			0.684324i
$19$	−4.02536			−0.923480			−0.461740	−	0.887015i	$-0.652775\pi$
$19$	−4.02536			−0.923480			−0.461740	+	0.887015i	$0.652775\pi$
$20$	0.205955	−	2.22656i	0.0460530	−	0.497875i
$21$	−0.757747			−0.165354
$22$			4.13135i			0.880807i
$23$			1.71944i			0.358529i	0.983801	+	0.179264i	$0.0573717\pi$
$23$			1.71944i			0.358529i	−0.983801	+	0.179264i	$0.942628\pi$
$24$	−0.310900			−0.0634623
$25$	−4.91516	−	0.917145i	−0.983033	−	0.183429i
$26$	−2.98705			−0.585809
$27$		−	1.83535i		−	0.353213i
$28$			2.43727i			0.460600i
$29$	−1.98253			−0.368146			−0.184073	−	0.982913i	$-0.558928\pi$
$29$	−1.98253			−0.368146			−0.184073	+	0.982913i	$0.558928\pi$
$30$	−0.0640316	+	0.692239i	−0.0116905	+	0.126385i
$31$	6.12637			1.10033			0.550164	−	0.835057i	$-0.314565\pi$
$31$	6.12637			1.10033			0.550164	+	0.835057i	$0.314565\pi$
$32$			1.00000i			0.176777i
$33$		−	1.28444i		−	0.223592i
$34$	−8.05940			−1.38218
$35$	5.42673	+	0.501968i	0.917285	+	0.0848481i
$36$	−2.90334			−0.483890
$37$			1.06271i			0.174708i	0.996177	+	0.0873539i	$0.0278411\pi$
$37$			1.06271i			0.174708i	−0.996177	+	0.0873539i	$0.972159\pi$
$38$		−	4.02536i		−	0.652999i
$39$	0.928676			0.148707
$40$	2.22656	+	0.205955i	0.352051	+	0.0325644i
$41$	8.13859			1.27103			0.635517	−	0.772087i	$-0.280787\pi$
$41$	8.13859			1.27103			0.635517	+	0.772087i	$0.280787\pi$
$42$		−	0.757747i		−	0.116923i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−4.13135			−0.622825
$45$	−0.597958	+	6.46447i	−0.0891384	+	0.963666i
$46$	−1.71944			−0.253518
$47$		−	0.297064i		−	0.0433312i	−0.999765	−	0.0216656i	$-0.993103\pi$
$47$		−	0.297064i		−	0.0433312i	0.999765	−	0.0216656i	$-0.00689692\pi$
$48$		−	0.310900i		−	0.0448746i
$49$	1.05973			0.151389
$50$	0.917145	−	4.91516i	0.129704	−	0.695109i
$51$	2.50567			0.350864
$52$		−	2.98705i		−	0.414230i
$53$		−	13.0290i		−	1.78967i	−0.446399	−	0.894834i	$-0.647294\pi$
$53$		−	13.0290i		−	1.78967i	0.446399	−	0.894834i	$-0.352706\pi$
$54$	1.83535			0.249760
$55$	−0.850874	+	9.19872i	−0.114732	+	1.24035i
$56$	−2.43727			−0.325694
$57$			1.25148i			0.165763i
$58$		−	1.98253i		−	0.260318i
$59$	−0.202020			−0.0263008			−0.0131504	−	0.999914i	$-0.504186\pi$
$59$	−0.202020			−0.0263008			−0.0131504	+	0.999914i	$0.504186\pi$
$60$	−0.692239	−	0.0640316i	−0.0893677	−	0.00826644i
$61$	−3.83397			−0.490889			−0.245445	−	0.969411i	$-0.578934\pi$
$61$	−3.83397			−0.490889			−0.245445	+	0.969411i	$0.578934\pi$
$62$			6.12637i			0.778049i
$63$		−	7.07622i		−	0.891520i
$64$	−1.00000			−0.125000
$65$	−6.65086	−	0.615199i	−0.824938	−	0.0763061i
$66$	1.28444			0.158104
$67$		−	6.74414i		−	0.823928i	−0.911200	−	0.411964i	$-0.864843\pi$
$67$		−	6.74414i		−	0.823928i	0.911200	−	0.411964i	$-0.135157\pi$
$68$		−	8.05940i		−	0.977346i
$69$	0.534575			0.0643553
$70$	−0.501968	+	5.42673i	−0.0599967	+	0.648618i
$71$	5.40129			0.641015			0.320508	−	0.947246i	$-0.396146\pi$
$71$	5.40129			0.641015			0.320508	+	0.947246i	$0.396146\pi$
$72$		−	2.90334i		−	0.342162i
$73$			1.14430i			0.133930i	0.997755	+	0.0669651i	$0.0213316\pi$
$73$			1.14430i			0.133930i	−0.997755	+	0.0669651i	$0.978668\pi$
$74$	−1.06271			−0.123537
$75$	−0.285141	+	1.52813i	−0.0329252	+	0.176453i
$76$	4.02536			0.461740
$77$		−	10.0692i		−	1.14749i
$78$			0.928676i			0.105152i
$79$	−14.1162			−1.58819			−0.794096	−	0.607792i	$-0.792055\pi$
$79$	−14.1162			−1.58819			−0.794096	+	0.607792i	$0.792055\pi$
$80$	−0.205955	+	2.22656i	−0.0230265	+	0.248937i
$81$	8.13941			0.904379
$82$			8.13859i			0.898757i
$83$		−	3.57563i		−	0.392476i	−0.980556	−	0.196238i	$-0.937127\pi$
$83$		−	3.57563i		−	0.392476i	0.980556	−	0.196238i	$-0.0628725\pi$
$84$	0.757747			0.0826770
$85$	−17.9448	−	1.65988i	−1.94638	−	0.180039i
$86$	1.00000			0.107833
$87$			0.616368i			0.0660816i
$88$		−	4.13135i		−	0.440404i
$89$	−3.88382			−0.411684			−0.205842	−	0.978585i	$-0.565993\pi$
$89$	−3.88382			−0.411684			−0.205842	+	0.978585i	$0.565993\pi$
$90$	−6.46447	−	0.597958i	−0.681415	−	0.0630303i
$91$	7.28025			0.763177
$92$		−	1.71944i		−	0.179264i
$93$		−	1.90469i		−	0.197507i
$94$	0.297064			0.0306398
$95$	0.829044	−	8.96271i	0.0850581	−	0.919555i
$96$	0.310900			0.0317311
$97$		−	4.77755i		−	0.485087i	−0.970141	−	0.242543i	$-0.922018\pi$
$97$		−	4.77755i		−	0.485087i	0.970141	−	0.242543i	$-0.0779817\pi$
$98$			1.05973i			0.107048i
$99$	11.9947			1.20552
$100$	4.91516	+	0.917145i	0.491516	+	0.0917145i
$101$	−11.0158			−1.09611			−0.548055	−	0.836442i	$-0.684631\pi$
$101$	−11.0158			−1.09611			−0.548055	+	0.836442i	$0.684631\pi$
$102$			2.50567i			0.248098i
$103$			13.4363i			1.32392i	0.749540	+	0.661959i	$0.230275\pi$
$103$			13.4363i			1.32392i	−0.749540	+	0.661959i	$0.769725\pi$
$104$	2.98705			0.292905
$105$	0.156062	−	1.68717i	0.0152301	−	0.164651i
$106$	13.0290			1.26549
$107$		−	9.10866i		−	0.880567i	−0.897859	−	0.440284i	$-0.854878\pi$
$107$		−	9.10866i		−	0.880567i	0.897859	−	0.440284i	$-0.145122\pi$
$108$			1.83535i			0.176607i
$109$	5.21255			0.499272			0.249636	−	0.968340i	$-0.419689\pi$
$109$	5.21255			0.499272			0.249636	+	0.968340i	$0.419689\pi$
$110$	−9.19872	−	0.850874i	−0.877063	−	0.0811276i
$111$	0.330396			0.0313598
$112$		−	2.43727i		−	0.230300i
$113$		−	7.13297i		−	0.671013i	−0.942038	−	0.335507i	$-0.891092\pi$
$113$		−	7.13297i		−	0.671013i	0.942038	−	0.335507i	$-0.108908\pi$
$114$	−1.25148			−0.117212
$115$	−3.82845	−	0.354128i	−0.357005	−	0.0330226i
$116$	1.98253			0.184073
$117$			8.67243i			0.801767i
$118$		−	0.202020i		−	0.0185975i
$119$	19.6429			1.80066
$120$	0.0640316	−	0.692239i	0.00584525	−	0.0631925i
$121$	6.06808			0.551644
$122$		−	3.83397i		−	0.347111i
$123$		−	2.53029i		−	0.228149i
$124$	−6.12637			−0.550164
$125$	3.05438	−	10.7550i	0.273192	−	0.961959i
$126$	7.07622			0.630400
$127$		−	13.5644i		−	1.20364i	−0.798631	−	0.601821i	$-0.794442\pi$
$127$		−	13.5644i		−	1.20364i	0.798631	−	0.601821i	$-0.205558\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.310900			−0.0273732
$130$	0.615199	−	6.65086i	0.0539565	−	0.583319i
$131$	9.56414			0.835622			0.417811	−	0.908534i	$-0.362797\pi$
$131$	9.56414			0.835622			0.417811	+	0.908534i	$0.362797\pi$
$132$			1.28444i			0.111796i
$133$			9.81087i			0.850711i
$134$	6.74414			0.582605
$135$	4.08652	+	0.378000i	0.351712	+	0.0325331i
$136$	8.05940			0.691088
$137$			4.55865i			0.389472i	0.980856	+	0.194736i	$0.0623850\pi$
