LMFDB - Embedded newform 462.2.c.a.197.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(197,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.c (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 $ x^12 + 16x^10 + 94x^8 + 246x^6 + 277x^4 + 114*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.7
Root			$2.33939i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.806630 - 1.53276i) q^{3} +1.00000 q^{4} -3.86104i q^{5} +(-0.806630 + 1.53276i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.69870 - 2.47274i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.806630 - 1.53276i) q^{3} +1.00000 q^{4} -3.86104i q^{5} +(-0.806630 + 1.53276i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.69870 - 2.47274i) q^{9} +3.86104i q^{10} +(-1.72613 + 2.83205i) q^{11} +(0.806630 - 1.53276i) q^{12} -5.06552i q^{13} +1.00000i q^{14} +(-5.91804 - 3.11443i) q^{15} +1.00000 q^{16} +2.69769 q^{17} +(1.69870 + 2.47274i) q^{18} +7.70835i q^{19} -3.86104i q^{20} +(-1.53276 - 0.806630i) q^{21} +(1.72613 - 2.83205i) q^{22} +3.49322i q^{23} +(-0.806630 + 1.53276i) q^{24} -9.90764 q^{25} +5.06552i q^{26} +(-5.16033 + 0.609106i) q^{27} -1.00000i q^{28} +0.831472 q^{29} +(5.91804 + 3.11443i) q^{30} +9.19326 q^{31} -1.00000 q^{32} +(2.94849 + 4.93015i) q^{33} -2.69769 q^{34} -3.86104 q^{35} +(-1.69870 - 2.47274i) q^{36} +3.04331 q^{37} -7.70835i q^{38} +(-7.76421 - 4.08600i) q^{39} +3.86104i q^{40} -5.28064 q^{41} +(1.53276 + 0.806630i) q^{42} -12.5717i q^{43} +(-1.72613 + 2.83205i) q^{44} +(-9.54734 + 6.55874i) q^{45} -3.49322i q^{46} -4.96439i q^{47} +(0.806630 - 1.53276i) q^{48} -1.00000 q^{49} +9.90764 q^{50} +(2.17604 - 4.13491i) q^{51} -5.06552i q^{52} -0.602608i q^{53} +(5.16033 - 0.609106i) q^{54} +(10.9346 + 6.66465i) q^{55} +1.00000i q^{56} +(11.8150 + 6.21778i) q^{57} -0.831472 q^{58} +0.161004i q^{59} +(-5.91804 - 3.11443i) q^{60} -4.61360i q^{61} -9.19326 q^{62} +(-2.47274 + 1.69870i) q^{63} +1.00000 q^{64} -19.5582 q^{65} +(-2.94849 - 4.93015i) q^{66} -4.22686 q^{67} +2.69769 q^{68} +(5.35426 + 2.81774i) q^{69} +3.86104 q^{70} -12.0213i q^{71} +(1.69870 + 2.47274i) q^{72} -6.15308i q^{73} -3.04331 q^{74} +(-7.99180 + 15.1860i) q^{75} +7.70835i q^{76} +(2.83205 + 1.72613i) q^{77} +(7.76421 + 4.08600i) q^{78} +2.49556i q^{79} -3.86104i q^{80} +(-3.22886 + 8.40086i) q^{81} +5.28064 q^{82} +3.53635 q^{83} +(-1.53276 - 0.806630i) q^{84} -10.4159i q^{85} +12.5717i q^{86} +(0.670690 - 1.27445i) q^{87} +(1.72613 - 2.83205i) q^{88} +7.35755i q^{89} +(9.54734 - 6.55874i) q^{90} -5.06552 q^{91} +3.49322i q^{92} +(7.41556 - 14.0910i) q^{93} +4.96439i q^{94} +29.7622 q^{95} +(-0.806630 + 1.53276i) q^{96} +12.0650 q^{97} +1.00000 q^{98} +(9.93507 - 0.542522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.806630	−	1.53276i	0.465708	−	0.884938i
$3$	0.806630	−	1.53276i	0.465708	−	0.884938i
$4$	1.00000			0.500000
$5$		−	3.86104i		−	1.72671i	−0.504597	−	0.863355i	$-0.668359\pi$
$5$		−	3.86104i		−	1.72671i	0.504597	−	0.863355i	$-0.331641\pi$
$6$	−0.806630	+	1.53276i	−0.329305	+	0.625746i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.00000			−0.353553
$9$	−1.69870	−	2.47274i	−0.566232	−	0.824246i
$10$			3.86104i			1.22097i
$11$	−1.72613	+	2.83205i	−0.520447	+	0.853894i
$11$	−1.72613	+	2.83205i	−0.520447	+	0.853894i
$12$	0.806630	−	1.53276i	0.232854	−	0.442469i
$13$		−	5.06552i		−	1.40492i	−0.711722	−	0.702461i	$-0.752085\pi$
$13$		−	5.06552i		−	1.40492i	0.711722	−	0.702461i	$-0.247915\pi$
$14$			1.00000i			0.267261i
$15$	−5.91804	−	3.11443i	−1.52803	−	0.804143i
$16$	1.00000			0.250000
$17$	2.69769			0.654287			0.327143	−	0.944975i	$-0.393914\pi$
$17$	2.69769			0.654287			0.327143	+	0.944975i	$0.393914\pi$
$18$	1.69870	+	2.47274i	0.400386	+	0.582830i
$19$			7.70835i			1.76842i	0.467093	+	0.884208i	$0.345301\pi$
$19$			7.70835i			1.76842i	−0.467093	+	0.884208i	$0.654699\pi$
$20$		−	3.86104i		−	0.863355i
$21$	−1.53276	−	0.806630i	−0.334475	−	0.176021i
$22$	1.72613	−	2.83205i	0.368012	−	0.603794i
$23$			3.49322i			0.728386i	0.931323	+	0.364193i	$0.118655\pi$
$23$			3.49322i			0.728386i	−0.931323	+	0.364193i	$0.881345\pi$
$24$	−0.806630	+	1.53276i	−0.164653	+	0.312873i
$25$	−9.90764			−1.98153
$26$			5.06552i			0.993430i
$27$	−5.16033	+	0.609106i	−0.993106	+	0.117222i
$28$		−	1.00000i		−	0.188982i
$29$	0.831472			0.154400			0.0772002	−	0.997016i	$-0.475402\pi$
$29$	0.831472			0.154400			0.0772002	+	0.997016i	$0.475402\pi$
$30$	5.91804	+	3.11443i	1.08048	+	0.568615i
$31$	9.19326			1.65116			0.825579	−	0.564287i	$-0.190849\pi$
$31$	9.19326			1.65116			0.825579	+	0.564287i	$0.190849\pi$
$32$	−1.00000			−0.176777
$33$	2.94849	+	4.93015i	0.513267	+	0.858229i
$34$	−2.69769			−0.462651
$35$	−3.86104			−0.652635
$36$	−1.69870	−	2.47274i	−0.283116	−	0.412123i
$37$	3.04331			0.500316			0.250158	−	0.968205i	$-0.419517\pi$
$37$	3.04331			0.500316			0.250158	+	0.968205i	$0.419517\pi$
$38$		−	7.70835i		−	1.25046i
$39$	−7.76421	−	4.08600i	−1.24327	−	0.654283i
$40$			3.86104i			0.610484i
$41$	−5.28064			−0.824698			−0.412349	−	0.911026i	$-0.635292\pi$
$41$	−5.28064			−0.824698			−0.412349	+	0.911026i	$0.635292\pi$
$42$	1.53276	+	0.806630i	0.236510	+	0.124466i
$43$		−	12.5717i		−	1.91717i	−0.284805	−	0.958586i	$-0.591929\pi$
$43$		−	12.5717i		−	1.91717i	0.284805	−	0.958586i	$-0.408071\pi$
$44$	−1.72613	+	2.83205i	−0.260224	+	0.426947i
$45$	−9.54734	+	6.55874i	−1.42323	+	0.977719i
$46$		−	3.49322i		−	0.515047i
$47$		−	4.96439i		−	0.724131i	−0.932153	−	0.362066i	$-0.882072\pi$
$47$		−	4.96439i		−	0.724131i	0.932153	−	0.362066i	$-0.117928\pi$
$48$	0.806630	−	1.53276i	0.116427	−	0.221235i
$49$	−1.00000			−0.142857
$50$	9.90764			1.40115
$51$	2.17604	−	4.13491i	0.304707	−	0.579004i
$52$		−	5.06552i		−	0.702461i
$53$		−	0.602608i		−	0.0827746i	−0.999143	−	0.0413873i	$-0.986822\pi$
$53$		−	0.602608i		−	0.0827746i	0.999143	−	0.0413873i	$-0.0131777\pi$
$54$	5.16033	−	0.609106i	0.702232	−	0.0828888i
$55$	10.9346	+	6.66465i	1.47443	+	0.898662i
$56$			1.00000i			0.133631i
$57$	11.8150	+	6.21778i	1.56494	+	0.823566i
$58$	−0.831472			−0.109178
$59$			0.161004i			0.0209609i	0.999945	+	0.0104804i	$0.00333609\pi$
$59$			0.161004i			0.0209609i	−0.999945	+	0.0104804i	$0.996664\pi$
$60$	−5.91804	−	3.11443i	−0.764016	−	0.402071i
$61$		−	4.61360i		−	0.590711i	−0.955387	−	0.295355i	$-0.904562\pi$
$61$		−	4.61360i		−	0.590711i	0.955387	−	0.295355i	$-0.0954381\pi$
$62$	−9.19326			−1.16754
$63$	−2.47274	+	1.69870i	−0.311536	+	0.214016i
$64$	1.00000			0.125000
$65$	−19.5582			−2.42589
$66$	−2.94849	−	4.93015i	−0.362935	−	0.606860i
$67$	−4.22686			−0.516393			−0.258197	−	0.966092i	$-0.583128\pi$
$67$	−4.22686			−0.516393			−0.258197	+	0.966092i	$0.583128\pi$
$68$	2.69769			0.327143
$69$	5.35426	+	2.81774i	0.644577	+	0.339215i
$70$	3.86104			0.461483
$71$		−	12.0213i		−	1.42667i	−0.700825	−	0.713333i	$-0.747185\pi$
$71$		−	12.0213i		−	1.42667i	0.700825	−	0.713333i	$-0.252815\pi$
$72$	1.69870	+	2.47274i	0.200193	+	0.291415i
$73$		−	6.15308i		−	0.720163i	−0.932921	−	0.360082i	$-0.882749\pi$
$73$		−	6.15308i		−	0.720163i	0.932921	−	0.360082i	$-0.117251\pi$
$74$	−3.04331			−0.353777
$75$	−7.99180	+	15.1860i	−0.922814	+	1.75353i
$76$			7.70835i			0.884208i
$77$	2.83205	+	1.72613i	0.322742	+	0.196711i
$78$	7.76421	+	4.08600i	0.879124	+	0.462648i
