LMFDB - Embedded newform 105.2.d.b.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("105.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.d (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.2
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.2.d.b.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +(-4.21432 - 0.592104i) q^{10} +2.00000 q^{11} -1.62222i q^{12} +6.42864i q^{13} -1.90321 q^{14} +(2.21432 + 0.311108i) q^{15} -4.61285 q^{16} +4.42864i q^{17} +1.90321i q^{18} +2.42864 q^{19} +(-0.504684 + 3.59210i) q^{20} +1.00000 q^{21} -3.80642i q^{22} -1.37778i q^{23} +0.719004 q^{24} +(-4.80642 - 1.37778i) q^{25} +12.2351 q^{26} -1.00000i q^{27} +1.62222i q^{28} -0.755569 q^{29} +(0.592104 - 4.21432i) q^{30} +5.18421 q^{31} +7.34122i q^{32} +2.00000i q^{33} +8.42864 q^{34} +(-2.21432 - 0.311108i) q^{35} +1.62222 q^{36} +7.61285i q^{37} -4.62222i q^{38} -6.42864 q^{39} +(-1.59210 - 0.223688i) q^{40} -8.23506 q^{41} -1.90321i q^{42} -10.1017i q^{43} -3.24443 q^{44} +(-0.311108 + 2.21432i) q^{45} -2.62222 q^{46} +2.75557i q^{47} -4.61285i q^{48} -1.00000 q^{49} +(-2.62222 + 9.14764i) q^{50} -4.42864 q^{51} -10.4286i q^{52} -9.18421i q^{53} -1.90321 q^{54} +(0.622216 - 4.42864i) q^{55} -0.719004 q^{56} +2.42864i q^{57} +1.43801i q^{58} -14.1017 q^{59} +(-3.59210 - 0.504684i) q^{60} +6.85728 q^{61} -9.86665i q^{62} +1.00000i q^{63} +4.74620 q^{64} +(14.2351 + 2.00000i) q^{65} +3.80642 q^{66} +2.75557i q^{67} -7.18421i q^{68} +1.37778 q^{69} +(-0.592104 + 4.21432i) q^{70} +2.00000 q^{71} +0.719004i q^{72} +1.57136i q^{73} +14.4889 q^{74} +(1.37778 - 4.80642i) q^{75} -3.93978 q^{76} -2.00000i q^{77} +12.2351i q^{78} +4.85728 q^{79} +(-1.43509 + 10.2143i) q^{80} +1.00000 q^{81} +15.6731i q^{82} -11.6128i q^{83} -1.62222 q^{84} +(9.80642 + 1.37778i) q^{85} -19.2257 q^{86} -0.755569i q^{87} -1.43801i q^{88} -4.62222 q^{89} +(4.21432 + 0.592104i) q^{90} +6.42864 q^{91} +2.23506i q^{92} +5.18421i q^{93} +5.24443 q^{94} +(0.755569 - 5.37778i) q^{95} -7.34122 q^{96} -11.9398i q^{97} +1.90321i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{14} + 26 q^{16} - 12 q^{19} - 30 q^{20} + 6 q^{21} + 18 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{29} - 10 q^{30} + 4 q^{31} + 24 q^{34} + 10 q^{36} - 12 q^{39} + 4 q^{40} + 4 q^{41} - 20 q^{44} - 2 q^{45} - 16 q^{46} - 6 q^{49} - 16 q^{50} + 2 q^{54} + 4 q^{55} - 18 q^{56} - 32 q^{59} - 8 q^{60} - 12 q^{61} - 26 q^{64} + 32 q^{65} - 4 q^{66} + 8 q^{69} + 10 q^{70} + 12 q^{71} + 88 q^{74} + 8 q^{75} + 4 q^{76} - 24 q^{79} + 46 q^{80} + 6 q^{81} - 10 q^{84} + 32 q^{85} - 8 q^{86} - 28 q^{89} + 12 q^{90} + 12 q^{91} + 32 q^{94} + 4 q^{95} - 58 q^{96} - 12 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^14 + 26 * q^16 - 12 * q^19 - 30 * q^20 + 6 * q^21 + 18 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^29 - 10 * q^30 + 4 * q^31 + 24 * q^34 + 10 * q^36 - 12 * q^39 + 4 * q^40 + 4 * q^41 - 20 * q^44 - 2 * q^45 - 16 * q^46 - 6 * q^49 - 16 * q^50 + 2 * q^54 + 4 * q^55 - 18 * q^56 - 32 * q^59 - 8 * q^60 - 12 * q^61 - 26 * q^64 + 32 * q^65 - 4 * q^66 + 8 * q^69 + 10 * q^70 + 12 * q^71 + 88 * q^74 + 8 * q^75 + 4 * q^76 - 24 * q^79 + 46 * q^80 + 6 * q^81 - 10 * q^84 + 32 * q^85 - 8 * q^86 - 28 * q^89 + 12 * q^90 + 12 * q^91 + 32 * q^94 + 4 * q^95 - 58 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.90321i		−	1.34577i	−0.739745	−	0.672887i	$-0.765054\pi$
$2$		−	1.90321i		−	1.34577i	0.739745	−	0.672887i	$-0.234946\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.62222			−0.811108
$5$	0.311108	−	2.21432i	0.139132	−	0.990274i
$5$	0.311108	−	2.21432i	0.139132	−	0.990274i
$6$	1.90321			0.776983
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	0.719004i		−	0.254206i
$9$	−1.00000			−0.333333
$10$	−4.21432	−	0.592104i	−1.33268	−	0.187240i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		−	1.62222i		−	0.468293i
$13$			6.42864i			1.78298i	0.453037	+	0.891492i	$0.350341\pi$
$13$			6.42864i			1.78298i	−0.453037	+	0.891492i	$0.649659\pi$
$14$	−1.90321			−0.508655
$15$	2.21432	+	0.311108i	0.571735	+	0.0803277i
$16$	−4.61285			−1.15321
$17$			4.42864i			1.07410i	0.843550	+	0.537051i	$0.180462\pi$
$17$			4.42864i			1.07410i	−0.843550	+	0.537051i	$0.819538\pi$
$18$			1.90321i			0.448591i
$19$	2.42864			0.557168			0.278584	−	0.960412i	$-0.410135\pi$
$19$	2.42864			0.557168			0.278584	+	0.960412i	$0.410135\pi$
$20$	−0.504684	+	3.59210i	−0.112851	+	0.803219i
$21$	1.00000			0.218218
$22$		−	3.80642i		−	0.811532i
$23$		−	1.37778i		−	0.287288i	−0.989629	−	0.143644i	$-0.954118\pi$
$23$		−	1.37778i		−	0.287288i	0.989629	−	0.143644i	$-0.0458820\pi$
$24$	0.719004			0.146766
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$	12.2351			2.39949
$27$		−	1.00000i		−	0.192450i
$28$			1.62222i			0.306570i
$29$	−0.755569			−0.140306			−0.0701528	−	0.997536i	$-0.522349\pi$
$29$	−0.755569			−0.140306			−0.0701528	+	0.997536i	$0.522349\pi$
$30$	0.592104	−	4.21432i	0.108103	−	0.769426i
$31$	5.18421			0.931111			0.465556	−	0.885019i	$-0.345855\pi$
$31$	5.18421			0.931111			0.465556	+	0.885019i	$0.345855\pi$
$32$			7.34122i			1.29776i
$33$			2.00000i			0.348155i
$34$	8.42864			1.44550
$35$	−2.21432	−	0.311108i	−0.374288	−	0.0525868i
$36$	1.62222			0.270369
$37$			7.61285i			1.25154i	0.780006	+	0.625772i	$0.215216\pi$
$37$			7.61285i			1.25154i	−0.780006	+	0.625772i	$0.784784\pi$
$38$		−	4.62222i		−	0.749822i
$39$	−6.42864			−1.02941
$40$	−1.59210	−	0.223688i	−0.251734	−	0.0353681i
$41$	−8.23506			−1.28610			−0.643050	−	0.765824i	$-0.722331\pi$
$41$	−8.23506			−1.28610			−0.643050	+	0.765824i	$0.722331\pi$
$42$		−	1.90321i		−	0.293672i
$43$		−	10.1017i		−	1.54050i	−0.637744	−	0.770248i	$-0.720132\pi$
$43$		−	10.1017i		−	1.54050i	0.637744	−	0.770248i	$-0.279868\pi$
$44$	−3.24443			−0.489116
$45$	−0.311108	+	2.21432i	−0.0463772	+	0.330091i
$46$	−2.62222			−0.386625
$47$			2.75557i			0.401941i	0.979597	+	0.200971i	$0.0644095\pi$
$47$			2.75557i			0.401941i	−0.979597	+	0.200971i	$0.935590\pi$
$48$		−	4.61285i		−	0.665807i
$49$	−1.00000			−0.142857
$50$	−2.62222	+	9.14764i	−0.370837	+	1.29367i
$51$	−4.42864			−0.620134
$52$		−	10.4286i		−	1.44619i
$53$		−	9.18421i		−	1.26155i	−0.775967	−	0.630774i	$-0.782737\pi$
$53$		−	9.18421i		−	1.26155i	0.775967	−	0.630774i	$-0.217263\pi$
$54$	−1.90321			−0.258994
$55$	0.622216	−	4.42864i	0.0838995	−	0.597158i
$56$	−0.719004			−0.0960809
$57$			2.42864i			0.321681i
$58$			1.43801i			0.188820i
$59$	−14.1017			−1.83589			−0.917943	−	0.396712i	$-0.870151\pi$
$59$	−14.1017			−1.83589			−0.917943	+	0.396712i	$0.870151\pi$
$60$	−3.59210	−	0.504684i	−0.463739	−	0.0651544i
$61$	6.85728			0.877985			0.438992	−	0.898491i	$-0.355336\pi$
$61$	6.85728			0.877985			0.438992	+	0.898491i	$0.355336\pi$
$62$		−	9.86665i		−	1.25307i
$63$			1.00000i			0.125988i
$64$	4.74620			0.593275
$65$	14.2351	+	2.00000i	1.76564	+	0.248069i
$66$	3.80642			0.468538
$67$			2.75557i			0.336646i	0.985732	+	0.168323i	$0.0538352\pi$
$67$			2.75557i			0.336646i	−0.985732	+	0.168323i	$0.946165\pi$
$68$		−	7.18421i		−	0.871213i
$69$	1.37778			0.165866
$70$	−0.592104	+	4.21432i	−0.0707700	+	0.503708i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			0.719004i			0.0847354i