$137$			4.55865i			0.389472i	−0.980856	+	0.194736i	$0.937615\pi$
$138$			0.534575i			0.0455061i
$139$	7.54593			0.640037			0.320019	−	0.947411i	$-0.396311\pi$
$139$	7.54593			0.640037			0.320019	+	0.947411i	$0.396311\pi$
$140$	−5.42673	−	0.501968i	−0.458642	−	0.0424241i
$141$	−0.0923572			−0.00777788
$142$			5.40129i			0.453266i
$143$			12.3406i			1.03197i
$144$	2.90334			0.241945
$145$	0.408312	−	4.41422i	0.0339084	−	0.366581i
$146$	−1.14430			−0.0947030
$147$		−	0.329469i		−	0.0271741i
$148$		−	1.06271i		−	0.0873539i
$149$	−21.7726			−1.78368			−0.891840	−	0.452351i	$-0.850586\pi$
$149$	−21.7726			−1.78368			−0.891840	+	0.452351i	$0.850586\pi$
$150$	−1.52813	−	0.285141i	−0.124771	−	0.0232816i
$151$	−19.5939			−1.59453			−0.797266	−	0.603628i	$-0.793721\pi$
$151$	−19.5939			−1.59453			−0.797266	+	0.603628i	$0.793721\pi$
$152$			4.02536i			0.326500i
$153$			23.3992i			1.89171i
$154$	10.0692			0.811400
$155$	−1.26176	+	13.6407i	−0.101347	+	1.09565i
$156$	−0.928676			−0.0743536
$157$		−	22.9383i		−	1.83067i	−0.402690	−	0.915336i	$-0.631925\pi$
$157$		−	22.9383i		−	1.83067i	0.402690	−	0.915336i	$-0.368075\pi$
$158$		−	14.1162i		−	1.12302i
$159$	−4.05071			−0.321243
$160$	−2.22656	−	0.205955i	−0.176025	−	0.0162822i
$161$	4.19074			0.330277
$162$			8.13941i			0.639493i
$163$		−	8.37843i		−	0.656249i	−0.944634	−	0.328125i	$-0.893583\pi$
$163$		−	8.37843i		−	0.656249i	0.944634	−	0.328125i	$-0.106417\pi$
$164$	−8.13859			−0.635517
$165$	2.85988	+	0.264537i	0.222642	+	0.0205942i
$166$	3.57563			0.277522
$167$			3.33004i			0.257686i	0.991665	+	0.128843i	$0.0411263\pi$
$167$			3.33004i			0.257686i	−0.991665	+	0.128843i	$0.958874\pi$
$168$			0.757747i			0.0584615i
$169$	4.07752			0.313655
$170$	1.65988	−	17.9448i	0.127307	−	1.37630i
$171$	−11.6870			−0.893726
$172$			1.00000i			0.0762493i
$173$		−	11.3222i		−	0.860812i	−0.902635	−	0.430406i	$-0.858370\pi$
$173$		−	11.3222i		−	0.860812i	0.902635	−	0.430406i	$-0.141630\pi$
$174$	−0.616368			−0.0467267
$175$	−2.23533	+	11.9796i	−0.168975	+	0.905571i
$176$	4.13135			0.311412
$177$			0.0628082i			0.00472095i
$178$		−	3.88382i		−	0.291104i
$179$	−24.3428			−1.81947			−0.909733	−	0.415194i	$-0.863714\pi$
$179$	−24.3428			−1.81947			−0.909733	+	0.415194i	$0.863714\pi$
$180$	0.597958	−	6.46447i	0.0445692	−	0.481833i
$181$	−16.3993			−1.21895			−0.609476	−	0.792805i	$-0.708620\pi$
$181$	−16.3993			−1.21895			−0.609476	+	0.792805i	$0.708620\pi$
$182$			7.28025i			0.539648i
$183$			1.19198i			0.0881138i
$184$	1.71944			0.126759
$185$	−2.36618	−	0.218870i	−0.173965	−	0.0160916i
$186$	1.90469			0.139659
$187$			33.2962i			2.43486i
$188$			0.297064i			0.0216656i
$189$	−4.47324			−0.325380
$190$	8.96271	+	0.829044i	0.650223	+	0.0601451i
$191$	13.4739			0.974938			0.487469	−	0.873140i	$-0.337920\pi$
$191$	13.4739			0.974938			0.487469	+	0.873140i	$0.337920\pi$
$192$			0.310900i			0.0224373i
$193$			23.0357i			1.65814i	0.559142	+	0.829072i	$0.311131\pi$
$193$			23.0357i			1.65814i	−0.559142	+	0.829072i	$0.688869\pi$
$194$	4.77755			0.343008
$195$	−0.191266	+	2.06775i	−0.0136968	+	0.148075i
$196$	−1.05973			−0.0756947
$197$		−	14.9741i		−	1.06686i	−0.845845	−	0.533429i	$-0.820903\pi$
$197$		−	14.9741i		−	1.06686i	0.845845	−	0.533429i	$-0.179097\pi$
$198$			11.9947i			0.852428i
$199$	−9.81530			−0.695789			−0.347894	−	0.937534i	$-0.613103\pi$
$199$	−9.81530			−0.695789			−0.347894	+	0.937534i	$0.613103\pi$
$200$	−0.917145	+	4.91516i	−0.0648519	+	0.347555i
$201$	−2.09676			−0.147894
$202$		−	11.0158i		−	0.775067i
$203$			4.83195i			0.339136i
$204$	−2.50567			−0.175432
$205$	−1.67619	+	18.1211i	−0.117070	+	1.26563i
$206$	−13.4363			−0.936151
$207$			4.99213i			0.346977i
$208$			2.98705i			0.207115i
$209$	−16.6302			−1.15033
$210$	1.68717	+	0.156062i	0.116426	+	0.0107693i
$211$	18.1730			1.25108			0.625539	−	0.780193i	$-0.284879\pi$
$211$	18.1730			1.25108			0.625539	+	0.780193i	$0.284879\pi$
$212$			13.0290i			0.894834i
$213$		−	1.67926i		−	0.115061i
$214$	9.10866			0.622655
$215$	2.22656	+	0.205955i	0.151850	+	0.0140460i
$216$	−1.83535			−0.124880
$217$		−	14.9316i		−	1.01362i
$218$			5.21255i			0.353039i
$219$	0.355763			0.0240403
$220$	0.850874	−	9.19872i	0.0573659	−	0.620177i
$221$	−24.0739			−1.61938
$222$			0.330396i			0.0221747i
$223$			10.2007i			0.683087i	0.939866	+	0.341543i	$0.110950\pi$
$223$			10.2007i			0.683087i	−0.939866	+	0.341543i	$0.889050\pi$
$224$	2.43727			0.162847
$225$	−14.2704	−	2.66278i	−0.951360	−	0.177519i
$226$	7.13297			0.474478
$227$		−	8.31726i		−	0.552036i	−0.961152	−	0.276018i	$-0.910985\pi$
$227$		−	8.31726i		−	0.552036i	0.961152	−	0.276018i	$-0.0890149\pi$
$228$		−	1.25148i		−	0.0828816i
$229$	−9.18100			−0.606697			−0.303349	−	0.952880i	$-0.598105\pi$
$229$	−9.18100			−0.606697			−0.303349	+	0.952880i	$0.598105\pi$
$230$	0.354128	−	3.82845i	0.0233505	−	0.252440i
$231$	−3.13052			−0.205973
$232$			1.98253i			0.130159i
$233$			27.6383i			1.81064i	0.424726	+	0.905322i	$0.360370\pi$
$233$			27.6383i			1.81064i	−0.424726	+	0.905322i	$0.639630\pi$
$234$	−8.67243			−0.566935
$235$	0.661431	+	0.0611819i	0.0431470	+	0.00399106i
$236$	0.202020			0.0131504
$237$			4.38872i			0.285078i
$238$			19.6429i			1.27326i
$239$	27.4665			1.77666			0.888329	−	0.459207i	$-0.151866\pi$
$239$	27.4665			1.77666			0.888329	+	0.459207i	$0.151866\pi$
$240$	0.692239	+	0.0640316i	0.0446838	+	0.00413322i
$241$	14.7606			0.950811			0.475406	−	0.879767i	$-0.342301\pi$
$241$	14.7606			0.950811			0.475406	+	0.879767i	$0.342301\pi$
$242$			6.06808i			0.390071i
$243$		−	8.03660i		−	0.515548i
$244$	3.83397			0.245445
$245$	−0.218256	+	2.35955i	−0.0139439	+	0.150746i
$246$	2.53029			0.161325
$247$		−	12.0240i		−	0.765066i
$248$		−	6.12637i		−	0.389025i
$249$	−1.11166			−0.0704488
$250$	10.7550	+	3.05438i	0.680208	+	0.193176i
$251$	18.2732			1.15339			0.576697	−	0.816958i	$-0.304341\pi$
$251$	18.2732			1.15339			0.576697	+	0.816958i	$0.304341\pi$
$252$			7.07622i			0.445760i
$253$			7.10363i			0.446601i
$254$	13.5644			0.851104
$255$	−0.516056	+	5.57903i	−0.0323167	+	0.349373i
$256$	1.00000			0.0625000
$257$		−	11.3712i		−	0.709316i	−0.934996	−	0.354658i	$-0.884597\pi$
$257$		−	11.3712i		−	0.709316i	0.934996	−	0.354658i	$-0.115403\pi$
$258$		−	0.310900i		−	0.0193558i
$259$	2.59010			0.160941
$260$	6.65086	+	0.615199i	0.412469	+	0.0381530i
$261$	−5.75595			−0.356284
$262$			9.56414i			0.590874i