$79$			2.49556i			0.280773i	0.990097	+	0.140386i	$0.0448345\pi$
$79$			2.49556i			0.280773i	−0.990097	+	0.140386i	$0.955166\pi$
$80$		−	3.86104i		−	0.431678i
$81$	−3.22886	+	8.40086i	−0.358763	+	0.933429i
$82$	5.28064			0.583150
$83$	3.53635			0.388165			0.194082	−	0.980985i	$-0.437827\pi$
$83$	3.53635			0.388165			0.194082	+	0.980985i	$0.437827\pi$
$84$	−1.53276	−	0.806630i	−0.167238	−	0.0880106i
$85$		−	10.4159i		−	1.12976i
$86$			12.5717i			1.35564i
$87$	0.670690	−	1.27445i	0.0719055	−	0.136635i
$88$	1.72613	−	2.83205i	0.184006	−	0.301897i
$89$			7.35755i			0.779899i	0.920836	+	0.389950i	$0.127508\pi$
$89$			7.35755i			0.779899i	−0.920836	+	0.389950i	$0.872492\pi$
$90$	9.54734	−	6.55874i	1.00638	−	0.691351i
$91$	−5.06552			−0.531010
$92$			3.49322i			0.364193i
$93$	7.41556	−	14.0910i	0.768957	−	1.46117i
$94$			4.96439i			0.512038i
$95$	29.7622			3.05354
$96$	−0.806630	+	1.53276i	−0.0823263	+	0.156436i
$97$	12.0650			1.22501			0.612505	−	0.790467i	$-0.290162\pi$
$97$	12.0650			1.22501			0.612505	+	0.790467i	$0.290162\pi$
$98$	1.00000			0.101015
$99$	9.93507	−	0.542522i	0.998512	−	0.0545255i
$100$	−9.90764			−0.990764
$101$	10.4799			1.04279			0.521396	−	0.853315i	$-0.325411\pi$
$101$	10.4799			1.04279			0.521396	+	0.853315i	$0.325411\pi$
$102$	−2.17604	+	4.13491i	−0.215460	+	0.409417i
$103$	−4.76959			−0.469961			−0.234981	−	0.972000i	$-0.575503\pi$
$103$	−4.76959			−0.469961			−0.234981	+	0.972000i	$0.575503\pi$
$104$			5.06552i			0.496715i
$105$	−3.11443	+	5.91804i	−0.303937	+	0.577542i
$106$			0.602608i			0.0585305i
$107$	5.70706			0.551722			0.275861	−	0.961198i	$-0.411037\pi$
$107$	5.70706			0.551722			0.275861	+	0.961198i	$0.411037\pi$
$108$	−5.16033	+	0.609106i	−0.496553	+	0.0586112i
$109$			0.152695i			0.0146255i	0.999973	+	0.00731277i	$0.00232775\pi$
$109$			0.152695i			0.0146255i	−0.999973	+	0.00731277i	$0.997672\pi$
$110$	−10.9346	−	6.66465i	−1.04258	−	0.635450i
$111$	2.45482	−	4.66465i	0.233001	−	0.442749i
$112$		−	1.00000i		−	0.0944911i
$113$			5.39852i			0.507850i	0.967224	+	0.253925i	$0.0817216\pi$
$113$			5.39852i			0.507850i	−0.967224	+	0.253925i	$0.918278\pi$
$114$	−11.8150	−	6.21778i	−1.10658	−	0.582349i
$115$	13.4875			1.25771
$116$	0.831472			0.0772002
$117$	−12.5257	+	8.60477i	−1.15800	+	0.795512i
$118$		−	0.161004i		−	0.0148216i
$119$		−	2.69769i		−	0.247297i
$120$	5.91804	+	3.11443i	0.540241	+	0.284307i
$121$	−5.04096	−	9.77695i	−0.458269	−	0.888813i
$122$			4.61360i			0.417696i
$123$	−4.25953	+	8.09395i	−0.384069	+	0.729807i
$124$	9.19326			0.825579
$125$			18.9486i			1.69481i
$126$	2.47274	−	1.69870i	0.220289	−	0.151332i
$127$			14.2439i			1.26394i	0.774993	+	0.631970i	$0.217754\pi$
$127$			14.2439i			1.26394i	−0.774993	+	0.631970i	$0.782246\pi$
$128$	−1.00000			−0.0883883
$129$	−19.2694	−	10.1407i	−1.69658	−	0.892842i
$130$	19.5582			1.71536
$131$	17.0775			1.49207			0.746034	−	0.665908i	$-0.231956\pi$
$131$	17.0775			1.49207			0.746034	+	0.665908i	$0.231956\pi$
$132$	2.94849	+	4.93015i	0.256633	+	0.429115i
$133$	7.70835			0.668398
$134$	4.22686			0.365145
$135$	2.35178	+	19.9242i	0.202409	+	1.71481i
$136$	−2.69769			−0.231325
$137$			10.9911i			0.939035i	0.882923	+	0.469518i	$0.155572\pi$
$137$			10.9911i			0.939035i	−0.882923	+	0.469518i	$0.844428\pi$
$138$	−5.35426	−	2.81774i	−0.455785	−	0.239862i
$139$		−	8.67348i		−	0.735675i	−0.929890	−	0.367837i	$-0.880098\pi$
$139$		−	8.67348i		−	0.735675i	0.929890	−	0.367837i	$-0.119902\pi$
$140$	−3.86104			−0.326318
$141$	−7.60921	−	4.00443i	−0.640811	−	0.337234i
$142$			12.0213i			1.00881i
$143$	14.3458	+	8.74373i	1.19965	+	0.731188i
$144$	−1.69870	−	2.47274i	−0.141558	−	0.206061i
$145$		−	3.21035i		−	0.266605i
$146$			6.15308i			0.509232i
$147$	−0.806630	+	1.53276i	−0.0665297	+	0.126420i
$148$	3.04331			0.250158
$149$	−3.59764			−0.294730			−0.147365	−	0.989082i	$-0.547079\pi$
$149$	−3.59764			−0.294730			−0.147365	+	0.989082i	$0.547079\pi$
$150$	7.99180	−	15.1860i	0.652528	−	1.23993i
$151$			17.5295i			1.42653i	0.700892	+	0.713267i	$0.252785\pi$
$151$			17.5295i			1.42653i	−0.700892	+	0.713267i	$0.747215\pi$
$152$		−	7.70835i		−	0.625229i
$153$	−4.58256	−	6.67069i	−0.370478	−	0.539293i
$154$	−2.83205	−	1.72613i	−0.228213	−	0.139095i
$155$		−	35.4955i		−	2.85107i
$156$	−7.76421	−	4.08600i	−0.621635	−	0.327142i
$157$	−7.25956			−0.579376			−0.289688	−	0.957121i	$-0.593551\pi$
$157$	−7.25956			−0.579376			−0.289688	+	0.957121i	$0.593551\pi$
$158$		−	2.49556i		−	0.198536i
$159$	−0.923652	−	0.486082i	−0.0732504	−	0.0385488i
$160$			3.86104i			0.305242i
$161$	3.49322			0.275304
$162$	3.22886	−	8.40086i	0.253683	−	0.660034i
$163$	15.4886			1.21316			0.606580	−	0.795023i	$-0.292541\pi$
$163$	15.4886			1.21316			0.606580	+	0.795023i	$0.292541\pi$
$164$	−5.28064			−0.412349
$165$	19.0355	−	11.3843i	1.48191	−	0.886263i
$166$	−3.53635			−0.274474
$167$	−3.94198			−0.305040			−0.152520	−	0.988300i	$-0.548739\pi$
$167$	−3.94198			−0.305040			−0.152520	+	0.988300i	$0.548739\pi$
$168$	1.53276	+	0.806630i	0.118255	+	0.0622329i
$169$	−12.6595			−0.973804
$170$			10.4159i			0.798864i
$171$	19.0607	−	13.0941i	1.45761	−	1.00133i
$172$		−	12.5717i		−	0.958586i
$173$	−5.16603			−0.392766			−0.196383	−	0.980527i	$-0.562920\pi$
$173$	−5.16603			−0.392766			−0.196383	+	0.980527i	$0.562920\pi$
$174$	−0.670690	+	1.27445i	−0.0508449	+	0.0966155i
$175$			9.90764i			0.748947i
$176$	−1.72613	+	2.83205i	−0.130112	+	0.213473i
$177$	0.246779	+	0.129870i	0.0185491	+	0.00976165i
$178$		−	7.35755i		−	0.551472i
$179$		−	5.01937i		−	0.375166i	−0.982249	−	0.187583i	$-0.939935\pi$
$179$		−	5.01937i		−	0.375166i	0.982249	−	0.187583i	$-0.0600653\pi$
$180$	−9.54734	+	6.55874i	−0.711617	+	0.488859i
$181$	−9.50810			−0.706732			−0.353366	−	0.935485i	$-0.614963\pi$
$181$	−9.50810			−0.706732			−0.353366	+	0.935485i	$0.614963\pi$
$182$	5.06552			0.375481
$183$	−7.07153	−	3.72147i	−0.522743	−	0.275099i
$184$		−	3.49322i		−	0.257524i
$185$		−	11.7503i		−	0.863901i
$186$	−7.41556	+	14.0910i	−0.543735	+	1.03321i
$187$	−4.65657	+	7.63999i	−0.340522	+	0.558692i
$188$		−	4.96439i		−	0.362066i
$189$	0.609106	+	5.16033i	0.0443059	+	0.375359i
$190$	−29.7622			−2.15918
$191$			8.73096i			0.631750i	0.948801	+	0.315875i	$0.102298\pi$
$191$			8.73096i			0.631750i	−0.948801	+	0.315875i	$0.897702\pi$
$192$	0.806630	−	1.53276i	0.0582135	−	0.110617i
$193$		−	11.2644i		−	0.810830i	−0.914133	−	0.405415i	$-0.867127\pi$
$193$		−	11.2644i		−	0.810830i	0.914133	−	0.405415i	$-0.132873\pi$
$194$	−12.0650			−0.866213
$195$	−15.7762	+	29.9779i	−1.12976	+	2.14677i
$196$	−1.00000			−0.0714286
$197$	26.1013			1.85964			0.929820	−	0.368016i	$-0.119963\pi$
$197$	26.1013			1.85964			0.929820	+	0.368016i	$0.119963\pi$
$198$	−9.93507	+	0.542522i	−0.706055	+	0.0385553i
$199$	−20.1620			−1.42925			−0.714625	−	0.699508i	$-0.753402\pi$
$199$	−20.1620			−1.42925			−0.714625	+	0.699508i	$0.753402\pi$
$200$	9.90764			0.700576
$201$	−3.40951	+	6.47875i	−0.240488	+	0.456976i
$202$	−10.4799			−0.737366
$203$		−	0.831472i		−	0.0583579i
$204$	2.17604	−	4.13491i	0.152353	−	0.289502i
$205$			20.3888i			1.42401i
$206$	4.76959			0.332313
$207$	8.63781	−	5.93392i	0.600370	−	0.412436i
$208$		−	5.06552i		−	0.351230i
$209$	−21.8304	−	13.3056i	−1.51004	−	0.920367i
$210$	3.11443	−	5.91804i	0.214916	−	0.408384i
