LMFDB - Embedded newform 430.2.b.b.259.3

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			259.3
Root			$-2.20024i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.b.259.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.20024i q^{3} -1.00000 q^{4} +(1.77243 - 1.36327i) q^{5} -1.20024 q^{6} -4.33187i q^{7} +1.00000i q^{8} +1.55943 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.20024i q^{3} -1.00000 q^{4} +(1.77243 - 1.36327i) q^{5} -1.20024 q^{6} -4.33187i q^{7} +1.00000i q^{8} +1.55943 q^{9} +(-1.36327 - 1.77243i) q^{10} +0.276696 q^{11} +1.20024i q^{12} +4.16476i q^{13} -4.33187 q^{14} +(-1.63625 - 2.12733i) q^{15} +1.00000 q^{16} +2.65591i q^{17} -1.55943i q^{18} -1.21298 q^{19} +(-1.77243 + 1.36327i) q^{20} -5.19928 q^{21} -0.276696i q^{22} -1.82155i q^{23} +1.20024 q^{24} +(1.28298 - 4.83259i) q^{25} +4.16476 q^{26} -5.47240i q^{27} +4.33187i q^{28} -8.13212 q^{29} +(-2.12733 + 1.63625i) q^{30} +0.868364 q^{31} -1.00000i q^{32} -0.332101i q^{33} +2.65591 q^{34} +(-5.90552 - 7.67792i) q^{35} -1.55943 q^{36} +5.72235i q^{37} +1.21298i q^{38} +4.99870 q^{39} +(1.36327 + 1.77243i) q^{40} +4.91678 q^{41} +5.19928i q^{42} +1.00000i q^{43} -0.276696 q^{44} +(2.76397 - 2.12592i) q^{45} -1.82155 q^{46} +7.94188i q^{47} -1.20024i q^{48} -11.7651 q^{49} +(-4.83259 - 1.28298i) q^{50} +3.18773 q^{51} -4.16476i q^{52} +1.31145i q^{53} -5.47240 q^{54} +(0.490423 - 0.377212i) q^{55} +4.33187 q^{56} +1.45586i q^{57} +8.13212i q^{58} +4.68922 q^{59} +(1.63625 + 2.12733i) q^{60} +5.55596 q^{61} -0.868364i q^{62} -6.75524i q^{63} -1.00000 q^{64} +(5.67770 + 7.38172i) q^{65} -0.332101 q^{66} +7.06731i q^{67} -2.65591i q^{68} -2.18629 q^{69} +(-7.67792 + 5.90552i) q^{70} +14.0990 q^{71} +1.55943i q^{72} -4.44146i q^{73} +5.72235 q^{74} +(-5.80026 - 1.53989i) q^{75} +1.21298 q^{76} -1.19861i q^{77} -4.99870i q^{78} -3.37116 q^{79} +(1.77243 - 1.36327i) q^{80} -1.88990 q^{81} -4.91678i q^{82} -9.61181i q^{83} +5.19928 q^{84} +(3.62073 + 4.70741i) q^{85} +1.00000 q^{86} +9.76048i q^{87} +0.276696i q^{88} +8.27820 q^{89} +(-2.12592 - 2.76397i) q^{90} +18.0412 q^{91} +1.82155i q^{92} -1.04224i q^{93} +7.94188 q^{94} +(-2.14991 + 1.65362i) q^{95} -1.20024 q^{96} -14.9186i q^{97} +11.7651i q^{98} +0.431487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	1.20024i		−	0.692958i	−0.938058	−	0.346479i	$-0.887377\pi$
$3$		−	1.20024i		−	0.692958i	0.938058	−	0.346479i	$-0.112623\pi$
$4$	−1.00000			−0.500000
$5$	1.77243	−	1.36327i	0.792653	−	0.609673i
$5$	1.77243	−	1.36327i	0.792653	−	0.609673i
$6$	−1.20024			−0.489995
$7$		−	4.33187i		−	1.63729i	−0.574297	−	0.818647i	$-0.694724\pi$
$7$		−	4.33187i		−	1.63729i	0.574297	−	0.818647i	$-0.305276\pi$
$8$			1.00000i			0.353553i
$9$	1.55943			0.519809
$10$	−1.36327	−	1.77243i	−0.431104	−	0.560490i
$11$	0.276696			0.0834270			0.0417135	−	0.999130i	$-0.486718\pi$
$11$	0.276696			0.0834270			0.0417135	+	0.999130i	$0.486718\pi$
$12$			1.20024i			0.346479i
$13$			4.16476i			1.15510i	0.816357	+	0.577548i	$0.195990\pi$
$13$			4.16476i			1.15510i	−0.816357	+	0.577548i	$0.804010\pi$
$14$	−4.33187			−1.15774
$15$	−1.63625	−	2.12733i	−0.422478	−	0.549275i
$16$	1.00000			0.250000
$17$			2.65591i			0.644153i	0.946714	+	0.322077i	$0.104381\pi$
$17$			2.65591i			0.644153i	−0.946714	+	0.322077i	$0.895619\pi$
$18$		−	1.55943i		−	0.367561i
$19$	−1.21298			−0.278276			−0.139138	−	0.990273i	$-0.544433\pi$
$19$	−1.21298			−0.278276			−0.139138	+	0.990273i	$0.544433\pi$
$20$	−1.77243	+	1.36327i	−0.396326	+	0.304837i
$21$	−5.19928			−1.13458
$22$		−	0.276696i		−	0.0589918i
$23$		−	1.82155i		−	0.379819i	−0.981802	−	0.189909i	$-0.939181\pi$
$23$		−	1.82155i		−	0.379819i	0.981802	−	0.189909i	$-0.0608194\pi$
$24$	1.20024			0.244998
$25$	1.28298	−	4.83259i	0.256597	−	0.966519i
$26$	4.16476			0.816777
$27$		−	5.47240i		−	1.05316i
$28$			4.33187i			0.818647i
$29$	−8.13212			−1.51010			−0.755048	−	0.655669i	$-0.772387\pi$
$29$	−8.13212			−1.51010			−0.755048	+	0.655669i	$0.772387\pi$
$30$	−2.12733	+	1.63625i	−0.388396	+	0.298737i
$31$	0.868364			0.155963			0.0779814	−	0.996955i	$-0.475153\pi$
$31$	0.868364			0.155963			0.0779814	+	0.996955i	$0.475153\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	0.332101i		−	0.0578114i
$34$	2.65591			0.455485
$35$	−5.90552	−	7.67792i	−0.998215	−	1.29781i
$36$	−1.55943			−0.259905
$37$			5.72235i			0.940748i	0.882467	+	0.470374i	$0.155881\pi$
$37$			5.72235i			0.940748i	−0.882467	+	0.470374i	$0.844119\pi$
$38$			1.21298i			0.196771i
$39$	4.99870			0.800433
$40$	1.36327	+	1.77243i	0.215552	+	0.280245i
$41$	4.91678			0.767872			0.383936	−	0.923360i	$-0.374568\pi$
$41$	4.91678			0.767872			0.383936	+	0.923360i	$0.374568\pi$
$42$			5.19928i			0.802267i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−0.276696			−0.0417135
$45$	2.76397	−	2.12592i	0.412028	−	0.316914i
$46$	−1.82155			−0.268572
$47$			7.94188i			1.15844i	0.815170	+	0.579221i	$0.196643\pi$
$47$			7.94188i			1.15844i	−0.815170	+	0.579221i	$0.803357\pi$
$48$		−	1.20024i		−	0.173240i
$49$	−11.7651			−1.68073
$50$	−4.83259	−	1.28298i	−0.683432	−	0.181441i
$51$	3.18773			0.446371
$52$		−	4.16476i		−	0.577548i
$53$			1.31145i			0.180141i	0.995935	+	0.0900705i	$0.0287092\pi$
$53$			1.31145i			0.180141i	−0.995935	+	0.0900705i	$0.971291\pi$
$54$	−5.47240			−0.744699
$55$	0.490423	−	0.377212i	0.0661286	−	0.0508632i
$56$	4.33187			0.578871
$57$			1.45586i			0.192833i
$58$			8.13212i			1.06780i
$59$	4.68922			0.610485			0.305242	−	0.952275i	$-0.401262\pi$
$59$	4.68922			0.610485			0.305242	+	0.952275i	$0.401262\pi$
$60$	1.63625	+	2.12733i	0.211239	+	0.274638i
$61$	5.55596			0.711368			0.355684	−	0.934606i	$-0.384248\pi$
$61$	5.55596			0.711368			0.355684	+	0.934606i	$0.384248\pi$
$62$		−	0.868364i		−	0.110282i
$63$		−	6.75524i		−	0.851081i
$64$	−1.00000			−0.125000
$65$	5.67770	+	7.38172i	0.704232	+	0.915590i
$66$	−0.332101			−0.0408788
$67$			7.06731i			0.863409i	0.902015	+	0.431704i	$0.142088\pi$
$67$			7.06731i			0.863409i	−0.902015	+	0.431704i	$0.857912\pi$
$68$		−	2.65591i		−	0.322077i
$69$	−2.18629			−0.263198
$70$	−7.67792	+	5.90552i	−0.917687	+	0.705845i
$71$	14.0990			1.67324			0.836620	−	0.547783i	$-0.184528\pi$
$71$	14.0990			1.67324			0.836620	+	0.547783i	$0.184528\pi$
$72$			1.55943i			0.183780i
$73$		−	4.44146i		−	0.519833i	−0.965631	−	0.259917i	$-0.916305\pi$
$73$		−	4.44146i		−	0.519833i	0.965631	−	0.259917i	$-0.0836950\pi$
$74$	5.72235			0.665209
$75$	−5.80026	−	1.53989i	−0.669757	−	0.177811i
$76$	1.21298			0.139138
$77$		−	1.19861i		−	0.136595i
$78$		−	4.99870i		−	0.565992i
$79$	−3.37116			−0.379285			−0.189642	−	0.981853i	$-0.560733\pi$
$79$	−3.37116			−0.379285			−0.189642	+	0.981853i	$0.560733\pi$
$80$	1.77243	−	1.36327i	0.198163	−	0.152418i
