LMFDB - Embedded newform 432.2.u.f.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	432.97
Dual form			432.2.u.f.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70086 + 0.327233i) q^{3} +(1.34943 + 0.491154i) q^{5} +(-0.111026 + 0.629660i) q^{7} +(2.78584 + 1.11316i) q^{9} +O(q^{10})$	\(q+(1.70086 + 0.327233i) q^{3} +(1.34943 + 0.491154i) q^{5} +(-0.111026 + 0.629660i) q^{7} +(2.78584 + 1.11316i) q^{9} +(-2.56485 + 0.933530i) q^{11} +(3.51973 - 2.95340i) q^{13} +(2.13447 + 1.27696i) q^{15} +(1.37496 + 2.38149i) q^{17} +(-2.25118 + 3.89915i) q^{19} +(-0.394885 + 1.03463i) q^{21} +(-0.868468 - 4.92533i) q^{23} +(-2.25048 - 1.88838i) q^{25} +(4.37405 + 2.80494i) q^{27} +(2.34180 + 1.96501i) q^{29} +(-0.510147 - 2.89319i) q^{31} +(-4.66793 + 0.748497i) q^{33} +(-0.459082 + 0.795154i) q^{35} +(-3.60922 - 6.25136i) q^{37} +(6.95301 - 3.87154i) q^{39} +(-8.31675 + 6.97858i) q^{41} +(9.16233 - 3.33481i) q^{43} +(3.21257 + 2.87040i) q^{45} +(-0.382925 + 2.17168i) q^{47} +(6.19370 + 2.25432i) q^{49} +(1.55930 + 4.50051i) q^{51} -8.94401 q^{53} -3.91961 q^{55} +(-5.10486 + 5.89524i) q^{57} +(-11.1894 - 4.07259i) q^{59} +(1.62996 - 9.24397i) q^{61} +(-1.01021 + 1.63054i) q^{63} +(6.20021 - 2.25669i) q^{65} +(5.12362 - 4.29923i) q^{67} +(0.134590 - 8.66148i) q^{69} +(6.61014 + 11.4491i) q^{71} +(2.02070 - 3.49995i) q^{73} +(-3.20981 - 3.94829i) q^{75} +(-0.303041 - 1.71863i) q^{77} +(-10.4934 - 8.80503i) q^{79} +(6.52177 + 6.20214i) q^{81} +(-2.98429 - 2.50411i) q^{83} +(0.685733 + 3.88898i) q^{85} +(3.34006 + 4.10852i) q^{87} +(-3.94057 + 6.82526i) q^{89} +(1.46886 + 2.54413i) q^{91} +(0.0790598 - 5.08784i) q^{93} +(-4.95290 + 4.15597i) q^{95} +(-16.0203 + 5.83093i) q^{97} +(-8.18443 - 0.254417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.70086	+	0.327233i	0.981991	+	0.188928i
$3$	1.70086	+	0.327233i	0.981991	+	0.188928i
$4$		0			0
$5$	1.34943	+	0.491154i	0.603485	+	0.219651i	0.625650	−	0.780104i	$-0.284834\pi$
$5$	1.34943	+	0.491154i	0.603485	+	0.219651i	−0.0221649	+	0.999754i	$0.507056\pi$
$6$		0			0
$7$	−0.111026	+	0.629660i	−0.0419639	+	0.237989i	−0.998574	−	0.0533813i	$-0.983000\pi$
$7$	−0.111026	+	0.629660i	−0.0419639	+	0.237989i	0.956610	+	0.291370i	$0.0941112\pi$
$8$		0			0
$9$	2.78584	+	1.11316i	0.928612	+	0.371052i
$10$		0			0
$11$	−2.56485	+	0.933530i	−0.773332	+	0.281470i	−0.698390	−	0.715718i	$-0.746100\pi$
$11$	−2.56485	+	0.933530i	−0.773332	+	0.281470i	−0.0749429	+	0.997188i	$0.523877\pi$
$12$		0			0
$13$	3.51973	−	2.95340i	0.976196	−	0.819126i	−0.00731491	−	0.999973i	$-0.502328\pi$
$13$	3.51973	−	2.95340i	0.976196	−	0.819126i	0.983511	+	0.180847i	$0.0578840\pi$
$14$		0			0
$15$	2.13447	+	1.27696i	0.551119	+	0.329711i
$16$		0			0
$17$	1.37496	+	2.38149i	0.333476	+	0.577597i	0.983191	−	0.182581i	$-0.0584451\pi$
$17$	1.37496	+	2.38149i	0.333476	+	0.577597i	−0.649715	+	0.760178i	$0.725112\pi$
$18$		0			0
$19$	−2.25118	+	3.89915i	−0.516455	+	0.894526i	0.483362	+	0.875420i	$0.339415\pi$
$19$	−2.25118	+	3.89915i	−0.516455	+	0.894526i	−0.999817	+	0.0191061i	$0.993918\pi$
$20$		0			0
$21$	−0.394885	+	1.03463i	−0.0861710	+	0.225775i
$22$		0			0
$23$	−0.868468	−	4.92533i	−0.181088	−	1.02700i	−0.930879	−	0.365327i	$-0.880957\pi$