$211$		−	20.1922i		−	1.39009i	−0.718968	−	0.695043i	$-0.755385\pi$
$211$		−	20.1922i		−	1.39009i	0.718968	−	0.695043i	$-0.244615\pi$
$212$		−	0.602608i		−	0.0413873i
$213$	−18.4258	−	9.69674i	−1.26251	−	0.664410i
$214$	−5.70706			−0.390126
$215$	−48.5400			−3.31040
$216$	5.16033	−	0.609106i	0.351116	−	0.0414444i
$217$		−	9.19326i		−	0.624079i
$218$		−	0.152695i		−	0.0103418i
$219$	−9.43118	−	4.96326i	−0.637300	−	0.335386i
$220$	10.9346	+	6.66465i	0.737214	+	0.449331i
$221$		−	13.6652i		−	0.919222i
$222$	−2.45482	+	4.66465i	−0.164757	+	0.313071i
$223$	−0.163853			−0.0109724			−0.00548620	−	0.999985i	$-0.501746\pi$
$223$	−0.163853			−0.0109724			−0.00548620	+	0.999985i	$0.501746\pi$
$224$			1.00000i			0.0668153i
$225$	16.8301	+	24.4990i	1.12200	+	1.63327i
$226$		−	5.39852i		−	0.359104i
$227$	9.14938			0.607266			0.303633	−	0.952789i	$-0.401800\pi$
$227$	9.14938			0.607266			0.303633	+	0.952789i	$0.401800\pi$
$228$	11.8150	+	6.21778i	0.782470	+	0.411783i
$229$	9.97390			0.659094			0.329547	−	0.944139i	$-0.393104\pi$
$229$	9.97390			0.659094			0.329547	+	0.944139i	$0.393104\pi$
$230$	−13.4875			−0.889337
$231$	4.93015	−	2.94849i	0.324380	−	0.193997i
$232$	−0.831472			−0.0545888
$233$	−2.49984			−0.163770			−0.0818849	−	0.996642i	$-0.526094\pi$
$233$	−2.49984			−0.163770			−0.0818849	+	0.996642i	$0.526094\pi$
$234$	12.5257	−	8.60477i	0.818830	−	0.562512i
$235$	−19.1677			−1.25036
$236$			0.161004i			0.0104804i
$237$	3.82509	+	2.01300i	0.248467	+	0.130758i
$238$			2.69769i			0.174866i
$239$	8.25748			0.534132			0.267066	−	0.963678i	$-0.413946\pi$
$239$	8.25748			0.534132			0.267066	+	0.963678i	$0.413946\pi$
$240$	−5.91804	−	3.11443i	−0.382008	−	0.201036i
$241$			15.0943i			0.972309i	0.873873	+	0.486155i	$0.161601\pi$
$241$			15.0943i			0.972309i	−0.873873	+	0.486155i	$0.838399\pi$
$242$	5.04096	+	9.77695i	0.324045	+	0.628486i
$243$	10.2720	+	11.7255i	0.658948	+	0.752188i
$244$		−	4.61360i		−	0.295355i
$245$			3.86104i			0.246673i
$246$	4.25953	−	8.09395i	0.271577	−	0.516051i
$247$	39.0468			2.48449
$248$	−9.19326			−0.583772
$249$	2.85253	−	5.42037i	0.180772	−	0.343502i
$250$		−	18.9486i		−	1.19841i
$251$		−	13.7304i		−	0.866655i	−0.901237	−	0.433327i	$-0.857339\pi$
$251$		−	13.7304i		−	0.866655i	0.901237	−	0.433327i	$-0.142661\pi$
$252$	−2.47274	+	1.69870i	−0.155768	+	0.107008i
$253$	−9.89295	−	6.02974i	−0.621965	−	0.379087i
$254$		−	14.2439i		−	0.893741i
$255$	−15.9651	−	8.40178i	−0.999771	−	0.526140i
$256$	1.00000			0.0625000
$257$		−	5.93347i		−	0.370120i	−0.982727	−	0.185060i	$-0.940752\pi$
$257$		−	5.93347i		−	0.370120i	0.982727	−	0.185060i	$-0.0592479\pi$
$258$	19.2694	+	10.1407i	1.19966	+	0.631335i
$259$		−	3.04331i		−	0.189102i
$260$	−19.5582			−1.21295
$261$	−1.41242	−	2.05601i	−0.0874265	−	0.127264i
$262$	−17.0775			−1.05505
$263$	−20.1194			−1.24062			−0.620308	−	0.784359i	$-0.712992\pi$
$263$	−20.1194			−1.24062			−0.620308	+	0.784359i	$0.712992\pi$
$264$	−2.94849	−	4.93015i	−0.181467	−	0.303430i
$265$	−2.32669			−0.142928
$266$	−7.70835			−0.472629
$267$	11.2774	+	5.93482i	0.690163	+	0.363205i
$268$	−4.22686			−0.258197
$269$		−	23.5034i		−	1.43303i	−0.697571	−	0.716515i	$-0.745736\pi$
$269$		−	23.5034i		−	1.43303i	0.697571	−	0.716515i	$-0.254264\pi$
$270$	−2.35178	−	19.9242i	−0.143125	−	1.21255i
$271$			30.2007i			1.83456i	0.398243	+	0.917280i	$0.369620\pi$
$271$			30.2007i			1.83456i	−0.398243	+	0.917280i	$0.630380\pi$
$272$	2.69769			0.163572
$273$	−4.08600	+	7.76421i	−0.247296	+	0.469912i
$274$		−	10.9911i		−	0.663998i
$275$	17.1019	−	28.0589i	1.03128	−	1.69201i
$276$	5.35426	+	2.81774i	0.322289	+	0.169608i
$277$			3.10788i			0.186735i	0.995632	+	0.0933673i	$0.0297631\pi$
$277$			3.10788i			0.186735i	−0.995632	+	0.0933673i	$0.970237\pi$
$278$			8.67348i			0.520201i
$279$	−15.6165	−	22.7325i	−0.934938	−	1.36096i
$280$	3.86104			0.230741
$281$	−1.17009			−0.0698016			−0.0349008	−	0.999391i	$-0.511112\pi$
$281$	−1.17009			−0.0698016			−0.0349008	+	0.999391i	$0.511112\pi$
$282$	7.60921	+	4.00443i	0.453122	+	0.238460i
$283$			32.3497i			1.92299i	0.274826	+	0.961494i	$0.411380\pi$
$283$			32.3497i			1.92299i	−0.274826	+	0.961494i	$0.588620\pi$
$284$		−	12.0213i		−	0.713333i
$285$	24.0071	−	45.6183i	1.42206	−	2.70220i
$286$	−14.3458	−	8.74373i	−0.848283	−	0.517028i
$287$			5.28064i			0.311707i
$288$	1.69870	+	2.47274i	0.100097	+	0.145707i
$289$	−9.72245			−0.571909
$290$			3.21035i			0.188518i
$291$	9.73195	−	18.4927i	0.570497	−	1.08406i
$292$		−	6.15308i		−	0.360082i
$293$	10.6481			0.622070			0.311035	−	0.950398i	$-0.399324\pi$
$293$	10.6481			0.622070			0.311035	+	0.950398i	$0.399324\pi$
$294$	0.806630	−	1.53276i	0.0470436	−	0.0893923i
$295$	0.621641			0.0361934
$296$	−3.04331			−0.176889
$297$	7.18237	−	15.6657i	0.416764	−	0.909015i
$298$	3.59764			0.208405
$299$	17.6950			1.02333
$300$	−7.99180	+	15.1860i	−0.461407	+	0.876765i
$301$	−12.5717			−0.724623
$302$		−	17.5295i		−	1.00871i
$303$	8.45343	−	16.0632i	0.485637	−	0.922807i
$304$			7.70835i			0.442104i
$305$	−17.8133			−1.01999
$306$	4.58256	+	6.67069i	0.261968	+	0.381338i
$307$			14.4447i			0.824401i	0.911093	+	0.412200i	$0.135240\pi$
$307$			14.4447i			0.824401i	−0.911093	+	0.412200i	$0.864760\pi$
$308$	2.83205	+	1.72613i	0.161371	+	0.0983553i
$309$	−3.84729	+	7.31063i	−0.218865	+	0.415887i
$310$			35.4955i			2.01601i
$311$			27.8091i			1.57691i	0.615094	+	0.788454i	$0.289118\pi$
$311$			27.8091i			1.57691i	−0.615094	+	0.788454i	$0.710882\pi$
$312$	7.76421	+	4.08600i	0.439562	+	0.231324i
$313$	14.5554			0.822719			0.411359	−	0.911473i	$-0.365054\pi$
$313$	14.5554			0.822719			0.411359	+	0.911473i	$0.365054\pi$
$314$	7.25956			0.409681
$315$	6.55874	+	9.54734i	0.369543	+	0.537932i
$316$			2.49556i			0.140386i
$317$		−	1.42646i		−	0.0801177i	−0.999197	−	0.0400589i	$-0.987245\pi$
$317$		−	1.42646i		−	0.0801177i	0.999197	−	0.0400589i	$-0.0127545\pi$
$318$	0.923652	+	0.486082i	0.0517959	+	0.0272581i
$319$	−1.43523	+	2.35477i	−0.0803573	+	0.131842i
$320$		−	3.86104i		−	0.215839i
$321$	4.60348	−	8.74754i	0.256941	−	0.488240i
$322$	−3.49322			−0.194669
$323$			20.7948i			1.15705i
$324$	−3.22886	+	8.40086i	−0.179381	+	0.466714i
$325$			50.1873i			2.78389i
$326$	−15.4886			−0.857833
$327$	0.234045	+	0.123169i	0.0129427	+	0.00681123i
$328$	5.28064			0.291575
$329$	−4.96439			−0.273696
$330$	−19.0355	+	11.3843i	−1.04787	+	0.626683i
$331$	7.00503			0.385031			0.192516	−	0.981294i	$-0.438335\pi$
$331$	7.00503			0.385031			0.192516	+	0.981294i	$0.438335\pi$
$332$	3.53635			0.194082
$333$	−5.16965	−	7.52530i	−0.283295	−	0.412384i
$334$	3.94198			0.215696
$335$			16.3201i			0.891661i
$336$	−1.53276	−	0.806630i	−0.0836188	−	0.0440053i
$337$		−	15.1925i		−	0.827589i	−0.910370	−	0.413795i	$-0.864203\pi$
$337$		−	15.1925i		−	0.827589i	0.910370	−	0.413795i	$-0.135797\pi$
$338$	12.6595			0.688584
$339$	8.27462	+	4.35460i	0.449416	+	0.236510i
$340$		−	10.4159i		−	0.564882i
$341$	−15.8687	+	26.0357i	−0.859340	+	1.40991i
$342$	−19.0607	+	13.0941i	−1.03069	+	0.708050i
$343$			1.00000i			0.0539949i
$344$			12.5717i			0.677822i
$345$	10.8794	−	20.6730i	0.585727	−	1.11300i
$346$	5.16603			0.277728
$347$	17.4151			0.934893			0.467446	−	0.884021i	$-0.345174\pi$
$347$	17.4151			0.934893			0.467446	+	0.884021i	$0.345174\pi$
$348$	0.670690	−	1.27445i	0.0359528	−	0.0683174i