$73$			1.57136i			0.183914i	0.995763	+	0.0919569i	$0.0293122\pi$
$73$			1.57136i			0.183914i	−0.995763	+	0.0919569i	$0.970688\pi$
$74$	14.4889			1.68430
$75$	1.37778	−	4.80642i	0.159093	−	0.554998i
$76$	−3.93978			−0.451923
$77$		−	2.00000i		−	0.227921i
$78$			12.2351i			1.38535i
$79$	4.85728			0.546487			0.273243	−	0.961945i	$-0.411904\pi$
$79$	4.85728			0.546487			0.273243	+	0.961945i	$0.411904\pi$
$80$	−1.43509	+	10.2143i	−0.160448	+	1.14200i
$81$	1.00000			0.111111
$82$			15.6731i			1.73080i
$83$		−	11.6128i		−	1.27468i	−0.770585	−	0.637338i	$-0.780036\pi$
$83$		−	11.6128i		−	1.27468i	0.770585	−	0.637338i	$-0.219964\pi$
$84$	−1.62222			−0.176998
$85$	9.80642	+	1.37778i	1.06366	+	0.149442i
$86$	−19.2257			−2.07316
$87$		−	0.755569i		−	0.0810055i
$88$		−	1.43801i		−	0.153292i
$89$	−4.62222			−0.489954			−0.244977	−	0.969529i	$-0.578780\pi$
$89$	−4.62222			−0.489954			−0.244977	+	0.969529i	$0.578780\pi$
$90$	4.21432	+	0.592104i	0.444228	+	0.0624133i
$91$	6.42864			0.673905
$92$			2.23506i			0.233021i
$93$			5.18421i			0.537577i
$94$	5.24443			0.540922
$95$	0.755569	−	5.37778i	0.0775197	−	0.551749i
$96$	−7.34122			−0.749260
$97$		−	11.9398i		−	1.21230i	−0.795350	−	0.606150i	$-0.792713\pi$
$97$		−	11.9398i		−	1.21230i	0.795350	−	0.606150i	$-0.207287\pi$
$98$			1.90321i			0.192253i
$99$	−2.00000			−0.201008
$100$	7.79706	+	2.23506i	0.779706	+	0.223506i
$101$	1.47949			0.147215			0.0736076	−	0.997287i	$-0.476549\pi$
$101$	1.47949			0.147215			0.0736076	+	0.997287i	$0.476549\pi$
$102$			8.42864i			0.834560i
$103$			8.85728i			0.872734i	0.899769	+	0.436367i	$0.143735\pi$
$103$			8.85728i			0.872734i	−0.899769	+	0.436367i	$0.856265\pi$
$104$	4.62222			0.453246
$105$	0.311108	−	2.21432i	0.0303610	−	0.216095i
$106$	−17.4795			−1.69776
$107$			1.76494i			0.170623i	0.996354	+	0.0853114i	$0.0271885\pi$
$107$			1.76494i			0.170623i	−0.996354	+	0.0853114i	$0.972811\pi$
$108$			1.62222i			0.156098i
$109$	−5.61285			−0.537613			−0.268807	−	0.963194i	$-0.586629\pi$
$109$	−5.61285			−0.537613			−0.268807	+	0.963194i	$0.586629\pi$
$110$	−8.42864	−	1.18421i	−0.803639	−	0.112910i
$111$	−7.61285			−0.722580
$112$			4.61285i			0.435873i
$113$			11.2859i			1.06169i	0.847469	+	0.530845i	$0.178125\pi$
$113$			11.2859i			1.06169i	−0.847469	+	0.530845i	$0.821875\pi$
$114$	4.62222			0.432910
$115$	−3.05086	−	0.428639i	−0.284494	−	0.0399708i
$116$	1.22570			0.113803
$117$		−	6.42864i		−	0.594328i
$118$			26.8385i			2.47069i
$119$	4.42864			0.405973
$120$	0.223688	−	1.59210i	0.0204198	−	0.145339i
$121$	−7.00000			−0.636364
$122$		−	13.0509i		−	1.18157i
$123$		−	8.23506i		−	0.742531i
$124$	−8.40990			−0.755232
$125$	−4.54617	+	10.2143i	−0.406622	+	0.913597i
$126$	1.90321			0.169552
$127$		−	12.8573i		−	1.14090i	−0.821333	−	0.570450i	$-0.806769\pi$
$127$		−	12.8573i		−	1.14090i	0.821333	−	0.570450i	$-0.193231\pi$
$128$			5.64941i			0.499342i
$129$	10.1017			0.889406
$130$	3.80642	−	27.0923i	0.333845	−	2.37616i
$131$	−2.10171			−0.183627			−0.0918136	−	0.995776i	$-0.529266\pi$
$131$	−2.10171			−0.183627			−0.0918136	+	0.995776i	$0.529266\pi$
$132$		−	3.24443i		−	0.282391i
$133$		−	2.42864i		−	0.210590i
$134$	5.24443			0.453050
$135$	−2.21432	−	0.311108i	−0.190578	−	0.0267759i
$136$	3.18421			0.273044
$137$			15.9398i			1.36183i	0.732364	+	0.680914i	$0.238417\pi$
$137$			15.9398i			1.36183i	−0.732364	+	0.680914i	$0.761583\pi$
$138$		−	2.62222i		−	0.223218i
$139$	−11.6731			−0.990097			−0.495048	−	0.868865i	$-0.664850\pi$
$139$	−11.6731			−0.990097			−0.495048	+	0.868865i	$0.664850\pi$
$140$	3.59210	+	0.504684i	0.303588	+	0.0426536i
$141$	−2.75557			−0.232061
$142$		−	3.80642i		−	0.319428i
$143$			12.8573i			1.07518i
$144$	4.61285			0.384404
$145$	−0.235063	+	1.67307i	−0.0195209	+	0.138941i
$146$	2.99063			0.247506
$147$		−	1.00000i		−	0.0824786i
$148$		−	12.3497i		−	1.01514i
$149$	21.2257			1.73888			0.869438	−	0.494041i	$-0.164481\pi$
$149$	21.2257			1.73888			0.869438	+	0.494041i	$0.164481\pi$
$150$	−9.14764	−	2.62222i	−0.746902	−	0.214103i
$151$	16.8573			1.37183			0.685913	−	0.727684i	$-0.259403\pi$
$151$	16.8573			1.37183			0.685913	+	0.727684i	$0.259403\pi$
$152$		−	1.74620i		−	0.141636i
$153$		−	4.42864i		−	0.358034i
$154$	−3.80642			−0.306730
$155$	1.61285	−	11.4795i	0.129547	−	0.922055i
$156$	10.4286			0.834959
$157$		−	10.4286i		−	0.832296i	−0.909297	−	0.416148i	$-0.863380\pi$
$157$		−	10.4286i		−	0.832296i	0.909297	−	0.416148i	$-0.136620\pi$
$158$		−	9.24443i		−	0.735447i
$159$	9.18421			0.728355
$160$	16.2558	+	2.28391i	1.28513	+	0.180559i
$161$	−1.37778			−0.108585
$162$		−	1.90321i		−	0.149530i
$163$		−	20.8573i		−	1.63367i	−0.576873	−	0.816834i	$-0.695727\pi$
$163$		−	20.8573i		−	1.63367i	0.576873	−	0.816834i	$-0.304273\pi$
$164$	13.3590			1.04317
$165$	4.42864	+	0.622216i	0.344769	+	0.0484394i
$166$	−22.1017			−1.71543
$167$			15.3461i			1.18752i	0.804642	+	0.593760i	$0.202357\pi$
$167$			15.3461i			1.18752i	−0.804642	+	0.593760i	$0.797643\pi$
$168$		−	0.719004i		−	0.0554723i
$169$	−28.3274			−2.17903
$170$	2.62222	−	18.6637i	0.201115	−	1.43144i
$171$	−2.42864			−0.185723
$172$			16.3872i			1.24951i
$173$		−	2.06022i		−	0.156636i	−0.996928	−	0.0783179i	$-0.975045\pi$
$173$		−	2.06022i		−	0.156636i	0.996928	−	0.0783179i	$-0.0249549\pi$
$174$	−1.43801			−0.109015
$175$	−1.37778	+	4.80642i	−0.104151	+	0.363331i
$176$	−9.22570			−0.695413
$177$		−	14.1017i		−	1.05995i
$178$			8.79706i			0.659367i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	0.504684	−	3.59210i	0.0376169	−	0.267740i
$181$	−12.1017			−0.899513			−0.449757	−	0.893151i	$-0.648489\pi$
$181$	−12.1017			−0.899513			−0.449757	+	0.893151i	$0.648489\pi$
$182$		−	12.2351i		−	0.906923i
$183$			6.85728i			0.506905i
$184$	−0.990632			−0.0730304
$185$	16.8573	+	2.36842i	1.23937	+	0.174129i
$186$	9.86665			0.723458
$187$			8.85728i			0.647708i
$188$		−	4.47013i		−	0.326017i
$189$	−1.00000			−0.0727393
$190$	−10.2351	−	1.43801i	−0.742530	−	0.104324i
$191$	0.488863			0.0353729			0.0176864	−	0.999844i	$-0.494370\pi$
$191$	0.488863			0.0353729			0.0176864	+	0.999844i	$0.494370\pi$
$192$			4.74620i			0.342528i
$193$			22.9590i			1.65262i	0.563212	+	0.826312i	$0.309565\pi$
$193$			22.9590i			1.65262i	−0.563212	+	0.826312i	$0.690435\pi$
$194$	−22.7239			−1.63148
$195$	−2.00000	+	14.2351i	−0.143223	+	1.01939i
$196$	1.62222			0.115873
$197$		−	1.18421i		−	0.0843713i	−0.999110	−	0.0421857i	$-0.986568\pi$
$197$		−	1.18421i		−	0.0843713i	0.999110	−	0.0421857i	$-0.0134321\pi$
$198$			3.80642i			0.270511i
$199$	−8.79706			−0.623607			−0.311803	−	0.950147i	$-0.600933\pi$
$199$	−8.79706			−0.623607			−0.311803	+	0.950147i	$0.600933\pi$
$200$	−0.990632	+	3.45584i	−0.0700483	+	0.244365i
$201$	−2.75557			−0.194363
$202$		−	2.81579i		−	0.198118i
$203$			0.755569i			0.0530305i
$204$	7.18421			0.502995
$205$	−2.56199	+	18.2351i	−0.178937	+	1.27359i
$206$	16.8573			1.17450
$207$			1.37778i			0.0957626i
$208$		−	29.6543i		−	2.05616i
$209$	4.85728			0.335985
$210$	−4.21432	−	0.592104i	−0.290816	−	0.0408591i
$211$	23.2257			1.59892			0.799461	−	0.600717i	$-0.205118\pi$