$23$	−0.868468	−	4.92533i	−0.181088	−	1.02700i	0.749791	−	0.661675i	$-0.230154\pi$
$24$		0			0
$25$	−2.25048	−	1.88838i	−0.450096	−	0.377676i
$26$		0			0
$27$	4.37405	+	2.80494i	0.841787	+	0.539810i
$28$		0			0
$29$	2.34180	+	1.96501i	0.434862	+	0.364893i	0.833783	−	0.552093i	$-0.186171\pi$
$29$	2.34180	+	1.96501i	0.434862	+	0.364893i	−0.398920	+	0.916986i	$0.630615\pi$
$30$		0			0
$31$	−0.510147	−	2.89319i	−0.0916251	−	0.519632i	−0.995729	−	0.0923200i	$-0.970572\pi$
$31$	−0.510147	−	2.89319i	−0.0916251	−	0.519632i	0.904104	−	0.427312i	$-0.140539\pi$
$32$		0			0
$33$	−4.66793	+	0.748497i	−0.812583	+	0.130297i
$34$		0			0
$35$	−0.459082	+	0.795154i	−0.0775991	+	0.134406i
$36$		0			0
$37$	−3.60922	−	6.25136i	−0.593353	−	1.02772i	−0.993777	−	0.111387i	$-0.964471\pi$
$37$	−3.60922	−	6.25136i	−0.593353	−	1.02772i	0.400424	−	0.916330i	$-0.368863\pi$
$38$		0			0
$39$	6.95301	−	3.87154i	1.11337	−	0.619943i
$40$		0			0
$41$	−8.31675	+	6.97858i	−1.29886	+	1.08987i	−0.308517	+	0.951219i	$0.599833\pi$
$41$	−8.31675	+	6.97858i	−1.29886	+	1.08987i	−0.990341	+	0.138653i	$0.955723\pi$
$42$		0			0
$43$	9.16233	−	3.33481i	1.39724	−	0.508554i	0.469883	−	0.882728i	$-0.344296\pi$
$43$	9.16233	−	3.33481i	1.39724	−	0.508554i	0.927358	+	0.374174i	$0.122074\pi$
$44$		0			0
$45$	3.21257	+	2.87040i	0.478902	+	0.427895i
$46$		0			0
$47$	−0.382925	+	2.17168i	−0.0558554	+	0.316772i	−0.999915	−	0.0130019i	$-0.995861\pi$
$47$	−0.382925	+	2.17168i	−0.0558554	+	0.316772i	0.944060	+	0.329773i	$0.106972\pi$
$48$		0			0
$49$	6.19370	+	2.25432i	0.884815	+	0.322046i
$50$		0			0
$51$	1.55930	+	4.50051i	0.218346	+	0.630198i
$52$		0			0
$53$	−8.94401			−1.22855			−0.614277	−	0.789090i	$-0.710552\pi$
$53$	−8.94401			−1.22855			−0.614277	+	0.789090i	$0.710552\pi$
$54$		0			0
$55$	−3.91961			−0.528520
$56$		0			0
$57$	−5.10486	+	5.89524i	−0.676155	+	0.780844i
$58$		0			0
$59$	−11.1894	−	4.07259i	−1.45673	−	0.530206i	−0.512267	−	0.858826i	$-0.671194\pi$
$59$	−11.1894	−	4.07259i	−1.45673	−	0.530206i	−0.944462	+	0.328620i	$0.893417\pi$
$60$		0			0
$61$	1.62996	−	9.24397i	0.208695	−	1.18357i	−0.682823	−	0.730584i	$-0.739248\pi$
$61$	1.62996	−	9.24397i	0.208695	−	1.18357i	0.891518	−	0.452985i	$-0.149641\pi$
$62$		0			0
$63$	−1.01021	+	1.63054i	−0.127274	+	0.205429i
$64$		0			0
$65$	6.20021	−	2.25669i	0.769042	−	0.279908i
$66$		0			0
$67$	5.12362	−	4.29923i	0.625950	−	0.525234i	−0.273717	−	0.961810i	$-0.588253\pi$
$67$	5.12362	−	4.29923i	0.625950	−	0.525234i	0.899668	+	0.436576i	$0.143809\pi$
$68$		0			0
$69$	0.134590	−	8.66148i	0.0162028	−	1.04272i
$70$		0			0
$71$	6.61014	+	11.4491i	0.784480	+	1.35876i	0.929309	+	0.369302i	$0.120403\pi$
$71$	6.61014	+	11.4491i	0.784480	+	1.35876i	−0.144830	+	0.989457i	$0.546263\pi$
$72$		0			0
$73$	2.02070	−	3.49995i	0.236505	−	0.409638i	−0.723204	−	0.690634i	$-0.757331\pi$
$73$	2.02070	−	3.49995i	0.236505	−	0.409638i	0.959709	+	0.280996i	$0.0906648\pi$
$74$		0			0
$75$	−3.20981	−	3.94829i	−0.370637	−	0.455910i
$76$		0			0
$77$	−0.303041	−	1.71863i	−0.0345347	−	0.195856i
$78$		0			0
$79$	−10.4934	−	8.80503i	−1.18060	−	0.990643i	−0.999975	−	0.00709184i	$-0.997743\pi$