$263$		−	24.0201i		−	1.48115i	−0.671976	−	0.740573i	$-0.734554\pi$
$263$		−	24.0201i		−	1.48115i	0.671976	−	0.740573i	$-0.265446\pi$
$264$	−1.28444			−0.0790518
$265$	29.0098	+	2.68339i	1.78206	+	0.164839i
$266$	−9.81087			−0.601543
$267$			1.20748i			0.0738965i
$268$			6.74414i			0.411964i
$269$	16.4243			1.00141			0.500705	−	0.865618i	$-0.333074\pi$
$269$	16.4243			1.00141			0.500705	+	0.865618i	$0.333074\pi$
$270$	−0.378000	+	4.08652i	−0.0230044	+	0.248698i
$271$	8.62039			0.523651			0.261826	−	0.965115i	$-0.415675\pi$
$271$	8.62039			0.523651			0.261826	+	0.965115i	$0.415675\pi$
$272$			8.05940i			0.488673i
$273$		−	2.26343i		−	0.136989i
$274$	−4.55865			−0.275398
$275$	−20.3063	−	3.78905i	−1.22451	−	0.228488i
$276$	−0.534575			−0.0321776
$277$			19.0215i			1.14289i	0.820640	+	0.571445i	$0.193617\pi$
$277$			19.0215i			1.14289i	−0.820640	+	0.571445i	$0.806383\pi$
$278$			7.54593i			0.452575i
$279$	17.7869			1.06488
$280$	0.501968	−	5.42673i	0.0299983	−	0.324309i
$281$	8.50111			0.507134			0.253567	−	0.967318i	$-0.418396\pi$
$281$	8.50111			0.507134			0.253567	+	0.967318i	$0.418396\pi$
$282$		−	0.0923572i		−	0.00549979i
$283$		−	0.625941i		−	0.0372083i	−0.999827	−	0.0186042i	$-0.994078\pi$
$283$		−	0.625941i		−	0.0372083i	0.999827	−	0.0186042i	$-0.00592223\pi$
$284$	−5.40129			−0.320508
$285$	−2.78651	−	0.257750i	−0.165059	−	0.0152678i
$286$	−12.3406			−0.729713
$287$		−	19.8359i		−	1.17088i
$288$			2.90334i			0.171081i
$289$	−47.9540			−2.82082
$290$	4.41422	+	0.408312i	0.259212	+	0.0239769i
$291$	−1.48534			−0.0870723
$292$		−	1.14430i		−	0.0669651i
$293$			18.3657i			1.07294i	0.843920	+	0.536469i	$0.180242\pi$
$293$			18.3657i			1.07294i	−0.843920	+	0.536469i	$0.819758\pi$
$294$	0.329469			0.0192150
$295$	0.0416072	−	0.449811i	0.00242246	−	0.0261890i
$296$	1.06271			0.0617685
$297$		−	7.58248i		−	0.439980i
$298$		−	21.7726i		−	1.26125i
$299$	−5.13607			−0.297026
$300$	0.285141	−	1.52813i	0.0164626	−	0.0882264i
$301$	−2.43727			−0.140482
$302$		−	19.5939i		−	1.12750i
$303$			3.42480i			0.196750i
$304$	−4.02536			−0.230870
$305$	0.789626	−	8.53657i	0.0452138	−	0.488802i
$306$	−23.3992			−1.33764
$307$			19.1117i			1.09076i	0.838187	+	0.545382i	$0.183615\pi$
$307$			19.1117i			1.09076i	−0.838187	+	0.545382i	$0.816385\pi$
$308$			10.0692i			0.573747i
$309$	4.17735			0.237641
$310$	−13.6407	−	1.26176i	−0.774742	−	0.0716630i
$311$	−13.5634			−0.769109			−0.384555	−	0.923102i	$-0.625645\pi$
$311$	−13.5634			−0.769109			−0.384555	+	0.923102i	$0.625645\pi$
$312$		−	0.928676i		−	0.0525759i
$313$		−	8.67192i		−	0.490166i	−0.969502	−	0.245083i	$-0.921185\pi$
$313$		−	8.67192i		−	0.490166i	0.969502	−	0.245083i	$-0.0788152\pi$
$314$	22.9383			1.29448
$315$	15.7556	+	1.45738i	0.887730	+	0.0821143i
$316$	14.1162			0.794096
$317$		−	2.05642i		−	0.115500i	−0.998331	−	0.0577502i	$-0.981607\pi$
$317$		−	2.05642i		−	0.115500i	0.998331	−	0.0577502i	$-0.0183927\pi$
$318$		−	4.05071i		−	0.227153i
$319$	−8.19052			−0.458581
$320$	0.205955	−	2.22656i	0.0115132	−	0.124469i
$321$	−2.83189			−0.158060
$322$			4.19074i			0.233541i
$323$		−	32.4420i		−	1.80512i
$324$	−8.13941			−0.452190
$325$	2.73956	−	14.6819i	0.151963	−	0.814403i
$326$	8.37843			0.464038
$327$		−	1.62058i		−	0.0896185i
$328$		−	8.13859i		−	0.449378i
$329$	−0.724024			−0.0399167
$330$	−0.264537	+	2.85988i	−0.0145623	+	0.157431i
$331$	−12.8369			−0.705582			−0.352791	−	0.935702i	$-0.614767\pi$
$331$	−12.8369			−0.705582			−0.352791	+	0.935702i	$0.614767\pi$
$332$			3.57563i			0.196238i
$333$			3.08540i			0.169079i
$334$	−3.33004			−0.182211
$335$	15.0163	+	1.38899i	0.820426	+	0.0758887i
$336$	−0.757747			−0.0413385
$337$			7.35752i			0.400790i	0.979715	+	0.200395i	$0.0642225\pi$
$337$			7.35752i			0.400790i	−0.979715	+	0.200395i	$0.935777\pi$
$338$			4.07752i			0.221788i
$339$	−2.21764			−0.120446
$340$	17.9448	+	1.65988i	0.973192	+	0.0900194i
$341$	25.3102			1.37062
$342$		−	11.6870i		−	0.631960i
$343$		−	19.6437i		−	1.06066i
$344$	−1.00000			−0.0539164
$345$	−0.110099	+	1.19027i	−0.00592751	+	0.0640817i
$346$	11.3222			0.608686
$347$			15.1748i			0.814625i	0.913289	+	0.407313i	$0.133534\pi$
$347$			15.1748i			0.814625i	−0.913289	+	0.407313i	$0.866466\pi$
$348$		−	0.616368i		−	0.0330408i
$349$	19.7339			1.05633			0.528165	−	0.849142i	$-0.322880\pi$
$349$	19.7339			1.05633			0.528165	+	0.849142i	$0.322880\pi$
$350$	−11.9796	−	2.23533i	−0.640335	−	0.119483i
$351$	5.48229			0.292623
$352$			4.13135i			0.220202i
$353$			1.61393i			0.0859008i	0.999077	+	0.0429504i	$0.0136757\pi$
$353$			1.61393i			0.0859008i	−0.999077	+	0.0429504i	$0.986324\pi$
$354$	−0.0628082			−0.00333822
$355$	−1.11242	+	12.0263i	−0.0590414	+	0.638291i
$356$	3.88382			0.205842
$357$		−	6.10699i		−	0.323216i
$358$		−	24.3428i		−	1.28656i
$359$	35.5467			1.87608			0.938041	−	0.346523i	$-0.112638\pi$
$359$	35.5467			1.87608			0.938041	+	0.346523i	$0.112638\pi$
$360$	6.46447	+	0.597958i	0.340708	+	0.0315152i
$361$	−2.79650			−0.147184
$362$		−	16.3993i		−	0.861929i
$363$		−	1.88657i		−	0.0990191i
$364$	−7.28025			−0.381589
$365$	−2.54786	−	0.235675i	−0.133361	−	0.0123358i
$366$	−1.19198			−0.0623059
$367$		−	12.4912i		−	0.652037i	−0.945363	−	0.326018i	$-0.894293\pi$
$367$		−	12.4912i		−	0.652037i	0.945363	−	0.326018i	$-0.105707\pi$
$368$			1.71944i			0.0896321i
$369$	23.6291			1.23008
$370$	0.218870	−	2.36618i	0.0113785	−	0.123012i
$371$	−31.7551			−1.64864
$372$			1.90469i			0.0987536i
$373$			33.9833i			1.75959i	0.475356	+	0.879793i	$0.342319\pi$
$373$			33.9833i			1.75959i	−0.475356	+	0.879793i	$0.657681\pi$
$374$	−33.2962			−1.72171
$375$	−3.34374	−	0.949609i	−0.172670	−	0.0490376i
$376$	−0.297064			−0.0153199
$377$		−	5.92191i		−	0.304994i
$378$		−	4.47324i		−	0.230079i
$379$	−32.5571			−1.67235			−0.836173	−	0.548466i	$-0.815212\pi$
$379$	−32.5571			−1.67235			−0.836173	+	0.548466i	$0.815212\pi$
$380$	−0.829044	+	8.96271i	−0.0425290	+	0.459777i
$381$	−4.21716			−0.216052
$382$			13.4739i			0.689385i
$383$		−	24.3285i		−	1.24313i	−0.783363	−	0.621565i	$-0.786497\pi$
$383$		−	24.3285i		−	1.24313i	0.783363	−	0.621565i	$-0.213503\pi$
$384$	−0.310900			−0.0158656
$385$	22.4197	+	2.07381i	1.14262	+	0.105691i
$386$	−23.0357			−1.17249
$387$		−	2.90334i		−	0.147585i
$388$			4.77755i			0.242543i
$389$	14.1473			0.717295			0.358647	−	0.933473i	$-0.383238\pi$
$389$	14.1473			0.717295			0.358647	+	0.933473i	$0.383238\pi$