$211$	23.2257			1.59892			0.799461	+	0.600717i	$0.205118\pi$
$212$			14.8988i			1.02325i
$213$			2.00000i			0.137038i
$214$	3.35905			0.229620
$215$	−22.3684	−	3.14272i	−1.52551	−	0.214332i
$216$	−0.719004			−0.0489220
$217$		−	5.18421i		−	0.351927i
$218$			10.6824i			0.723506i
$219$	−1.57136			−0.106183
$220$	−1.00937	+	7.18421i	−0.0680516	+	0.484359i
$221$	−28.4701			−1.91511
$222$			14.4889i			0.972429i
$223$			15.2257i			1.01959i	0.860297	+	0.509794i	$0.170278\pi$
$223$			15.2257i			1.01959i	−0.860297	+	0.509794i	$0.829722\pi$
$224$	7.34122			0.490506
$225$	4.80642	+	1.37778i	0.320428	+	0.0918523i
$226$	21.4795			1.42879
$227$		−	14.3684i		−	0.953665i	−0.878994	−	0.476833i	$-0.841785\pi$
$227$		−	14.3684i		−	0.953665i	0.878994	−	0.476833i	$-0.158215\pi$
$228$		−	3.93978i		−	0.260918i
$229$	5.61285			0.370907			0.185454	−	0.982653i	$-0.440625\pi$
$229$	5.61285			0.370907			0.185454	+	0.982653i	$0.440625\pi$
$230$	−0.815792	+	5.80642i	−0.0537917	+	0.382864i
$231$	2.00000			0.131590
$232$			0.543257i			0.0356666i
$233$		−	23.2859i		−	1.52551i	−0.646687	−	0.762756i	$-0.723846\pi$
$233$		−	23.2859i		−	1.52551i	0.646687	−	0.762756i	$-0.276154\pi$
$234$	−12.2351			−0.799831
$235$	6.10171	+	0.857279i	0.398032	+	0.0559227i
$236$	22.8760			1.48910
$237$			4.85728i			0.315514i
$238$		−	8.42864i		−	0.546348i
$239$	8.48886			0.549099			0.274549	−	0.961573i	$-0.411471\pi$
$239$	8.48886			0.549099			0.274549	+	0.961573i	$0.411471\pi$
$240$	−10.2143	−	1.43509i	−0.659332	−	0.0926349i
$241$	−7.24443			−0.466655			−0.233327	−	0.972398i	$-0.574961\pi$
$241$	−7.24443			−0.466655			−0.233327	+	0.972398i	$0.574961\pi$
$242$			13.3225i			0.856402i
$243$			1.00000i			0.0641500i
$244$	−11.1240			−0.712140
$245$	−0.311108	+	2.21432i	−0.0198759	+	0.141468i
$246$	−15.6731			−0.999278
$247$			15.6128i			0.993422i
$248$		−	3.72746i		−	0.236694i
$249$	11.6128			0.735934
$250$	19.4400	+	8.65233i	1.22949	+	0.547221i
$251$	27.6128			1.74291			0.871454	−	0.490478i	$-0.163178\pi$
$251$	27.6128			1.74291			0.871454	+	0.490478i	$0.163178\pi$
$252$		−	1.62222i		−	0.102190i
$253$		−	2.75557i		−	0.173241i
$254$	−24.4701			−1.53539
$255$	−1.37778	+	9.80642i	−0.0862802	+	0.614102i
$256$	20.2444			1.26528
$257$		−	0.428639i		−	0.0267378i	−0.999911	−	0.0133689i	$-0.995744\pi$
$257$		−	0.428639i		−	0.0267378i	0.999911	−	0.0133689i	$-0.00425558\pi$
$258$		−	19.2257i		−	1.19694i
$259$	7.61285			0.473039
$260$	−23.0923	−	3.24443i	−1.43213	−	0.201211i
$261$	0.755569			0.0467685
$262$			4.00000i			0.247121i
$263$			9.37778i			0.578259i	0.957290	+	0.289129i	$0.0933658\pi$
$263$			9.37778i			0.578259i	−0.957290	+	0.289129i	$0.906634\pi$
$264$	1.43801			0.0885032
$265$	−20.3368	−	2.85728i	−1.24928	−	0.175521i
$266$	−4.62222			−0.283406
$267$		−	4.62222i		−	0.282875i
$268$		−	4.47013i		−	0.273056i
$269$	−1.74620			−0.106468			−0.0532339	−	0.998582i	$-0.516953\pi$
$269$	−1.74620			−0.106468			−0.0532339	+	0.998582i	$0.516953\pi$
$270$	−0.592104	+	4.21432i	−0.0360343	+	0.256475i
$271$	−2.69535			−0.163731			−0.0818653	−	0.996643i	$-0.526088\pi$
$271$	−2.69535			−0.163731			−0.0818653	+	0.996643i	$0.526088\pi$
$272$		−	20.4286i		−	1.23867i
$273$			6.42864i			0.389079i
$274$	30.3368			1.83271
$275$	−9.61285	−	2.75557i	−0.579677	−	0.166167i
$276$	−2.23506			−0.134535
$277$		−	5.12399i		−	0.307870i	−0.988081	−	0.153935i	$-0.950805\pi$
$277$		−	5.12399i		−	0.307870i	0.988081	−	0.153935i	$-0.0491947\pi$
$278$			22.2163i			1.33245i
$279$	−5.18421			−0.310370
$280$	−0.223688	+	1.59210i	−0.0133679	+	0.0951464i
$281$	23.9813			1.43060			0.715301	−	0.698816i	$-0.246290\pi$
$281$	23.9813			1.43060			0.715301	+	0.698816i	$0.246290\pi$
$282$			5.24443i			0.312301i
$283$		−	2.36842i		−	0.140788i	−0.997519	−	0.0703939i	$-0.977574\pi$
$283$		−	2.36842i		−	0.140788i	0.997519	−	0.0703939i	$-0.0224256\pi$
$284$	−3.24443			−0.192522
$285$	5.37778	+	0.755569i	0.318552	+	0.0447560i
$286$	24.4701			1.44695
$287$			8.23506i			0.486100i
$288$		−	7.34122i		−	0.432585i
$289$	−2.61285			−0.153697
$290$	3.18421	+	0.447375i	0.186983	+	0.0262708i
$291$	11.9398			0.699922
$292$		−	2.54909i		−	0.149174i
$293$		−	8.42864i		−	0.492406i	−0.969218	−	0.246203i	$-0.920817\pi$
$293$		−	8.42864i		−	0.492406i	0.969218	−	0.246203i	$-0.0791831\pi$
$294$	−1.90321			−0.110998
$295$	−4.38715	+	31.2257i	−0.255430	+	1.81803i
$296$	5.47367			0.318150
$297$		−	2.00000i		−	0.116052i
$298$		−	40.3970i		−	2.34014i
$299$	8.85728			0.512230
$300$	−2.23506	+	7.79706i	−0.129041	+	0.450163i
$301$	−10.1017			−0.582253
$302$		−	32.0830i		−	1.84617i
$303$			1.47949i			0.0849947i
$304$	−11.2029			−0.642533
$305$	2.13335	−	15.1842i	0.122155	−	0.869445i
$306$	−8.42864			−0.481833
$307$		−	22.5718i		−	1.28824i	−0.764923	−	0.644121i	$-0.777223\pi$
$307$		−	22.5718i		−	1.28824i	0.764923	−	0.644121i	$-0.222777\pi$
$308$			3.24443i			0.184869i
$309$	−8.85728			−0.503873
$310$	−21.8479	−	3.06959i	−1.24088	−	0.174341i
$311$	−24.0830			−1.36562			−0.682810	−	0.730596i	$-0.739242\pi$
$311$	−24.0830			−1.36562			−0.682810	+	0.730596i	$0.739242\pi$
$312$			4.62222i			0.261681i
$313$		−	9.65433i		−	0.545695i	−0.962057	−	0.272848i	$-0.912035\pi$
$313$		−	9.65433i		−	0.545695i	0.962057	−	0.272848i	$-0.0879655\pi$
$314$	−19.8479			−1.12008
$315$	2.21432	+	0.311108i	0.124763	+	0.0175289i
$316$	−7.87955			−0.443260
$317$		−	6.04149i		−	0.339324i	−0.985502	−	0.169662i	$-0.945732\pi$
$317$		−	6.04149i		−	0.339324i	0.985502	−	0.169662i	$-0.0542676\pi$
$318$		−	17.4795i		−	0.980201i
$319$	−1.51114			−0.0846075
$320$	1.47658	−	10.5096i	0.0825433	−	0.587505i
$321$	−1.76494			−0.0985092
$322$			2.62222i			0.146130i
$323$			10.7556i			0.598456i
$324$	−1.62222			−0.0901231
$325$	8.85728	−	30.8988i	0.491313	−	1.71396i
$326$	−39.6958			−2.19855
$327$		−	5.61285i		−	0.310391i
$328$			5.92104i			0.326935i
$329$	2.75557			0.151919
$330$	1.18421	−	8.42864i	0.0651885	−	0.463981i
$331$	13.5111			0.742639			0.371320	−	0.928505i	$-0.378905\pi$
$331$	13.5111			0.742639			0.371320	+	0.928505i	$0.378905\pi$
$332$			18.8385i			1.03390i
$333$		−	7.61285i		−	0.417181i
$334$	29.2070			1.59813
$335$	6.10171	+	0.857279i	0.333372	+	0.0468382i
$336$	−4.61285			−0.251651
$337$			10.4889i			0.571365i	0.958324	+	0.285682i	$0.0922202\pi$
$337$			10.4889i			0.571365i	−0.958324	+	0.285682i	$0.907780\pi$
$338$			53.9131i			2.93248i
$339$	−11.2859			−0.612967
$340$	−15.9081	−	2.23506i	−0.862740	−	0.121213i
$341$	10.3684			0.561481
$342$			4.62222i			0.249941i
$343$			1.00000i			0.0539949i
$344$	−7.26317			−0.391604
$345$	0.428639	−	3.05086i	0.0230772	−	0.164253i
$346$	−3.92104			−0.210796
$347$		−	16.7239i		−	0.897787i	−0.893585	−	0.448894i	$-0.851818\pi$
$347$		−	16.7239i		−	0.897787i	0.893585	−	0.448894i	$-0.148182\pi$
$348$			1.22570i			0.0657042i
$349$	16.3684			0.876181			0.438091	−	0.898931i	$-0.355655\pi$
$349$	16.3684			0.876181			0.438091	+	0.898931i	$0.355655\pi$
$350$	9.14764	+	2.62222i	0.488962	+	0.140163i
$351$	6.42864			0.343135
$352$			14.6824i			0.782577i
$353$		−	0.549086i		−	0.0292249i	−0.999893	−	0.0146124i	$-0.995349\pi$
$353$		−	0.549086i		−	0.0292249i	0.999893	−	0.0146124i	$-0.00465145\pi$
$354$	−26.8385			−1.42645