$79$	−10.4934	−	8.80503i	−1.18060	−	0.990643i	−0.180628	−	0.983552i	$-0.557813\pi$
$80$		0			0
$81$	6.52177	+	6.20214i	0.724641	+	0.689126i
$82$		0			0
$83$	−2.98429	−	2.50411i	−0.327568	−	0.274862i	0.464140	−	0.885762i	$-0.346363\pi$
$83$	−2.98429	−	2.50411i	−0.327568	−	0.274862i	−0.791708	+	0.610900i	$0.790808\pi$
$84$		0			0
$85$	0.685733	+	3.88898i	0.0743782	+	0.421820i
$86$		0			0
$87$	3.34006	+	4.10852i	0.358092	+	0.440479i
$88$		0			0
$89$	−3.94057	+	6.82526i	−0.417699	+	0.723476i	−0.995708	−	0.0925546i	$-0.970497\pi$
$89$	−3.94057	+	6.82526i	−0.417699	+	0.723476i	0.578008	+	0.816031i	$0.303830\pi$
$90$		0			0
$91$	1.46886	+	2.54413i	0.153978	+	0.266698i
$92$		0			0
$93$	0.0790598	−	5.08784i	0.00819812	−	0.527584i
$94$		0			0
$95$	−4.95290	+	4.15597i	−0.508157	+	0.426394i
$96$		0			0
$97$	−16.0203	+	5.83093i	−1.62662	+	0.592041i	−0.984627	−	0.174669i	$-0.944114\pi$
$97$	−16.0203	+	5.83093i	−1.62662	+	0.592041i	−0.641993	+	0.766711i	$0.721892\pi$
$98$		0			0
$99$	−8.18443	−	0.254417i	−0.822566	−	0.0255698i
$100$		0			0
$101$	1.95902	−	11.1102i	0.194930	−	1.10550i	−0.717589	−	0.696467i	$-0.754754\pi$
$101$	1.95902	−	11.1102i	0.194930	−	1.10550i	0.912519	−	0.409035i	$-0.134135\pi$
$102$		0			0
$103$	−5.73373	−	2.08691i	−0.564961	−	0.205629i	0.0437203	−	0.999044i	$-0.486079\pi$
$103$	−5.73373	−	2.08691i	−0.564961	−	0.205629i	−0.608681	+	0.793415i	$0.708301\pi$
$104$		0			0
$105$	−1.04103	+	1.20222i	−0.101595	+	0.117324i
$106$		0			0
$107$	3.04986			0.294841			0.147421	−	0.989074i	$-0.452903\pi$
$107$	3.04986			0.294841			0.147421	+	0.989074i	$0.452903\pi$
$108$		0			0
$109$	−1.91368			−0.183297			−0.0916486	−	0.995791i	$-0.529214\pi$
$109$	−1.91368			−0.183297			−0.0916486	+	0.995791i	$0.529214\pi$
$110$		0			0
$111$	−4.09313	−	11.8137i	−0.388502	−	1.12131i
$112$		0			0
$113$	−5.61276	−	2.04288i	−0.528004	−	0.192178i	0.0642428	−	0.997934i	$-0.479537\pi$
$113$	−5.61276	−	2.04288i	−0.528004	−	0.192178i	−0.592247	+	0.805757i	$0.701759\pi$
$114$		0			0
$115$	1.24715	−	7.07296i	0.116298	−	0.659557i
$116$		0			0
$117$	13.0930	−	4.30969i	1.21045	−	0.398431i
$118$		0			0
$119$	−1.65219	+	0.601347i	−0.151456	+	0.0551254i
$120$		0			0
$121$	−2.71949	+	2.28193i	−0.247227	+	0.207448i
$122$		0			0
$123$	−16.4292	+	9.14806i	−1.48137	+	0.824853i
$124$		0			0
$125$	−5.69949	−	9.87180i	−0.509778	−	0.882961i
$126$		0			0
$127$	−6.88015	+	11.9168i	−0.610514	+	1.05744i	0.380640	+	0.924723i	$0.375704\pi$
$127$	−6.88015	+	11.9168i	−0.610514	+	1.05744i	−0.991154	+	0.132718i	$0.957630\pi$
$128$		0			0
$129$	16.6751	−	2.67383i	1.46816	−	0.235417i
$130$		0			0
$131$	−2.05603	−	11.6603i	−0.179636	−	1.01877i	−0.932655	−	0.360768i	$-0.882515\pi$
$131$	−2.05603	−	11.6603i	−0.179636	−	1.01877i	0.753019	−	0.657998i	$-0.228597\pi$
$132$		0			0
$133$	−2.20520	−	1.85038i	−0.191215	−	0.160448i
$134$		0			0
$135$	4.52484	+	5.93341i	0.389436	+	0.510667i
$136$		0			0
$137$	−3.30729	−	2.77514i	−0.282560	−	0.237096i	0.490481	−	0.871452i	$-0.336821\pi$
$137$	−3.30729	−	2.77514i	−0.282560	−	0.237096i	−0.773041	+	0.634356i	$0.781266\pi$
$138$		0			0
$139$	−1.54299	−	8.75072i	−0.130874	−	0.742226i	−0.977644	−	0.210266i	$-0.932567\pi$