$81$	−1.88990			−0.209989
$82$		−	4.91678i		−	0.542967i
$83$		−	9.61181i		−	1.05503i	−0.849545	−	0.527517i	$-0.823123\pi$
$83$		−	9.61181i		−	1.05503i	0.849545	−	0.527517i	$-0.176877\pi$
$84$	5.19928			0.567288
$85$	3.62073	+	4.70741i	0.392723	+	0.510590i
$86$	1.00000			0.107833
$87$			9.76048i			1.04643i
$88$			0.276696i			0.0294959i
$89$	8.27820			0.877487			0.438744	−	0.898612i	$-0.355424\pi$
$89$	8.27820			0.877487			0.438744	+	0.898612i	$0.355424\pi$
$90$	−2.12592	−	2.76397i	−0.224092	−	0.291348i
$91$	18.0412			1.89123
$92$			1.82155i			0.189909i
$93$		−	1.04224i		−	0.108076i
$94$	7.94188			0.819143
$95$	−2.14991	+	1.65362i	−0.220576	+	0.169657i
$96$	−1.20024			−0.122499
$97$		−	14.9186i		−	1.51475i	−0.652980	−	0.757375i	$-0.726482\pi$
$97$		−	14.9186i		−	1.51475i	0.652980	−	0.757375i	$-0.273518\pi$
$98$			11.7651i			1.18846i
$99$	0.431487			0.0433661
$100$	−1.28298	+	4.83259i	−0.128298	+	0.483259i
$101$	16.4300			1.63484			0.817421	−	0.576041i	$-0.195403\pi$
$101$	16.4300			1.63484			0.817421	+	0.576041i	$0.195403\pi$
$102$		−	3.18773i		−	0.315632i
$103$			13.5565i			1.33576i	0.744270	+	0.667879i	$0.232798\pi$
$103$			13.5565i			1.33576i	−0.744270	+	0.667879i	$0.767202\pi$
$104$	−4.16476			−0.408388
$105$	−9.21534	+	7.08803i	−0.899325	+	0.691721i
$106$	1.31145			0.127379
$107$		−	10.8456i		−	1.04848i	−0.851571	−	0.524240i	$-0.824349\pi$
$107$		−	10.8456i		−	1.04848i	0.851571	−	0.524240i	$-0.175651\pi$
$108$			5.47240i			0.526582i
$109$	−12.7649			−1.22266			−0.611328	−	0.791377i	$-0.709364\pi$
$109$	−12.7649			−1.22266			−0.611328	+	0.791377i	$0.709364\pi$
$110$	−0.377212	−	0.490423i	−0.0359657	−	0.0467600i
$111$	6.86818			0.651899
$112$		−	4.33187i		−	0.409324i
$113$			10.2517i			0.964395i	0.876062	+	0.482198i	$0.160161\pi$
$113$			10.2517i			0.964395i	−0.876062	+	0.482198i	$0.839839\pi$
$114$	1.45586			0.136354
$115$	−2.48326	−	3.22856i	−0.231565	−	0.301064i
$116$	8.13212			0.755048
$117$			6.49464i			0.600430i
$118$		−	4.68922i		−	0.431678i
$119$	11.5051			1.05467
$120$	2.12733	−	1.63625i	0.194198	−	0.149369i
$121$	−10.9234			−0.993040
$122$		−	5.55596i		−	0.503013i
$123$		−	5.90131i		−	0.532103i
$124$	−0.868364			−0.0779814
$125$	−4.31414	−	10.3145i	−0.385869	−	0.922554i
$126$	−6.75524			−0.601805
$127$		−	9.30180i		−	0.825401i	−0.910867	−	0.412701i	$-0.864586\pi$
$127$		−	9.30180i		−	0.825401i	0.910867	−	0.412701i	$-0.135414\pi$
$128$			1.00000i			0.0883883i
$129$	1.20024			0.105675
$130$	7.38172	−	5.67770i	0.647420	−	0.497967i
$131$	−7.16097			−0.625657			−0.312828	−	0.949810i	$-0.601276\pi$
$131$	−7.16097			−0.625657			−0.312828	+	0.949810i	$0.601276\pi$
$132$			0.332101i			0.0289057i
$133$			5.25446i			0.455620i
$134$	7.06731			0.610522
$135$	−7.46037	−	9.69942i	−0.642086	−	0.834793i
$136$	−2.65591			−0.227743
$137$			8.87184i			0.757973i	0.925402	+	0.378986i	$0.123727\pi$
$137$			8.87184i			0.757973i	−0.925402	+	0.378986i	$0.876273\pi$
$138$			2.18629i			0.186109i
$139$	−19.1774			−1.62661			−0.813304	−	0.581838i	$-0.802334\pi$
$139$	−19.1774			−1.62661			−0.813304	+	0.581838i	$0.802334\pi$
$140$	5.90552	+	7.67792i	0.499108	+	0.648903i
$141$	9.53215			0.802752
$142$		−	14.0990i		−	1.18316i
$143$			1.15237i			0.0963662i
$144$	1.55943			0.129952
$145$	−14.4136	+	11.0863i	−1.19698	+	0.920666i
$146$	−4.44146			−0.367577
$147$			14.1210i			1.16468i
$148$		−	5.72235i		−	0.470374i
$149$	21.8131			1.78700			0.893501	−	0.449062i	$-0.148242\pi$
$149$	21.8131			1.78700			0.893501	+	0.449062i	$0.148242\pi$
$150$	−1.53989	+	5.80026i	−0.125731	+	0.473590i
$151$	8.52294			0.693587			0.346794	−	0.937941i	$-0.387270\pi$
$151$	8.52294			0.693587			0.346794	+	0.937941i	$0.387270\pi$
$152$		−	1.21298i		−	0.0983854i
$153$			4.14170i			0.334837i
$154$	−1.19861			−0.0965869
$155$	1.53911	−	1.18382i	0.123624	−	0.0950864i
$156$	−4.99870			−0.400217
$157$			19.5923i			1.56363i	0.623509	+	0.781816i	$0.285707\pi$
$157$			19.5923i			1.56363i	−0.623509	+	0.781816i	$0.714293\pi$
$158$			3.37116i			0.268195i
$159$	1.57405			0.124830
$160$	−1.36327	−	1.77243i	−0.107776	−	0.140123i
$161$	−7.89071			−0.621875
$162$			1.88990i			0.148485i
$163$			14.5972i			1.14334i	0.820484	+	0.571670i	$0.193704\pi$
$163$			14.5972i			1.14334i	−0.820484	+	0.571670i	$0.806296\pi$
$164$	−4.91678			−0.383936
$165$	−0.452744	−	0.588625i	−0.0352461	−	0.0458244i
$166$	−9.61181			−0.746021
$167$		−	2.92331i		−	0.226213i	−0.993583	−	0.113106i	$-0.963920\pi$
$167$		−	2.92331i		−	0.226213i	0.993583	−	0.113106i	$-0.0360801\pi$
$168$		−	5.19928i		−	0.401133i
$169$	−4.34522			−0.334248
$170$	4.70741	−	3.62073i	0.361042	−	0.277697i
$171$	−1.89155			−0.144650
$172$		−	1.00000i		−	0.0762493i
$173$		−	1.88524i		−	0.143333i	−0.997429	−	0.0716663i	$-0.977168\pi$
$173$		−	1.88524i		−	0.143333i	0.997429	−	0.0716663i	$-0.0228317\pi$
$174$	9.76048			0.739940
$175$	−20.9342	−	5.55772i	−1.58248	−	0.420124i
$176$	0.276696			0.0208567
$177$		−	5.62819i		−	0.423040i
$178$		−	8.27820i		−	0.620477i
$179$	23.5607			1.76101			0.880504	−	0.474039i	$-0.157204\pi$
$179$	23.5607			1.76101			0.880504	+	0.474039i	$0.157204\pi$
$180$	−2.76397	+	2.12592i	−0.206014	+	0.158457i
$181$	−14.3060			−1.06336			−0.531679	−	0.846946i	$-0.678439\pi$
$181$	−14.3060			−1.06336			−0.531679	+	0.846946i	$0.678439\pi$
$182$		−	18.0412i		−	1.33730i
$183$		−	6.66848i		−	0.492948i
$184$	1.82155			0.134286
$185$	7.80111	+	10.1424i	0.573549	+	0.745687i
$186$	−1.04224			−0.0764210
$187$			0.734880i			0.0537398i
$188$		−	7.94188i		−	0.579221i
$189$	−23.7058			−1.72434
$190$	1.65362	+	2.14991i	0.119966	+	0.155971i
$191$	−10.6098			−0.767701			−0.383851	−	0.923395i	$-0.625402\pi$
$191$	−10.6098			−0.767701			−0.383851	+	0.923395i	$0.625402\pi$
$192$			1.20024i			0.0866198i
$193$		−	19.6176i		−	1.41210i	−0.708160	−	0.706052i	$-0.750474\pi$
$193$		−	19.6176i		−	1.41210i	0.708160	−	0.706052i	$-0.249526\pi$
$194$	−14.9186			−1.07109
$195$	8.85983	−	6.81459i	0.634466	−	0.488003i
$196$	11.7651			0.840367
$197$			21.2588i			1.51463i	0.653051	+	0.757314i	$0.273489\pi$
$197$			21.2588i			1.51463i	−0.653051	+	0.757314i	$0.726511\pi$
$198$		−	0.431487i		−	0.0306645i
$199$	−11.5372			−0.817850			−0.408925	−	0.912568i	$-0.634096\pi$
$199$	−11.5372			−0.817850			−0.408925	+	0.912568i	$0.634096\pi$
$200$	4.83259	+	1.28298i	0.341716	+	0.0907206i
$201$	8.48245			0.598306
$202$		−	16.4300i		−	1.15601i
$203$			35.2273i			2.47247i
$204$	−3.18773			−0.223186
$205$	8.71462	−	6.70290i	0.608656	−	0.468151i
$206$	13.5565			0.944524
$207$		−	2.84057i		−	0.197433i
$208$			4.16476i			0.288774i
$209$	−0.335626			−0.0232157
$210$	7.08803	+	9.21534i	0.489121	+	0.635919i
$211$	11.8621			0.816622			0.408311	−	0.912843i	$-0.366118\pi$
$211$	11.8621			0.816622			0.408311	+	0.912843i	$0.366118\pi$