$355$	0.622216	−	4.42864i	0.0330238	−	0.235048i
$356$	7.49823			0.397405
$357$			4.42864i			0.234388i
$358$			19.0321i			1.00588i
$359$	0.285442			0.0150651			0.00753253	−	0.999972i	$-0.497602\pi$
$359$	0.285442			0.0150651			0.00753253	+	0.999972i	$0.497602\pi$
$360$	1.59210	+	0.223688i	0.0839113	+	0.0117894i
$361$	−13.1017			−0.689564
$362$			23.0321i			1.21054i
$363$		−	7.00000i		−	0.367405i
$364$	−10.4286			−0.546609
$365$	3.47949	+	0.488863i	0.182125	+	0.0255882i
$366$	13.0509			0.682179
$367$			1.71456i			0.0894992i	0.998998	+	0.0447496i	$0.0142490\pi$
$367$			1.71456i			0.0894992i	−0.998998	+	0.0447496i	$0.985751\pi$
$368$			6.35551i			0.331304i
$369$	8.23506			0.428700
$370$	4.50760	−	32.0830i	0.234339	−	1.66791i
$371$	−9.18421			−0.476820
$372$		−	8.40990i		−	0.436033i
$373$		−	16.0000i		−	0.828449i	−0.910175	−	0.414224i	$-0.864053\pi$
$373$		−	16.0000i		−	0.828449i	0.910175	−	0.414224i	$-0.135947\pi$
$374$	16.8573			0.871669
$375$	−10.2143	−	4.54617i	−0.527465	−	0.234763i
$376$	1.98126			0.102176
$377$		−	4.85728i		−	0.250163i
$378$			1.90321i			0.0978907i
$379$	4.85728			0.249502			0.124751	−	0.992188i	$-0.460187\pi$
$379$	4.85728			0.249502			0.124751	+	0.992188i	$0.460187\pi$
$380$	−1.22570	+	8.72393i	−0.0628768	+	0.447528i
$381$	12.8573			0.658698
$382$		−	0.930409i		−	0.0476039i
$383$			8.38715i			0.428563i	0.976772	+	0.214282i	$0.0687411\pi$
$383$			8.38715i			0.428563i	−0.976772	+	0.214282i	$0.931259\pi$
$384$	−5.64941			−0.288295
$385$	−4.42864	−	0.622216i	−0.225704	−	0.0317110i
$386$	43.6958			2.22406
$387$			10.1017i			0.513499i
$388$			19.3689i			0.983307i
$389$	−8.95899			−0.454239			−0.227119	−	0.973867i	$-0.572931\pi$
$389$	−8.95899			−0.454239			−0.227119	+	0.973867i	$0.572931\pi$
$390$	27.0923	+	3.80642i	1.37187	+	0.192746i
$391$	6.10171			0.308577
$392$			0.719004i			0.0363152i
$393$		−	2.10171i		−	0.106017i
$394$	−2.25380			−0.113545
$395$	1.51114	−	10.7556i	0.0760336	−	0.541171i
$396$	3.24443			0.163039
$397$		−	2.54909i		−	0.127935i	−0.997952	−	0.0639675i	$-0.979625\pi$
$397$		−	2.54909i		−	0.127935i	0.997952	−	0.0639675i	$-0.0203754\pi$
$398$			16.7427i			0.839234i
$399$	2.42864			0.121584
$400$	22.1713	+	6.35551i	1.10857	+	0.317775i
$401$	0.958989			0.0478896			0.0239448	−	0.999713i	$-0.492377\pi$
$401$	0.958989			0.0478896			0.0239448	+	0.999713i	$0.492377\pi$
$402$			5.24443i			0.261568i
$403$			33.3274i			1.66016i
$404$	−2.40006			−0.119407
$405$	0.311108	−	2.21432i	0.0154591	−	0.110030i
$406$	1.43801			0.0713671
$407$			15.2257i			0.754710i
$408$			3.18421i			0.157642i
$409$	31.9813			1.58137			0.790686	−	0.612222i	$-0.209724\pi$
$409$	31.9813			1.58137			0.790686	+	0.612222i	$0.209724\pi$
$410$	34.7052	+	4.87601i	1.71397	+	0.240809i
$411$	−15.9398			−0.786251
$412$		−	14.3684i		−	0.707881i
$413$			14.1017i			0.693900i
$414$	2.62222			0.128875
$415$	−25.7146	−	3.61285i	−1.26228	−	0.177348i
$416$	−47.1941			−2.31388
$417$		−	11.6731i		−	0.571633i
$418$		−	9.24443i		−	0.452160i
$419$	0.470127			0.0229672			0.0114836	−	0.999934i	$-0.496345\pi$
$419$	0.470127			0.0229672			0.0114836	+	0.999934i	$0.496345\pi$
$420$	−0.504684	+	3.59210i	−0.0246261	+	0.175277i
$421$	−33.6128			−1.63819			−0.819095	−	0.573658i	$-0.805524\pi$
$421$	−33.6128			−1.63819			−0.819095	+	0.573658i	$0.805524\pi$
$422$		−	44.2034i		−	2.15179i
$423$		−	2.75557i		−	0.133980i
$424$	−6.60348			−0.320693
$425$	6.10171	−	21.2859i	0.295976	−	1.03252i
$426$	3.80642			0.184422
$427$		−	6.85728i		−	0.331847i
$428$		−	2.86311i		−	0.138394i
$429$	−12.8573			−0.620755
$430$	−5.98126	+	42.5718i	−0.288442	+	2.05300i
$431$	11.7146			0.564270			0.282135	−	0.959375i	$-0.408957\pi$
$431$	11.7146			0.564270			0.282135	+	0.959375i	$0.408957\pi$
$432$			4.61285i			0.221936i
$433$			0.0602231i			0.00289414i	0.999999	+	0.00144707i	$0.000460616\pi$
$433$			0.0602231i			0.00289414i	−0.999999	+	0.00144707i	$0.999539\pi$
$434$	−9.86665			−0.473614
$435$	−1.67307	−	0.235063i	−0.0802176	−	0.0112704i
$436$	9.10525			0.436062
$437$		−	3.34614i		−	0.160068i
$438$			2.99063i			0.142898i
$439$	22.4286			1.07046			0.535230	−	0.844706i	$-0.320225\pi$
$439$	22.4286			1.07046			0.535230	+	0.844706i	$0.320225\pi$
$440$	−3.18421	−	0.447375i	−0.151801	−	0.0213278i
$441$	1.00000			0.0476190
$442$			54.1847i			2.57730i
$443$			23.9496i			1.13788i	0.822379	+	0.568940i	$0.192647\pi$
$443$			23.9496i			1.13788i	−0.822379	+	0.568940i	$0.807353\pi$
$444$	12.3497			0.586090
$445$	−1.43801	+	10.2351i	−0.0681681	+	0.485189i
$446$	28.9777			1.37214
$447$			21.2257i			1.00394i
$448$		−	4.74620i		−	0.224237i
$449$	−29.4291			−1.38885			−0.694423	−	0.719567i	$-0.744340\pi$
$449$	−29.4291			−1.38885			−0.694423	+	0.719567i	$0.744340\pi$
$450$	2.62222	−	9.14764i	0.123612	−	0.431224i
$451$	−16.4701			−0.775548
$452$		−	18.3082i		−	0.861145i
$453$			16.8573i			0.792024i
$454$	−27.3461			−1.28342
$455$	2.00000	−	14.2351i	0.0937614	−	0.667350i
$456$	1.74620			0.0817733
$457$		−	3.14272i		−	0.147010i	−0.997295	−	0.0735051i	$-0.976581\pi$
$457$		−	3.14272i		−	0.147010i	0.997295	−	0.0735051i	$-0.0234185\pi$
$458$		−	10.6824i		−	0.499158i
$459$	4.42864			0.206711
$460$	4.94914	+	0.695346i	0.230755	+	0.0324207i
$461$	−3.37778			−0.157319			−0.0786596	−	0.996902i	$-0.525064\pi$
$461$	−3.37778			−0.157319			−0.0786596	+	0.996902i	$0.525064\pi$
$462$		−	3.80642i		−	0.177091i
$463$		−	20.8573i		−	0.969320i	−0.874703	−	0.484660i	$-0.838943\pi$
$463$		−	20.8573i		−	0.969320i	0.874703	−	0.484660i	$-0.161057\pi$
$464$	3.48532			0.161802
$465$	11.4795	+	1.61285i	0.532349	+	0.0747940i
$466$	−44.3180			−2.05299
$467$		−	14.3684i		−	0.664891i	−0.943122	−	0.332446i	$-0.892126\pi$
$467$		−	14.3684i		−	0.664891i	0.943122	−	0.332446i	$-0.107874\pi$
$468$			10.4286i			0.482064i
$469$	2.75557			0.127240
$470$	1.63158	−	11.6128i	0.0752593	−	0.535661i
$471$	10.4286			0.480526
$472$			10.1392i			0.466694i
$473$		−	20.2034i		−	0.928954i
$474$	9.24443			0.424611
$475$	−11.6731	−	3.34614i	−0.535597	−	0.153532i
$476$	−7.18421			−0.329288
$477$			9.18421i			0.420516i
$478$		−	16.1561i		−	0.738963i
$479$	−6.36842			−0.290980			−0.145490	−	0.989360i	$-0.546476\pi$
$479$	−6.36842			−0.290980			−0.145490	+	0.989360i	$0.546476\pi$
$480$	−2.28391	+	16.2558i	−0.104246	+	0.741973i
$481$	−48.9403			−2.23148
$482$			13.7877i			0.628012i
$483$		−	1.37778i		−	0.0626914i
$484$	11.3555			0.516160
$485$	−26.4385	−	3.71456i	−1.20051	−	0.168669i
$486$	1.90321			0.0863314
$487$			17.3274i			0.785180i	0.919714	+	0.392590i	$0.128421\pi$
$487$			17.3274i			0.785180i	−0.919714	+	0.392590i	$0.871579\pi$
$488$		−	4.93041i		−	0.223189i
$489$	20.8573			0.943199
$490$	4.21432	+	0.592104i	0.190384	+	0.0267485i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$			13.3590i			0.602272i
$493$		−	3.34614i		−	0.150703i
$494$	29.7146			1.33692
$495$	−0.622216	+	4.42864i	−0.0279665	+	0.199053i
$496$	−23.9140			−1.07377
$497$		−	2.00000i		−	0.0897123i
$498$		−	22.1017i		−	0.990401i
$499$	−23.3461			−1.04512			−0.522558	−	0.852603i	$-0.675022\pi$
$499$	−23.3461			−1.04512			−0.522558	+	0.852603i	$0.675022\pi$
$500$	7.37487	−	16.5698i	0.329814	−	0.741025i
$501$	−15.3461			−0.685615