$139$	−1.54299	−	8.75072i	−0.130874	−	0.742226i	0.846770	−	0.531960i	$-0.178544\pi$
$140$		0			0
$141$	−1.36195	+	3.56841i	−0.114697	+	0.300514i
$142$		0			0
$143$	−6.27049	+	10.8608i	−0.524365	+	0.908227i
$144$		0			0
$145$	2.19499	+	3.80184i	0.182284	+	0.315725i
$146$		0			0
$147$	9.79692	+	5.86107i	0.808036	+	0.483413i
$148$		0			0
$149$	−4.62702	+	3.88253i	−0.379060	+	0.318069i	−0.812333	−	0.583193i	$-0.801803\pi$
$149$	−4.62702	+	3.88253i	−0.379060	+	0.318069i	0.433273	+	0.901263i	$0.357359\pi$
$150$		0			0
$151$	12.5289	−	4.56016i	1.01959	−	0.371101i	0.222482	−	0.974937i	$-0.428584\pi$
$151$	12.5289	−	4.56016i	1.01959	−	0.371101i	0.797108	+	0.603836i	$0.206362\pi$
$152$		0			0
$153$	1.17943	+	8.16499i	0.0953513	+	0.660100i
$154$		0			0
$155$	0.732591	−	4.15473i	0.0588431	−	0.333716i
$156$		0			0
$157$	15.1550	+	5.51598i	1.20950	+	0.440223i	0.866532	−	0.499122i	$-0.166344\pi$
$157$	15.1550	+	5.51598i	1.20950	+	0.440223i	0.342972	+	0.939346i	$0.388566\pi$
$158$		0			0
$159$	−15.2125	−	2.92678i	−1.20643	−	0.232109i
$160$		0			0
$161$	3.19770			0.252014
$162$		0			0
$163$	6.39994			0.501282			0.250641	−	0.968080i	$-0.419359\pi$
$163$	6.39994			0.501282			0.250641	+	0.968080i	$0.419359\pi$
$164$		0			0
$165$	−6.66670	−	1.28263i	−0.519002	−	0.0998524i
$166$		0			0
$167$	15.6056	+	5.67996i	1.20759	+	0.439528i	0.865869	−	0.500272i	$-0.166766\pi$
$167$	15.6056	+	5.67996i	1.20759	+	0.439528i	0.341725	+	0.939800i	$0.388989\pi$
$168$		0			0
$169$	1.40847	−	7.98782i	0.108344	−	0.614448i
$170$		0			0
$171$	−10.6118	+	8.35649i	−0.811502	+	0.639037i
$172$		0			0
$173$	10.6314	−	3.86952i	0.808292	−	0.294194i	0.0953739	−	0.995442i	$-0.469595\pi$
$173$	10.6314	−	3.86952i	0.808292	−	0.294194i	0.712918	+	0.701247i	$0.247373\pi$
$174$		0			0
$175$	1.43890	−	1.20738i	0.108770	−	0.0912692i
$176$		0			0
$177$	−17.6988	−	10.5884i	−1.33032	−	0.795875i
$178$		0			0
$179$	1.36906	+	2.37128i	0.102328	+	0.177238i	0.912643	−	0.408756i	$-0.134037\pi$
$179$	1.36906	+	2.37128i	0.102328	+	0.177238i	−0.810315	+	0.585994i	$0.800704\pi$
$180$		0			0
$181$	−12.2529	+	21.2226i	−0.910748	+	1.57746i	−0.0977379	+	0.995212i	$0.531161\pi$
$181$	−12.2529	+	21.2226i	−0.910748	+	1.57746i	−0.813010	+	0.582250i	$0.802173\pi$
$182$		0			0
$183$	5.79727	−	15.1893i	0.428546	−	1.12283i
$184$		0			0
$185$	−1.80003	−	10.2085i	−0.132341	−	0.750543i
$186$		0			0
$187$	−5.74976	−	4.82462i	−0.420464	−	0.352811i
$188$		0			0
$189$	−2.25179	+	2.44274i	−0.163794	+	0.177683i
$190$		0			0
$191$	14.4271	+	12.1057i	1.04391	+	0.875941i	0.992440	−	0.122734i	$-0.0391662\pi$
$191$	14.4271	+	12.1057i	1.04391	+	0.875941i	0.0514660	+	0.998675i	$0.483611\pi$
$192$		0			0
$193$	1.41085	+	8.00132i	0.101555	+	0.575948i	0.992540	+	0.121916i	$0.0389038\pi$
$193$	1.41085	+	8.00132i	0.101555	+	0.575948i	−0.890985	+	0.454032i	$0.849985\pi$
$194$		0			0
$195$	11.2842	−	1.80940i	0.808075	−	0.129574i
$196$		0			0
$197$	−5.34367	+	9.25550i	−0.380721	+	0.659427i	−0.991165	−	0.132631i	$-0.957657\pi$
$197$	−5.34367	+	9.25550i	−0.380721	+	0.659427i	0.610445	+	0.792059i	$0.290991\pi$
$198$		0			0
$199$	0.360894	+	0.625087i	0.0255831	+	0.0443112i	0.878534	−	0.477681i	$-0.158522\pi$