$390$	−2.06775	−	0.191266i	−0.104705	−	0.00968511i
$391$	−13.8577			−0.700813
$392$		−	1.05973i		−	0.0535242i
$393$		−	2.97349i		−	0.149993i
$394$	14.9741			0.754383
$395$	2.90730	−	31.4305i	0.146282	−	1.58144i
$396$	−11.9947			−0.602758
$397$			8.97099i			0.450241i	0.974331	+	0.225121i	$0.0722776\pi$
$397$			8.97099i			0.450241i	−0.974331	+	0.225121i	$0.927722\pi$
$398$		−	9.81530i		−	0.491997i
$399$	3.05020			0.152701
$400$	−4.91516	−	0.917145i	−0.245758	−	0.0458572i
$401$	−12.9434			−0.646364			−0.323182	−	0.946337i	$-0.604753\pi$
$401$	−12.9434			−0.646364			−0.323182	+	0.946337i	$0.604753\pi$
$402$		−	2.09676i		−	0.104577i
$403$			18.2998i			0.911577i
$404$	11.0158			0.548055
$405$	−1.67635	+	18.1229i	−0.0832987	+	0.900535i
$406$	−4.83195			−0.239806
$407$			4.39041i			0.217625i
$408$		−	2.50567i		−	0.124049i
$409$	29.6250			1.46486			0.732430	−	0.680842i	$-0.238386\pi$
$409$	29.6250			1.46486			0.732430	+	0.680842i	$0.238386\pi$
$410$	−18.1211	−	1.67619i	−0.894936	−	0.0827809i
$411$	1.41729			0.0699095
$412$		−	13.4363i		−	0.661959i
$413$			0.492378i			0.0242283i
$414$	−4.99213			−0.245350
$415$	7.96136	+	0.736419i	0.390808	+	0.0361494i
$416$	−2.98705			−0.146452
$417$		−	2.34603i		−	0.114886i
$418$		−	16.6302i		−	0.813408i
$419$	32.7955			1.60216			0.801082	−	0.598555i	$-0.204258\pi$
$419$	32.7955			1.60216			0.801082	+	0.598555i	$0.204258\pi$
$420$	−0.156062	+	1.68717i	−0.00761505	+	0.0823256i
$421$	−23.4820			−1.14444			−0.572222	−	0.820099i	$-0.693918\pi$
$421$	−23.4820			−1.14444			−0.572222	+	0.820099i	$0.693918\pi$
$422$			18.1730i			0.884646i
$423$		−	0.862477i		−	0.0419351i
$424$	−13.0290			−0.632743
$425$	7.39164	−	39.6133i	0.358547	−	1.92153i
$426$	1.67926			0.0813606
$427$			9.34440i			0.452207i
$428$			9.10866i			0.440284i
$429$	3.83669			0.185237
$430$	−0.205955	+	2.22656i	−0.00993204	+	0.107374i
$431$	−22.5348			−1.08547			−0.542733	−	0.839906i	$-0.682610\pi$
$431$	−22.5348			−1.08547			−0.542733	+	0.839906i	$0.682610\pi$
$432$		−	1.83535i		−	0.0883033i
$433$		−	32.3968i		−	1.55689i	−0.627711	−	0.778446i	$-0.716008\pi$
$433$		−	32.3968i		−	1.55689i	0.627711	−	0.778446i	$-0.283992\pi$
$434$	14.9316			0.716740
$435$	−1.37238	−	0.126944i	−0.0658007	−	0.00608651i
$436$	−5.21255			−0.249636
$437$		−	6.92137i		−	0.331094i
$438$			0.355763i			0.0169990i
$439$	−27.9756			−1.33520			−0.667601	−	0.744520i	$-0.732679\pi$
$439$	−27.9756			−1.33520			−0.667601	+	0.744520i	$0.732679\pi$
$440$	9.19872	+	0.850874i	0.438532	+	0.0405638i
$441$	3.07674			0.146512
$442$		−	24.0739i		−	1.14508i
$443$			22.2234i			1.05586i	0.849287	+	0.527932i	$0.177032\pi$
$443$			22.2234i			1.05586i	−0.849287	+	0.527932i	$0.822968\pi$
$444$	−0.330396			−0.0156799
$445$	0.799892	−	8.64756i	0.0379185	−	0.409934i
$446$	−10.2007			−0.483015
$447$			6.76911i			0.320168i
$448$			2.43727i			0.115150i
$449$	28.9309			1.36533			0.682666	−	0.730731i	$-0.260820\pi$
$449$	28.9309			1.36533			0.682666	+	0.730731i	$0.260820\pi$
$450$	2.66278	−	14.2704i	0.125525	−	0.672713i
$451$	33.6234			1.58326
$452$			7.13297i			0.335507i
$453$			6.09176i			0.286216i
$454$	8.31726			0.390348
$455$	−1.49941	+	16.2099i	−0.0702932	+	0.759933i
$456$	1.25148			0.0586061
$457$		−	8.37745i		−	0.391881i	−0.980616	−	0.195940i	$-0.937224\pi$
$457$		−	8.37745i		−	0.391881i	0.980616	−	0.195940i	$-0.0627759\pi$
$458$		−	9.18100i		−	0.429000i
$459$	14.7918			0.690423
$460$	3.82845	+	0.354128i	0.178502	+	0.0165113i
$461$	−31.0950			−1.44824			−0.724118	−	0.689676i	$-0.757753\pi$
$461$	−31.0950			−1.44824			−0.724118	+	0.689676i	$0.757753\pi$
$462$		−	3.13052i		−	0.145645i
$463$		−	23.8818i		−	1.10988i	−0.831890	−	0.554940i	$-0.812741\pi$
$463$		−	23.8818i		−	1.10988i	0.831890	−	0.554940i	$-0.187259\pi$
$464$	−1.98253			−0.0920365
$465$	4.24091	+	0.392281i	0.196668	+	0.0181916i
$466$	−27.6383			−1.28032
$467$			12.5709i			0.581712i	0.956767	+	0.290856i	$0.0939401\pi$
$467$			12.5709i			0.581712i	−0.956767	+	0.290856i	$0.906060\pi$
$468$		−	8.67243i		−	0.400883i
$469$	−16.4373			−0.759003
$470$	−0.0611819	+	0.661431i	−0.00282211	+	0.0305095i
$471$	−7.13151			−0.328603
$472$			0.202020i			0.00929874i
$473$		−	4.13135i		−	0.189960i
$474$	−4.38872			−0.201581
$475$	19.7853	+	3.69184i	0.907812	+	0.169393i
$476$	−19.6429			−0.900332
$477$		−	37.8276i		−	1.73201i
$478$			27.4665i			1.25629i
$479$	−35.0874			−1.60318			−0.801592	−	0.597872i	$-0.796013\pi$
$479$	−35.0874			−1.60318			−0.801592	+	0.597872i	$0.796013\pi$
$480$	−0.0640316	+	0.692239i	−0.00292263	+	0.0315962i
$481$	−3.17436			−0.144738
$482$			14.7606i			0.672325i
$483$		−	1.30290i		−	0.0592841i
$484$	−6.06808			−0.275822
$485$	10.6375	+	0.983962i	0.483025	+	0.0446794i
$486$	8.03660			0.364547
$487$		−	27.9557i		−	1.26680i	−0.773826	−	0.633398i	$-0.781660\pi$
$487$		−	27.9557i		−	1.26680i	0.773826	−	0.633398i	$-0.218340\pi$
$488$			3.83397i			0.173556i
$489$	−2.60486			−0.117796
$490$	−2.35955	−	0.218256i	−0.106593	−	0.00985980i
$491$	−32.2993			−1.45765			−0.728825	−	0.684701i	$-0.759933\pi$
$491$	−32.2993			−1.45765			−0.728825	+	0.684701i	$0.759933\pi$
$492$			2.53029i			0.114074i
$493$		−	15.9780i		−	0.719612i
$494$	12.0240			0.540983
$495$	−2.47038	+	26.7070i	−0.111035	+	1.20039i
$496$	6.12637			0.275082
$497$		−	13.1644i		−	0.590504i
$498$		−	1.11166i		−	0.0498148i
$499$	−4.72254			−0.211410			−0.105705	−	0.994398i	$-0.533710\pi$
$499$	−4.72254			−0.211410			−0.105705	+	0.994398i	$0.533710\pi$
$500$	−3.05438	+	10.7550i	−0.136596	+	0.480980i
$501$	1.03531			0.0462542
$502$			18.2732i			0.815572i
$503$			18.7440i			0.835756i	0.908503	+	0.417878i	$0.137226\pi$
$503$			18.7440i			0.835756i	−0.908503	+	0.417878i	$0.862774\pi$
$504$	−7.07622			−0.315200
$505$	2.26875	−	24.5273i	0.100958	−	1.09145i
$506$	−7.10363			−0.315795
$507$		−	1.26770i		−	0.0563006i
$508$			13.5644i			0.601821i
$509$	−23.0651			−1.02234			−0.511172	−	0.859478i	$-0.670789\pi$
$509$	−23.0651			−1.02234			−0.511172	+	0.859478i	$0.670789\pi$
$510$	−5.57903	−	0.516056i	−0.247044	−	0.0228513i
$511$	2.78897			0.123377
$512$			1.00000i			0.0441942i
$513$			7.38794i			0.326186i
$514$	11.3712			0.501562
$515$	−29.9168	−	2.76728i	−1.31829	−	0.121941i
$516$	0.310900			0.0136866
$517$		−	1.22728i		−	0.0539755i
$518$			2.59010i			0.113802i
$519$	−3.52008			−0.154514
$520$	−0.615199	+	6.65086i	−0.0269783	+	0.291660i