$349$		−	12.0560i		−	0.645341i	−0.946511	−	0.322670i	$-0.895419\pi$
$349$		−	12.0560i		−	0.645341i	0.946511	−	0.322670i	$-0.104581\pi$
$350$		−	9.90764i		−	0.529586i
$351$	3.08544	+	26.1397i	0.164688	+	1.39524i
$352$	1.72613	−	2.83205i	0.0920029	−	0.150949i
$353$			23.4434i			1.24776i	0.781518	+	0.623882i	$0.214445\pi$
$353$			23.4434i			1.24776i	−0.781518	+	0.623882i	$0.785555\pi$
$354$	−0.246779	−	0.129870i	−0.0131162	−	0.00690253i
$355$	−46.4148			−2.46344
$356$			7.35755i			0.389950i
$357$	−4.13491	−	2.17604i	−0.218843	−	0.115168i
$358$			5.01937i			0.265282i
$359$	5.26816			0.278043			0.139021	−	0.990289i	$-0.455604\pi$
$359$	5.26816			0.278043			0.139021	+	0.990289i	$0.455604\pi$
$360$	9.54734	−	6.55874i	0.503189	−	0.345676i
$361$	−40.4186			−2.12729
$362$	9.50810			0.499735
$363$	−19.0519	−	0.159802i	−0.999965	−	0.00838745i
$364$	−5.06552			−0.265505
$365$	−23.7573			−1.24351
$366$	7.07153	+	3.72147i	0.369635	+	0.194524i
$367$	19.4642			1.01602			0.508012	−	0.861350i	$-0.330380\pi$
$367$	19.4642			1.01602			0.508012	+	0.861350i	$0.330380\pi$
$368$			3.49322i			0.182097i
$369$	8.97021	+	13.0576i	0.466970	+	0.679754i
$370$			11.7503i			0.610871i
$371$	−0.602608			−0.0312858
$372$	7.41556	−	14.0910i	0.384479	−	0.730586i
$373$		−	5.38807i		−	0.278984i	−0.990223	−	0.139492i	$-0.955453\pi$
$373$		−	5.38807i		−	0.278984i	0.990223	−	0.139492i	$-0.0445469\pi$
$374$	4.65657	−	7.63999i	0.240785	−	0.395055i
$375$	29.0436	+	15.2845i	1.49981	+	0.789289i
$376$			4.96439i			0.256019i
$377$		−	4.21183i		−	0.216921i
$378$	−0.609106	−	5.16033i	−0.0313290	−	0.265419i
$379$	−8.29732			−0.426205			−0.213102	−	0.977030i	$-0.568357\pi$
$379$	−8.29732			−0.426205			−0.213102	+	0.977030i	$0.568357\pi$
$380$	29.7622			1.52677
$381$	21.8324	+	11.4895i	1.11851	+	0.588627i
$382$		−	8.73096i		−	0.446715i
$383$		−	27.2636i		−	1.39311i	−0.717506	−	0.696553i	$-0.754716\pi$
$383$		−	27.2636i		−	1.39311i	0.717506	−	0.696553i	$-0.245284\pi$
$384$	−0.806630	+	1.53276i	−0.0411632	+	0.0782182i
$385$	6.66465	−	10.9346i	0.339662	−	0.557281i
$386$			11.2644i			0.573343i
$387$	−31.0866	+	21.3555i	−1.58022	+	1.08556i
$388$	12.0650			0.612505
$389$			26.4139i			1.33924i	0.742705	+	0.669619i	$0.233543\pi$
$389$			26.4139i			1.33924i	−0.742705	+	0.669619i	$0.766457\pi$
$390$	15.7762	−	29.9779i	0.798859	−	1.51799i
$391$			9.42364i			0.476574i
$392$	1.00000			0.0505076
$393$	13.7752	−	26.1757i	0.694868	−	1.32039i
$394$	−26.1013			−1.31496
$395$	9.63547			0.484813
$396$	9.93507	−	0.542522i	0.499256	−	0.0272627i
$397$	2.10425			0.105609			0.0528047	−	0.998605i	$-0.483184\pi$
$397$	2.10425			0.105609			0.0528047	+	0.998605i	$0.483184\pi$
$398$	20.1620			1.01063
$399$	6.21778	−	11.8150i	0.311279	−	0.591491i
$400$	−9.90764			−0.495382
$401$			18.9795i			0.947793i	0.880581	+	0.473896i	$0.157153\pi$
$401$			18.9795i			0.947793i	−0.880581	+	0.473896i	$0.842847\pi$
$402$	3.40951	−	6.47875i	0.170051	−	0.323131i
$403$		−	46.5686i		−	2.31975i
$404$	10.4799			0.521396
$405$	32.4361	+	12.4668i	1.61176	+	0.619479i
$406$			0.831472i			0.0412653i
$407$	−5.25314	+	8.61878i	−0.260388	+	0.427217i
$408$	−2.17604	+	4.13491i	−0.107730	+	0.204709i
$409$		−	5.10349i		−	0.252352i	−0.992008	−	0.126176i	$-0.959730\pi$
$409$		−	5.10349i		−	0.252352i	0.992008	−	0.126176i	$-0.0402703\pi$
$410$		−	20.3888i		−	1.00693i
$411$	16.8467	+	8.86577i	0.830988	+	0.437316i
$412$	−4.76959			−0.234981
$413$	0.161004			0.00792246
$414$	−8.63781	+	5.93392i	−0.424525	+	0.291636i
$415$		−	13.6540i		−	0.670248i
$416$			5.06552i			0.248357i
$417$	−13.2943	−	6.99629i	−0.651027	−	0.342610i
$418$	21.8304	+	13.3056i	1.06776	+	0.650798i
$419$			6.15406i			0.300645i	0.988637	+	0.150323i	$0.0480313\pi$
$419$			6.15406i			0.300645i	−0.988637	+	0.150323i	$0.951969\pi$
$420$	−3.11443	+	5.91804i	−0.151969	+	0.288771i
$421$	18.8837			0.920334			0.460167	−	0.887832i	$-0.347790\pi$
$421$	18.8837			0.920334			0.460167	+	0.887832i	$0.347790\pi$
$422$			20.1922i			0.982940i
$423$	−12.2756	+	8.43299i	−0.596862	+	0.410026i
$424$			0.602608i			0.0292652i
$425$	−26.7278			−1.29649
$426$	18.4258	+	9.69674i	0.892731	+	0.469809i
$427$	−4.61360			−0.223268
$428$	5.70706			0.275861
$429$	24.9738	−	14.9356i	1.20574	−	0.721100i
$430$	48.5400			2.34081
$431$	−4.81981			−0.232162			−0.116081	−	0.993240i	$-0.537033\pi$
$431$	−4.81981			−0.232162			−0.116081	+	0.993240i	$0.537033\pi$
$432$	−5.16033	+	0.609106i	−0.248276	+	0.0293056i
$433$	−18.0162			−0.865802			−0.432901	−	0.901441i	$-0.642510\pi$
$433$	−18.0162			−0.865802			−0.432901	+	0.901441i	$0.642510\pi$
$434$			9.19326i			0.441290i
$435$	−4.92069	−	2.58956i	−0.235929	−	0.124160i
$436$			0.152695i			0.00731277i
$437$	−26.9269			−1.28809
$438$	9.43118	+	4.96326i	0.450639	+	0.237154i
$439$			10.9524i			0.522729i	0.965240	+	0.261364i	$0.0841724\pi$
$439$			10.9524i			0.522729i	−0.965240	+	0.261364i	$0.915828\pi$
$440$	−10.9346	−	6.66465i	−0.521289	−	0.317725i
$441$	1.69870	+	2.47274i	0.0808903	+	0.117749i
$442$			13.6652i			0.649988i
$443$		−	3.51803i		−	0.167147i	−0.996502	−	0.0835734i	$-0.973367\pi$
$443$		−	3.51803i		−	0.167147i	0.996502	−	0.0835734i	$-0.0266333\pi$
$444$	2.45482	−	4.66465i	0.116501	−	0.221375i
$445$	28.4078			1.34666
$446$	0.163853			0.00775866
$447$	−2.90196	+	5.51431i	−0.137258	+	0.260818i
$448$		−	1.00000i		−	0.0472456i
$449$		−	10.5334i		−	0.497102i	−0.968619	−	0.248551i	$-0.920046\pi$
$449$		−	10.5334i		−	0.497102i	0.968619	−	0.248551i	$-0.0799543\pi$
$450$	−16.8301	−	24.4990i	−0.793377	−	1.15489i
$451$	9.11507	−	14.9550i	0.429212	−	0.704205i
$452$			5.39852i			0.253925i
$453$	26.8686	+	14.1399i	1.26240	+	0.664349i
$454$	−9.14938			−0.429402
$455$			19.5582i			0.916901i
$456$	−11.8150	−	6.21778i	−0.553290	−	0.291174i
$457$			3.05021i			0.142683i	0.997452	+	0.0713414i	$0.0227280\pi$
$457$			3.05021i			0.142683i	−0.997452	+	0.0713414i	$0.977272\pi$
$458$	−9.97390			−0.466050
$459$	−13.9210	+	1.64318i	−0.649776	+	0.0766971i
$460$	13.4875			0.628856
$461$	41.6488			1.93978			0.969888	−	0.243551i	$-0.0783122\pi$
$461$	41.6488			1.93978			0.969888	+	0.243551i	$0.0783122\pi$
$462$	−4.93015	+	2.94849i	−0.229371	+	0.137176i
$463$	−1.06374			−0.0494362			−0.0247181	−	0.999694i	$-0.507869\pi$
$463$	−1.06374			−0.0494362			−0.0247181	+	0.999694i	$0.507869\pi$
$464$	0.831472			0.0386001
$465$	−54.4061	−	28.6318i	−2.52302	−	1.32777i
$466$	2.49984			0.115803
$467$			19.4950i			0.902121i	0.892493	+	0.451060i	$0.148954\pi$
$467$			19.4950i			0.902121i	−0.892493	+	0.451060i	$0.851046\pi$
$468$	−12.5257	+	8.60477i	−0.579000	+	0.397756i
$469$			4.22686i			0.195178i
$470$	19.1677			0.884141
$471$	−5.85578	+	11.1271i	−0.269820	+	0.512712i
$472$		−	0.161004i		−	0.00741079i
$473$	35.6037	+	21.7004i	1.63706	+	0.997786i
$474$	−3.82509	−	2.01300i	−0.175692	−	0.0924600i
$475$		−	76.3715i		−	3.50417i
$476$		−	2.69769i		−	0.123649i
$477$	−1.49009	+	1.02365i	−0.0682266	+	0.0468696i
$478$	−8.25748			−0.377689
$479$	−7.07807			−0.323405			−0.161703	−	0.986840i	$-0.551699\pi$
$479$	−7.07807			−0.323405			−0.161703	+	0.986840i	$0.551699\pi$
$480$	5.91804	+	3.11443i	0.270120	+	0.142154i
$481$		−	15.4159i		−	0.702905i
$482$		−	15.0943i		−	0.687527i
$483$	2.81774	−	5.35426i	0.128211	−	0.243627i
$484$	−5.04096	−	9.77695i	−0.229135	−	0.444407i
$485$		−	46.5833i		−	2.11524i