$212$		−	1.31145i		−	0.0900705i
$213$		−	16.9221i		−	1.15949i
$214$	−10.8456			−0.741387
$215$	1.36327	+	1.77243i	0.0929743	+	0.120878i
$216$	5.47240			0.372350
$217$		−	3.76164i		−	0.255357i
$218$			12.7649i			0.864549i
$219$	−5.33081			−0.360222
$220$	−0.490423	+	0.377212i	−0.0330643	+	0.0254316i
$221$	−11.0612			−0.744059
$222$		−	6.86818i		−	0.460962i
$223$		−	7.93765i		−	0.531544i	−0.964036	−	0.265772i	$-0.914373\pi$
$223$		−	7.93765i		−	0.531544i	0.964036	−	0.265772i	$-0.0856269\pi$
$224$	−4.33187			−0.289436
$225$	2.00072	−	7.53608i	0.133381	−	0.502405i
$226$	10.2517			0.681931
$227$		−	12.8619i		−	0.853676i	−0.904328	−	0.426838i	$-0.859628\pi$
$227$		−	12.8619i		−	0.853676i	0.904328	−	0.426838i	$-0.140372\pi$
$228$		−	1.45586i		−	0.0964167i
$229$	−22.2719			−1.47177			−0.735885	−	0.677106i	$-0.763234\pi$
$229$	−22.2719			−1.47177			−0.735885	+	0.677106i	$0.763234\pi$
$230$	−3.22856	+	2.48326i	−0.212885	+	0.163741i
$231$	−1.43862			−0.0946543
$232$		−	8.13212i		−	0.533900i
$233$		−	15.1937i		−	0.995373i	−0.867357	−	0.497686i	$-0.834183\pi$
$233$		−	15.1937i		−	0.995373i	0.867357	−	0.497686i	$-0.165817\pi$
$234$	6.49464			0.424568
$235$	10.8269	+	14.0764i	0.706272	+	0.918243i
$236$	−4.68922			−0.305242
$237$			4.04619i			0.262829i
$238$		−	11.5051i		−	0.745763i
$239$	−21.9439			−1.41943			−0.709715	−	0.704489i	$-0.751176\pi$
$239$	−21.9439			−1.41943			−0.709715	+	0.704489i	$0.751176\pi$
$240$	−1.63625	−	2.12733i	−0.105620	−	0.137319i
$241$	−5.10417			−0.328789			−0.164394	−	0.986395i	$-0.552567\pi$
$241$	−5.10417			−0.328789			−0.164394	+	0.986395i	$0.552567\pi$
$242$			10.9234i			0.702185i
$243$		−	14.1489i		−	0.907650i
$244$	−5.55596			−0.355684
$245$	−20.8528	+	16.0391i	−1.33224	+	1.02470i
$246$	−5.90131			−0.376253
$247$		−	5.05175i		−	0.321435i
$248$			0.868364i			0.0551412i
$249$	−11.5365			−0.731094
$250$	−10.3145	+	4.31414i	−0.652344	+	0.272850i
$251$	−29.6307			−1.87028			−0.935138	−	0.354284i	$-0.884725\pi$
$251$	−29.6307			−1.87028			−0.935138	+	0.354284i	$0.884725\pi$
$252$			6.75524i			0.425540i
$253$		−	0.504015i		−	0.0316871i
$254$	−9.30180			−0.583647
$255$	5.65001	−	4.34574i	0.353817	−	0.272141i
$256$	1.00000			0.0625000
$257$			18.1428i			1.13172i	0.824503	+	0.565858i	$0.191455\pi$
$257$			18.1428i			1.13172i	−0.824503	+	0.565858i	$0.808545\pi$
$258$		−	1.20024i		−	0.0747236i
$259$	24.7885			1.54028
$260$	−5.67770	−	7.38172i	−0.352116	−	0.457795i
$261$	−12.6814			−0.784962
$262$			7.16097i			0.442406i
$263$		−	13.7467i		−	0.847661i	−0.905742	−	0.423830i	$-0.860685\pi$
$263$		−	13.7467i		−	0.847661i	0.905742	−	0.423830i	$-0.139315\pi$
$264$	0.332101			0.0204394
$265$	1.78786	+	2.32444i	0.109827	+	0.142789i
$266$	5.25446			0.322172
$267$		−	9.93581i		−	0.608062i
$268$		−	7.06731i		−	0.431704i
$269$	3.68903			0.224924			0.112462	−	0.993656i	$-0.464126\pi$
$269$	3.68903			0.224924			0.112462	+	0.993656i	$0.464126\pi$
$270$	−9.69942	+	7.46037i	−0.590288	+	0.454023i
$271$	0.746757			0.0453622			0.0226811	−	0.999743i	$-0.492780\pi$
$271$	0.746757			0.0453622			0.0226811	+	0.999743i	$0.492780\pi$
$272$			2.65591i			0.161038i
$273$		−	21.6538i		−	1.31055i
$274$	8.87184			0.535968
$275$	0.354996	−	1.33716i	0.0214071	−	0.0806337i
$276$	2.18629			0.131599
$277$			0.719612i			0.0432373i	0.999766	+	0.0216186i	$0.00688196\pi$
$277$			0.719612i			0.0432373i	−0.999766	+	0.0216186i	$0.993118\pi$
$278$			19.1774i			1.15019i
$279$	1.35415			0.0810709
$280$	7.67792	−	5.90552i	0.458844	−	0.352922i
$281$	0.670605			0.0400049			0.0200025	−	0.999800i	$-0.493633\pi$
$281$	0.670605			0.0400049			0.0200025	+	0.999800i	$0.493633\pi$
$282$		−	9.53215i		−	0.567631i
$283$		−	7.76210i		−	0.461409i	−0.973024	−	0.230704i	$-0.925897\pi$
$283$		−	7.76210i		−	0.461409i	0.973024	−	0.230704i	$-0.0741030\pi$
$284$	−14.0990			−0.836620
$285$	1.98473	+	2.58040i	0.117565	+	0.152850i
$286$	1.15237			0.0681412
$287$		−	21.2989i		−	1.25723i
$288$		−	1.55943i		−	0.0918902i
$289$	9.94613			0.585067
$290$	11.0863	+	14.4136i	0.651009	+	0.846394i
$291$	−17.9058			−1.04966
$292$			4.44146i			0.259917i
$293$			17.4486i			1.01936i	0.860364	+	0.509680i	$0.170236\pi$
$293$			17.4486i			1.01936i	−0.860364	+	0.509680i	$0.829764\pi$
$294$	14.1210			0.823552
$295$	8.31130	−	6.39268i	0.483903	−	0.372196i
$296$	−5.72235			−0.332605
$297$		−	1.51419i		−	0.0878623i
$298$		−	21.8131i		−	1.26360i
$299$	7.58630			0.438727
$300$	5.80026	+	1.53989i	0.334878	+	0.0889053i
$301$	4.33187			0.249685
$302$		−	8.52294i		−	0.490440i
$303$		−	19.7199i		−	1.13288i
$304$	−1.21298			−0.0695690
$305$	9.84753	−	7.57428i	0.563868	−	0.433702i
$306$	4.14170			0.236765
$307$			28.0493i			1.60086i	0.599428	+	0.800429i	$0.295395\pi$
$307$			28.0493i			1.60086i	−0.599428	+	0.800429i	$0.704605\pi$
$308$			1.19861i			0.0682973i
$309$	16.2710			0.925625
$310$	−1.18382	−	1.53911i	−0.0672362	−	0.0874156i
$311$	16.8210			0.953834			0.476917	−	0.878948i	$-0.341754\pi$
$311$	16.8210			0.953834			0.476917	+	0.878948i	$0.341754\pi$
$312$			4.99870i			0.282996i
$313$		−	22.6662i		−	1.28117i	−0.767887	−	0.640585i	$-0.778692\pi$
$313$		−	22.6662i		−	1.28117i	0.767887	−	0.640585i	$-0.221308\pi$
$314$	19.5923			1.10566
$315$	−9.20923	−	11.9732i	−0.518881	−	0.674611i
$316$	3.37116			0.189642
$317$			22.5794i			1.26819i	0.773256	+	0.634094i	$0.218627\pi$
$317$			22.5794i			1.26819i	−0.773256	+	0.634094i	$0.781373\pi$
$318$		−	1.57405i		−	0.0882682i
$319$	−2.25012			−0.125983
$320$	−1.77243	+	1.36327i	−0.0990816	+	0.0762092i
$321$	−13.0173			−0.726553
$322$			7.89071i			0.439732i
$323$		−	3.22156i		−	0.179252i
$324$	1.88990			0.104995
$325$	20.1266	+	5.34332i	1.11642	+	0.296394i
$326$	14.5972			0.808464
$327$			15.3209i			0.847250i
$328$			4.91678i			0.271484i
$329$	34.4032			1.89671
$330$	−0.588625	+	0.452744i	−0.0324027	+	0.0249227i
$331$	−8.81733			−0.484644			−0.242322	−	0.970196i	$-0.577909\pi$
$331$	−8.81733			−0.484644			−0.242322	+	0.970196i	$0.577909\pi$
$332$			9.61181i			0.527517i
$333$			8.92359i			0.489010i
$334$	−2.92331			−0.159957
$335$	9.63466	+	12.5263i	0.526398	+	0.684383i
$336$	−5.19928			−0.283644
$337$			15.7948i			0.860398i	0.902734	+	0.430199i	$0.141557\pi$
$337$			15.7948i			0.860398i	−0.902734	+	0.430199i	$0.858443\pi$
$338$			4.34522i			0.236349i
$339$	12.3044			0.668286
$340$	−3.62073	−	4.70741i	−0.196362	−	0.255295i
$341$	0.240273			0.0130115
$342$			1.89155i			0.102283i
$343$			20.6420i			1.11456i
$344$	−1.00000			−0.0539164
$345$	−3.87504	+	2.98051i	−0.208625	+	0.160465i
$346$	−1.88524			−0.101351
$347$			9.65491i			0.518303i	0.965837	+	0.259151i	$0.0834428\pi$
$347$			9.65491i			0.518303i	−0.965837	+	0.259151i	$0.916557\pi$
$348$		−	9.76048i		−	0.523217i