$521$	28.8139			1.26236			0.631179	−	0.775637i	$-0.282571\pi$
$521$	28.8139			1.26236			0.631179	+	0.775637i	$0.282571\pi$
$522$		−	5.75595i		−	0.251931i
$523$		−	40.0402i		−	1.75084i	−0.483365	−	0.875419i	$-0.660586\pi$
$523$		−	40.0402i		−	1.75084i	0.483365	−	0.875419i	$-0.339414\pi$
$524$	−9.56414			−0.417811
$525$	3.72445	+	0.694964i	0.162548	+	0.0303307i
$526$	24.0201			1.04733
$527$			49.3749i			2.15080i
$528$		−	1.28444i		−	0.0558980i
$529$	20.0435			0.871457
$530$	−2.68339	+	29.0098i	−0.116559	+	1.26011i
$531$	−0.586534			−0.0254534
$532$		−	9.81087i		−	0.425355i
$533$			24.3104i			1.05300i
$534$	−1.20748			−0.0522527
$535$	20.2810	+	1.87598i	0.876824	+	0.0811055i
$536$	−6.74414			−0.291303
$537$			7.56818i			0.326591i
$538$			16.4243i			0.708103i
$539$	4.37810			0.188578
$540$	−4.08652	−	0.378000i	−0.175856	−	0.0162665i
$541$	10.4699			0.450135			0.225068	−	0.974343i	$-0.427740\pi$
$541$	10.4699			0.450135			0.225068	+	0.974343i	$0.427740\pi$
$542$			8.62039i			0.370277i
$543$			5.09855i			0.218800i
$544$	−8.05940			−0.345544
$545$	−1.07355	+	11.6061i	−0.0459860	+	0.497150i
$546$	2.26343			0.0968659
$547$		−	29.4519i		−	1.25927i	−0.776890	−	0.629636i	$-0.783204\pi$
$547$		−	29.4519i		−	1.25927i	0.776890	−	0.629636i	$-0.216796\pi$
$548$		−	4.55865i		−	0.194736i
$549$	−11.1313			−0.475073
$550$	3.78905	−	20.3063i	0.161566	−	0.865863i
$551$	7.98038			0.339975
$552$		−	0.534575i		−	0.0227530i
$553$			34.4049i			1.46304i
$554$	−19.0215			−0.808146
$555$	−0.0680467	+	0.735646i	−0.00288842	+	0.0312264i
$556$	−7.54593			−0.320019
$557$			24.6080i			1.04267i	0.853351	+	0.521336i	$0.174566\pi$
$557$			24.6080i			1.04267i	−0.853351	+	0.521336i	$0.825434\pi$
$558$			17.7869i			0.752981i
$559$	2.98705			0.126339
$560$	5.42673	+	0.501968i	0.229321	+	0.0212120i
$561$	10.3518			0.437054
$562$			8.50111i			0.358598i
$563$			1.51341i			0.0637827i	0.999491	+	0.0318913i	$0.0101531\pi$
$563$			1.51341i			0.0637827i	−0.999491	+	0.0318913i	$0.989847\pi$
$564$	0.0923572			0.00388894
$565$	15.8820	+	1.46907i	0.668161	+	0.0618044i
$566$	0.625941			0.0263102
$567$		−	19.8379i		−	0.833115i
$568$		−	5.40129i		−	0.226633i
$569$	23.5587			0.987632			0.493816	−	0.869566i	$-0.335602\pi$
$569$	23.5587			0.987632			0.493816	+	0.869566i	$0.335602\pi$
$570$	0.257750	−	2.78651i	0.0107960	−	0.116714i
$571$	21.0235			0.879806			0.439903	−	0.898045i	$-0.355013\pi$
$571$	21.0235			0.879806			0.439903	+	0.898045i	$0.355013\pi$
$572$		−	12.3406i		−	0.515985i
$573$		−	4.18904i		−	0.175000i
$574$	19.8359			0.827935
$575$	1.57698	−	8.45134i	0.0657645	−	0.352445i
$576$	−2.90334			−0.120973
$577$		−	16.8486i		−	0.701417i	−0.936485	−	0.350708i	$-0.885941\pi$
$577$		−	16.8486i		−	0.701417i	0.936485	−	0.350708i	$-0.114059\pi$
$578$		−	47.9540i		−	1.99462i
$579$	7.16180			0.297634
$580$	−0.408312	+	4.41422i	−0.0169542	+	0.183290i
$581$	−8.71476			−0.361549
$582$		−	1.48534i		−	0.0615694i
$583$		−	53.8273i		−	2.22930i
$584$	1.14430			0.0473515
$585$	−19.3097	−	1.78613i	−0.798359	−	0.0738475i
$586$	−18.3657			−0.758682
$587$			35.6890i			1.47304i	0.676415	+	0.736520i	$0.263532\pi$
$587$			35.6890i			1.47304i	−0.676415	+	0.736520i	$0.736468\pi$
$588$			0.329469i			0.0135871i
$589$	−24.6608			−1.01613
$590$	0.449811	+	0.0416072i	0.0185184	+	0.00171294i
$591$	−4.65544			−0.191499
$592$			1.06271i			0.0436769i
$593$			20.0945i			0.825183i	0.910916	+	0.412592i	$0.135376\pi$
$593$			20.0945i			0.825183i	−0.910916	+	0.412592i	$0.864624\pi$
$594$	7.58248			0.311113
$595$	−4.04556	+	43.7362i	−0.165852	+	1.79301i
$596$	21.7726			0.891840
$597$			3.05158i			0.124893i
$598$		−	5.13607i		−	0.210029i
$599$	33.8395			1.38265			0.691323	−	0.722546i	$-0.257028\pi$
$599$	33.8395			1.38265			0.691323	+	0.722546i	$0.257028\pi$
$600$	1.52813	+	0.285141i	0.0623855	+	0.0116408i
$601$	−8.30285			−0.338680			−0.169340	−	0.985558i	$-0.554164\pi$
$601$	−8.30285			−0.338680			−0.169340	+	0.985558i	$0.554164\pi$
$602$		−	2.43727i		−	0.0993356i
$603$		−	19.5805i		−	0.797381i
$604$	19.5939			0.797266
$605$	−1.24975	+	13.5110i	−0.0508097	+	0.549299i
$606$	−3.42480			−0.139123
$607$			35.6949i			1.44881i	0.689375	+	0.724405i	$0.257885\pi$
$607$			35.6949i			1.44881i	−0.689375	+	0.724405i	$0.742115\pi$
$608$		−	4.02536i		−	0.163250i
$609$	1.50225			0.0608744
$610$	8.53657	+	0.789626i	0.345636	+	0.0319710i
$611$	0.887345			0.0358981
$612$		−	23.3992i		−	0.945856i
$613$		−	19.3991i		−	0.783521i	−0.920067	−	0.391761i	$-0.871866\pi$
$613$		−	19.3991i		−	0.783521i	0.920067	−	0.391761i	$-0.128134\pi$
$614$	−19.1117			−0.771287
$615$	5.63385	+	0.521126i	0.227179	+	0.0210138i
$616$	−10.0692			−0.405700
$617$			20.5855i			0.828740i	0.910109	+	0.414370i	$0.135998\pi$
$617$			20.5855i			0.828740i	−0.910109	+	0.414370i	$0.864002\pi$
$618$			4.17735i			0.168038i
$619$	−22.3584			−0.898658			−0.449329	−	0.893366i	$-0.648337\pi$
$619$	−22.3584			−0.898658			−0.449329	+	0.893366i	$0.648337\pi$
$620$	1.26176	−	13.6407i	0.0506734	−	0.547825i
$621$	3.15578			0.126637
$622$		−	13.5634i		−	0.543842i
$623$			9.46590i			0.379243i
$624$	0.928676			0.0371768
$625$	23.3177	+	9.01584i	0.932708	+	0.360633i
$626$	8.67192			0.346600
$627$			5.17033i			0.206483i
$628$			22.9383i			0.915336i
$629$	−8.56477			−0.341500
$630$	−1.45738	+	15.7556i	−0.0580636	+	0.627720i
$631$	−44.3248			−1.76454			−0.882272	−	0.470741i	$-0.843987\pi$
$631$	−44.3248			−1.76454			−0.882272	+	0.470741i	$0.843987\pi$
$632$			14.1162i			0.561511i
$633$		−	5.64998i		−	0.224567i
$634$	2.05642			0.0816710
$635$	30.2019	+	2.79365i	1.19853	+	0.110863i
$636$	4.05071			0.160621
$637$			3.16546i			0.125420i
$638$		−	8.19052i		−	0.324266i
$639$	15.6818			0.620362
$640$	2.22656	+	0.205955i	0.0880126	+	0.00814110i
$641$	6.51143			0.257186			0.128593	−	0.991697i	$-0.458954\pi$
$641$	6.51143			0.257186			0.128593	+	0.991697i	$0.458954\pi$
$642$		−	2.83189i		−	0.111766i
$643$			18.2114i			0.718188i	0.933301	+	0.359094i	$0.116914\pi$
$643$			18.2114i			0.718188i	−0.933301	+	0.359094i	$0.883086\pi$
$644$	−4.19074			−0.165138
$645$	0.0640316	−	0.692239i	0.00252124	−	0.0272569i
$646$	32.4420			1.27641
$647$			5.41794i			0.213001i	0.994313	+	0.106501i	$0.0339646\pi$
$647$			5.41794i			0.213001i	−0.994313	+	0.106501i	$0.966035\pi$
$648$		−	8.13941i		−	0.319746i
$649$	−0.834618			−0.0327616
$650$	14.6819	+	2.73956i	0.575870	+	0.107454i
$651$	−4.64224			−0.181944