$486$	−10.2720	−	11.7255i	−0.465947	−	0.531877i
$487$	30.7305			1.39253			0.696266	−	0.717784i	$-0.254843\pi$
$487$	30.7305			1.39253			0.696266	+	0.717784i	$0.254843\pi$
$488$			4.61360i			0.208848i
$489$	12.4936	−	23.7403i	0.564978	−	1.07357i
$490$		−	3.86104i		−	0.174424i
$491$	−12.6920			−0.572781			−0.286391	−	0.958113i	$-0.592456\pi$
$491$	−12.6920			−0.572781			−0.286391	+	0.958113i	$0.592456\pi$
$492$	−4.25953	+	8.09395i	−0.192034	+	0.364903i
$493$	2.24306			0.101022
$494$	−39.0468			−1.75680
$495$	−2.09470	−	38.3597i	−0.0941497	−	1.72414i
$496$	9.19326			0.412789
$497$	−12.0213			−0.539229
$498$	−2.85253	+	5.42037i	−0.127825	+	0.242893i
$499$	−25.1145			−1.12428			−0.562140	−	0.827042i	$-0.690022\pi$
$499$	−25.1145			−1.12428			−0.562140	+	0.827042i	$0.690022\pi$
$500$			18.9486i			0.847407i
$501$	−3.17972	+	6.04211i	−0.142060	+	0.269942i
$502$			13.7304i			0.612817i
$503$	2.25842			0.100698			0.0503489	−	0.998732i	$-0.483967\pi$
$503$	2.25842			0.100698			0.0503489	+	0.998732i	$0.483967\pi$
$504$	2.47274	−	1.69870i	0.110144	−	0.0756659i
$505$		−	40.4635i		−	1.80060i
$506$	9.89295	+	6.02974i	0.439795	+	0.268055i
$507$	−10.2115	+	19.4039i	−0.453509	+	0.861757i
$508$			14.2439i			0.631970i
$509$		−	38.1220i		−	1.68973i	−0.534982	−	0.844863i	$-0.679682\pi$
$509$		−	38.1220i		−	1.68973i	0.534982	−	0.844863i	$-0.320318\pi$
$510$	15.9651	+	8.40178i	0.706945	+	0.372037i
$511$	−6.15308			−0.272196
$512$	−1.00000			−0.0441942
$513$	−4.69520	−	39.7776i	−0.207298	−	1.75622i
$514$			5.93347i			0.261714i
$515$			18.4156i			0.811487i
$516$	−19.2694	−	10.1407i	−0.848289	−	0.446421i
$517$	14.0594	+	8.56918i	0.618331	+	0.376872i
$518$			3.04331i			0.133715i
$519$	−4.16708	+	7.91828i	−0.182914	+	0.347574i
$520$	19.5582			0.857682
$521$			28.2110i			1.23595i	0.786199	+	0.617974i	$0.212046\pi$
$521$			28.2110i			1.23595i	−0.786199	+	0.617974i	$0.787954\pi$
$522$	1.41242	+	2.05601i	0.0618198	+	0.0899892i
$523$		−	0.946140i		−	0.0413718i	−0.999786	−	0.0206859i	$-0.993415\pi$
$523$		−	0.946140i		−	0.0413718i	0.999786	−	0.0206859i	$-0.00658500\pi$
$524$	17.0775			0.746034
$525$	15.1860	+	7.99180i	0.662772	+	0.348791i
$526$	20.1194			0.877248
$527$	24.8006			1.08033
$528$	2.94849	+	4.93015i	0.128317	+	0.214557i
$529$	10.7974			0.469453
$530$	2.32669			0.101065
$531$	0.398119	−	0.273496i	0.0172769	−	0.0118687i
$532$	7.70835			0.334199
$533$			26.7492i			1.15864i
$534$	−11.2774	−	5.93482i	−0.488019	−	0.256825i
$535$		−	22.0352i		−	0.952664i
$536$	4.22686			0.182573
$537$	−7.69349	−	4.04878i	−0.331998	−	0.174718i
$538$			23.5034i			1.01331i
$539$	1.72613	−	2.83205i	0.0743496	−	0.121985i
$540$	2.35178	+	19.9242i	0.101205	+	0.857403i
$541$			13.1089i			0.563597i	0.959474	+	0.281799i	$0.0909310\pi$
$541$			13.1089i			0.563597i	−0.959474	+	0.281799i	$0.909069\pi$
$542$		−	30.2007i		−	1.29723i
$543$	−7.66952	+	14.5736i	−0.329131	+	0.625414i
$544$	−2.69769			−0.115663
$545$	0.589562			0.0252541
$546$	4.08600	−	7.76421i	0.174865	−	0.332278i
$547$			18.6449i			0.797198i	0.917125	+	0.398599i	$0.130503\pi$
$547$			18.6449i			0.797198i	−0.917125	+	0.398599i	$0.869497\pi$
$548$			10.9911i			0.469518i
$549$	−11.4082	+	7.83710i	−0.486891	+	0.334479i
$550$	−17.1019	+	28.0589i	−0.729226	+	1.19643i
$551$			6.40927i			0.273044i
$552$	−5.35426	−	2.81774i	−0.227892	−	0.119931i
$553$	2.49556			0.106122
$554$		−	3.10788i		−	0.132041i
$555$	−18.0104	−	9.47817i	−0.764500	−	0.402326i
$556$		−	8.67348i		−	0.367837i
$557$	−32.6578			−1.38376			−0.691878	−	0.722015i	$-0.743216\pi$
$557$	−32.6578			−1.38376			−0.691878	+	0.722015i	$0.743216\pi$
$558$	15.6165	+	22.7325i	0.661101	+	0.962344i
$559$	−63.6823			−2.69347
$560$	−3.86104			−0.163159
$561$	7.95414	+	13.3000i	0.335824	+	0.561528i
$562$	1.17009			0.0493572
$563$	−42.8575			−1.80623			−0.903114	−	0.429400i	$-0.858725\pi$
$563$	−42.8575			−1.80623			−0.903114	+	0.429400i	$0.858725\pi$
$564$	−7.60921	−	4.00443i	−0.320406	−	0.168617i
$565$	20.8439			0.876909
$566$		−	32.3497i		−	1.35976i
$567$	8.40086	+	3.22886i	0.352803	+	0.135600i
$568$			12.0213i			0.504403i
$569$	−9.63357			−0.403860			−0.201930	−	0.979400i	$-0.564721\pi$
$569$	−9.63357			−0.403860			−0.201930	+	0.979400i	$0.564721\pi$
$570$	−24.0071	+	45.6183i	−1.00555	+	1.91074i
$571$		−	10.6965i		−	0.447634i	−0.974631	−	0.223817i	$-0.928148\pi$
$571$		−	10.6965i		−	0.447634i	0.974631	−	0.223817i	$-0.0718518\pi$
$572$	14.3458	+	8.74373i	0.599827	+	0.365594i
$573$	13.3824	+	7.04265i	0.559060	+	0.294211i
$574$		−	5.28064i		−	0.220410i
$575$		−	34.6096i		−	1.44332i
$576$	−1.69870	−	2.47274i	−0.0707790	−	0.103031i
$577$	−30.7639			−1.28072			−0.640359	−	0.768076i	$-0.721214\pi$
$577$	−30.7639			−1.28072			−0.640359	+	0.768076i	$0.721214\pi$
$578$	9.72245			0.404400
$579$	−17.2656	−	9.08621i	−0.717535	−	0.377610i
$580$		−	3.21035i		−	0.133302i
$581$		−	3.53635i		−	0.146713i
$582$	−9.73195	+	18.4927i	−0.403402	+	0.766545i
$583$	1.70661	+	1.04018i	0.0706807	+	0.0430798i
$584$			6.15308i			0.254616i
$585$	33.2234	+	48.3622i	1.37362	+	1.99953i
$586$	−10.6481			−0.439870
$587$			4.00060i			0.165122i	0.996586	+	0.0825612i	$0.0263100\pi$
$587$			4.00060i			0.165122i	−0.996586	+	0.0825612i	$0.973690\pi$
$588$	−0.806630	+	1.53276i	−0.0332649	+	0.0632099i
$589$			70.8648i			2.91993i
$590$	−0.621641			−0.0255926
$591$	21.0541	−	40.0070i	0.866049	−	1.64567i
$592$	3.04331			0.125079
$593$	35.7449			1.46787			0.733933	−	0.679222i	$-0.237683\pi$
$593$	35.7449			1.46787			0.733933	+	0.679222i	$0.237683\pi$
$594$	−7.18237	+	15.6657i	−0.294696	+	0.642771i
$595$	−10.4159			−0.427011
$596$	−3.59764			−0.147365
$597$	−16.2633	+	30.9035i	−0.665613	+	1.26480i
$598$	−17.6950			−0.723601
$599$		−	18.2841i		−	0.747066i	−0.927617	−	0.373533i	$-0.878146\pi$
$599$		−	18.2841i		−	0.747066i	0.927617	−	0.373533i	$-0.121854\pi$
$600$	7.99180	−	15.1860i	0.326264	−	0.619967i
$601$		−	3.92580i		−	0.160137i	−0.996789	−	0.0800683i	$-0.974486\pi$
$601$		−	3.92580i		−	0.160137i	0.996789	−	0.0800683i	$-0.0255138\pi$
$602$	12.5717			0.512386
$603$	7.18015	+	10.4519i	0.292398	+	0.425635i
$604$			17.5295i			0.713267i
$605$	−37.7492	+	19.4634i	−1.53472	+	0.791298i
$606$	−8.45343	+	16.0632i	−0.343397	+	0.652523i
$607$		−	0.684969i		−	0.0278020i	−0.999903	−	0.0139010i	$-0.995575\pi$
$607$		−	0.684969i		−	0.0278020i	0.999903	−	0.0139010i	$-0.00442497\pi$
$608$		−	7.70835i		−	0.312615i
$609$	−1.27445	−	0.670690i	−0.0516431	−	0.0271777i
$610$	17.8133			0.721239
$611$	−25.1472			−1.01735
$612$	−4.58256	−	6.67069i	−0.185239	−	0.269647i
$613$			13.9389i			0.562987i	0.959563	+	0.281494i	$0.0908298\pi$
$613$			13.9389i			0.562987i	−0.959563	+	0.281494i	$0.909170\pi$
$614$		−	14.4447i		−	0.582939i
$615$	31.2511	+	16.4462i	1.26017	+	0.663175i
$616$	−2.83205	−	1.72613i	−0.114106	−	0.0695477i
$617$		−	2.06877i		−	0.0832854i	−0.999133	−	0.0416427i	$-0.986741\pi$
$617$		−	2.06877i		−	0.0832854i	0.999133	−	0.0416427i	$-0.0132591\pi$
$618$	3.84729	−	7.31063i	0.154761	−	0.294077i
$619$	−32.1629			−1.29274			−0.646368	−	0.763026i	$-0.723713\pi$
$619$	−32.1629			−1.29274			−0.646368	+	0.763026i	$0.723713\pi$
$620$		−	35.4955i		−	1.42554i
$621$	−2.12774	−	18.0262i	−0.0853833	−	0.723365i
$622$		−	27.8091i		−	1.11504i
$623$	7.35755			0.294774
$624$	−7.76421	−	4.08600i	−0.310817	−	0.163571i