$349$	−30.1877			−1.61591			−0.807955	−	0.589245i	$-0.799425\pi$
$349$	−30.1877			−1.61591			−0.807955	+	0.589245i	$0.799425\pi$
$350$	−5.55772	+	20.9342i	−0.297073	+	1.11898i
$351$	22.7912			1.21651
$352$		−	0.276696i		−	0.0147479i
$353$		−	4.00797i		−	0.213323i	−0.994295	−	0.106661i	$-0.965984\pi$
$353$		−	4.00797i		−	0.213323i	0.994295	−	0.106661i	$-0.0340161\pi$
$354$	−5.62819			−0.299135
$355$	24.9894	−	19.2207i	1.32630	−	1.02013i
$356$	−8.27820			−0.438744
$357$		−	13.8088i		−	0.730841i
$358$		−	23.5607i		−	1.24522i
$359$	−25.0926			−1.32433			−0.662167	−	0.749356i	$-0.730363\pi$
$359$	−25.0926			−1.32433			−0.662167	+	0.749356i	$0.730363\pi$
$360$	2.12592	+	2.76397i	0.112046	+	0.145674i
$361$	−17.5287			−0.922563
$362$			14.3060i			0.751908i
$363$			13.1107i			0.688135i
$364$	−18.0412			−0.945617
$365$	−6.05491	−	7.87215i	−0.316928	−	0.412047i
$366$	−6.66848			−0.348567
$367$			21.8468i			1.14039i	0.821509	+	0.570196i	$0.193133\pi$
$367$			21.8468i			1.14039i	−0.821509	+	0.570196i	$0.806867\pi$
$368$		−	1.82155i		−	0.0949547i
$369$	7.66736			0.399147
$370$	10.1424	−	7.80111i	0.527280	−	0.405561i
$371$	5.68102			0.294944
$372$			1.04224i			0.0540378i
$373$			24.9641i			1.29259i	0.763086	+	0.646297i	$0.223683\pi$
$373$			24.9641i			1.29259i	−0.763086	+	0.646297i	$0.776317\pi$
$374$	0.734880			0.0379998
$375$	−12.3798	+	5.17800i	−0.639291	+	0.267391i
$376$	−7.94188			−0.409571
$377$		−	33.8683i		−	1.74431i
$378$			23.7058i			1.21929i
$379$	32.9305			1.69152			0.845762	−	0.533561i	$-0.179146\pi$
$379$	32.9305			1.69152			0.845762	+	0.533561i	$0.179146\pi$
$380$	2.14991	−	1.65362i	0.110288	−	0.0848287i
$381$	−11.1644			−0.571969
$382$			10.6098i			0.542847i
$383$		−	3.12657i		−	0.159760i	−0.996804	−	0.0798801i	$-0.974546\pi$
$383$		−	3.12657i		−	0.159760i	0.996804	−	0.0798801i	$-0.0254537\pi$
$384$	1.20024			0.0612494
$385$	−1.63403	−	2.12445i	−0.0832781	−	0.108272i
$386$	−19.6176			−0.998508
$387$			1.55943i			0.0792702i
$388$			14.9186i			0.757375i
$389$	22.8148			1.15675			0.578377	−	0.815770i	$-0.303686\pi$
$389$	22.8148			1.15675			0.578377	+	0.815770i	$0.303686\pi$
$390$	−6.81459	−	8.85983i	−0.345070	−	0.448635i
$391$	4.83787			0.244661
$392$		−	11.7651i		−	0.594229i
$393$			8.59487i			0.433554i
$394$	21.2588			1.07100
$395$	−5.97513	+	4.59580i	−0.300641	+	0.231240i
$396$	−0.431487			−0.0216831
$397$			3.13451i			0.157317i	0.996902	+	0.0786584i	$0.0250636\pi$
$397$			3.13451i			0.157317i	−0.996902	+	0.0786584i	$0.974936\pi$
$398$			11.5372i			0.578307i
$399$	6.30661			0.315725
$400$	1.28298	−	4.83259i	0.0641491	−	0.241630i
$401$	24.3939			1.21817			0.609086	−	0.793104i	$-0.291536\pi$
$401$	24.3939			1.21817			0.609086	+	0.793104i	$0.291536\pi$
$402$		−	8.48245i		−	0.423066i
$403$			3.61653i			0.180152i
$404$	−16.4300			−0.817421
$405$	−3.34971	+	2.57645i	−0.166448	+	0.128025i
$406$	35.2273			1.74830
$407$			1.58335i			0.0784838i
$408$			3.18773i			0.157816i
$409$	−11.4073			−0.564052			−0.282026	−	0.959407i	$-0.591007\pi$
$409$	−11.4073			−0.564052			−0.282026	+	0.959407i	$0.591007\pi$
$410$	−6.70290	−	8.71462i	−0.331033	−	0.430384i
$411$	10.6483			0.525243
$412$		−	13.5565i		−	0.667879i
$413$		−	20.3131i		−	0.999544i
$414$	−2.84057			−0.139606
$415$	−13.1035	−	17.0362i	−0.643226	−	0.836275i
$416$	4.16476			0.204194
$417$			23.0175i			1.12717i
$418$			0.335626i			0.0164160i
$419$	32.6578			1.59544			0.797720	−	0.603028i	$-0.206039\pi$
$419$	32.6578			1.59544			0.797720	+	0.603028i	$0.206039\pi$
$420$	9.21534	−	7.08803i	0.449663	−	0.345861i
$421$	8.84416			0.431038			0.215519	−	0.976500i	$-0.430856\pi$
$421$	8.84416			0.431038			0.215519	+	0.976500i	$0.430856\pi$
$422$		−	11.8621i		−	0.577439i
$423$			12.3848i			0.602169i
$424$	−1.31145			−0.0636894
$425$	12.8349	+	3.40749i	0.622586	+	0.165288i
$426$	−16.9221			−0.819880
$427$		−	24.0677i		−	1.16472i
$428$			10.8456i			0.524240i
$429$	1.38312			0.0667777
$430$	1.77243	−	1.36327i	0.0854739	−	0.0657428i
$431$	−24.2816			−1.16960			−0.584801	−	0.811177i	$-0.698827\pi$
$431$	−24.2816			−1.16960			−0.584801	+	0.811177i	$0.698827\pi$
$432$		−	5.47240i		−	0.263291i
$433$		−	18.2285i		−	0.876007i	−0.898973	−	0.438003i	$-0.855686\pi$
$433$		−	18.2285i		−	0.876007i	0.898973	−	0.438003i	$-0.144314\pi$
$434$	−3.76164			−0.180565
$435$	13.3062	+	17.2997i	0.637983	+	0.829458i
$436$	12.7649			0.611328
$437$			2.20949i			0.105694i
$438$			5.33081i			0.254716i
$439$	−25.6050			−1.22206			−0.611030	−	0.791607i	$-0.709245\pi$
$439$	−25.6050			−1.22206			−0.611030	+	0.791607i	$0.709245\pi$
$440$	0.377212	+	0.490423i	0.0179829	+	0.0233800i
$441$	−18.3469			−0.873661
$442$			11.0612i			0.526129i
$443$		−	12.3973i		−	0.589014i	−0.955649	−	0.294507i	$-0.904845\pi$
$443$		−	12.3973i		−	0.589014i	0.955649	−	0.294507i	$-0.0951554\pi$
$444$	−6.86818			−0.325949
$445$	14.6725	−	11.2854i	0.695543	−	0.534981i
$446$	−7.93765			−0.375859
$447$		−	26.1810i		−	1.23832i
$448$			4.33187i			0.204662i
$449$	30.4208			1.43564			0.717822	−	0.696226i	$-0.245139\pi$
$449$	30.4208			1.43564			0.717822	+	0.696226i	$0.245139\pi$
$450$	−7.53608	−	2.00072i	−0.355254	−	0.0943148i
$451$	1.36045			0.0640612
$452$		−	10.2517i		−	0.482198i
$453$		−	10.2296i		−	0.480627i
$454$	−12.8619			−0.603640
$455$	31.9767	−	24.5951i	1.49909	−	1.15303i
$456$	−1.45586			−0.0681769
$457$			37.9047i			1.77311i	0.462626	+	0.886554i	$0.346907\pi$
$457$			37.9047i			1.77311i	−0.462626	+	0.886554i	$0.653093\pi$
$458$			22.2719i			1.04070i
$459$	14.5342			0.678399
$460$	2.48326	+	3.22856i	0.115783	+	0.150532i
$461$	−30.4939			−1.42024			−0.710121	−	0.704079i	$-0.751360\pi$
$461$	−30.4939			−1.42024			−0.710121	+	0.704079i	$0.751360\pi$
$462$			1.43862i			0.0669307i
$463$			36.9446i			1.71696i	0.512847	+	0.858480i	$0.328591\pi$
$463$			36.9446i			1.71696i	−0.512847	+	0.858480i	$0.671409\pi$
$464$	−8.13212			−0.377524
$465$	−1.42086	−	1.84730i	−0.0658909	−	0.0856665i
$466$	−15.1937			−0.703835
$467$		−	6.55650i		−	0.303398i	−0.988427	−	0.151699i	$-0.951525\pi$
$467$		−	6.55650i		−	0.303398i	0.988427	−	0.151699i	$-0.0484745\pi$
$468$		−	6.49464i		−	0.300215i
$469$	30.6147			1.41365
$470$	14.0764	−	10.8269i	0.649296	−	0.499409i
$471$	23.5154			1.08353
$472$			4.68922i			0.215839i
$473$			0.276696i			0.0127225i
$474$	4.04619			0.185848
$475$	−1.55623	+	5.86182i	−0.0714046	+	0.268959i
$476$	−11.5051			−0.527334
$477$			2.04510i			0.0936389i
$478$			21.9439i			1.00369i
$479$	6.29516			0.287633			0.143817	−	0.989604i	$-0.454062\pi$
$479$	6.29516			0.287633			0.143817	+	0.989604i	$0.454062\pi$
$480$	−2.12733	+	1.63625i	−0.0970990	+	0.0746843i
$481$	−23.8322			−1.08665
$482$			5.10417i			0.232489i
$483$			9.47073i			0.430933i
$484$	10.9234			0.496520
$485$	−20.3380	−	26.4420i	−0.923503	−	1.20067i