$652$			8.37843i			0.328125i
$653$			23.9437i			0.936991i	0.883466	+	0.468495i	$0.155204\pi$
$653$			23.9437i			0.936991i	−0.883466	+	0.468495i	$0.844796\pi$
$654$	1.62058			0.0633699
$655$	−1.96978	+	21.2952i	−0.0769658	+	0.832070i
$656$	8.13859			0.317758
$657$			3.32229i			0.129615i
$658$		−	0.724024i		−	0.0282254i
$659$	39.0606			1.52159			0.760793	−	0.648995i	$-0.224810\pi$
$659$	39.0606			1.52159			0.760793	+	0.648995i	$0.224810\pi$
$660$	−2.85988	−	0.264537i	−0.111321	−	0.0102971i
$661$	17.9891			0.699697			0.349848	−	0.936806i	$-0.386233\pi$
$661$	17.9891			0.699697			0.349848	+	0.936806i	$0.386233\pi$
$662$		−	12.8369i		−	0.498922i
$663$			7.48457i			0.290677i
$664$	−3.57563			−0.138761
$665$	−21.8445	−	2.02060i	−0.847094	−	0.0783556i
$666$	−3.08540			−0.119557
$667$		−	3.40884i		−	0.131991i
$668$		−	3.33004i		−	0.128843i
$669$	3.17139			0.122613
$670$	−1.38899	+	15.0163i	−0.0536614	+	0.580129i
$671$	−15.8395			−0.611476
$672$		−	0.757747i		−	0.0292307i
$673$		−	22.2081i		−	0.856060i	−0.903765	−	0.428030i	$-0.859208\pi$
$673$		−	22.2081i		−	0.856060i	0.903765	−	0.428030i	$-0.140792\pi$
$674$	−7.35752			−0.283401
$675$	−1.68328	+	9.02105i	−0.0647896	+	0.347220i
$676$	−4.07752			−0.156828
$677$			13.2511i			0.509281i	0.967036	+	0.254641i	$0.0819571\pi$
$677$			13.2511i			0.509281i	−0.967036	+	0.254641i	$0.918043\pi$
$678$		−	2.21764i		−	0.0851681i
$679$	−11.6442			−0.446862
$680$	−1.65988	+	17.9448i	−0.0636534	+	0.688150i
$681$	−2.58584			−0.0990895
$682$			25.3102i			0.969177i
$683$		−	1.49181i		−	0.0570824i	−0.999593	−	0.0285412i	$-0.990914\pi$
$683$		−	1.49181i		−	0.0570824i	0.999593	−	0.0285412i	$-0.00908619\pi$
$684$	11.6870			0.446863
$685$	−10.1501	−	0.938878i	−0.387816	−	0.0358727i
$686$	19.6437			0.750000
$687$			2.85438i			0.108901i
$688$		−	1.00000i		−	0.0381246i
$689$	38.9183			1.48267
$690$	−1.19027	−	0.110099i	−0.0453126	−	0.00419138i
$691$	−8.35760			−0.317938			−0.158969	−	0.987284i	$-0.550817\pi$
$691$	−8.35760			−0.317938			−0.158969	+	0.987284i	$0.550817\pi$
$692$			11.3222i			0.430406i
$693$		−	29.2344i		−	1.11052i
$694$	−15.1748			−0.576027
$695$	−1.55412	+	16.8015i	−0.0589513	+	0.637317i
$696$	0.616368			0.0233634
$697$			65.5922i			2.48448i
$698$			19.7339i			0.746938i
$699$	8.59275			0.325008
$700$	2.23533	−	11.9796i	0.0844874	−	0.452785i
$701$	2.12161			0.0801320			0.0400660	−	0.999197i	$-0.487243\pi$
$701$	2.12161			0.0801320			0.0400660	+	0.999197i	$0.487243\pi$
$702$			5.48229i			0.206916i
$703$		−	4.27777i		−	0.161339i
$704$	−4.13135			−0.155706
$705$	0.0190215	−	0.205639i	0.000716389	−	0.00774482i
$706$	−1.61393			−0.0607410
$707$			26.8484i			1.00974i
$708$		−	0.0628082i		−	0.00236048i
$709$	15.6154			0.586449			0.293224	−	0.956044i	$-0.405272\pi$
$709$	15.6154			0.586449			0.293224	+	0.956044i	$0.405272\pi$
$710$	−12.0263	−	1.11242i	−0.451340	−	0.0417486i
$711$	−40.9840			−1.53702
$712$			3.88382i			0.145552i
$713$			10.5339i			0.394499i
$714$	6.10699			0.228548
$715$	−27.4771	−	2.54161i	−1.02758	−	0.0950506i
$716$	24.3428			0.909733
$717$		−	8.53934i		−	0.318907i
$718$			35.5467i			1.32659i
$719$	−36.6123			−1.36541			−0.682704	−	0.730695i	$-0.739196\pi$
$719$	−36.6123			−1.36541			−0.682704	+	0.730695i	$0.739196\pi$
$720$	−0.597958	+	6.46447i	−0.0222846	+	0.240917i
$721$	32.7479			1.21959
$722$		−	2.79650i		−	0.104075i
$723$		−	4.58906i		−	0.170669i
$724$	16.3993			0.609476
$725$	9.74444	+	1.81826i	0.361900	+	0.0675286i
$726$	1.88657			0.0700171
$727$			5.61669i			0.208311i	0.994561	+	0.104156i	$0.0332140\pi$
$727$			5.61669i			0.208311i	−0.994561	+	0.104156i	$0.966786\pi$
$728$		−	7.28025i		−	0.269824i
$729$	21.9197			0.811839
$730$	0.235675	−	2.54786i	0.00872271	−	0.0943004i
$731$	8.05940			0.298088
$732$		−	1.19198i		−	0.0440569i
$733$			25.8014i			0.952996i	0.879176	+	0.476498i	$0.158094\pi$
$733$			25.8014i			0.952996i	−0.879176	+	0.476498i	$0.841906\pi$
$734$	12.4912			0.461060
$735$	0.733584	+	0.0678559i	0.0270586	+	0.00250290i
$736$	−1.71944			−0.0633795
$737$		−	27.8624i		−	1.02633i
$738$			23.6291i			0.869799i
$739$	−2.26414			−0.0832876			−0.0416438	−	0.999133i	$-0.513259\pi$
$739$	−2.26414			−0.0832876			−0.0416438	+	0.999133i	$0.513259\pi$
$740$	2.36618	+	0.218870i	0.0869825	+	0.00804581i
$741$	−3.73825			−0.137328
$742$		−	31.7551i		−	1.16577i
$743$		−	10.9589i		−	0.402043i	−0.979587	−	0.201022i	$-0.935574\pi$
$743$		−	10.9589i		−	0.402043i	0.979587	−	0.201022i	$-0.0644262\pi$
$744$	−1.90469			−0.0698293
$745$	4.48418	−	48.4780i	0.164288	−	1.77610i
$746$	−33.9833			−1.24422
$747$		−	10.3813i		−	0.379831i
$748$		−	33.2962i		−	1.21743i
$749$	−22.2002			−0.811179
$750$	0.949609	−	3.34374i	0.0346748	−	0.122096i
$751$	−15.7669			−0.575341			−0.287670	−	0.957729i	$-0.592881\pi$
$751$	−15.7669			−0.575341			−0.287670	+	0.957729i	$0.592881\pi$
$752$		−	0.297064i		−	0.0108328i
$753$		−	5.68114i		−	0.207032i
$754$	5.92191			0.215663
$755$	4.03547	−	43.6271i	0.146866	−	1.58775i
$756$	4.47324			0.162690
$757$		−	4.38490i		−	0.159372i	−0.996820	−	0.0796859i	$-0.974608\pi$
$757$		−	4.38490i		−	0.159372i	0.996820	−	0.0796859i	$-0.0253917\pi$
$758$		−	32.5571i		−	1.18253i
$759$	2.20852			0.0801642
$760$	−8.96271	−	0.829044i	−0.325112	−	0.0300726i
$761$	−26.1935			−0.949514			−0.474757	−	0.880117i	$-0.657464\pi$
$761$	−26.1935			−0.949514			−0.474757	+	0.880117i	$0.657464\pi$
$762$		−	4.21716i		−	0.152772i
$763$		−	12.7044i		−	0.459930i
$764$	−13.4739			−0.487469
$765$	−52.0998	−	4.81919i	−1.88367	−	0.174238i
$766$	24.3285			0.879025
$767$		−	0.603446i		−	0.0217892i
$768$		−	0.310900i		−	0.0112186i
$769$	−31.8802			−1.14963			−0.574815	−	0.818284i	$-0.694926\pi$
$769$	−31.8802			−1.14963			−0.574815	+	0.818284i	$0.694926\pi$
$770$	−2.07381	+	22.4197i	−0.0747348	+	0.807951i
$771$	−3.53531			−0.127321
$772$		−	23.0357i		−	0.829072i
$773$			4.16709i			0.149880i	0.997188	+	0.0749399i	$0.0238765\pi$
$773$			4.16709i			0.149880i	−0.997188	+	0.0749399i	$0.976123\pi$
$774$	2.90334			0.104358
$775$	−30.1121	−	5.61877i	−1.08166	−	0.201832i
$776$	−4.77755			−0.171504
$777$		−	0.805262i		−	0.0288886i
$778$			14.1473i			0.507204i
$779$	−32.7607			−1.17377
$780$	0.191266	−	2.06775i	0.00684841	−	0.0740375i
$781$	22.3146			0.798481
$782$		−	13.8577i		−	0.495550i
$783$			3.63863i			0.130034i
$784$	1.05973			0.0378473
$785$	51.0735	+	4.72426i	1.82289	+	0.168616i