$199$	0.360894	+	0.625087i	0.0255831	+	0.0443112i	−0.852950	+	0.521992i	$0.825189\pi$
$200$		0			0
$201$	10.1214	−	5.63576i	0.713909	−	0.397516i
$202$		0			0
$203$	−1.49729	+	1.25637i	−0.105089	+	0.0881801i
$204$		0			0
$205$	−14.6505	+	5.33234i	−1.02323	+	0.372426i
$206$		0			0
$207$	3.06324	−	14.6879i	0.212910	−	1.02088i
$208$		0			0
$209$	2.13396	−	12.1023i	0.147609	−	0.837133i
$210$		0			0
$211$	27.0521	+	9.84616i	1.86234	+	0.677837i	0.977127	+	0.212658i	$0.0682121\pi$
$211$	27.0521	+	9.84616i	1.86234	+	0.677837i	0.885217	+	0.465179i	$0.154010\pi$
$212$		0			0
$213$	7.49639	+	21.6364i	0.513644	+	1.48250i
$214$		0			0
$215$	14.0019			0.954920
$216$		0			0
$217$	1.87836			0.127512
$218$		0			0
$219$	4.58222	−	5.29168i	0.309638	−	0.357578i
$220$		0			0
$221$	11.8730	+	4.32141i	0.798662	+	0.290689i
$222$		0			0
$223$	−2.26907	+	12.8685i	−0.151948	+	0.861742i	0.809575	+	0.587017i	$0.199698\pi$
$223$	−2.26907	+	12.8685i	−0.151948	+	0.861742i	−0.961523	+	0.274725i	$0.911413\pi$
$224$		0			0
$225$	−4.16741	−	7.76585i	−0.277828	−	0.517723i
$226$		0			0
$227$	22.1051	−	8.04558i	1.46716	−	0.534004i	0.519835	−	0.854266i	$-0.325993\pi$
$227$	22.1051	−	8.04558i	1.46716	−	0.534004i	0.947329	+	0.320262i	$0.103771\pi$
$228$		0			0
$229$	8.50752	−	7.13866i	0.562193	−	0.471736i	−0.316852	−	0.948475i	$-0.602626\pi$
$229$	8.50752	−	7.13866i	0.562193	−	0.471736i	0.879045	+	0.476739i	$0.158181\pi$
$230$		0			0
$231$	0.0469637	−	3.02231i	0.00308998	−	0.198854i
$232$		0			0
$233$	11.5386	+	19.9855i	0.755921	+	1.30929i	0.944915	+	0.327316i	$0.106144\pi$
$233$	11.5386	+	19.9855i	0.755921	+	1.30929i	−0.188994	+	0.981978i	$0.560523\pi$
$234$		0			0
$235$	−1.58336	+	2.74246i	−0.103287	+	0.178898i
$236$		0			0
$237$	−14.9665	−	18.4099i	−0.972181	−	1.19585i
$238$		0			0
$239$	−2.12958	−	12.0775i	−0.137751	−	0.781226i	−0.972904	−	0.231208i	$-0.925732\pi$
$239$	−2.12958	−	12.0775i	−0.137751	−	0.781226i	0.835153	−	0.550018i	$-0.185379\pi$
$240$		0			0
$241$	17.9676	+	15.0766i	1.15739	+	0.971169i	0.999866	−	0.0163457i	$-0.00520323\pi$
$241$	17.9676	+	15.0766i	1.15739	+	0.971169i	0.157528	+	0.987515i	$0.449648\pi$
$242$		0			0
$243$	9.06306	+	12.6831i	0.581396	+	0.813621i
$244$		0			0
$245$	7.25078	+	6.08412i	0.463235	+	0.388700i
$246$		0			0
$247$	3.59223	+	20.3726i	0.228568	+	1.29628i
$248$		0			0
$249$	−4.25642	−	5.23570i	−0.269739	−	0.331799i
$250$		0			0
$251$	−2.30715	+	3.99610i	−0.145626	+	0.252232i	−0.929606	−	0.368554i	$-0.879853\pi$
$251$	−2.30715	+	3.99610i	−0.145626	+	0.252232i	0.783980	+	0.620786i	$0.213186\pi$
$252$		0			0
$253$	6.82544	+	11.8220i	0.429112	+	0.743243i
$254$		0			0
$255$	−0.106271	+	6.83900i	−0.00665495	+	0.428275i
$256$		0			0
$257$	−2.48116	+	2.08194i	−0.154770	+	0.129868i	−0.716885	−	0.697192i	$-0.754433\pi$
$257$	−2.48116	+	2.08194i	−0.154770	+	0.129868i	0.562114	+	0.827060i	$0.309988\pi$
$258$		0			0
$259$	4.33695	−	1.57852i	0.269485	−	0.0980845i
$260$		0			0
$261$	4.33653	+	8.08098i	0.268424	+	0.500200i
$262$		0			0
$263$	2.24720	−	12.7445i	0.138568	−	0.785859i	−0.833740	−	0.552157i	$-0.813805\pi$
$263$	2.24720	−	12.7445i	0.138568	−	0.785859i	0.972308	−	0.233702i	$-0.0750840\pi$
$264$		0			0