$486$	−14.1489			−0.641806
$487$		−	8.73653i		−	0.395890i	−0.980213	−	0.197945i	$-0.936573\pi$
$487$		−	8.73653i		−	0.395890i	0.980213	−	0.197945i	$-0.0634268\pi$
$488$			5.55596i			0.251507i
$489$	17.5201			0.792287
$490$	16.0391	+	20.8528i	0.724571	+	0.942035i
$491$	−26.0249			−1.17449			−0.587244	−	0.809410i	$-0.699787\pi$
$491$	−26.0249			−1.17449			−0.587244	+	0.809410i	$0.699787\pi$
$492$			5.90131i			0.266051i
$493$		−	21.5982i		−	0.972733i
$494$	−5.05175			−0.227289
$495$	0.764779	−	0.588234i	0.0343743	−	0.0264392i
$496$	0.868364			0.0389907
$497$		−	61.0750i		−	2.73959i
$498$			11.5365i			0.516961i
$499$	−41.4093			−1.85374			−0.926868	−	0.375388i	$-0.877509\pi$
$499$	−41.4093			−1.85374			−0.926868	+	0.375388i	$0.877509\pi$
$500$	4.31414	+	10.3145i	0.192934	+	0.461277i
$501$	−3.50867			−0.156756
$502$			29.6307i			1.32248i
$503$			22.7586i			1.01476i	0.861723	+	0.507378i	$0.169385\pi$
$503$			22.7586i			1.01476i	−0.861723	+	0.507378i	$0.830615\pi$
$504$	6.75524			0.300903
$505$	29.1209	−	22.3985i	1.29586	−	0.996719i
$506$	−0.504015			−0.0224062
$507$			5.21530i			0.231620i
$508$			9.30180i			0.412701i
$509$	−27.9287			−1.23792			−0.618958	−	0.785424i	$-0.712445\pi$
$509$	−27.9287			−1.23792			−0.618958	+	0.785424i	$0.712445\pi$
$510$	−4.34574	−	5.65001i	−0.192432	−	0.250187i
$511$	−19.2398			−0.851120
$512$		−	1.00000i		−	0.0441942i
$513$			6.63789i			0.293070i
$514$	18.1428			0.800243
$515$	18.4811	+	24.0278i	0.814376	+	1.05879i
$516$	−1.20024			−0.0528376
$517$			2.19749i			0.0966454i
$518$		−	24.7885i		−	1.08914i
$519$	−2.26274			−0.0993234
$520$	−7.38172	+	5.67770i	−0.323710	+	0.248983i
$521$	21.4902			0.941501			0.470751	−	0.882266i	$-0.343983\pi$
$521$	21.4902			0.941501			0.470751	+	0.882266i	$0.343983\pi$
$522$			12.6814i			0.555052i
$523$			33.9294i			1.48363i	0.670605	+	0.741814i	$0.266034\pi$
$523$			33.9294i			1.48363i	−0.670605	+	0.741814i	$0.733966\pi$
$524$	7.16097			0.312828
$525$	−6.67059	+	25.1260i	−0.291128	+	1.09659i
$526$	−13.7467			−0.599387
$527$			2.30630i			0.100464i
$528$		−	0.332101i		−	0.0144528i
$529$	19.6820			0.855738
$530$	2.32444	−	1.78786i	0.100967	−	0.0776595i
$531$	7.31251			0.317336
$532$		−	5.25446i		−	0.227810i
$533$			20.4772i			0.886966i
$534$	−9.93581			−0.429965
$535$	−14.7854	−	19.2229i	−0.639230	−	0.831081i
$536$	−7.06731			−0.305261
$537$		−	28.2784i		−	1.22030i
$538$		−	3.68903i		−	0.159045i
$539$	−3.25537			−0.140219
$540$	7.46037	+	9.69942i	0.321043	+	0.417397i
$541$	−4.50140			−0.193530			−0.0967651	−	0.995307i	$-0.530850\pi$
$541$	−4.50140			−0.193530			−0.0967651	+	0.995307i	$0.530850\pi$
$542$		−	0.746757i		−	0.0320759i
$543$			17.1706i			0.736863i
$544$	2.65591			0.113871
$545$	−22.6248	+	17.4020i	−0.969142	+	0.745421i
$546$	−21.6538			−0.926695
$547$			20.6906i			0.884665i	0.896851	+	0.442332i	$0.145849\pi$
$547$			20.6906i			0.884665i	−0.896851	+	0.442332i	$0.854151\pi$
$548$		−	8.87184i		−	0.378986i
$549$	8.66412			0.369776
$550$	−1.33716	−	0.354996i	−0.0570167	−	0.0151371i
$551$	9.86406			0.420223
$552$		−	2.18629i		−	0.0930547i
$553$			14.6034i			0.621001i
$554$	0.719612			0.0305734
$555$	12.1733	−	9.36320i	0.516729	−	0.397446i
$556$	19.1774			0.813304
$557$			11.6903i			0.495333i	0.968845	+	0.247666i	$0.0796637\pi$
$557$			11.6903i			0.495333i	−0.968845	+	0.247666i	$0.920336\pi$
$558$		−	1.35415i		−	0.0573258i
$559$	−4.16476			−0.176151
$560$	−5.90552	−	7.67792i	−0.249554	−	0.324451i
$561$	0.882031			0.0372394
$562$		−	0.670605i		−	0.0282878i
$563$			4.14835i			0.174832i	0.996172	+	0.0874161i	$0.0278610\pi$
$563$			4.14835i			0.174832i	−0.996172	+	0.0874161i	$0.972139\pi$
$564$	−9.53215			−0.401376
$565$	13.9758	+	18.1703i	0.587966	+	0.764431i
$566$	−7.76210			−0.326265
$567$			8.18682i			0.343814i
$568$			14.0990i			0.591580i
$569$	15.7777			0.661436			0.330718	−	0.943730i	$-0.392709\pi$
$569$	15.7777			0.661436			0.330718	+	0.943730i	$0.392709\pi$
$570$	2.58040	−	1.98473i	0.108081	−	0.0831313i
$571$	−21.5196			−0.900566			−0.450283	−	0.892886i	$-0.648677\pi$
$571$	−21.5196			−0.900566			−0.450283	+	0.892886i	$0.648677\pi$
$572$		−	1.15237i		−	0.0481831i
$573$			12.7343i			0.531985i
$574$	−21.2989			−0.888997
$575$	−8.80279	−	2.33701i	−0.367102	−	0.0974602i
$576$	−1.55943			−0.0649762
$577$		−	24.5251i		−	1.02099i	−0.859880	−	0.510496i	$-0.829462\pi$
$577$		−	24.5251i		−	1.02099i	0.859880	−	0.510496i	$-0.170538\pi$
$578$		−	9.94613i		−	0.413705i
$579$	−23.5458			−0.978529
$580$	14.4136	−	11.0863i	0.598491	−	0.460333i
$581$	−41.6372			−1.72740
$582$			17.9058i			0.742220i
$583$			0.362872i			0.0150286i
$584$	4.44146			0.183789
$585$	8.85396	+	11.5113i	0.366066	+	0.475932i
$586$	17.4486			0.720796
$587$			2.25160i			0.0929334i	0.998920	+	0.0464667i	$0.0147961\pi$
$587$			2.25160i			0.0929334i	−0.998920	+	0.0464667i	$0.985204\pi$
$588$		−	14.1210i		−	0.582339i
$589$	−1.05331			−0.0434007
$590$	−6.39268	−	8.31130i	−0.263183	−	0.342171i
$591$	25.5156			1.04957
$592$			5.72235i			0.235187i
$593$		−	25.4538i		−	1.04526i	−0.852559	−	0.522630i	$-0.824951\pi$
$593$		−	25.4538i		−	1.04526i	0.852559	−	0.522630i	$-0.175049\pi$
$594$	−1.51419			−0.0621280
$595$	20.3919	−	15.6845i	0.835986	−	0.643003i
$596$	−21.8131			−0.893501
$597$			13.8474i			0.566736i
$598$		−	7.58630i		−	0.310227i
$599$	−29.1371			−1.19051			−0.595255	−	0.803537i	$-0.702949\pi$
$599$	−29.1371			−1.19051			−0.595255	+	0.803537i	$0.702949\pi$
$600$	1.53989	−	5.80026i	0.0628656	−	0.236795i
$601$	30.5290			1.24530			0.622652	−	0.782499i	$-0.286055\pi$
$601$	30.5290			1.24530			0.622652	+	0.782499i	$0.286055\pi$
$602$		−	4.33187i		−	0.176554i
$603$			11.0210i			0.448808i
$604$	−8.52294			−0.346794
$605$	−19.3610	+	14.8916i	−0.787136	+	0.605430i
$606$	−19.7199			−0.801065
$607$		−	18.9454i		−	0.768969i	−0.923131	−	0.384485i	$-0.874379\pi$
$607$		−	18.9454i		−	0.768969i	0.923131	−	0.384485i	$-0.125621\pi$
$608$			1.21298i			0.0491927i
$609$	42.2812			1.71332
$610$	−7.57428	−	9.84753i	−0.306674	−	0.398715i
$611$	−33.0760			−1.33811
$612$		−	4.14170i		−	0.167418i
$613$		−	22.1125i		−	0.893116i	−0.894755	−	0.446558i	$-0.852650\pi$
$613$		−	22.1125i		−	0.893116i	0.894755	−	0.446558i	$-0.147350\pi$
$614$	28.0493			1.13198
$615$	−8.04508	−	10.4596i	−0.324409	−	0.421773i
$616$	1.19861			0.0482935
$617$		−	17.9704i		−	0.723459i	−0.932283	−	0.361730i	$-0.882186\pi$
$617$		−	17.9704i		−	0.723459i	0.932283	−	0.361730i	$-0.117814\pi$
$618$		−	16.2710i		−	0.654515i
$619$	−34.8376			−1.40024			−0.700120	−	0.714025i	$-0.746870\pi$
$619$	−34.8376			−1.40024			−0.700120	+	0.714025i	$0.746870\pi$
$620$	−1.53911	+	1.18382i	−0.0618122	+	0.0475432i
$621$	−9.96823			−0.400011
$622$		−	16.8210i		−	0.674463i
$623$		−	35.8601i		−	1.43671i