$502$		−	52.5531i		−	2.34556i
$503$		−	0.387152i		−	0.0172623i	−0.999963	−	0.00863113i	$-0.997253\pi$
$503$		−	0.387152i		−	0.0172623i	0.999963	−	0.00863113i	$-0.00274741\pi$
$504$	0.719004			0.0320270
$505$	0.460282	−	3.27607i	0.0204823	−	0.145783i
$506$	−5.24443			−0.233143
$507$		−	28.3274i		−	1.25806i
$508$			20.8573i			0.925392i
$509$	29.9496			1.32749			0.663747	−	0.747957i	$-0.268965\pi$
$509$	29.9496			1.32749			0.663747	+	0.747957i	$0.268965\pi$
$510$	18.6637	+	2.62222i	0.826443	+	0.116114i
$511$	1.57136			0.0695129
$512$		−	27.2306i		−	1.20343i
$513$		−	2.42864i		−	0.107227i
$514$	−0.815792			−0.0359830
$515$	19.6128	+	2.75557i	0.864245	+	0.121425i
$516$	−16.3872			−0.721404
$517$			5.51114i			0.242380i
$518$		−	14.4889i		−	0.636604i
$519$	2.06022			0.0904338
$520$	1.43801	−	10.2351i	0.0630608	−	0.448837i
$521$	−18.5205			−0.811398			−0.405699	−	0.914007i	$-0.632972\pi$
$521$	−18.5205			−0.811398			−0.405699	+	0.914007i	$0.632972\pi$
$522$		−	1.43801i		−	0.0629399i
$523$			4.00000i			0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$			4.00000i			0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	3.40943			0.148942
$525$	−4.80642	−	1.37778i	−0.209770	−	0.0601314i
$526$	17.8479			0.778206
$527$			22.9590i			1.00011i
$528$		−	9.22570i		−	0.401497i
$529$	21.1017			0.917466
$530$	−5.43801	+	38.7052i	−0.236212	+	1.68125i
$531$	14.1017			0.611962
$532$			3.93978i			0.170811i
$533$		−	52.9403i		−	2.29310i
$534$	−8.79706			−0.380686
$535$	3.90813	+	0.549086i	0.168963	+	0.0237390i
$536$	1.98126			0.0855776
$537$		−	10.0000i		−	0.431532i
$538$			3.32339i			0.143282i
$539$	−2.00000			−0.0861461
$540$	3.59210	+	0.504684i	0.154580	+	0.0217181i
$541$	14.5906			0.627298			0.313649	−	0.949539i	$-0.398449\pi$
$541$	14.5906			0.627298			0.313649	+	0.949539i	$0.398449\pi$
$542$			5.12981i			0.220344i
$543$		−	12.1017i		−	0.519334i
$544$	−32.5116			−1.39392
$545$	−1.74620	+	12.4286i	−0.0747990	+	0.532384i
$546$	12.2351			0.523612
$547$		−	18.7556i		−	0.801930i	−0.916093	−	0.400965i	$-0.868675\pi$
$547$		−	18.7556i		−	0.801930i	0.916093	−	0.400965i	$-0.131325\pi$
$548$		−	25.8578i		−	1.10459i
$549$	−6.85728			−0.292662
$550$	−5.24443	+	18.2953i	−0.223623	+	0.780114i
$551$	−1.83500			−0.0781738
$552$		−	0.990632i		−	0.0421641i
$553$		−	4.85728i		−	0.206553i
$554$	−9.75203			−0.414324
$555$	−2.36842	+	16.8573i	−0.100534	+	0.715552i
$556$	18.9362			0.803075
$557$			31.8765i			1.35065i	0.737520	+	0.675325i	$0.235997\pi$
$557$			31.8765i			1.35065i	−0.737520	+	0.675325i	$0.764003\pi$
$558$			9.86665i			0.417688i
$559$	64.9403			2.74668
$560$	10.2143	+	1.43509i	0.431634	+	0.0606437i
$561$	−8.85728			−0.373955
$562$		−	45.6414i		−	1.92527i
$563$			2.01874i			0.0850796i	0.999095	+	0.0425398i	$0.0135449\pi$
$563$			2.01874i			0.0850796i	−0.999095	+	0.0425398i	$0.986455\pi$
$564$	4.47013			0.188226
$565$	24.9906	+	3.51114i	1.05136	+	0.147715i
$566$	−4.50760			−0.189468
$567$		−	1.00000i		−	0.0419961i
$568$		−	1.43801i		−	0.0603375i
$569$	28.9590			1.21402			0.607012	−	0.794693i	$-0.292368\pi$
$569$	28.9590			1.21402			0.607012	+	0.794693i	$0.292368\pi$
$570$	1.43801	−	10.2351i	0.0602315	−	0.428700i
$571$	8.97773			0.375706			0.187853	−	0.982197i	$-0.439847\pi$
$571$	8.97773			0.375706			0.187853	+	0.982197i	$0.439847\pi$
$572$		−	20.8573i		−	0.872087i
$573$			0.488863i			0.0204225i
$574$	15.6731			0.654181
$575$	−1.89829	+	6.62222i	−0.0791642	+	0.276165i
$576$	−4.74620			−0.197758
$577$			28.6766i			1.19382i	0.802307	+	0.596911i	$0.203606\pi$
$577$			28.6766i			1.19382i	−0.802307	+	0.596911i	$0.796394\pi$
$578$			4.97280i			0.206841i
$579$	−22.9590			−0.954143
$580$	0.381323	−	2.71408i	0.0158336	−	0.112696i
$581$	−11.6128			−0.481782
$582$		−	22.7239i		−	0.941937i
$583$		−	18.3684i		−	0.760742i
$584$	1.12981			0.0467520
$585$	−14.2351	−	2.00000i	−0.588547	−	0.0826898i
$586$	−16.0415			−0.662668
$587$			45.2070i			1.86589i	0.360018	+	0.932945i	$0.382771\pi$
$587$			45.2070i			1.86589i	−0.360018	+	0.932945i	$0.617229\pi$
$588$			1.62222i			0.0668990i
$589$	12.5906			0.518786
$590$	59.4291	+	8.34968i	2.44666	+	0.343751i
$591$	1.18421			0.0487118
$592$		−	35.1169i		−	1.44330i
$593$			18.2636i			0.749998i	0.927025	+	0.374999i	$0.122357\pi$
$593$			18.2636i			0.749998i	−0.927025	+	0.374999i	$0.877643\pi$
$594$	−3.80642			−0.156179
$595$	1.37778	−	9.80642i	0.0564837	−	0.402024i
$596$	−34.4327			−1.41042
$597$		−	8.79706i		−	0.360040i
$598$		−	16.8573i		−	0.689345i
$599$	22.7368			0.929002			0.464501	−	0.885573i	$-0.346234\pi$
$599$	22.7368			0.929002			0.464501	+	0.885573i	$0.346234\pi$
$600$	−3.45584	−	0.990632i	−0.141084	−	0.0404424i
$601$	0.488863			0.0199411			0.00997056	−	0.999950i	$-0.496826\pi$
$601$	0.488863			0.0199411			0.00997056	+	0.999950i	$0.496826\pi$
$602$			19.2257i			0.783581i
$603$		−	2.75557i		−	0.112215i
$604$	−27.3461			−1.11270
$605$	−2.17775	+	15.5002i	−0.0885383	+	0.630174i
$606$	2.81579			0.114384
$607$			20.2034i			0.820032i	0.912078	+	0.410016i	$0.134477\pi$
$607$			20.2034i			0.820032i	−0.912078	+	0.410016i	$0.865523\pi$
$608$			17.8292i			0.723069i
$609$	−0.755569			−0.0306172
$610$	−28.8988	−	4.06022i	−1.17008	−	0.164394i
$611$	−17.7146			−0.716654
$612$			7.18421i			0.290404i
$613$			10.3684i			0.418776i	0.977833	+	0.209388i	$0.0671472\pi$
$613$			10.3684i			0.418776i	−0.977833	+	0.209388i	$0.932853\pi$
$614$	−42.9590			−1.73368
$615$	−18.2351	−	2.56199i	−0.735309	−	0.103310i
$616$	−1.43801			−0.0579390
$617$			39.2859i			1.58159i	0.612080	+	0.790796i	$0.290333\pi$
$617$			39.2859i			1.58159i	−0.612080	+	0.790796i	$0.709667\pi$
$618$			16.8573i			0.678099i
$619$	−42.8988			−1.72425			−0.862123	−	0.506698i	$-0.830866\pi$
$619$	−42.8988			−1.72425			−0.862123	+	0.506698i	$0.830866\pi$
$620$	−2.61639	+	18.6222i	−0.105077	+	0.747886i
$621$	−1.37778			−0.0552886
$622$			45.8350i			1.83782i
$623$			4.62222i			0.185185i
$624$	29.6543			1.18712
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	−18.3742			−0.734383
$627$			4.85728i			0.193981i
$628$			16.9175i			0.675082i
$629$	−33.7146			−1.34429
$630$	0.592104	−	4.21432i	0.0235900	−	0.167903i
$631$	15.3461			0.610920			0.305460	−	0.952205i	$-0.401190\pi$
$631$	15.3461			0.610920			0.305460	+	0.952205i	$0.401190\pi$
$632$		−	3.49240i		−	0.138920i
$633$			23.2257i			0.923139i
$634$	−11.4982			−0.456653
$635$	−28.4701	−	4.00000i	−1.12980	−	0.158735i
$636$	−14.8988			−0.590775
$637$		−	6.42864i		−	0.254712i
$638$			2.87601i			0.113863i
$639$	−2.00000			−0.0791188
$640$	12.5096	+	1.75758i	0.494486	+	0.0694743i
$641$	30.6735			1.21153			0.605766	−	0.795643i	$-0.292867\pi$
$641$	30.6735			1.21153			0.605766	+	0.795643i	$0.292867\pi$
$642$			3.35905i			0.132571i
$643$		−	49.0607i		−	1.93477i	−0.253320	−	0.967383i	$-0.581523\pi$
$643$		−	49.0607i		−	1.93477i	0.253320	−	0.967383i	$-0.418477\pi$
$644$	2.23506			0.0880738
$645$	3.14272	−	22.3684i	0.123745	−	0.880756i
$646$	20.4701			0.805386
$647$			15.3461i			0.603319i	0.953416	+	0.301660i	$0.0975406\pi$
$647$			15.3461i			0.603319i	−0.953416	+	0.301660i	$0.902459\pi$
$648$		−	0.719004i		−	0.0282451i
$649$	−28.2034			−1.10708
$650$	−58.8069	−	16.8573i	−2.30660	−	0.661197i