$265$	−12.0694	−	4.39289i	−0.741415	−	0.269853i
$266$		0			0
$267$	−8.93580	+	10.3193i	−0.546862	+	0.631532i
$268$		0			0
$269$	15.5079			0.945530			0.472765	−	0.881188i	$-0.343256\pi$
$269$	15.5079			0.945530			0.472765	+	0.881188i	$0.343256\pi$
$270$		0			0
$271$	−11.6591			−0.708240			−0.354120	−	0.935200i	$-0.615220\pi$
$271$	−11.6591			−0.708240			−0.354120	+	0.935200i	$0.615220\pi$
$272$		0			0
$273$	1.66579	+	4.80787i	0.100818	+	0.290986i
$274$		0			0
$275$	7.53501	+	2.74252i	0.454378	+	0.165380i
$276$		0			0
$277$	5.33506	−	30.2566i	0.320552	−	1.81794i	−0.218692	−	0.975794i	$-0.570179\pi$
$277$	5.33506	−	30.2566i	0.320552	−	1.81794i	0.539245	−	0.842149i	$-0.318710\pi$
$278$		0			0
$279$	1.79938	−	8.62782i	0.107726	−	0.516534i
$280$		0			0
$281$	12.4224	−	4.52140i	0.741061	−	0.269724i	0.0562218	−	0.998418i	$-0.482095\pi$
$281$	12.4224	−	4.52140i	0.741061	−	0.269724i	0.684839	+	0.728694i	$0.259872\pi$
$282$		0			0
$283$	−9.07896	+	7.61815i	−0.539688	+	0.452852i	−0.871431	−	0.490518i	$-0.836808\pi$
$283$	−9.07896	+	7.61815i	−0.539688	+	0.452852i	0.331743	+	0.943370i	$0.392363\pi$
$284$		0			0
$285$	−9.78415	+	5.44797i	−0.579563	+	0.322710i
$286$		0			0
$287$	−3.47076	−	6.01153i	−0.204872	−	0.354849i
$288$		0			0
$289$	4.71899	−	8.17354i	0.277588	−	0.480796i
$290$		0			0
$291$	−29.1564	+	4.67519i	−1.70918	+	0.274065i
$292$		0			0
$293$	−2.16037	−	12.2521i	−0.126210	−	0.715775i	−0.980582	−	0.196112i	$-0.937168\pi$
$293$	−2.16037	−	12.2521i	−0.126210	−	0.715775i	0.854371	−	0.519663i	$-0.173943\pi$
$294$		0			0
$295$	−13.0990	−	10.9914i	−0.762655	−	0.639944i
$296$		0			0
$297$	−13.8373	−	3.11094i	−0.802921	−	0.180515i
$298$		0			0
$299$	−17.6032	−	14.7709i	−1.01802	−	0.854222i
$300$		0			0
$301$	1.08254	+	6.13940i	0.0623967	+	0.353869i
$302$		0			0
$303$	6.96763	−	18.2558i	0.400280	−	1.04877i
$304$		0			0
$305$	6.73974	−	11.6736i	0.385916	−	0.668427i
$306$		0			0
$307$	4.43172	+	7.67597i	0.252932	+	0.438091i	0.964332	−	0.264697i	$-0.0852718\pi$
$307$	4.43172	+	7.67597i	0.252932	+	0.438091i	−0.711400	+	0.702787i	$0.751939\pi$
$308$		0			0
$309$	−9.06935	−	5.42580i	−0.515937	−	0.308663i
$310$		0			0
$311$	−23.7334	+	19.9147i	−1.34580	+	1.12926i	−0.365703	+	0.930732i	$0.619171\pi$
$311$	−23.7334	+	19.9147i	−1.34580	+	1.12926i	−0.980095	+	0.198527i	$0.936384\pi$
$312$		0			0
$313$	4.15943	−	1.51391i	0.235105	−	0.0855713i	−0.221781	−	0.975097i	$-0.571187\pi$
$313$	4.15943	−	1.51391i	0.235105	−	0.0855713i	0.456886	+	0.889525i	$0.348965\pi$
$314$		0			0
$315$	−2.16406	+	1.70414i	−0.121931	+	0.0960174i
$316$		0			0
$317$	−4.22992	+	23.9890i	−0.237576	+	1.34736i	0.599545	+	0.800341i	$0.295348\pi$
$317$	−4.22992	+	23.9890i	−0.237576	+	1.34736i	−0.837121	+	0.547018i	$0.815763\pi$
$318$		0			0
$319$	−7.84078	−	2.85381i	−0.438999	−	0.159783i
$320$		0			0
$321$	5.18738	+	0.998017i	0.289531	+	0.0557039i
$322$		0			0
$323$	−12.3811			−0.688901
$324$		0			0
$325$	−13.4982			−0.748746
$326$		0			0
$327$	−3.25489	−	0.626219i	−0.179996	−	0.0346300i
$328$		0			0
$329$	−1.32490	−	0.482225i	−0.0730443	−	0.0265859i
$330$		0			0
$331$	−4.27476	+	24.2434i	−0.234962	+	1.33254i	0.607732	+	0.794142i	$0.292080\pi$