$624$	4.99870			0.200108
$625$	−21.7079	−	12.4003i	−0.868316	−	0.496011i
$626$	−22.6662			−0.905924
$627$			0.402831i			0.0160875i
$628$		−	19.5923i		−	0.781816i
$629$	−15.1981			−0.605986
$630$	−11.9732	+	9.20923i	−0.477022	+	0.366905i
$631$	14.8286			0.590316			0.295158	−	0.955449i	$-0.404628\pi$
$631$	14.8286			0.590316			0.295158	+	0.955449i	$0.404628\pi$
$632$		−	3.37116i		−	0.134097i
$633$		−	14.2374i		−	0.565885i
$634$	22.5794			0.896744
$635$	−12.6809	−	16.4867i	−0.503225	−	0.654257i
$636$	−1.57405			−0.0624150
$637$		−	48.9990i		−	1.94141i
$638$			2.25012i			0.0890833i
$639$	21.9863			0.869766
$640$	1.36327	+	1.77243i	0.0538880	+	0.0700613i
$641$	20.0431			0.791656			0.395828	−	0.918325i	$-0.370458\pi$
$641$	20.0431			0.791656			0.395828	+	0.918325i	$0.370458\pi$
$642$			13.0173i			0.513750i
$643$		−	38.3487i		−	1.51233i	−0.654383	−	0.756163i	$-0.727072\pi$
$643$		−	38.3487i		−	1.51233i	0.654383	−	0.756163i	$-0.272928\pi$
$644$	7.89071			0.310938
$645$	2.12733	−	1.63625i	0.0837637	−	0.0644273i
$646$	−3.22156			−0.126751
$647$		−	42.7856i		−	1.68208i	−0.540976	−	0.841038i	$-0.681945\pi$
$647$		−	42.7856i		−	1.68208i	0.540976	−	0.841038i	$-0.318055\pi$
$648$		−	1.88990i		−	0.0742424i
$649$	1.29749			0.0509309
$650$	5.34332	−	20.1266i	0.209582	−	0.789430i
$651$	−4.51487			−0.176952
$652$		−	14.5972i		−	0.571670i
$653$		−	42.6330i		−	1.66836i	−0.551493	−	0.834179i	$-0.685942\pi$
$653$		−	42.6330i		−	1.66836i	0.551493	−	0.834179i	$-0.314058\pi$
$654$	15.3209			0.599096
$655$	−12.6923	+	9.76234i	−0.495928	+	0.381446i
$656$	4.91678			0.191968
$657$		−	6.92613i		−	0.270214i
$658$		−	34.4032i		−	1.34118i
$659$	20.6169			0.803121			0.401560	−	0.915833i	$-0.368468\pi$
$659$	20.6169			0.803121			0.401560	+	0.915833i	$0.368468\pi$
$660$	0.452744	+	0.588625i	0.0176230	+	0.0229122i
$661$	26.5678			1.03337			0.516684	−	0.856176i	$-0.327166\pi$
$661$	26.5678			1.03337			0.516684	+	0.856176i	$0.327166\pi$
$662$			8.81733i			0.342695i
$663$			13.2761i			0.515602i
$664$	9.61181			0.373011
$665$	7.16326	+	9.31314i	0.277779	+	0.361148i
$666$	8.92359			0.345782
$667$			14.8130i			0.573563i
$668$			2.92331i			0.113106i
$669$	−9.52707			−0.368338
$670$	12.5263	−	9.63466i	0.483932	−	0.372219i
$671$	1.53731			0.0593473
$672$			5.19928i			0.200567i
$673$			0.104695i			0.00403570i	0.999998	+	0.00201785i	$0.000642302\pi$
$673$			0.104695i			0.00403570i	−0.999998	+	0.00201785i	$0.999358\pi$
$674$	15.7948			0.608393
$675$	−26.4459	−	7.02100i	−1.01790	−	0.270238i
$676$	4.34522			0.167124
$677$			27.1453i			1.04328i	0.853166	+	0.521639i	$0.174679\pi$
$677$			27.1453i			1.04328i	−0.853166	+	0.521639i	$0.825321\pi$
$678$		−	12.3044i		−	0.472549i
$679$	−64.6253			−2.48009
$680$	−4.70741	+	3.62073i	−0.180521	+	0.138849i
$681$	−15.4374			−0.591561
$682$		−	0.240273i		−	0.00920052i
$683$			1.90682i			0.0729624i	0.999334	+	0.0364812i	$0.0116149\pi$
$683$			1.90682i			0.0729624i	−0.999334	+	0.0364812i	$0.988385\pi$
$684$	1.89155			0.0723252
$685$	12.0947	+	15.7247i	0.462116	+	0.600809i
$686$	20.6420			0.788114
$687$			26.7316i			1.01988i
$688$			1.00000i			0.0381246i
$689$	−5.46186			−0.208080
$690$	2.98051	+	3.87504i	0.113466	+	0.147520i
$691$	−45.1309			−1.71686			−0.858431	−	0.512929i	$-0.828560\pi$
$691$	−45.1309			−1.71686			−0.858431	+	0.512929i	$0.828560\pi$
$692$			1.88524i			0.0716663i
$693$		−	1.86915i		−	0.0710031i
$694$	9.65491			0.366495
$695$	−33.9906	+	26.1440i	−1.28934	+	0.991700i
$696$	−9.76048			−0.369970
$697$			13.0585i			0.494627i
$698$			30.1877i			1.14262i
$699$	−18.2361			−0.689752
$700$	20.9342	+	5.55772i	0.791238	+	0.210062i
$701$	−10.6808			−0.403408			−0.201704	−	0.979446i	$-0.564648\pi$
$701$	−10.6808			−0.403408			−0.201704	+	0.979446i	$0.564648\pi$
$702$		−	22.7912i		−	0.860200i
$703$		−	6.94107i		−	0.261787i
$704$	−0.276696			−0.0104284
$705$	16.8950	−	12.9949i	0.636304	−	0.489417i
$706$	−4.00797			−0.150842
$707$		−	71.1725i		−	2.67672i
$708$			5.62819i			0.211520i
$709$	30.6120			1.14966			0.574829	−	0.818274i	$-0.305069\pi$
$709$	30.6120			1.14966			0.574829	+	0.818274i	$0.305069\pi$
$710$	−19.2207	−	24.9894i	−0.721341	−	0.937835i
$711$	−5.25708			−0.197156
$712$			8.27820i			0.310239i
$713$		−	1.58177i		−	0.0592376i
$714$	−13.8088			−0.516783
$715$	1.57100	+	2.04249i	0.0587519	+	0.0763849i
$716$	−23.5607			−0.880504
$717$			26.3379i			0.983605i
$718$			25.0926i			0.936446i
$719$	−32.8195			−1.22396			−0.611980	−	0.790874i	$-0.709627\pi$
$719$	−32.8195			−1.22396			−0.611980	+	0.790874i	$0.709627\pi$
$720$	2.76397	−	2.12592i	0.103007	−	0.0792285i
$721$	58.7249			2.18703
$722$			17.5287i			0.652350i
$723$			6.12623i			0.227837i
$724$	14.3060			0.531679
$725$	−10.4334	+	39.2992i	−0.387486	+	1.45954i
$726$	13.1107			0.486585
$727$		−	29.9738i		−	1.11167i	−0.831294	−	0.555834i	$-0.812399\pi$
$727$		−	29.9738i		−	1.11167i	0.831294	−	0.555834i	$-0.187601\pi$
$728$			18.0412i			0.668652i
$729$	−22.6517			−0.838953
$730$	−7.87215	+	6.05491i	−0.291361	+	0.224102i
$731$	−2.65591			−0.0982324
$732$			6.66848i			0.246474i
$733$		−	50.1385i		−	1.85191i	−0.377638	−	0.925953i	$-0.623264\pi$
$733$		−	50.1385i		−	1.85191i	0.377638	−	0.925953i	$-0.376736\pi$
$734$	21.8468			0.806379
$735$	19.2507	+	25.0284i	0.710073	+	0.923185i
$736$	−1.82155			−0.0671431
$737$			1.95550i			0.0720316i
$738$		−	7.66736i		−	0.282239i
$739$	5.11638			0.188209			0.0941046	−	0.995562i	$-0.470001\pi$
$739$	5.11638			0.188209			0.0941046	+	0.995562i	$0.470001\pi$
$740$	−7.80111	−	10.1424i	−0.286775	−	0.372843i
$741$	−6.06331			−0.222741
$742$		−	5.68102i		−	0.208557i
$743$			33.2603i			1.22020i	0.792323	+	0.610101i	$0.208871\pi$
$743$			33.2603i			1.22020i	−0.792323	+	0.610101i	$0.791129\pi$
$744$	1.04224			0.0382105
$745$	38.6622	−	29.7372i	1.41647	−	1.08949i
$746$	24.9641			0.914002
$747$		−	14.9889i		−	0.548416i
$748$		−	0.734880i		−	0.0268699i
$749$	−46.9816			−1.71667
$750$	5.17800	+	12.3798i	0.189074	+	0.452047i
$751$	−34.5609			−1.26114			−0.630572	−	0.776130i	$-0.717180\pi$
$751$	−34.5609			−1.26114			−0.630572	+	0.776130i	$0.717180\pi$
$752$			7.94188i			0.289611i
$753$			35.5640i			1.29602i
$754$	−33.8683			−1.23341
$755$	15.1063	−	11.6191i	0.549774	−	0.422862i
$756$	23.7058			0.862170
$757$			28.6433i			1.04106i	0.853843	+	0.520530i	$0.174266\pi$
$757$			28.6433i			1.04106i	−0.853843	+	0.520530i	$0.825734\pi$
$758$		−	32.9305i		−	1.19609i
$759$	−0.604938			−0.0219579
$760$	−1.65362	−	2.14991i	−0.0599829	−	0.0779854i
$761$	−33.1485			−1.20163			−0.600817	−	0.799387i	$-0.705158\pi$
$761$	−33.1485			−1.20163			−0.600817	+	0.799387i	$0.705158\pi$
$762$			11.1644i			0.404443i
$763$			55.2960i			2.00185i
$764$	10.6098			0.383851
$765$	5.64626	+	7.34086i	0.204141	+	0.265409i