$651$	5.18421			0.203185
$652$			33.8350i			1.32508i
$653$		−	19.4697i		−	0.761906i	−0.924594	−	0.380953i	$-0.875596\pi$
$653$		−	19.4697i		−	0.761906i	0.924594	−	0.380953i	$-0.124404\pi$
$654$	−10.6824			−0.417716
$655$	−0.653858	+	4.65386i	−0.0255484	+	0.181841i
$656$	37.9871			1.48315
$657$		−	1.57136i		−	0.0613046i
$658$		−	5.24443i		−	0.204449i
$659$	−30.9403			−1.20526			−0.602631	−	0.798020i	$-0.705881\pi$
$659$	−30.9403			−1.20526			−0.602631	+	0.798020i	$0.705881\pi$
$660$	−7.18421	−	1.00937i	−0.279645	−	0.0392896i
$661$	47.7975			1.85911			0.929554	−	0.368685i	$-0.120192\pi$
$661$	47.7975			1.85911			0.929554	+	0.368685i	$0.120192\pi$
$662$		−	25.7146i		−	0.999425i
$663$		−	28.4701i		−	1.10569i
$664$	−8.34968			−0.324030
$665$	−5.37778	−	0.755569i	−0.208542	−	0.0292997i
$666$	−14.4889			−0.561432
$667$			1.04101i			0.0403081i
$668$		−	24.8948i		−	0.963207i
$669$	−15.2257			−0.588659
$670$	1.63158	−	11.6128i	0.0630336	−	0.448643i
$671$	13.7146			0.529445
$672$			7.34122i			0.283194i
$673$			27.8163i			1.07224i	0.844142	+	0.536119i	$0.180110\pi$
$673$			27.8163i			1.07224i	−0.844142	+	0.536119i	$0.819890\pi$
$674$	19.9625			0.768928
$675$	−1.37778	+	4.80642i	−0.0530309	+	0.184999i
$676$	45.9532			1.76743
$677$			19.0005i			0.730248i	0.930959	+	0.365124i	$0.118973\pi$
$677$			19.0005i			0.730248i	−0.930959	+	0.365124i	$0.881027\pi$
$678$			21.4795i			0.824915i
$679$	−11.9398			−0.458207
$680$	0.990632	−	7.05086i	0.0379890	−	0.270388i
$681$	14.3684			0.550599
$682$		−	19.7333i		−	0.755627i
$683$			4.52051i			0.172972i	0.996253	+	0.0864862i	$0.0275638\pi$
$683$			4.52051i			0.172972i	−0.996253	+	0.0864862i	$0.972436\pi$
$684$	3.93978			0.150641
$685$	35.2958	+	4.95899i	1.34858	+	0.189473i
$686$	1.90321			0.0726650
$687$			5.61285i			0.214143i
$688$			46.5977i			1.77652i
$689$	59.0420			2.24932
$690$	−5.80642	−	0.815792i	−0.221047	−	0.0310567i
$691$	−1.18421			−0.0450494			−0.0225247	−	0.999746i	$-0.507170\pi$
$691$	−1.18421			−0.0450494			−0.0225247	+	0.999746i	$0.507170\pi$
$692$			3.34213i			0.127049i
$693$			2.00000i			0.0759737i
$694$	−31.8292			−1.20822
$695$	−3.63158	+	25.8479i	−0.137754	+	0.980467i
$696$	−0.543257			−0.0205921
$697$		−	36.4701i		−	1.38140i
$698$		−	31.1526i		−	1.17914i
$699$	23.2859			0.880754
$700$	2.23506	−	7.79706i	0.0844775	−	0.294701i
$701$	−26.6735			−1.00745			−0.503723	−	0.863865i	$-0.668037\pi$
$701$	−26.6735			−1.00745			−0.503723	+	0.863865i	$0.668037\pi$
$702$		−	12.2351i		−	0.461783i
$703$			18.4889i			0.697321i
$704$	9.49240			0.357758
$705$	−0.857279	+	6.10171i	−0.0322870	+	0.229804i
$706$	−1.04503			−0.0393301
$707$		−	1.47949i		−	0.0556421i
$708$			22.8760i			0.859733i
$709$	18.2034			0.683644			0.341822	−	0.939765i	$-0.388956\pi$
$709$	18.2034			0.683644			0.341822	+	0.939765i	$0.388956\pi$
$710$	−8.42864	−	1.18421i	−0.316321	−	0.0444425i
$711$	−4.85728			−0.182162
$712$			3.32339i			0.124549i
$713$		−	7.14272i		−	0.267497i
$714$	8.42864			0.315434
$715$	28.4701	+	4.00000i	1.06472	+	0.149592i
$716$	16.2222			0.606250
$717$			8.48886i			0.317022i
$718$		−	0.543257i		−	0.0202742i
$719$	−4.85728			−0.181146			−0.0905730	−	0.995890i	$-0.528870\pi$
$719$	−4.85728			−0.181146			−0.0905730	+	0.995890i	$0.528870\pi$
$720$	1.43509	−	10.2143i	0.0534828	−	0.380665i
$721$	8.85728			0.329862
$722$			24.9353i			0.927997i
$723$		−	7.24443i		−	0.269423i
$724$	19.6316			0.729602
$725$	3.63158	+	1.04101i	0.134874	+	0.0386622i
$726$	−13.3225			−0.494444
$727$		−	21.0607i		−	0.781098i	−0.920582	−	0.390549i	$-0.872285\pi$
$727$		−	21.0607i		−	0.781098i	0.920582	−	0.390549i	$-0.127715\pi$
$728$		−	4.62222i		−	0.171311i
$729$	−1.00000			−0.0370370
$730$	0.930409	−	6.62222i	0.0344360	−	0.245099i
$731$	44.7368			1.65465
$732$		−	11.1240i		−	0.411154i
$733$			9.45091i			0.349077i	0.984650	+	0.174539i	$0.0558434\pi$
$733$			9.45091i			0.349077i	−0.984650	+	0.174539i	$0.944157\pi$
$734$	3.26317			0.120446
$735$	−2.21432	−	0.311108i	−0.0816764	−	0.0114754i
$736$	10.1146			0.372830
$737$			5.51114i			0.203005i
$738$		−	15.6731i		−	0.576934i
$739$	8.20342			0.301768			0.150884	−	0.988551i	$-0.451788\pi$
$739$	8.20342			0.301768			0.150884	+	0.988551i	$0.451788\pi$
$740$	−27.3461	−	3.84208i	−1.00526	−	0.141238i
$741$	−15.6128			−0.573552
$742$			17.4795i			0.641692i
$743$			8.33677i			0.305847i	0.988238	+	0.152923i	$0.0488687\pi$
$743$			8.33677i			0.305847i	−0.988238	+	0.152923i	$0.951131\pi$
$744$	3.72746			0.136655
$745$	6.60348	−	47.0005i	0.241933	−	1.72196i
$746$	−30.4514			−1.11490
$747$			11.6128i			0.424892i
$748$		−	14.3684i		−	0.525361i
$749$	1.76494			0.0644894
$750$	−8.65233	+	19.4400i	−0.315938	+	0.709849i
$751$	−25.9180			−0.945760			−0.472880	−	0.881127i	$-0.656786\pi$
$751$	−25.9180			−0.945760			−0.472880	+	0.881127i	$0.656786\pi$
$752$		−	12.7110i		−	0.463523i
$753$			27.6128i			1.00627i
$754$	−9.24443			−0.336662
$755$	5.24443	−	37.3274i	0.190864	−	1.35848i
$756$	1.62222			0.0589994
$757$		−	8.94025i		−	0.324939i	−0.986714	−	0.162470i	$-0.948054\pi$
$757$		−	8.94025i		−	0.324939i	0.986714	−	0.162470i	$-0.0519459\pi$
$758$		−	9.24443i		−	0.335773i
$759$	2.75557			0.100021
$760$	−3.86665	−	0.543257i	−0.140258	−	0.0197060i
$761$	−0.825636			−0.0299293			−0.0149646	−	0.999888i	$-0.504764\pi$
$761$	−0.825636			−0.0299293			−0.0149646	+	0.999888i	$0.504764\pi$
$762$		−	24.4701i		−	0.886459i
$763$			5.61285i			0.203199i
$764$	−0.793040			−0.0286912
$765$	−9.80642	−	1.37778i	−0.354552	−	0.0498139i
$766$	15.9625			0.576750
$767$		−	90.6548i		−	3.27336i
$768$			20.2444i			0.730508i
$769$	−21.2257			−0.765418			−0.382709	−	0.923869i	$-0.625009\pi$
$769$	−21.2257			−0.765418			−0.382709	+	0.923869i	$0.625009\pi$
$770$	−1.18421	+	8.42864i	−0.0426759	+	0.303747i
$771$	0.428639			0.0154371
$772$		−	37.2444i		−	1.34046i
$773$			29.4893i			1.06066i	0.847792	+	0.530329i	$0.177932\pi$
$773$			29.4893i			1.06066i	−0.847792	+	0.530329i	$0.822068\pi$
$774$	19.2257			0.691053
$775$	−24.9175	−	7.14272i	−0.895063	−	0.256574i
$776$	−8.58474			−0.308174
$777$			7.61285i			0.273109i
$778$			17.0509i			0.611303i
$779$	−20.0000			−0.716574
$780$	3.24443	−	23.0923i	0.116169	−	0.826838i
$781$	4.00000			0.143131
$782$		−	11.6128i		−	0.415275i
$783$			0.755569i			0.0270018i
$784$	4.61285			0.164745
$785$	−23.0923	−	3.24443i	−0.824201	−	0.115799i
$786$	−4.00000			−0.142675
$787$			34.4514i			1.22806i	0.789283	+	0.614030i	$0.210453\pi$
$787$			34.4514i			1.22806i	−0.789283	+	0.614030i	$0.789547\pi$
$788$			1.92104i			0.0684343i
$789$	−9.37778			−0.333858
$790$	−20.4701	−	2.87601i	−0.728294	−	0.102324i
$791$	11.2859			0.401281
$792$			1.43801i			0.0510974i
$793$			44.0830i			1.56543i
$794$	−4.85145			−0.172172
$795$	2.85728	−	20.3368i	0.101337	−	0.721271i
$796$	14.2707			0.505812
$797$		−	18.9175i		−	0.670092i	−0.942202	−	0.335046i	$-0.891248\pi$
$797$		−	18.9175i		−	0.670092i	0.942202	−	0.335046i	$-0.108752\pi$
$798$		−	4.62222i		−	0.163625i
$799$	−12.2034			−0.431726
$800$	10.1146	−	35.2850i	0.357606	−	1.24751i
$801$	4.62222			0.163318
$802$		−	1.82516i		−	0.0644486i
$803$			3.14272i			0.110904i
$804$	4.47013			0.157649
$805$	−0.428639	+	3.05086i	−0.0151076	+	0.107529i