$331$	−4.27476	+	24.2434i	−0.234962	+	1.33254i	−0.842694	+	0.538393i	$0.819031\pi$
$332$		0			0
$333$	−3.09598	−	21.4329i	−0.169658	−	1.17452i
$334$		0			0
$335$	9.02558	−	3.28504i	0.493120	−	0.179481i
$336$		0			0
$337$	−0.336211	+	0.282115i	−0.0183146	+	0.0153678i	−0.651899	−	0.758306i	$-0.726027\pi$
$337$	−0.336211	+	0.282115i	−0.0183146	+	0.0153678i	0.633584	+	0.773674i	$0.281583\pi$
$338$		0			0
$339$	−8.87801	−	5.31133i	−0.482187	−	0.288472i
$340$		0			0
$341$	4.00933	+	6.94437i	0.217117	+	0.376059i
$342$		0			0
$343$	−4.34493	+	7.52563i	−0.234604	+	0.406346i
$344$		0			0
$345$	4.43574	−	11.6220i	0.238812	−	0.625707i
$346$		0			0
$347$	−3.48453	−	19.7617i	−0.187059	−	1.06087i	−0.923281	−	0.384125i	$-0.874503\pi$
$347$	−3.48453	−	19.7617i	−0.187059	−	1.06087i	0.736222	−	0.676741i	$-0.236608\pi$
$348$		0			0
$349$	8.40572	+	7.05324i	0.449948	+	0.377551i	0.839417	−	0.543488i	$-0.182897\pi$
$349$	8.40572	+	7.05324i	0.449948	+	0.377551i	−0.389469	+	0.921040i	$0.627341\pi$
$350$		0			0
$351$	23.6796	−	3.04572i	1.26392	−	0.162568i
$352$		0			0
$353$	5.42734	+	4.55408i	0.288868	+	0.242389i	0.775693	−	0.631110i	$-0.217401\pi$
$353$	5.42734	+	4.55408i	0.288868	+	0.242389i	−0.486825	+	0.873500i	$0.661845\pi$
$354$		0			0
$355$	3.29668	+	18.6964i	0.174970	+	0.992303i
$356$		0			0
$357$	−3.00692	+	0.482155i	−0.159143	+	0.0255183i
$358$		0			0
$359$	7.25834	−	12.5718i	0.383081	−	0.663515i	−0.608420	−	0.793615i	$-0.708197\pi$
$359$	7.25834	−	12.5718i	0.383081	−	0.663515i	0.991501	+	0.130100i	$0.0415298\pi$
$360$		0			0
$361$	−0.635582	−	1.10086i	−0.0334517	−	0.0579400i
$362$		0			0
$363$	−5.37220	+	2.99132i	−0.281967	+	0.157004i
$364$		0			0
$365$	4.44581	−	3.73048i	0.232704	−	0.195262i
$366$		0			0
$367$	−26.7389	+	9.73216i	−1.39576	+	0.508015i	−0.926917	−	0.375267i	$-0.877551\pi$
$367$	−26.7389	+	9.73216i	−1.39576	+	0.508015i	−0.468843	+	0.883282i	$0.655329\pi$
$368$		0			0
$369$	−30.9374	+	10.1834i	−1.61053	+	0.530124i
$370$		0			0
$371$	0.993018	−	5.63168i	0.0515549	−	0.292382i
$372$		0			0
$373$	5.75174	+	2.09346i	0.297814	+	0.108395i	0.486606	−	0.873622i	$-0.338235\pi$
$373$	5.75174	+	2.09346i	0.297814	+	0.108395i	−0.188792	+	0.982017i	$0.560457\pi$
$374$		0			0
$375$	−6.46364	−	18.6556i	−0.333781	−	0.963371i
$376$		0			0
$377$	14.0460			0.723404
$378$		0			0
$379$	−0.581106			−0.0298494			−0.0149247	−	0.999889i	$-0.504751\pi$
$379$	−0.581106			−0.0298494			−0.0149247	+	0.999889i	$0.504751\pi$
$380$		0			0
$381$	−15.6017	+	18.0173i	−0.799300	+	0.923055i
$382$		0			0
$383$	7.95738	+	2.89625i	0.406603	+	0.147991i	0.537221	−	0.843441i	$-0.319474\pi$
$383$	7.95738	+	2.89625i	0.406603	+	0.147991i	−0.130618	+	0.991433i	$0.541696\pi$
$384$		0			0
$385$	0.435179	−	2.46802i	0.0221788	−	0.125782i
$386$		0			0
$387$	29.2369	+	0.908843i	1.48620	+	0.0461991i
$388$		0			0
$389$	−28.9256	+	10.5281i	−1.46659	+	0.533795i	−0.947172	−	0.320727i	$-0.896073\pi$
$389$	−28.9256	+	10.5281i	−1.46659	+	0.533795i	−0.519417	+	0.854521i	$0.673851\pi$
$390$		0			0
$391$	10.5355	−	8.84036i	0.532805	−	0.447076i
$392$		0			0
$393$	0.318632	−	20.5053i	0.0160729	−	1.03436i
$394$		0			0
$395$	−9.83557	−	17.0357i	−0.494881	−	0.857159i
$396$		0			0