$766$	−3.12657			−0.112967
$767$			19.5295i			0.705169i
$768$		−	1.20024i		−	0.0433099i
$769$	17.2479			0.621974			0.310987	−	0.950414i	$-0.399340\pi$
$769$	17.2479			0.621974			0.310987	+	0.950414i	$0.399340\pi$
$770$	−2.12445	+	1.63403i	−0.0765599	+	0.0588865i
$771$	21.7757			0.784231
$772$			19.6176i			0.706052i
$773$			34.5369i			1.24221i	0.783729	+	0.621103i	$0.213315\pi$
$773$			34.5369i			1.24221i	−0.783729	+	0.621103i	$0.786685\pi$
$774$	1.55943			0.0560525
$775$	1.11410	−	4.19645i	0.0400195	−	0.150741i
$776$	14.9186			0.535545
$777$		−	29.7521i		−	1.06735i
$778$		−	22.8148i		−	0.817948i
$779$	−5.96393			−0.213680
$780$	−8.85983	+	6.81459i	−0.317233	+	0.244001i
$781$	3.90113			0.139593
$782$		−	4.83787i		−	0.173002i
$783$			44.5022i			1.59038i
$784$	−11.7651			−0.420183
$785$	26.7096	+	34.7258i	0.953305	+	1.23942i
$786$	8.59487			0.306569
$787$			6.19044i			0.220665i	0.993895	+	0.110333i	$0.0351916\pi$
$787$			6.19044i			0.220665i	−0.993895	+	0.110333i	$0.964808\pi$
$788$		−	21.2588i		−	0.757314i
$789$	−16.4994			−0.587393
$790$	4.59580	+	5.97513i	0.163511	+	0.212585i
$791$	44.4089			1.57900
$792$			0.431487i			0.0153322i
$793$			23.1392i			0.821699i
$794$	3.13451			0.111240
$795$	2.78988	−	2.14585i	0.0989469	−	0.0761056i
$796$	11.5372			0.408925
$797$		−	9.67863i		−	0.342835i	−0.985198	−	0.171417i	$-0.945165\pi$
$797$		−	9.67863i		−	0.342835i	0.985198	−	0.171417i	$-0.0548347\pi$
$798$		−	6.30661i		−	0.223251i
$799$	−21.0929			−0.746215
$800$	−4.83259	−	1.28298i	−0.170858	−	0.0453603i
$801$	12.9092			0.456126
$802$		−	24.3939i		−	0.861377i
$803$		−	1.22893i		−	0.0433681i
$804$	−8.48245			−0.299153
$805$	−13.9857	+	10.7572i	−0.492931	+	0.379141i
$806$	3.61653			0.127387
$807$		−	4.42772i		−	0.155863i
$808$			16.4300i			0.578004i
$809$	18.8335			0.662151			0.331076	−	0.943604i	$-0.392588\pi$
$809$	18.8335			0.662151			0.331076	+	0.943604i	$0.392588\pi$
$810$	2.57645	+	3.34971i	0.0905272	+	0.117697i
$811$	−33.0983			−1.16224			−0.581120	−	0.813818i	$-0.697385\pi$
$811$	−33.0983			−1.16224			−0.581120	+	0.813818i	$0.697385\pi$
$812$		−	35.2273i		−	1.23624i
$813$		−	0.896286i		−	0.0314341i
$814$	1.58335			0.0554964
$815$	19.8999	+	25.8724i	0.697064	+	0.906272i
$816$	3.18773			0.111593
$817$		−	1.21298i		−	0.0424367i
$818$			11.4073i			0.398845i
$819$	28.1340			0.983080
$820$	−8.71462	+	6.70290i	−0.304328	+	0.234075i
$821$	35.8078			1.24970			0.624851	−	0.780744i	$-0.285160\pi$
$821$	35.8078			1.24970			0.624851	+	0.780744i	$0.285160\pi$
$822$		−	10.6483i		−	0.371403i
$823$			5.07844i			0.177023i	0.996075	+	0.0885116i	$0.0282110\pi$
$823$			5.07844i			0.177023i	−0.996075	+	0.0885116i	$0.971789\pi$
$824$	−13.5565			−0.472262
$825$	−1.60491	−	0.426080i	−0.0558758	−	0.0148342i
$826$	−20.3131			−0.706784
$827$			21.6277i			0.752067i	0.926606	+	0.376034i	$0.122712\pi$
$827$			21.6277i			0.752067i	−0.926606	+	0.376034i	$0.877288\pi$
$828$			2.84057i			0.0987166i
$829$	24.6643			0.856626			0.428313	−	0.903630i	$-0.359108\pi$
$829$	24.6643			0.856626			0.428313	+	0.903630i	$0.359108\pi$
$830$	−17.0362	+	13.1035i	−0.591336	+	0.454829i
$831$	0.863706			0.0299616
$832$		−	4.16476i		−	0.144387i
$833$		−	31.2472i		−	1.08265i
$834$	23.0175			0.797031
$835$	−3.98527	−	5.18135i	−0.137916	−	0.179308i
$836$	0.335626			0.0116079
$837$		−	4.75204i		−	0.164254i
$838$		−	32.6578i		−	1.12815i
$839$	−15.6599			−0.540641			−0.270321	−	0.962770i	$-0.587130\pi$
$839$	−15.6599			−0.540641			−0.270321	+	0.962770i	$0.587130\pi$
$840$	−7.08803	−	9.21534i	−0.244560	−	0.317959i
$841$	37.1313			1.28039
$842$		−	8.84416i		−	0.304790i
$843$		−	0.804886i		−	0.0277217i
$844$	−11.8621			−0.408311
$845$	−7.70158	+	5.92372i	−0.264942	+	0.203782i
$846$	12.3848			0.425798
$847$			47.3190i			1.62590i
$848$			1.31145i			0.0450352i
$849$	−9.31637			−0.319737
$850$	3.40749	−	12.8349i	0.116876	−	0.440235i
$851$	10.4235			0.357314
$852$			16.9221i			0.579743i
$853$			4.13161i			0.141464i	0.997495	+	0.0707319i	$0.0225335\pi$
$853$			4.13161i			0.141464i	−0.997495	+	0.0707319i	$0.977467\pi$
$854$	−24.0677			−0.823581
$855$	−3.35263	+	2.57869i	−0.114657	+	0.0881895i
$856$	10.8456			0.370694
$857$		−	50.0927i		−	1.71113i	−0.517693	−	0.855567i	$-0.673209\pi$
$857$		−	50.0927i		−	1.71113i	0.517693	−	0.855567i	$-0.326791\pi$
$858$		−	1.38312i		−	0.0472190i
$859$	−5.99026			−0.204385			−0.102192	−	0.994765i	$-0.532586\pi$
$859$	−5.99026			−0.204385			−0.102192	+	0.994765i	$0.532586\pi$
$860$	−1.36327	−	1.77243i	−0.0464872	−	0.0604392i
$861$	−25.5637			−0.871209
$862$			24.2816i			0.827033i
$863$			38.5000i			1.31055i	0.755388	+	0.655277i	$0.227448\pi$
$863$			38.5000i			1.31055i	−0.755388	+	0.655277i	$0.772552\pi$
$864$	−5.47240			−0.186175
$865$	−2.57010	−	3.34146i	−0.0873860	−	0.113613i
$866$	−18.2285			−0.619430
$867$		−	11.9377i		−	0.405427i
$868$			3.76164i			0.127679i
$869$	−0.932786			−0.0316426
$870$	17.2997	−	13.3062i	0.586515	−	0.451122i
$871$	−29.4336			−0.997321
$872$		−	12.7649i		−	0.432274i
$873$		−	23.2644i		−	0.787381i
$874$	2.20949			0.0747372
$875$	−44.6810	+	18.6883i	−1.51049	+	0.631781i
$876$	5.33081			0.180111
$877$			8.94224i			0.301958i	0.988537	+	0.150979i	$0.0482426\pi$
$877$			8.94224i			0.301958i	−0.988537	+	0.150979i	$0.951757\pi$
$878$			25.6050i			0.864127i
$879$	20.9425			0.706373
$880$	0.490423	−	0.377212i	0.0165322	−	0.0127158i
$881$	38.7774			1.30645			0.653223	−	0.757166i	$-0.273417\pi$
$881$	38.7774			1.30645			0.653223	+	0.757166i	$0.273417\pi$
$882$			18.3469i			0.617771i
$883$			41.7830i			1.40611i	0.711136	+	0.703055i	$0.248181\pi$
$883$			41.7830i			1.40611i	−0.711136	+	0.703055i	$0.751819\pi$
$884$	11.0612			0.372030
$885$	−7.67275	−	9.97554i	−0.257917	−	0.335324i
$886$	−12.3973			−0.416495
$887$		−	23.3757i		−	0.784878i	−0.919778	−	0.392439i	$-0.871631\pi$
$887$		−	23.3757i		−	0.784878i	0.919778	−	0.392439i	$-0.128369\pi$
$888$			6.86818i			0.230481i
$889$	−40.2942			−1.35143
$890$	−11.2854	−	14.6725i	−0.378288	−	0.491823i
$891$	−0.522929			−0.0175188
$892$			7.93765i			0.265772i
$893$		−	9.63331i		−	0.322367i
$894$	−26.1810			−0.875622
$895$	41.7595	−	32.1196i	1.39587	−	1.07364i
$896$	4.33187			0.144718
$897$		−	9.10537i		−	0.304020i
$898$		−	30.4208i		−	1.01515i
$899$	−7.06164			−0.235519
$900$	−2.00072	+	7.53608i	−0.0666906	+	0.251203i
$901$	−3.48308			−0.116038
$902$		−	1.36045i		−	0.0452981i
$903$		−	5.19928i		−	0.173021i
$904$	−10.2517			−0.340965
$905$	−25.3564	+	19.5030i	−0.842874	+	0.648302i
$906$	−10.2296			−0.339854
$907$			2.96259i			0.0983711i	0.998790	+	0.0491855i	$0.0156626\pi$
$907$			2.96259i			0.0983711i	−0.998790	+	0.0491855i	$0.984337\pi$
$908$			12.8619i			0.426838i
$909$	25.6213			0.849806
$910$	−24.5951	−	31.9767i	−0.815319	−	1.06002i