$806$	63.4291			2.23420
$807$		−	1.74620i		−	0.0614692i
$808$		−	1.06376i		−	0.0374230i
$809$	−21.2257			−0.746256			−0.373128	−	0.927780i	$-0.621715\pi$
$809$	−21.2257			−0.746256			−0.373128	+	0.927780i	$0.621715\pi$
$810$	−4.21432	−	0.592104i	−0.148076	−	0.0208044i
$811$	−21.5081			−0.755251			−0.377625	−	0.925958i	$-0.623259\pi$
$811$	−21.5081			−0.755251			−0.377625	+	0.925958i	$0.623259\pi$
$812$		−	1.22570i		−	0.0430135i
$813$		−	2.69535i		−	0.0945299i
$814$	28.9777			1.01567
$815$	−46.1847	−	6.48886i	−1.61778	−	0.227295i
$816$	20.4286			0.715145
$817$		−	24.5334i		−	0.858315i
$818$		−	60.8671i		−	2.12817i
$819$	−6.42864			−0.224635
$820$	4.15610	−	29.5812i	0.145137	−	1.03302i
$821$	−46.2034			−1.61251			−0.806255	−	0.591568i	$-0.798509\pi$
$821$	−46.2034			−1.61251			−0.806255	+	0.591568i	$0.798509\pi$
$822$			30.3368i			1.05812i
$823$		−	17.8350i		−	0.621689i	−0.950461	−	0.310845i	$-0.899388\pi$
$823$		−	17.8350i		−	0.621689i	0.950461	−	0.310845i	$-0.100612\pi$
$824$	6.36842			0.221854
$825$	2.75557	−	9.61285i	0.0959366	−	0.334676i
$826$	26.8385			0.933832
$827$		−	35.2128i		−	1.22447i	−0.790676	−	0.612234i	$-0.790271\pi$
$827$		−	35.2128i		−	1.22447i	0.790676	−	0.612234i	$-0.209729\pi$
$828$		−	2.23506i		−	0.0776738i
$829$	−14.3872			−0.499686			−0.249843	−	0.968286i	$-0.580379\pi$
$829$	−14.3872			−0.499686			−0.249843	+	0.968286i	$0.580379\pi$
$830$	−6.87601	+	48.9403i	−0.238670	+	1.69874i
$831$	5.12399			0.177749
$832$			30.5116i			1.05780i
$833$		−	4.42864i		−	0.153443i
$834$	−22.2163			−0.769289
$835$	33.9813	+	4.77430i	1.17597	+	0.165222i
$836$	−7.87955			−0.272520
$837$		−	5.18421i		−	0.179192i
$838$		−	0.894751i		−	0.0309087i
$839$	−1.51114			−0.0521703			−0.0260851	−	0.999660i	$-0.508304\pi$
$839$	−1.51114			−0.0521703			−0.0260851	+	0.999660i	$0.508304\pi$
$840$	−1.59210	−	0.223688i	−0.0549328	−	0.00771796i
$841$	−28.4291			−0.980314
$842$			63.9724i			2.20463i
$843$			23.9813i			0.825959i
$844$	−37.6771			−1.29690
$845$	−8.81288	+	62.7259i	−0.303172	+	2.15784i
$846$	−5.24443			−0.180307
$847$			7.00000i			0.240523i
$848$			42.3654i			1.45483i
$849$	2.36842			0.0812838
$850$	−40.5116	−	11.6128i	−1.38954	−	0.398317i
$851$	10.4889			0.359554
$852$		−	3.24443i		−	0.111152i
$853$		−	15.4064i		−	0.527504i	−0.964591	−	0.263752i	$-0.915040\pi$
$853$		−	15.4064i		−	0.527504i	0.964591	−	0.263752i	$-0.0849600\pi$
$854$	−13.0509			−0.446591
$855$	−0.755569	+	5.37778i	−0.0258399	+	0.183916i
$856$	1.26900			0.0433734
$857$		−	19.8578i		−	0.678328i	−0.940727	−	0.339164i	$-0.889856\pi$
$857$		−	19.8578i		−	0.678328i	0.940727	−	0.339164i	$-0.110144\pi$
$858$			24.4701i			0.835396i
$859$	−2.42864			−0.0828641			−0.0414321	−	0.999141i	$-0.513192\pi$
$859$	−2.42864			−0.0828641			−0.0414321	+	0.999141i	$0.513192\pi$
$860$	36.2864	+	5.09817i	1.23736	+	0.173846i
$861$	−8.23506			−0.280650
$862$		−	22.2953i		−	0.759380i
$863$		−	39.2958i		−	1.33764i	−0.743423	−	0.668822i	$-0.766799\pi$
$863$		−	39.2958i		−	1.33764i	0.743423	−	0.668822i	$-0.233201\pi$
$864$	7.34122			0.249753
$865$	−4.56199	−	0.640951i	−0.155112	−	0.0217930i
$866$	0.114617			0.00389485
$867$		−	2.61285i		−	0.0887370i
$868$			8.40990i			0.285451i
$869$	9.71456			0.329544
$870$	−0.447375	+	3.18421i	−0.0151674	+	0.107955i
$871$	−17.7146			−0.600235
$872$			4.03566i			0.136665i
$873$			11.9398i			0.404100i
$874$	−6.36842			−0.215415
$875$	10.2143	+	4.54617i	0.345307	+	0.153689i
$876$	2.54909			0.0861256
$877$			56.2864i			1.90066i	0.311249	+	0.950328i	$0.399253\pi$
$877$			56.2864i			1.90066i	−0.311249	+	0.950328i	$0.600747\pi$
$878$		−	42.6865i		−	1.44060i
$879$	8.42864			0.284291
$880$	−2.87019	+	20.4286i	−0.0967539	+	0.688649i
$881$	−2.33677			−0.0787279			−0.0393640	−	0.999225i	$-0.512533\pi$
$881$	−2.33677			−0.0787279			−0.0393640	+	0.999225i	$0.512533\pi$
$882$		−	1.90321i		−	0.0640845i
$883$			33.7146i			1.13459i	0.823516	+	0.567293i	$0.192009\pi$
$883$			33.7146i			1.13459i	−0.823516	+	0.567293i	$0.807991\pi$
$884$	46.1847			1.55336
$885$	−31.2257	−	4.38715i	−1.04964	−	0.147473i
$886$	45.5812			1.53133
$887$		−	47.8992i		−	1.60830i	−0.594427	−	0.804150i	$-0.702621\pi$
$887$		−	47.8992i		−	1.60830i	0.594427	−	0.804150i	$-0.297379\pi$
$888$			5.47367i			0.183684i
$889$	−12.8573			−0.431219
$890$	19.4795	+	2.73683i	0.652954	+	0.0917388i
$891$	2.00000			0.0670025
$892$		−	24.6994i		−	0.826996i
$893$			6.69228i			0.223949i
$894$	40.3970			1.35108
$895$	−3.11108	+	22.1432i	−0.103992	+	0.740165i
$896$	5.64941			0.188734
$897$			8.85728i			0.295736i
$898$			56.0098i			1.86907i
$899$	−3.91703			−0.130640
$900$	−7.79706	−	2.23506i	−0.259902	−	0.0745021i
$901$	40.6735			1.35503
$902$			31.3461i			1.04371i
$903$		−	10.1017i		−	0.336164i
$904$	8.11462			0.269888
$905$	−3.76494	+	26.7971i	−0.125151	+	0.890764i
$906$	32.0830			1.06589
$907$		−	23.7591i		−	0.788908i	−0.918916	−	0.394454i	$-0.870934\pi$
$907$		−	23.7591i		−	0.788908i	0.918916	−	0.394454i	$-0.129066\pi$
$908$			23.3087i			0.773525i
$909$	−1.47949			−0.0490717
$910$	−27.0923	−	3.80642i	−0.898102	−	0.126182i
$911$	22.9403			0.760045			0.380022	−	0.924977i	$-0.375916\pi$
$911$	22.9403			0.760045			0.380022	+	0.924977i	$0.375916\pi$
$912$		−	11.2029i		−	0.370967i
$913$		−	23.2257i		−	0.768658i
$914$	−5.98126			−0.197843
$915$	15.1842	+	2.13335i	0.501974	+	0.0705265i
$916$	−9.10525			−0.300846
$917$			2.10171i			0.0694046i
$918$		−	8.42864i		−	0.278187i
$919$	−16.9777			−0.560043			−0.280022	−	0.959994i	$-0.590342\pi$
$919$	−16.9777			−0.560043			−0.280022	+	0.959994i	$0.590342\pi$
$920$	−0.308193	+	2.19358i	−0.0101608	+	0.0723201i
$921$	22.5718			0.743767
$922$			6.42864i			0.211716i
$923$			12.8573i			0.423202i
$924$	−3.24443			−0.106734
$925$	10.4889	−	36.5906i	0.344872	−	1.20309i
$926$	−39.6958			−1.30449
$927$		−	8.85728i		−	0.290911i
$928$		−	5.54680i		−	0.182082i
$929$	−39.3403			−1.29071			−0.645357	−	0.763881i	$-0.723291\pi$
$929$	−39.3403			−1.29071			−0.645357	+	0.763881i	$0.723291\pi$
$930$	3.06959	−	21.8479i	0.100656	−	0.716421i
$931$	−2.42864			−0.0795954
$932$			37.7748i			1.23735i
$933$		−	24.0830i		−	0.788441i
$934$	−27.3461			−0.894793
$935$	19.6128	+	2.75557i	0.641409	+	0.0901167i
$936$	−4.62222			−0.151082
$937$			17.7748i			0.580677i	0.956924	+	0.290338i	$0.0937679\pi$
$937$			17.7748i			0.580677i	−0.956924	+	0.290338i	$0.906232\pi$
$938$		−	5.24443i		−	0.171237i
$939$	9.65433			0.315057
$940$	−9.89829	−	1.39069i	−0.322847	−	0.0453594i
$941$	35.5812			1.15991			0.579957	−	0.814647i	$-0.303069\pi$
$941$	35.5812			1.15991			0.579957	+	0.814647i	$0.303069\pi$
$942$		−	19.8479i		−	0.646680i
$943$			11.3461i			0.369481i
$944$	65.0490			2.11717
$945$	−0.311108	+	2.21432i	−0.0101203	+	0.0720318i
$946$	−38.4514			−1.25016
$947$		−	30.5018i		−	0.991174i	−0.868558	−	0.495587i	$-0.834953\pi$
$947$		−	30.5018i		−	0.991174i	0.868558	−	0.495587i	$-0.165047\pi$
$948$		−	7.87955i		−	0.255916i
$949$	−10.1017			−0.327915
$950$	−6.36842	+	22.2163i	−0.206619	+	0.720793i
$951$	6.04149			0.195909
$952$		−	3.18421i		−	0.103201i
$953$		−	51.1655i		−	1.65741i	−0.559684	−	0.828706i	$-0.689077\pi$
$953$		−	51.1655i		−	1.65741i	0.559684	−	0.828706i	$-0.310923\pi$