$625$	23.6231			0.944925
$626$	−14.5554			−0.581750
$627$	−38.0033	+	22.7280i	−1.51771	+	0.907669i
$628$	−7.25956			−0.289688
$629$	8.20991			0.327351
$630$	−6.55874	−	9.54734i	−0.261306	−	0.380375i
$631$	30.5134			1.21472			0.607359	−	0.794428i	$-0.292229\pi$
$631$	30.5134			1.21472			0.607359	+	0.794428i	$0.292229\pi$
$632$		−	2.49556i		−	0.0992682i
$633$	−30.9497	−	16.2876i	−1.23014	−	0.647375i
$634$			1.42646i			0.0566518i
$635$	54.9962			2.18246
$636$	−0.923652	−	0.486082i	−0.0366252	−	0.0192744i
$637$			5.06552i			0.200703i
$638$	1.43523	−	2.35477i	0.0568212	−	0.0932261i
$639$	−29.7255	+	20.4205i	−1.17592	+	0.807824i
$640$			3.86104i			0.152621i
$641$			5.28722i			0.208833i	0.994534	+	0.104416i	$0.0332974\pi$
$641$			5.28722i			0.208833i	−0.994534	+	0.104416i	$0.966703\pi$
$642$	−4.60348	+	8.74754i	−0.181685	+	0.345238i
$643$	33.0075			1.30169			0.650845	−	0.759211i	$-0.274415\pi$
$643$	33.0075			1.30169			0.650845	+	0.759211i	$0.274415\pi$
$644$	3.49322			0.137652
$645$	−39.1538	+	74.4000i	−1.54168	+	2.92950i
$646$		−	20.7948i		−	0.818159i
$647$		−	19.8311i		−	0.779640i	−0.920891	−	0.389820i	$-0.872537\pi$
$647$		−	19.8311i		−	0.779640i	0.920891	−	0.389820i	$-0.127463\pi$
$648$	3.22886	−	8.40086i	0.126842	−	0.330017i
$649$	−0.455969	−	0.277913i	−0.0178984	−	0.0109090i
$650$		−	50.1873i		−	1.96851i
$651$	−14.0910	−	7.41556i	−0.552271	−	0.290639i
$652$	15.4886			0.606580
$653$		−	25.9231i		−	1.01445i	−0.861814	−	0.507225i	$-0.830671\pi$
$653$		−	25.9231i		−	1.01445i	0.861814	−	0.507225i	$-0.169329\pi$
$654$	−0.234045	−	0.123169i	−0.00915188	−	0.00481627i
$655$		−	65.9369i		−	2.57637i
$656$	−5.28064			−0.206175
$657$	−15.2149	+	10.4522i	−0.593592	+	0.407780i
$658$	4.96439			0.193532
$659$	−20.2139			−0.787421			−0.393710	−	0.919235i	$-0.628809\pi$
$659$	−20.2139			−0.787421			−0.393710	+	0.919235i	$0.628809\pi$
$660$	19.0355	−	11.3843i	0.740956	−	0.443132i
$661$	26.7459			1.04029			0.520147	−	0.854077i	$-0.325877\pi$
$661$	26.7459			1.04029			0.520147	+	0.854077i	$0.325877\pi$
$662$	−7.00503			−0.272258
$663$	−20.9455	−	11.0228i	−0.813455	−	0.428089i
$664$	−3.53635			−0.137237
$665$		−	29.7622i		−	1.15413i
$666$	5.16965	+	7.52530i	0.200320	+	0.291599i
$667$			2.90451i			0.112463i
$668$	−3.94198			−0.152520
$669$	−0.132169	+	0.251147i	−0.00510993	+	0.00970990i
$670$		−	16.3201i		−	0.630500i
$671$	13.0659	+	7.96367i	0.504404	+	0.307434i
$672$	1.53276	+	0.806630i	0.0591274	+	0.0311164i
$673$			38.6571i			1.49012i	0.666996	+	0.745061i	$0.267580\pi$
$673$			38.6571i			1.49012i	−0.666996	+	0.745061i	$0.732420\pi$
$674$			15.1925i			0.585194i
$675$	51.1267	−	6.03480i	1.96787	−	0.232280i
$676$	−12.6595			−0.486902
$677$	7.55254			0.290268			0.145134	−	0.989412i	$-0.453639\pi$
$677$	7.55254			0.290268			0.145134	+	0.989412i	$0.453639\pi$
$678$	−8.27462	−	4.35460i	−0.317785	−	0.167238i
$679$		−	12.0650i		−	0.463010i
$680$			10.4159i			0.399432i
$681$	7.38017	−	14.0238i	0.282809	−	0.537393i
$682$	15.8687	−	26.0357i	0.607645	−	0.996959i
$683$			9.59137i			0.367004i	0.983019	+	0.183502i	$0.0587433\pi$
$683$			9.59137i			0.367004i	−0.983019	+	0.183502i	$0.941257\pi$
$684$	19.0607	−	13.0941i	0.728805	−	0.500667i
$685$	42.4372			1.62144
$686$		−	1.00000i		−	0.0381802i
$687$	8.04525	−	15.2876i	0.306945	−	0.583257i
$688$		−	12.5717i		−	0.479293i
$689$	−3.05252			−0.116292
$690$	−10.8794	+	20.6730i	−0.414171	+	0.787008i
$691$	11.3824			0.433008			0.216504	−	0.976282i	$-0.430535\pi$
$691$	11.3824			0.433008			0.216504	+	0.976282i	$0.430535\pi$
$692$	−5.16603			−0.196383
$693$	−0.542522	−	9.93507i	−0.0206087	−	0.377402i
$694$	−17.4151			−0.661069
$695$	−33.4887			−1.27030
$696$	−0.670690	+	1.27445i	−0.0254224	+	0.0483077i
$697$	−14.2456			−0.539589
$698$			12.0560i			0.456325i
$699$	−2.01644	+	3.83165i	−0.0762689	+	0.144926i
$700$			9.90764i			0.374474i
$701$	−36.0942			−1.36326			−0.681630	−	0.731697i	$-0.738729\pi$
$701$	−36.0942			−1.36326			−0.681630	+	0.731697i	$0.738729\pi$
$702$	−3.08544	−	26.1397i	−0.116452	−	0.986581i
$703$			23.4589i			0.884768i
$704$	−1.72613	+	2.83205i	−0.0650559	+	0.106737i
$705$	−15.4613	+	29.3795i	−0.582305	+	1.10650i
$706$		−	23.4434i		−	0.882303i
$707$		−	10.4799i		−	0.394139i
$708$	0.246779	+	0.129870i	0.00927454	+	0.00488082i
$709$	−10.7092			−0.402192			−0.201096	−	0.979571i	$-0.564450\pi$
$709$	−10.7092			−0.402192			−0.201096	+	0.979571i	$0.564450\pi$
$710$	46.4148			1.74191
$711$	6.17087	−	4.23920i	0.231426	−	0.158983i
$712$		−	7.35755i		−	0.275736i
$713$			32.1141i			1.20268i
$714$	4.13491	+	2.17604i	0.154745	+	0.0814363i
$715$	33.7599	−	55.3896i	1.26255	−	2.07145i
$716$		−	5.01937i		−	0.187583i
$717$	6.66073	−	12.6567i	0.248750	−	0.472674i
$718$	−5.26816			−0.196606
$719$		−	48.6552i		−	1.81453i	−0.420556	−	0.907267i	$-0.638165\pi$
$719$		−	48.6552i		−	1.81453i	0.420556	−	0.907267i	$-0.361835\pi$
$720$	−9.54734	+	6.55874i	−0.355808	+	0.244430i
$721$			4.76959i			0.177629i
$722$	40.4186			1.50422
$723$	23.1359	+	12.1755i	0.860434	+	0.452812i
$724$	−9.50810			−0.353366
$725$	−8.23792			−0.305949
$726$	19.0519	+	0.159802i	0.707082	+	0.00593082i
$727$	3.44225			0.127666			0.0638329	−	0.997961i	$-0.479668\pi$
$727$	3.44225			0.127666			0.0638329	+	0.997961i	$0.479668\pi$
$728$	5.06552			0.187741
$729$	26.2580	−	6.28637i	0.972518	−	0.232829i
$730$	23.7573			0.879297
$731$		−	33.9147i		−	1.25438i
$732$	−7.07153	−	3.72147i	−0.261371	−	0.137549i
$733$			1.65107i			0.0609837i	0.999535	+	0.0304919i	$0.00970737\pi$
$733$			1.65107i			0.0609837i	−0.999535	+	0.0304919i	$0.990293\pi$
$734$	−19.4642			−0.718438
$735$	5.91804	+	3.11443i	0.218290	+	0.114878i
$736$		−	3.49322i		−	0.128762i
$737$	7.29610	−	11.9707i	0.268755	−	0.440945i
$738$	−8.97021	−	13.0576i	−0.330198	−	0.480659i
$739$			21.9281i			0.806639i	0.915059	+	0.403319i	$0.132144\pi$
$739$			21.9281i			0.806639i	−0.915059	+	0.403319i	$0.867856\pi$
$740$		−	11.7503i		−	0.431951i
$741$	31.4963	−	59.8492i	1.15704	−	2.19862i
$742$	0.602608			0.0221224
$743$	−34.8682			−1.27919			−0.639596	−	0.768712i	$-0.720898\pi$
$743$	−34.8682			−1.27919			−0.639596	+	0.768712i	$0.720898\pi$
$744$	−7.41556	+	14.0910i	−0.271868	+	0.516603i
$745$			13.8906i			0.508913i
$746$			5.38807i			0.197271i
$747$	−6.00718	−	8.74447i	−0.219791	−	0.319943i
$748$	−4.65657	+	7.63999i	−0.170261	+	0.279346i
$749$		−	5.70706i		−	0.208531i
$750$	−29.0436	−	15.2845i	−1.06052	−	0.558111i
$751$	25.6297			0.935239			0.467620	−	0.883930i	$-0.345112\pi$
$751$	25.6297			0.935239			0.467620	+	0.883930i	$0.345112\pi$
$752$		−	4.96439i		−	0.181033i
$753$	−21.0454	−	11.0753i	−0.766936	−	0.403608i
$754$			4.21183i			0.153386i
$755$	67.6823			2.46321
$756$	0.609106	+	5.16033i	0.0221530	+	0.187679i
$757$	−28.8949			−1.05020			−0.525102	−	0.851039i	$-0.675973\pi$
$757$	−28.8949			−1.05020			−0.525102	+	0.851039i	$0.675973\pi$
$758$	8.29732			0.301372
$759$	−17.2221	+	10.2997i	−0.625122	+	0.373857i
$760$	−29.7622			−1.07959
$761$	−11.0225			−0.399565			−0.199782	−	0.979840i	$-0.564024\pi$
$761$	−11.0225			−0.399565			−0.199782	+	0.979840i	$0.564024\pi$
$762$	−21.8324	−	11.4895i	−0.790906	−	0.416222i
$763$	0.152695			0.00552794
$764$			8.73096i			0.315875i
$765$	−25.7558	+	17.6935i	−0.931203	+	0.639708i
$766$			27.2636i			0.985074i
$767$	0.815566			0.0294484