$786$	2.97349			0.106061
$787$		−	17.9192i		−	0.638752i	−0.947628	−	0.319376i	$-0.896527\pi$
$787$		−	17.9192i		−	0.638752i	0.947628	−	0.319376i	$-0.103473\pi$
$788$			14.9741i			0.533429i
$789$	−7.46787			−0.265863
$790$	31.4305	+	2.90730i	1.11825	+	0.103437i
$791$	−17.3850			−0.618138
$792$		−	11.9947i		−	0.426214i
$793$		−	11.4523i		−	0.406682i
$794$	−8.97099			−0.318369
$795$	0.834266	−	9.01917i	0.0295884	−	0.319877i
$796$	9.81530			0.347894
$797$		−	14.5723i		−	0.516178i	−0.966121	−	0.258089i	$-0.916907\pi$
$797$		−	14.5723i		−	0.516178i	0.966121	−	0.258089i	$-0.0830928\pi$
$798$			3.05020i			0.107976i
$799$	2.39416			0.0846992
$800$	0.917145	−	4.91516i	0.0324260	−	0.173777i
$801$	−11.2760			−0.398419
$802$		−	12.9434i		−	0.457049i
$803$			4.72751i			0.166830i
$804$	2.09676			0.0739469
$805$	−0.863105	+	9.33095i	−0.0304205	+	0.328873i
$806$	−18.2998			−0.644582
$807$		−	5.10633i		−	0.179751i
$808$			11.0158i			0.387533i
$809$	43.9263			1.54436			0.772182	−	0.635401i	$-0.219165\pi$
$809$	43.9263			1.54436			0.772182	+	0.635401i	$0.219165\pi$
$810$	−18.1229	−	1.67635i	−0.636774	−	0.0589011i
$811$	−48.4888			−1.70267			−0.851336	−	0.524621i	$-0.824207\pi$
$811$	−48.4888			−1.70267			−0.851336	+	0.524621i	$0.824207\pi$
$812$		−	4.83195i		−	0.169568i
$813$		−	2.68008i		−	0.0939945i
$814$	−4.39041			−0.153884
$815$	18.6551	+	1.72558i	0.653460	+	0.0604445i
$816$	2.50567			0.0877160
$817$			4.02536i			0.140829i
$818$			29.6250i			1.03581i
$819$	21.1370			0.738588
$820$	1.67619	−	18.1211i	0.0585349	−	0.632816i
$821$	−17.9423			−0.626191			−0.313095	−	0.949722i	$-0.601366\pi$
$821$	−17.9423			−0.626191			−0.313095	+	0.949722i	$0.601366\pi$
$822$			1.41729i			0.0494335i
$823$			23.9360i			0.834356i	0.908825	+	0.417178i	$0.136981\pi$
$823$			23.9360i			0.834356i	−0.908825	+	0.417178i	$0.863019\pi$
$824$	13.4363			0.468076
$825$	−1.17802	+	6.31323i	−0.0410133	+	0.219798i
$826$	−0.492378			−0.0171320
$827$			42.5137i			1.47835i	0.673516	+	0.739173i	$0.264783\pi$
$827$			42.5137i			1.47835i	−0.673516	+	0.739173i	$0.735217\pi$
$828$		−	4.99213i		−	0.173488i
$829$	1.88468			0.0654577			0.0327288	−	0.999464i	$-0.489580\pi$
$829$	1.88468			0.0654577			0.0327288	+	0.999464i	$0.489580\pi$
$830$	−0.736419	+	7.96136i	−0.0255615	+	0.276343i
$831$	5.91379			0.205147
$832$		−	2.98705i		−	0.103557i
$833$			8.54076i			0.295920i
$834$	2.34603			0.0812364
$835$	−7.41453	−	0.685838i	−0.256591	−	0.0237344i
$836$	16.6302			0.575167
$837$		−	11.2440i		−	0.388651i
$838$			32.7955i			1.13290i
$839$	−28.8179			−0.994905			−0.497453	−	0.867491i	$-0.665731\pi$
$839$	−28.8179			−0.994905			−0.497453	+	0.867491i	$0.665731\pi$
$840$	−1.68717	−	0.156062i	−0.0582130	−	0.00538465i
$841$	−25.0696			−0.864469
$842$		−	23.4820i		−	0.809244i
$843$		−	2.64300i		−	0.0910297i
$844$	−18.1730			−0.625539
$845$	−0.839786	+	9.07885i	−0.0288895	+	0.312322i
$846$	0.862477			0.0296526
$847$		−	14.7895i		−	0.508174i
$848$		−	13.0290i		−	0.447417i
$849$	−0.194605			−0.00667883
$850$	39.6133	+	7.39164i	1.35872	+	0.253531i
$851$	−1.82726			−0.0626377
$852$			1.67926i			0.0575306i
$853$		−	3.81024i		−	0.130460i	−0.997870	−	0.0652301i	$-0.979222\pi$
$853$		−	3.81024i		−	0.130460i	0.997870	−	0.0652301i	$-0.0207781\pi$
$854$	−9.34440			−0.319759
$855$	2.40700	−	26.0218i	0.0823175	−	0.889927i
$856$	−9.10866			−0.311328
$857$			4.13345i			0.141196i	0.997505	+	0.0705980i	$0.0224907\pi$
$857$			4.13345i			0.141196i	−0.997505	+	0.0705980i	$0.977509\pi$
$858$			3.83669i			0.130982i
$859$	−47.6723			−1.62656			−0.813279	−	0.581874i	$-0.802320\pi$
$859$	−47.6723			−1.62656			−0.813279	+	0.581874i	$0.802320\pi$
$860$	−2.22656	−	0.205955i	−0.0759252	−	0.00702302i
$861$	−6.16699			−0.210171
$862$		−	22.5348i		−	0.767540i
$863$			19.8828i			0.676819i	0.940999	+	0.338410i	$0.109889\pi$
$863$			19.8828i			0.676819i	−0.940999	+	0.338410i	$0.890111\pi$
$864$	1.83535			0.0624399
$865$	25.2096	+	2.33187i	0.857153	+	0.0792860i
$866$	32.3968			1.10089
$867$			14.9089i			0.506333i
$868$			14.9316i			0.506811i
$869$	−58.3189			−1.97833
$870$	0.126944	−	1.37238i	0.00430381	−	0.0465281i
$871$	20.1451			0.682591
$872$		−	5.21255i		−	0.176519i
$873$		−	13.8709i		−	0.469457i
$874$	6.92137			0.234119
$875$	−26.2129	−	7.44435i	−0.886158	−	0.251665i
$876$	−0.355763			−0.0120201
$877$		−	7.06183i		−	0.238461i	−0.992867	−	0.119231i	$-0.961957\pi$
$877$		−	7.06183i		−	0.238461i	0.992867	−	0.119231i	$-0.0380428\pi$
$878$		−	27.9756i		−	0.944130i
$879$	5.70992			0.192591
$880$	−0.850874	+	9.19872i	−0.0286830	+	0.310089i
$881$	24.0348			0.809754			0.404877	−	0.914371i	$-0.367314\pi$
$881$	24.0348			0.809754			0.404877	+	0.914371i	$0.367314\pi$
$882$			3.07674i			0.103599i
$883$		−	30.7296i		−	1.03413i	−0.855945	−	0.517067i	$-0.827024\pi$
$883$		−	30.7296i		−	1.03413i	0.855945	−	0.517067i	$-0.172976\pi$
$884$	24.0739			0.809692
$885$	−0.139846	−	0.0129357i	−0.00470089	−	0.000434828i
$886$	−22.2234			−0.746608
$887$			6.74222i			0.226382i	0.993573	+	0.113191i	$0.0361071\pi$
$887$			6.74222i			0.226382i	−0.993573	+	0.113191i	$0.963893\pi$
$888$		−	0.330396i		−	0.0110873i
$889$	−33.0600			−1.10880
$890$	8.64756	+	0.799892i	0.289867	+	0.0268125i
$891$	33.6268			1.12654
$892$		−	10.2007i		−	0.341543i
$893$			1.19579i			0.0400155i
$894$	−6.76911			−0.226393
$895$	5.01353	−	54.2008i	0.167584	−	1.81173i
$896$	−2.43727			−0.0814234
$897$			1.59680i			0.0533157i
$898$			28.9309i			0.965436i
$899$	−12.1457			−0.405081
$900$	14.2704	+	2.66278i	0.475680	+	0.0887595i
$901$	105.006			3.49825
$902$			33.6234i			1.11954i
$903$			0.757747i			0.0252163i
$904$	−7.13297			−0.237239
$905$	3.37753	−	36.5141i	0.112273	−	1.21377i
$906$	−6.09176			−0.202385
$907$		−	28.2890i		−	0.939321i	−0.882847	−	0.469661i	$-0.844376\pi$
$907$		−	28.2890i		−	0.939321i	0.882847	−	0.469661i	$-0.155624\pi$
$908$			8.31726i			0.276018i
$909$	−31.9825			−1.06079
$910$	−16.2099	−	1.49941i	−0.537354	−	0.0497048i
$911$	37.0111			1.22623			0.613117	−	0.789992i	$-0.289916\pi$
$911$	37.0111			1.22623			0.613117	+	0.789992i	$0.289916\pi$
$912$			1.25148i			0.0414408i
$913$		−	14.7722i		−	0.488888i
$914$	8.37745			0.277101
$915$	−2.65402	−	0.245495i	−0.0877393	−	0.00811581i
$916$	9.18100			0.303349
$917$		−	23.3104i		−	0.769776i
$918$			14.7918i			0.488203i
$919$	−35.1656			−1.16001			−0.580004	−	0.814614i	$-0.696949\pi$