$911$	5.26582			0.174464			0.0872322	−	0.996188i	$-0.472198\pi$
$911$	5.26582			0.174464			0.0872322	+	0.996188i	$0.472198\pi$
$912$			1.45586i			0.0482084i
$913$		−	2.65955i		−	0.0880182i
$914$	37.9047			1.25378
$915$	−9.09095	−	11.8194i	−0.300537	−	0.390737i
$916$	22.2719			0.735885
$917$			31.0204i			1.02438i
$918$		−	14.5342i		−	0.479701i
$919$	31.2980			1.03243			0.516213	−	0.856460i	$-0.327341\pi$
$919$	31.2980			1.03243			0.516213	+	0.856460i	$0.327341\pi$
$920$	3.22856	−	2.48326i	0.106442	−	0.0818707i
$921$	33.6658			1.10933
$922$			30.4939i			1.00426i
$923$			58.7188i			1.93275i
$924$	1.43862			0.0473271
$925$	27.6538	+	7.34167i	0.909251	+	0.241393i
$926$	36.9446			1.21407
$927$			21.1403i			0.694340i
$928$			8.13212i			0.266950i
$929$	−24.9452			−0.818425			−0.409213	−	0.912439i	$-0.634197\pi$
$929$	−24.9452			−0.818425			−0.409213	+	0.912439i	$0.634197\pi$
$930$	−1.84730	+	1.42086i	−0.0605753	+	0.0465919i
$931$	14.2708			0.467708
$932$			15.1937i			0.497686i
$933$		−	20.1893i		−	0.660967i
$934$	−6.55650			−0.214535
$935$	1.00184	+	1.30252i	0.0327637	+	0.0425970i
$936$	−6.49464			−0.212284
$937$			18.2249i			0.595380i	0.954663	+	0.297690i	$0.0962162\pi$
$937$			18.2249i			0.595380i	−0.954663	+	0.297690i	$0.903784\pi$
$938$		−	30.6147i		−	0.999605i
$939$	−27.2049			−0.887797
$940$	−10.8269	−	14.0764i	−0.353136	−	0.459121i
$941$	8.22908			0.268260			0.134130	−	0.990964i	$-0.457176\pi$
$941$	8.22908			0.268260			0.134130	+	0.990964i	$0.457176\pi$
$942$		−	23.5154i		−	0.766173i
$943$		−	8.95614i		−	0.291652i
$944$	4.68922			0.152621
$945$	−42.0167	+	32.3174i	−1.36680	+	1.05128i
$946$	0.276696			0.00899616
$947$			21.8699i			0.710676i	0.934738	+	0.355338i	$0.115634\pi$
$947$			21.8699i			0.710676i	−0.934738	+	0.355338i	$0.884366\pi$
$948$		−	4.04619i		−	0.131414i
$949$	18.4976			0.600457
$950$	5.86182	+	1.55623i	0.190183	+	0.0504907i
$951$	27.1007			0.878801
$952$			11.5051i			0.372882i
$953$		−	59.0323i		−	1.91224i	−0.292969	−	0.956122i	$-0.594643\pi$
$953$		−	59.0323i		−	1.91224i	0.292969	−	0.956122i	$-0.405357\pi$
$954$	2.04510			0.0662127
$955$	−18.8052	+	14.4641i	−0.608521	+	0.468047i
$956$	21.9439			0.709715
$957$			2.70069i			0.0873008i
$958$		−	6.29516i		−	0.203387i
$959$	38.4317			1.24102
$960$	1.63625	+	2.12733i	0.0528098	+	0.0686594i
$961$	−30.2459			−0.975676
$962$			23.8322i			0.768381i
$963$		−	16.9129i		−	0.545010i
$964$	5.10417			0.164394
$965$	−26.7441	−	34.7707i	−0.860922	−	1.11931i
$966$	9.47073			0.304716
$967$			41.8404i			1.34550i	0.739871	+	0.672748i	$0.234886\pi$
$967$			41.8404i			1.34550i	−0.739871	+	0.672748i	$0.765114\pi$
$968$		−	10.9234i		−	0.351093i
$969$	−3.86664			−0.124214
$970$	−26.4420	+	20.3380i	−0.849002	+	0.653015i
$971$	−0.721953			−0.0231686			−0.0115843	−	0.999933i	$-0.503687\pi$
$971$	−0.721953			−0.0231686			−0.0115843	+	0.999933i	$0.503687\pi$
$972$			14.1489i			0.453825i
$973$			83.0742i			2.66324i
$974$	−8.73653			−0.279937
$975$	6.41325	−	24.1567i	0.205388	−	0.773634i
$976$	5.55596			0.177842
$977$			15.4149i			0.493168i	0.969121	+	0.246584i	$0.0793081\pi$
$977$			15.4149i			0.493168i	−0.969121	+	0.246584i	$0.920692\pi$
$978$		−	17.5201i		−	0.560231i
$979$	2.29054			0.0732061
$980$	20.8528	−	16.0391i	0.666119	−	0.512349i
$981$	−19.9060			−0.635548
$982$			26.0249i			0.830489i
$983$		−	13.5408i		−	0.431884i	−0.976406	−	0.215942i	$-0.930718\pi$
$983$		−	13.5408i		−	0.431884i	0.976406	−	0.215942i	$-0.0692822\pi$
$984$	5.90131			0.188127
$985$	28.9815	+	37.6797i	0.923428	+	1.20057i
$986$	−21.5982			−0.687826
$987$		−	41.2921i		−	1.31434i
$988$			5.05175i			0.160718i
$989$	1.82155			0.0579218
$990$	−0.588234	−	0.764779i	−0.0186953	−	0.0243063i
$991$	51.5449			1.63738			0.818689	−	0.574237i	$-0.194701\pi$
$991$	51.5449			1.63738			0.818689	+	0.574237i	$0.194701\pi$
$992$		−	0.868364i		−	0.0275706i
$993$			10.5829i			0.335838i
$994$	−61.0750			−1.93718
$995$	−20.4488	+	15.7283i	−0.648271	+	0.498621i
$996$	11.5365			0.365547
$997$		−	12.0530i		−	0.381723i	−0.981617	−	0.190862i	$-0.938872\pi$
$997$		−	12.0530i		−	0.381723i	0.981617	−	0.190862i	$-0.0611281\pi$
$998$			41.4093i			1.31079i
$999$	31.3150			0.990762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.b.259.3	✓	16
5.2	odd	4		2150.2.a.bh.1.3		8
5.3	odd	4		2150.2.a.bg.1.6		8
5.4	even	2	inner	430.2.b.b.259.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.b.259.3	✓	16	1.1	even	1	trivial
430.2.b.b.259.14	yes	16	5.4	even	2	inner
2150.2.a.bg.1.6		8	5.3	odd	4
2150.2.a.bh.1.3		8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.20024i q^{3} -1.00000 q^{4} +(1.77243 - 1.36327i) q^{5} -1.20024 q^{6} -4.33187i q^{7} +1.00000i q^{8} +1.55943 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.20024i q^{3} -1.00000 q^{4} +(1.77243 - 1.36327i) q^{5} -1.20024 q^{6} -4.33187i q^{7} +1.00000i q^{8} +1.55943 q^{9} +(-1.36327 - 1.77243i) q^{10} +0.276696 q^{11} +1.20024i q^{12} +4.16476i q^{13} -4.33187 q^{14} +(-1.63625 - 2.12733i) q^{15} +1.00000 q^{16} +2.65591i q^{17} -1.55943i q^{18} -1.21298 q^{19} +(-1.77243 + 1.36327i) q^{20} -5.19928 q^{21} -0.276696i q^{22} -1.82155i q^{23} +1.20024 q^{24} +(1.28298 - 4.83259i) q^{25} +4.16476 q^{26} -5.47240i q^{27} +4.33187i q^{28} -8.13212 q^{29} +(-2.12733 + 1.63625i) q^{30} +0.868364 q^{31} -1.00000i q^{32} -0.332101i q^{33} +2.65591 q^{34} +(-5.90552 - 7.67792i) q^{35} -1.55943 q^{36} +5.72235i q^{37} +1.21298i q^{38} +4.99870 q^{39} +(1.36327 + 1.77243i) q^{40} +4.91678 q^{41} +5.19928i q^{42} +1.00000i q^{43} -0.276696 q^{44} +(2.76397 - 2.12592i) q^{45} -1.82155 q^{46} +7.94188i q^{47} -1.20024i q^{48} -11.7651 q^{49} +(-4.83259 - 1.28298i) q^{50} +3.18773 q^{51} -4.16476i q^{52} +1.31145i q^{53} -5.47240 q^{54} +(0.490423 - 0.377212i) q^{55} +4.33187 q^{56} +1.45586i q^{57} +8.13212i q^{58} +4.68922 q^{59} +(1.63625 + 2.12733i) q^{60} +5.55596 q^{61} -0.868364i q^{62} -6.75524i q^{63} -1.00000 q^{64} +(5.67770 + 7.38172i) q^{65} -0.332101 q^{66} +7.06731i q^{67} -2.65591i q^{68} -2.18629 q^{69} +(-7.67792 + 5.90552i) q^{70} +14.0990 q^{71} +1.55943i q^{72} -4.44146i q^{73} +5.72235 q^{74} +(-5.80026 - 1.53989i) q^{75} +1.21298 q^{76} -1.19861i q^{77} -4.99870i q^{78} -3.37116 q^{79} +(1.77243 - 1.36327i) q^{80} -1.88990 q^{81} -4.91678i q^{82} -9.61181i q^{83} +5.19928 q^{84} +(3.62073 + 4.70741i) q^{85} +1.00000 q^{86} +9.76048i q^{87} +0.276696i q^{88} +8.27820 q^{89} +(-2.12592 - 2.76397i) q^{90} +18.0412 q^{91} +1.82155i q^{92} -1.04224i q^{93} +7.94188 q^{94} +(-2.14991 + 1.65362i) q^{95} -1.20024 q^{96} -14.9186i q^{97} +11.7651i q^{98} +0.431487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \) 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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