$768$	0.806630	−	1.53276i	0.0291068	−	0.0553087i
$769$			31.5094i			1.13626i	0.822939	+	0.568129i	$0.192333\pi$
$769$			31.5094i			1.13626i	−0.822939	+	0.568129i	$0.807667\pi$
$770$	−6.66465	+	10.9346i	−0.240177	+	0.394057i
$771$	−9.09458	−	4.78612i	−0.327533	−	0.172368i
$772$		−	11.2644i		−	0.405415i
$773$			46.5070i			1.67274i	0.548164	+	0.836371i	$0.315327\pi$
$773$			46.5070i			1.67274i	−0.548164	+	0.836371i	$0.684673\pi$
$774$	31.0866	−	21.3555i	1.11738	−	0.767609i
$775$	−91.0835			−3.27182
$776$	−12.0650			−0.433106
$777$	−4.66465	−	2.45482i	−0.167343	−	0.0880663i
$778$		−	26.4139i		−	0.946984i
$779$		−	40.7050i		−	1.45841i
$780$	−15.7762	+	29.9779i	−0.564879	+	1.07338i
$781$	34.0449	+	20.7503i	1.21822	+	0.742505i
$782$		−	9.42364i		−	0.336989i
$783$	−4.29067	+	0.506454i	−0.153336	+	0.0180992i
$784$	−1.00000			−0.0357143
$785$			28.0295i			1.00041i
$786$	−13.7752	+	26.1757i	−0.491346	+	0.933655i
$787$			28.8312i			1.02772i	0.857874	+	0.513860i	$0.171785\pi$
$787$			28.8312i			1.02772i	−0.857874	+	0.513860i	$0.828215\pi$
$788$	26.1013			0.929820
$789$	−16.2289	+	30.8382i	−0.577765	+	1.09787i
$790$	−9.63547			−0.342815
$791$	5.39852			0.191949
$792$	−9.93507	+	0.542522i	−0.353027	+	0.0192777i
$793$	−23.3703			−0.829903
$794$	−2.10425			−0.0746771
$795$	−1.87678	+	3.56626i	−0.0665626	+	0.126482i
$796$	−20.1620			−0.714625
$797$			21.2458i			0.752566i	0.926505	+	0.376283i	$0.122798\pi$
$797$			21.2458i			0.752566i	−0.926505	+	0.376283i	$0.877202\pi$
$798$	−6.21778	+	11.8150i	−0.220107	+	0.418248i
$799$		−	13.3924i		−	0.473790i
$800$	9.90764			0.350288
$801$	18.1933	−	12.4982i	0.642829	−	0.441604i
$802$		−	18.9795i		−	0.670191i
$803$	17.4258	+	10.6210i	0.614943	+	0.374807i
$804$	−3.40951	+	6.47875i	−0.120244	+	0.228488i
$805$		−	13.4875i		−	0.475371i
$806$			46.5686i			1.64031i
$807$	−36.0251	−	18.9586i	−1.26814	−	0.667374i
$808$	−10.4799			−0.368683
$809$	−37.3877			−1.31448			−0.657241	−	0.753681i	$-0.728276\pi$
$809$	−37.3877			−1.31448			−0.657241	+	0.753681i	$0.728276\pi$
$810$	−32.4361	−	12.4668i	−1.13969	−	0.438038i
$811$			19.8659i			0.697588i	0.937200	+	0.348794i	$0.113409\pi$
$811$			19.8659i			0.697588i	−0.937200	+	0.348794i	$0.886591\pi$
$812$		−	0.831472i		−	0.0291789i
$813$	46.2903	+	24.3608i	1.62347	+	0.854369i
$814$	5.25314	−	8.61878i	0.184122	−	0.302088i
$815$		−	59.8021i		−	2.09478i
$816$	2.17604	−	4.13491i	0.0761767	−	0.144751i
$817$	96.9073			3.39036
$818$			5.10349i			0.178439i
$819$	8.60477	+	12.5257i	0.300675	+	0.437683i
$820$			20.3888i			0.712007i
$821$	−19.1112			−0.666986			−0.333493	−	0.942753i	$-0.608227\pi$
$821$	−19.1112			−0.666986			−0.333493	+	0.942753i	$0.608227\pi$
$822$	−16.8467	−	8.86577i	−0.587597	−	0.309229i
$823$	−7.36922			−0.256875			−0.128437	−	0.991718i	$-0.540996\pi$
$823$	−7.36922			−0.256875			−0.128437	+	0.991718i	$0.540996\pi$
$824$	4.76959			0.166156
$825$	−29.2126	−	48.8462i	−1.01705	−	1.70060i
$826$	−0.161004			−0.00560203
$827$	−0.0610377			−0.00212249			−0.00106124	−	0.999999i	$-0.500338\pi$
$827$	−0.0610377			−0.00212249			−0.00106124	+	0.999999i	$0.500338\pi$
$828$	8.63781	−	5.93392i	0.300185	−	0.206218i
$829$	44.7995			1.55595			0.777975	−	0.628295i	$-0.216247\pi$
$829$	44.7995			1.55595			0.777975	+	0.628295i	$0.216247\pi$
$830$			13.6540i			0.473937i
$831$	4.76364	+	2.50691i	0.165249	+	0.0869638i
$832$		−	5.06552i		−	0.175615i
$833$	−2.69769			−0.0934696
$834$	13.2943	+	6.99629i	0.460346	+	0.242262i
$835$			15.2202i			0.526716i
$836$	−21.8304	−	13.3056i	−0.755020	−	0.460184i
$837$	−47.4402	+	5.59967i	−1.63977	+	0.193553i
$838$		−	6.15406i		−	0.212588i
$839$			37.9316i			1.30954i	0.755826	+	0.654772i	$0.227235\pi$
$839$			37.9316i			1.30954i	−0.755826	+	0.654772i	$0.772765\pi$
$840$	3.11443	−	5.91804i	0.107458	−	0.204192i
$841$	−28.3087			−0.976161
$842$	−18.8837			−0.650774
$843$	−0.943828	+	1.79346i	−0.0325072	+	0.0617701i
$844$		−	20.1922i		−	0.695043i
$845$			48.8787i			1.68148i
$846$	12.2756	−	8.43299i	0.422045	−	0.289932i
$847$	−9.77695	+	5.04096i	−0.335940	+	0.173210i
$848$		−	0.602608i		−	0.0206936i
$849$	49.5842	+	26.0942i	1.70173	+	0.895551i
$850$	26.7278			0.916755
$851$			10.6309i			0.364424i
$852$	−18.4258	−	9.69674i	−0.631256	−	0.332205i
$853$		−	7.86879i		−	0.269422i	−0.990885	−	0.134711i	$-0.956989\pi$
$853$		−	7.86879i		−	0.269422i	0.990885	−	0.134711i	$-0.0430106\pi$
$854$	4.61360			0.157874
$855$	−50.5570	−	73.5942i	−1.72901	−	2.51687i
$856$	−5.70706			−0.195063
$857$	31.4422			1.07404			0.537022	−	0.843568i	$-0.319549\pi$
$857$	31.4422			1.07404			0.537022	+	0.843568i	$0.319549\pi$
$858$	−24.9738	+	14.9356i	−0.852590	+	0.509895i
$859$	22.2235			0.758257			0.379129	−	0.925344i	$-0.376224\pi$
$859$	22.2235			0.758257			0.379129	+	0.925344i	$0.376224\pi$
$860$	−48.5400			−1.65520
$861$	8.09395	+	4.25953i	0.275841	+	0.145164i
$862$	4.81981			0.164163
$863$			56.2253i			1.91393i	0.290198	+	0.956967i	$0.406279\pi$
$863$			56.2253i			1.91393i	−0.290198	+	0.956967i	$0.593721\pi$
$864$	5.16033	−	0.609106i	0.175558	−	0.0207222i
$865$			19.9463i			0.678193i
$866$	18.0162			0.612214
$867$	−7.84242	+	14.9022i	−0.266342	+	0.506104i
$868$		−	9.19326i		−	0.312039i
$869$	−7.06755	−	4.30766i	−0.239750	−	0.146127i
$870$	4.92069	+	2.58956i	0.166827	+	0.0877944i
$871$			21.4112i			0.725492i
$872$		−	0.152695i		−	0.00517091i
$873$	−20.4947	−	29.8335i	−0.693640	−	1.00971i
$874$	26.9269			0.910817
$875$	18.9486			0.640580
$876$	−9.43118	−	4.96326i	−0.318650	−	0.167693i
$877$		−	8.04833i		−	0.271773i	−0.990724	−	0.135886i	$-0.956612\pi$
$877$		−	8.04833i		−	0.271773i	0.990724	−	0.135886i	$-0.0433882\pi$
$878$		−	10.9524i		−	0.369625i
$879$	8.58910	−	16.3210i	0.289703	−	0.550494i
$880$	10.9346	+	6.66465i	0.368607	+	0.224665i
$881$		−	38.6483i		−	1.30210i	−0.759037	−	0.651048i	$-0.774330\pi$
$881$		−	38.6483i		−	1.30210i	0.759037	−	0.651048i	$-0.225670\pi$
$882$	−1.69870	−	2.47274i	−0.0571981	−	0.0832614i
$883$	22.6170			0.761123			0.380561	−	0.924756i	$-0.375731\pi$
$883$	22.6170			0.761123			0.380561	+	0.924756i	$0.375731\pi$
$884$		−	13.6652i		−	0.459611i
$885$	0.501434	−	0.952826i	0.0168555	−	0.0320289i
$886$			3.51803i			0.118191i
$887$	31.5870			1.06059			0.530294	−	0.847814i	$-0.322082\pi$
$887$	31.5870			1.06059			0.530294	+	0.847814i	$0.322082\pi$
$888$	−2.45482	+	4.66465i	−0.0823784	+	0.156535i
$889$	14.2439			0.477725
$890$	−28.4078			−0.952232
$891$	−18.2182	−	23.6452i	−0.610332	−	0.792146i
$892$	−0.163853			−0.00548620
$893$	38.2673			1.28057
$894$	2.90196	−	5.51431i	0.0970561	−	0.184426i
$895$	−19.3800			−0.647802
$896$			1.00000i			0.0334077i
$897$	14.2733	−	27.1221i	0.476571	−	0.905580i
$898$			10.5334i			0.351504i
$899$	7.64393			0.254939
$900$	16.8301	+	24.4990i	0.561002	+	0.816633i
$901$		−	1.62565i		−	0.0541583i
$902$	−9.11507	+	14.9550i	−0.303499	+	0.497948i
$903$	−10.1407	+	19.2694i	−0.337463	+	0.641246i
$904$		−	5.39852i		−	0.179552i
$905$			36.7112i			1.22032i
$906$	−26.8686	−	14.1399i	−0.892648	−	0.469765i
$907$	−28.7146			−0.953454			−0.476727	−	0.879051i	$-0.658177\pi$
$907$	−28.7146			−0.953454			−0.476727	+	0.879051i	$0.658177\pi$
$908$	9.14938			0.303633
$909$	−17.8022	−	25.9141i	−0.590463	−	0.859518i
$910$		−	19.5582i		−	0.648347i
$911$			2.44106i			0.0808758i	0.999182	+	0.0404379i	$0.0128753\pi$