$919$	−35.1656			−1.16001			−0.580004	+	0.814614i	$0.696949\pi$
$920$	−0.354128	+	3.82845i	−0.0116753	+	0.126220i
$921$	5.94184			0.195790
$922$		−	31.0950i		−	1.02406i
$923$			16.1339i			0.531055i
$924$	3.13052			0.102987
$925$	0.974655	−	5.22337i	0.0320465	−	0.171743i
$926$	23.8818			0.784804
$927$			39.0102i			1.28126i
$928$		−	1.98253i		−	0.0650796i
$929$	27.3655			0.897833			0.448917	−	0.893574i	$-0.351810\pi$
$929$	27.3655			0.897833			0.448917	+	0.893574i	$0.351810\pi$
$930$	−0.392281	+	4.24091i	−0.0128634	+	0.139065i
$931$	−4.26577			−0.139805
$932$		−	27.6383i		−	0.905322i
$933$			4.21686i			0.138054i
$934$	−12.5709			−0.411333
$935$	−74.1362	−	6.85754i	−2.42451	−	0.224265i
$936$	8.67243			0.283467
$937$			49.9935i			1.63322i	0.577192	+	0.816608i	$0.304148\pi$
$937$			49.9935i			1.63322i	−0.577192	+	0.816608i	$0.695852\pi$
$938$		−	16.4373i		−	0.536696i
$939$	−2.69610			−0.0879840
$940$	−0.661431	−	0.0611819i	−0.0215735	−	0.00199553i
$941$	7.06756			0.230396			0.115198	−	0.993343i	$-0.463250\pi$
$941$	7.06756			0.230396			0.115198	+	0.993343i	$0.463250\pi$
$942$		−	7.13151i		−	0.232357i
$943$			13.9938i			0.455702i
$944$	−0.202020			−0.00657521
$945$	0.921288	−	9.95995i	0.0299695	−	0.323997i
$946$	4.13135			0.134322
$947$		−	50.1488i		−	1.62962i	−0.579731	−	0.814808i	$-0.696842\pi$
$947$		−	50.1488i		−	1.62962i	0.579731	−	0.814808i	$-0.303158\pi$
$948$		−	4.38872i		−	0.142539i
$949$	−3.41809			−0.110956
$950$	−3.69184	+	19.7853i	−0.119779	+	0.641920i
$951$	−0.639343			−0.0207321
$952$		−	19.6429i		−	0.636631i
$953$		−	29.9709i		−	0.970853i	−0.874278	−	0.485426i	$-0.838664\pi$
$953$		−	29.9709i		−	0.970853i	0.874278	−	0.485426i	$-0.161336\pi$
$954$	37.8276			1.22471
$955$	−2.77502	+	30.0005i	−0.0897976	+	0.970794i
$956$	−27.4665			−0.888329
$957$			2.54643i			0.0823145i
$958$		−	35.0874i		−	1.13362i
$959$	11.1106			0.358782
$960$	−0.692239	−	0.0640316i	−0.0223419	−	0.00206661i
$961$	6.53238			0.210722
$962$		−	3.17436i		−	0.102345i
$963$		−	26.4455i		−	0.852196i
$964$	−14.7606			−0.475406
$965$	−51.2904	−	4.74432i	−1.65110	−	0.152725i
$966$	1.30290			0.0419202
$967$		−	29.4556i		−	0.947228i	−0.880733	−	0.473614i	$-0.842949\pi$
$967$		−	29.4556i		−	0.947228i	0.880733	−	0.473614i	$-0.157051\pi$
$968$		−	6.06808i		−	0.195035i
$969$	−10.0862			−0.324016
$970$	−0.983962	+	10.6375i	−0.0315931	+	0.341550i
$971$	57.6633			1.85050			0.925251	−	0.379355i	$-0.123854\pi$
$971$	57.6633			1.85050			0.925251	+	0.379355i	$0.123854\pi$
$972$			8.03660i			0.257774i
$973$		−	18.3914i		−	0.589603i
$974$	27.9557			0.895760
$975$	−4.56459	−	0.851730i	−0.146184	−	0.0272772i
$976$	−3.83397			−0.122722
$977$			17.0305i			0.544854i	0.962176	+	0.272427i	$0.0878263\pi$
$977$			17.0305i			0.544854i	−0.962176	+	0.272427i	$0.912174\pi$
$978$		−	2.60486i		−	0.0832941i
$979$	−16.0454			−0.512814
$980$	0.218256	−	2.35955i	0.00697193	−	0.0753729i
$981$	15.1338			0.483186
$982$		−	32.2993i		−	1.03071i
$983$		−	45.7499i		−	1.45919i	−0.683878	−	0.729597i	$-0.739708\pi$
$983$		−	45.7499i		−	1.45919i	0.683878	−	0.729597i	$-0.260292\pi$
$984$	−2.53029			−0.0806627
$985$	33.3407	+	3.08399i	1.06232	+	0.0982641i
$986$	15.9780			0.508842
$987$			0.225099i			0.00716499i
$988$			12.0240i			0.382533i
$989$	1.71944			0.0546751
$990$	−26.7070	−	2.47038i	−0.848805	−	0.0785137i
$991$	15.2937			0.485822			0.242911	−	0.970049i	$-0.421898\pi$
$991$	15.2937			0.485822			0.242911	+	0.970049i	$0.421898\pi$
$992$			6.12637i			0.194512i
$993$			3.99101i			0.126651i
$994$	13.1644			0.417549
$995$	2.02151	−	21.8544i	0.0640863	−	0.692831i
$996$	1.11166			0.0352244
$997$			38.8513i			1.23043i	0.788359	+	0.615216i	$0.210931\pi$
$997$			38.8513i			1.23043i	−0.788359	+	0.615216i	$0.789069\pi$
$998$		−	4.72254i		−	0.149490i
$999$	1.95044			0.0617091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.b.259.13	yes	16
5.2	odd	4		2150.2.a.bg.1.5		8
5.3	odd	4		2150.2.a.bh.1.4		8
5.4	even	2	inner	430.2.b.b.259.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.b.259.4	✓	16	5.4	even	2	inner
430.2.b.b.259.13	yes	16	1.1	even	1	trivial
2150.2.a.bg.1.5		8	5.2	odd	4
2150.2.a.bh.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.310900i q^{3} -1.00000 q^{4} +(-0.205955 + 2.22656i) q^{5} +0.310900 q^{6} -2.43727i q^{7} -1.00000i q^{8} +2.90334 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.310900i q^{3} -1.00000 q^{4} +(-0.205955 + 2.22656i) q^{5} +0.310900 q^{6} -2.43727i q^{7} -1.00000i q^{8} +2.90334 q^{9} +(-2.22656 - 0.205955i) q^{10} +4.13135 q^{11} +0.310900i q^{12} +2.98705i q^{13} +2.43727 q^{14} +(0.692239 + 0.0640316i) q^{15} +1.00000 q^{16} +8.05940i q^{17} +2.90334i q^{18} -4.02536 q^{19} +(0.205955 - 2.22656i) q^{20} -0.757747 q^{21} +4.13135i q^{22} +1.71944i q^{23} -0.310900 q^{24} +(-4.91516 - 0.917145i) q^{25} -2.98705 q^{26} -1.83535i q^{27} +2.43727i q^{28} -1.98253 q^{29} +(-0.0640316 + 0.692239i) q^{30} +6.12637 q^{31} +1.00000i q^{32} -1.28444i q^{33} -8.05940 q^{34} +(5.42673 + 0.501968i) q^{35} -2.90334 q^{36} +1.06271i q^{37} -4.02536i q^{38} +0.928676 q^{39} +(2.22656 + 0.205955i) q^{40} +8.13859 q^{41} -0.757747i q^{42} -1.00000i q^{43} -4.13135 q^{44} +(-0.597958 + 6.46447i) q^{45} -1.71944 q^{46} -0.297064i q^{47} -0.310900i q^{48} +1.05973 q^{49} +(0.917145 - 4.91516i) q^{50} +2.50567 q^{51} -2.98705i q^{52} -13.0290i q^{53} +1.83535 q^{54} +(-0.850874 + 9.19872i) q^{55} -2.43727 q^{56} +1.25148i q^{57} -1.98253i q^{58} -0.202020 q^{59} +(-0.692239 - 0.0640316i) q^{60} -3.83397 q^{61} +6.12637i q^{62} -7.07622i q^{63} -1.00000 q^{64} +(-6.65086 - 0.615199i) q^{65} +1.28444 q^{66} -6.74414i q^{67} -8.05940i q^{68} +0.534575 q^{69} +(-0.501968 + 5.42673i) q^{70} +5.40129 q^{71} -2.90334i q^{72} +1.14430i q^{73} -1.06271 q^{74} +(-0.285141 + 1.52813i) q^{75} +4.02536 q^{76} -10.0692i q^{77} +0.928676i q^{78} -14.1162 q^{79} +(-0.205955 + 2.22656i) q^{80} +8.13941 q^{81} +8.13859i q^{82} -3.57563i q^{83} +0.757747 q^{84} +(-17.9448 - 1.65988i) q^{85} +1.00000 q^{86} +0.616368i q^{87} -4.13135i q^{88} -3.88382 q^{89} +(-6.46447 - 0.597958i) q^{90} +7.28025 q^{91} -1.71944i q^{92} -1.90469i q^{93} +0.297064 q^{94} +(0.829044 - 8.96271i) q^{95} +0.310900 q^{96} -4.77755i q^{97} +1.05973i q^{98} +11.9947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \) 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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