$954$	17.4795			0.565920
$955$	0.152089	−	1.08250i	0.00492148	−	0.0350288i
$956$	−13.7708			−0.445378
$957$		−	1.51114i		−	0.0488481i
$958$			12.1204i			0.391594i
$959$	15.9398			0.514722
$960$	10.5096	+	1.47658i	0.339196	+	0.0476564i
$961$	−4.12399			−0.133032
$962$			93.1437i			3.00307i
$963$		−	1.76494i		−	0.0568743i
$964$	11.7520			0.378507
$965$	50.8385	+	7.14272i	1.63655	+	0.229932i
$966$	−2.62222			−0.0843684
$967$		−	47.8992i		−	1.54034i	−0.637841	−	0.770168i	$-0.720172\pi$
$967$		−	47.8992i		−	1.54034i	0.637841	−	0.770168i	$-0.279828\pi$
$968$			5.03303i			0.161768i
$969$	−10.7556			−0.345519
$970$	−7.06959	+	50.3180i	−0.226991	+	1.61561i
$971$	40.6735			1.30528			0.652638	−	0.757670i	$-0.273662\pi$
$971$	40.6735			1.30528			0.652638	+	0.757670i	$0.273662\pi$
$972$		−	1.62222i		−	0.0520326i
$973$			11.6731i			0.374221i
$974$	32.9777			1.05667
$975$	30.8988	+	8.85728i	0.989552	+	0.283660i
$976$	−31.6316			−1.01250
$977$			27.4893i			0.879462i	0.898130	+	0.439731i	$0.144926\pi$
$977$			27.4893i			0.879462i	−0.898130	+	0.439731i	$0.855074\pi$
$978$		−	39.6958i		−	1.26933i
$979$	−9.24443			−0.295453
$980$	0.504684	−	3.59210i	0.0161215	−	0.114746i
$981$	5.61285			0.179204
$982$		−	3.80642i		−	0.121468i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	−5.92104			−0.188756
$985$	−2.62222	−	0.368416i	−0.0835507	−	0.0117387i
$986$	−6.36842			−0.202812
$987$			2.75557i			0.0877107i
$988$		−	25.3274i		−	0.805772i
$989$	−13.9180			−0.442566
$990$	8.42864	+	1.18421i	0.267880	+	0.0376366i
$991$	−34.6923			−1.10204			−0.551018	−	0.834493i	$-0.685761\pi$
$991$	−34.6923			−1.10204			−0.551018	+	0.834493i	$0.685761\pi$
$992$			38.0584i			1.20836i
$993$			13.5111i			0.428763i
$994$	−3.80642			−0.120732
$995$	−2.73683	+	19.4795i	−0.0867634	+	0.617541i
$996$	−18.8385			−0.596922
$997$			28.6766i			0.908197i	0.890951	+	0.454099i	$0.150039\pi$
$997$			28.6766i			0.908197i	−0.890951	+	0.454099i	$0.849961\pi$
$998$			44.4327i			1.40649i
$999$	7.61285			0.240860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.d.b.64.2	✓	6
3.2	odd	2		315.2.d.e.64.5		6
4.3	odd	2		1680.2.t.k.1009.2		6
5.2	odd	4		525.2.a.j.1.3		3
5.3	odd	4		525.2.a.k.1.1		3
5.4	even	2	inner	105.2.d.b.64.5	yes	6
7.2	even	3		735.2.q.e.214.2		12
7.3	odd	6		735.2.q.f.79.5		12
7.4	even	3		735.2.q.e.79.5		12
7.5	odd	6		735.2.q.f.214.2		12
7.6	odd	2		735.2.d.b.589.2		6
12.11	even	2		5040.2.t.v.1009.4		6
15.2	even	4		1575.2.a.x.1.1		3
15.8	even	4		1575.2.a.w.1.3		3
15.14	odd	2		315.2.d.e.64.2		6
20.3	even	4		8400.2.a.dj.1.1		3
20.7	even	4		8400.2.a.dg.1.3		3
20.19	odd	2		1680.2.t.k.1009.5		6
21.20	even	2		2205.2.d.l.1324.5		6
35.4	even	6		735.2.q.e.79.2		12
35.9	even	6		735.2.q.e.214.5		12
35.13	even	4		3675.2.a.bj.1.1		3
35.19	odd	6		735.2.q.f.214.5		12
35.24	odd	6		735.2.q.f.79.2		12
35.27	even	4		3675.2.a.bi.1.3		3
35.34	odd	2		735.2.d.b.589.5		6
60.59	even	2		5040.2.t.v.1009.3		6
105.104	even	2		2205.2.d.l.1324.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.2	✓	6	1.1	even	1	trivial
105.2.d.b.64.5	yes	6	5.4	even	2	inner
315.2.d.e.64.2		6	15.14	odd	2
315.2.d.e.64.5		6	3.2	odd	2
525.2.a.j.1.3		3	5.2	odd	4
525.2.a.k.1.1		3	5.3	odd	4
735.2.d.b.589.2		6	7.6	odd	2
735.2.d.b.589.5		6	35.34	odd	2
735.2.q.e.79.2		12	35.4	even	6
735.2.q.e.79.5		12	7.4	even	3
735.2.q.e.214.2		12	7.2	even	3
735.2.q.e.214.5		12	35.9	even	6
735.2.q.f.79.2		12	35.24	odd	6
735.2.q.f.79.5		12	7.3	odd	6
735.2.q.f.214.2		12	7.5	odd	6
735.2.q.f.214.5		12	35.19	odd	6
1575.2.a.w.1.3		3	15.8	even	4
1575.2.a.x.1.1		3	15.2	even	4
1680.2.t.k.1009.2		6	4.3	odd	2
1680.2.t.k.1009.5		6	20.19	odd	2
2205.2.d.l.1324.2		6	105.104	even	2
2205.2.d.l.1324.5		6	21.20	even	2
3675.2.a.bi.1.3		3	35.27	even	4
3675.2.a.bj.1.1		3	35.13	even	4
5040.2.t.v.1009.3		6	60.59	even	2
5040.2.t.v.1009.4		6	12.11	even	2
8400.2.a.dg.1.3		3	20.7	even	4
8400.2.a.dj.1.1		3	20.3	even	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +(-4.21432 - 0.592104i) q^{10} +2.00000 q^{11} -1.62222i q^{12} +6.42864i q^{13} -1.90321 q^{14} +(2.21432 + 0.311108i) q^{15} -4.61285 q^{16} +4.42864i q^{17} +1.90321i q^{18} +2.42864 q^{19} +(-0.504684 + 3.59210i) q^{20} +1.00000 q^{21} -3.80642i q^{22} -1.37778i q^{23} +0.719004 q^{24} +(-4.80642 - 1.37778i) q^{25} +12.2351 q^{26} -1.00000i q^{27} +1.62222i q^{28} -0.755569 q^{29} +(0.592104 - 4.21432i) q^{30} +5.18421 q^{31} +7.34122i q^{32} +2.00000i q^{33} +8.42864 q^{34} +(-2.21432 - 0.311108i) q^{35} +1.62222 q^{36} +7.61285i q^{37} -4.62222i q^{38} -6.42864 q^{39} +(-1.59210 - 0.223688i) q^{40} -8.23506 q^{41} -1.90321i q^{42} -10.1017i q^{43} -3.24443 q^{44} +(-0.311108 + 2.21432i) q^{45} -2.62222 q^{46} +2.75557i q^{47} -4.61285i q^{48} -1.00000 q^{49} +(-2.62222 + 9.14764i) q^{50} -4.42864 q^{51} -10.4286i q^{52} -9.18421i q^{53} -1.90321 q^{54} +(0.622216 - 4.42864i) q^{55} -0.719004 q^{56} +2.42864i q^{57} +1.43801i q^{58} -14.1017 q^{59} +(-3.59210 - 0.504684i) q^{60} +6.85728 q^{61} -9.86665i q^{62} +1.00000i q^{63} +4.74620 q^{64} +(14.2351 + 2.00000i) q^{65} +3.80642 q^{66} +2.75557i q^{67} -7.18421i q^{68} +1.37778 q^{69} +(-0.592104 + 4.21432i) q^{70} +2.00000 q^{71} +0.719004i q^{72} +1.57136i q^{73} +14.4889 q^{74} +(1.37778 - 4.80642i) q^{75} -3.93978 q^{76} -2.00000i q^{77} +12.2351i q^{78} +4.85728 q^{79} +(-1.43509 + 10.2143i) q^{80} +1.00000 q^{81} +15.6731i q^{82} -11.6128i q^{83} -1.62222 q^{84} +(9.80642 + 1.37778i) q^{85} -19.2257 q^{86} -0.755569i q^{87} -1.43801i q^{88} -4.62222 q^{89} +(4.21432 + 0.592104i) q^{90} +6.42864 q^{91} +2.23506i q^{92} +5.18421i q^{93} +5.24443 q^{94} +(0.755569 - 5.37778i) q^{95} -7.34122 q^{96} -11.9398i q^{97} +1.90321i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{14} + 26 q^{16} - 12 q^{19} - 30 q^{20} + 6 q^{21} + 18 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{29} - 10 q^{30} + 4 q^{31} + 24 q^{34} + 10 q^{36} - 12 q^{39} + 4 q^{40} + 4 q^{41} - 20 q^{44} - 2 q^{45} - 16 q^{46} - 6 q^{49} - 16 q^{50} + 2 q^{54} + 4 q^{55} - 18 q^{56} - 32 q^{59} - 8 q^{60} - 12 q^{61} - 26 q^{64} + 32 q^{65} - 4 q^{66} + 8 q^{69} + 10 q^{70} + 12 q^{71} + 88 q^{74} + 8 q^{75} + 4 q^{76} - 24 q^{79} + 46 q^{80} + 6 q^{81} - 10 q^{84} + 32 q^{85} - 8 q^{86} - 28 q^{89} + 12 q^{90} + 12 q^{91} + 32 q^{94} + 4 q^{95} - 58 q^{96} - 12 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^14 + 26 * q^16 - 12 * q^19 - 30 * q^20 + 6 * q^21 + 18 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^29 - 10 * q^30 + 4 * q^31 + 24 * q^34 + 10 * q^36 - 12 * q^39 + 4 * q^40 + 4 * q^41 - 20 * q^44 - 2 * q^45 - 16 * q^46 - 6 * q^49 - 16 * q^50 + 2 * q^54 + 4 * q^55 - 18 * q^56 - 32 * q^59 - 8 * q^60 - 12 * q^61 - 26 * q^64 + 32 * q^65 - 4 * q^66 + 8 * q^69 + 10 * q^70 + 12 * q^71 + 88 * q^74 + 8 * q^75 + 4 * q^76 - 24 * q^79 + 46 * q^80 + 6 * q^81 - 10 * q^84 + 32 * q^85 - 8 * q^86 - 28 * q^89 + 12 * q^90 + 12 * q^91 + 32 * q^94 + 4 * q^95 - 58 * q^96 - 12 * q^99

Introduction

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Modular forms

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Database

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