$911$			2.44106i			0.0808758i	−0.999182	+	0.0404379i	$0.987125\pi$
$912$	11.8150	+	6.21778i	0.391235	+	0.205891i
$913$	−6.10419	+	10.0151i	−0.202019	+	0.331452i
$914$		−	3.05021i		−	0.100892i
$915$	−14.3687	+	27.3035i	−0.475016	+	0.902625i
$916$	9.97390			0.329547
$917$		−	17.0775i		−	0.563948i
$918$	13.9210	−	1.64318i	0.459461	−	0.0542331i
$919$		−	41.7704i		−	1.37788i	−0.724819	−	0.688939i	$-0.758077\pi$
$919$		−	41.7704i		−	1.37788i	0.724819	−	0.688939i	$-0.241923\pi$
$920$	−13.4875			−0.444668
$921$	22.1402	+	11.6515i	0.729544	+	0.383930i
$922$	−41.6488			−1.37163
$923$	−60.8941			−2.00435
$924$	4.93015	−	2.94849i	0.162190	−	0.0969983i
$925$	−30.1520			−0.991391
$926$	1.06374			0.0349566
$927$	8.10208	+	11.7939i	0.266107	+	0.387364i
$928$	−0.831472			−0.0272944
$929$		−	24.5494i		−	0.805441i	−0.915323	−	0.402721i	$-0.868065\pi$
$929$		−	24.5494i		−	0.805441i	0.915323	−	0.402721i	$-0.131935\pi$
$930$	54.4061	+	28.6318i	1.78405	+	0.938873i
$931$		−	7.70835i		−	0.252631i
$932$	−2.49984			−0.0818849
$933$	42.6246	+	22.4316i	1.39547	+	0.734379i
$934$		−	19.4950i		−	0.637896i
$935$	29.4983	+	17.9792i	0.964698	+	0.587983i
$936$	12.5257	−	8.60477i	0.409415	−	0.281256i
$937$		−	44.9563i		−	1.46866i	−0.678794	−	0.734328i	$-0.737497\pi$
$937$		−	44.9563i		−	1.46866i	0.678794	−	0.734328i	$-0.262503\pi$
$938$		−	4.22686i		−	0.138012i
$939$	11.7408	−	22.3099i	0.383147	−	0.728055i
$940$	−19.1677			−0.625182
$941$	58.9543			1.92185			0.960927	−	0.276801i	$-0.0892744\pi$
$941$	58.9543			1.92185			0.960927	+	0.276801i	$0.0892744\pi$
$942$	5.85578	−	11.1271i	0.190792	−	0.362542i
$943$		−	18.4464i		−	0.600699i
$944$			0.161004i			0.00524022i
$945$	19.9242	−	2.35178i	0.648136	−	0.0765035i
$946$	−35.6037	−	21.7004i	−1.15758	−	0.705542i
$947$		−	15.3478i		−	0.498735i	−0.968409	−	0.249368i	$-0.919777\pi$
$947$		−	15.3478i		−	0.498735i	0.968409	−	0.249368i	$-0.0802227\pi$
$948$	3.82509	+	2.01300i	0.124233	+	0.0653791i
$949$	−31.1685			−1.01177
$950$			76.3715i			2.47782i
$951$	−2.18641	−	1.15062i	−0.0708993	−	0.0373115i
$952$			2.69769i			0.0874328i
$953$	−20.9482			−0.678579			−0.339290	−	0.940682i	$-0.610187\pi$
$953$	−20.9482			−0.678579			−0.339290	+	0.940682i	$0.610187\pi$
$954$	1.49009	−	1.02365i	0.0482435	−	0.0331418i
$955$	33.7106			1.09085
$956$	8.25748			0.267066
$957$	2.45159	+	4.09928i	0.0792486	+	0.132511i
$958$	7.07807			0.228682
$959$	10.9911			0.354922
$960$	−5.91804	−	3.11443i	−0.191004	−	0.100518i
$961$	53.5160			1.72632
$962$			15.4159i			0.497029i
$963$	−9.69455	−	14.1121i	−0.312403	−	0.454755i
$964$			15.0943i			0.486155i
$965$	−43.4924			−1.40007
$966$	−2.81774	+	5.35426i	−0.0906591	+	0.172271i
$967$		−	4.00123i		−	0.128671i	−0.997928	−	0.0643354i	$-0.979507\pi$
$967$		−	4.00123i		−	0.128671i	0.997928	−	0.0643354i	$-0.0204928\pi$
$968$	5.04096	+	9.77695i	0.162023	+	0.314243i
$969$	31.8733	+	16.7737i	1.02392	+	0.538848i
$970$			46.5833i			1.49570i
$971$			26.3379i			0.845223i	0.906311	+	0.422611i	$0.138886\pi$
$971$			26.3379i			0.845223i	−0.906311	+	0.422611i	$0.861114\pi$
$972$	10.2720	+	11.7255i	0.329474	+	0.376094i
$973$	−8.67348			−0.278059
$974$	−30.7305			−0.984669
$975$	76.9250	+	40.4826i	2.46357	+	1.29648i
$976$		−	4.61360i		−	0.147678i
$977$		−	48.9097i		−	1.56476i	−0.622801	−	0.782381i	$-0.714005\pi$
$977$		−	48.9097i		−	1.56476i	0.622801	−	0.782381i	$-0.285995\pi$
$978$	−12.4936	+	23.7403i	−0.399500	+	0.759130i
$979$	−20.8369	−	12.7001i	−0.665951	−	0.405896i
$980$			3.86104i			0.123336i
$981$	0.377575	−	0.259383i	0.0120550	−	0.00828145i
$982$	12.6920			0.405018
$983$			15.8828i			0.506582i	0.967390	+	0.253291i	$0.0815130\pi$
$983$			15.8828i			0.506582i	−0.967390	+	0.253291i	$0.918487\pi$
$984$	4.25953	−	8.09395i	0.135789	−	0.258026i
$985$		−	100.778i		−	3.21106i
$986$	−2.24306			−0.0714335
$987$	−4.00443	+	7.60921i	−0.127462	+	0.242204i
$988$	39.0468			1.24224
$989$	43.9158			1.39644
$990$	2.09470	+	38.3597i	0.0665739	+	1.21915i
$991$	43.0978			1.36905			0.684523	−	0.728991i	$-0.260011\pi$
$991$	43.0978			1.36905			0.684523	+	0.728991i	$0.260011\pi$
$992$	−9.19326			−0.291886
$993$	5.65047	−	10.7370i	0.179312	−	0.340729i
$994$	12.0213			0.381293
$995$			77.8465i			2.46790i
$996$	2.85253	−	5.42037i	0.0903858	−	0.171751i
$997$		−	21.3314i		−	0.675571i	−0.941223	−	0.337785i	$-0.890322\pi$
$997$		−	21.3314i		−	0.675571i	0.941223	−	0.337785i	$-0.109678\pi$
$998$	25.1145			0.794986
$999$	−15.7045	+	1.85370i	−0.496867	+	0.0586483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.a.197.7	✓	12
3.2	odd	2		462.2.c.b.197.8	yes	12
11.10	odd	2		462.2.c.b.197.7	yes	12
33.32	even	2	inner	462.2.c.a.197.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.7	✓	12	1.1	even	1	trivial
462.2.c.a.197.8	yes	12	33.32	even	2	inner
462.2.c.b.197.7	yes	12	11.10	odd	2
462.2.c.b.197.8	yes	12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.806630 - 1.53276i) q^{3} +1.00000 q^{4} -3.86104i q^{5} +(-0.806630 + 1.53276i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.69870 - 2.47274i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.806630 - 1.53276i) q^{3} +1.00000 q^{4} -3.86104i q^{5} +(-0.806630 + 1.53276i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.69870 - 2.47274i) q^{9} +3.86104i q^{10} +(-1.72613 + 2.83205i) q^{11} +(0.806630 - 1.53276i) q^{12} -5.06552i q^{13} +1.00000i q^{14} +(-5.91804 - 3.11443i) q^{15} +1.00000 q^{16} +2.69769 q^{17} +(1.69870 + 2.47274i) q^{18} +7.70835i q^{19} -3.86104i q^{20} +(-1.53276 - 0.806630i) q^{21} +(1.72613 - 2.83205i) q^{22} +3.49322i q^{23} +(-0.806630 + 1.53276i) q^{24} -9.90764 q^{25} +5.06552i q^{26} +(-5.16033 + 0.609106i) q^{27} -1.00000i q^{28} +0.831472 q^{29} +(5.91804 + 3.11443i) q^{30} +9.19326 q^{31} -1.00000 q^{32} +(2.94849 + 4.93015i) q^{33} -2.69769 q^{34} -3.86104 q^{35} +(-1.69870 - 2.47274i) q^{36} +3.04331 q^{37} -7.70835i q^{38} +(-7.76421 - 4.08600i) q^{39} +3.86104i q^{40} -5.28064 q^{41} +(1.53276 + 0.806630i) q^{42} -12.5717i q^{43} +(-1.72613 + 2.83205i) q^{44} +(-9.54734 + 6.55874i) q^{45} -3.49322i q^{46} -4.96439i q^{47} +(0.806630 - 1.53276i) q^{48} -1.00000 q^{49} +9.90764 q^{50} +(2.17604 - 4.13491i) q^{51} -5.06552i q^{52} -0.602608i q^{53} +(5.16033 - 0.609106i) q^{54} +(10.9346 + 6.66465i) q^{55} +1.00000i q^{56} +(11.8150 + 6.21778i) q^{57} -0.831472 q^{58} +0.161004i q^{59} +(-5.91804 - 3.11443i) q^{60} -4.61360i q^{61} -9.19326 q^{62} +(-2.47274 + 1.69870i) q^{63} +1.00000 q^{64} -19.5582 q^{65} +(-2.94849 - 4.93015i) q^{66} -4.22686 q^{67} +2.69769 q^{68} +(5.35426 + 2.81774i) q^{69} +3.86104 q^{70} -12.0213i q^{71} +(1.69870 + 2.47274i) q^{72} -6.15308i q^{73} -3.04331 q^{74} +(-7.99180 + 15.1860i) q^{75} +7.70835i q^{76} +(2.83205 + 1.72613i) q^{77} +(7.76421 + 4.08600i) q^{78} +2.49556i q^{79} -3.86104i q^{80} +(-3.22886 + 8.40086i) q^{81} +5.28064 q^{82} +3.53635 q^{83} +(-1.53276 - 0.806630i) q^{84} -10.4159i q^{85} +12.5717i q^{86} +(0.670690 - 1.27445i) q^{87} +(1.72613 - 2.83205i) q^{88} +7.35755i q^{89} +(9.54734 - 6.55874i) q^{90} -5.06552 q^{91} +3.49322i q^{92} +(7.41556 - 14.0910i) q^{93} +4.96439i q^{94} +29.7622 q^{95} +(-0.806630 + 1.53276i) q^{96} +12.0650 q^{97} +1.00000 q^{98} +(9.93507 - 0.542522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

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