$397$	−13.6533	+	23.6482i	−0.685238	+	1.18687i	0.288124	+	0.957593i	$0.406969\pi$
$397$	−13.6533	+	23.6482i	−0.685238	+	1.18687i	−0.973362	+	0.229274i	$0.926365\pi$
$398$		0			0
$399$	−3.14522	−	3.86885i	−0.157458	−	0.193685i
$400$		0			0
$401$	−5.57531	−	31.6192i	−0.278418	−	1.57899i	−0.727891	−	0.685693i	$-0.759499\pi$
$401$	−5.57531	−	31.6192i	−0.278418	−	1.57899i	0.449473	−	0.893294i	$-0.351612\pi$
$402$		0			0
$403$	−10.3403	−	8.67656i	−0.515088	−	0.432210i
$404$		0			0
$405$	5.75450	+	11.5726i	0.285943	+	0.575046i
$406$		0			0
$407$	15.0930	+	12.6645i	0.748131	+	0.627756i
$408$		0			0
$409$	−5.96549	−	33.8320i	−0.294975	−	1.67288i	−0.667306	−	0.744784i	$-0.732553\pi$
$409$	−5.96549	−	33.8320i	−0.294975	−	1.67288i	0.372331	−	0.928100i	$-0.378559\pi$
$410$		0			0
$411$	−4.71710	−	5.80238i	−0.232678	−	0.286210i
$412$		0			0
$413$	3.80666	−	6.59332i	0.187313	−	0.324436i
$414$		0			0
$415$	−2.79719	−	4.84488i	−0.137309	−	0.237826i
$416$		0			0
$417$	0.239124	−	15.3886i	0.0117099	−	0.753585i
$418$		0			0
$419$	−11.2207	+	9.41532i	−0.548169	+	0.459968i	−0.874320	−	0.485349i	$-0.838692\pi$
$419$	−11.2207	+	9.41532i	−0.548169	+	0.459968i	0.326151	+	0.945318i	$0.394248\pi$
$420$		0			0
$421$	6.30189	−	2.29370i	0.307135	−	0.111788i	−0.183854	−	0.982954i	$-0.558857\pi$
$421$	6.30189	−	2.29370i	0.307135	−	0.111788i	0.490990	+	0.871165i	$0.336635\pi$
$422$		0			0
$423$	−3.48418	+	5.62368i	−0.169407	+	0.273433i
$424$		0			0
$425$	1.40285	−	7.95594i	0.0680481	−	0.385920i
$426$		0			0
$427$	5.63959	+	2.05264i	0.272919	+	0.0993343i
$428$		0			0
$429$	−14.2192	+	16.4208i	−0.686511	+	0.792803i
$430$		0			0
$431$	−19.4368			−0.936239			−0.468120	−	0.883665i	$-0.655068\pi$
$431$	−19.4368			−0.936239			−0.468120	+	0.883665i	$0.655068\pi$
$432$		0			0
$433$	0.493074			0.0236956			0.0118478	−	0.999930i	$-0.496229\pi$
$433$	0.493074			0.0236956			0.0118478	+	0.999930i	$0.496229\pi$
$434$		0			0
$435$	2.48928	+	7.18466i	0.119352	+	0.344478i
$436$		0			0
$437$	21.1597	+	7.70149i	1.01220	+	0.368412i
$438$		0			0
$439$	−1.82440	+	10.3467i	−0.0870740	+	0.493821i	0.909816	+	0.415012i	$0.136223\pi$
$439$	−1.82440	+	10.3467i	−0.0870740	+	0.493821i	−0.996890	+	0.0788089i	$0.974888\pi$
$440$		0			0
$441$	14.7452	+	13.1747i	0.702154	+	0.627368i
$442$		0			0
$443$	2.69511	−	0.980939i	0.128048	−	0.0466058i	−0.277201	−	0.960812i	$-0.589407\pi$
$443$	2.69511	−	0.980939i	0.128048	−	0.0466058i	0.405250	+	0.914206i	$0.367185\pi$
$444$		0			0
$445$	−8.66979	+	7.27482i	−0.410987	+	0.344859i
$446$		0			0
$447$	−9.14040	+	5.08952i	−0.432326	+	0.240726i
$448$		0			0
$449$	5.14109	+	8.90463i	0.242623	+	0.420235i	0.961461	−	0.274943i	$-0.0886589\pi$
$449$	5.14109	+	8.90463i	0.242623	+	0.420235i	−0.718838	+	0.695178i	$0.755326\pi$
$450$		0			0
$451$	14.8165	−	25.6630i	0.697683	−	1.20842i
$452$		0			0
$453$	22.8022	−	3.65630i	1.07134	−	0.171788i
$454$		0			0
$455$	0.732564	+	4.15458i	0.0343431	+	0.194770i
$456$		0			0
$457$	7.96619	+	6.68443i	0.372643	+	0.312684i	0.809806	−	0.586698i	$-0.199572\pi$
$457$	7.96619	+	6.68443i	0.372643	+	0.312684i	−0.437163	+	0.899382i	$0.644017\pi$
$458$		0			0
$459$	−0.665812	+	14.2734i	−0.0310775	+	0.666227i
$460$		0			0
$461$	−9.88996	−	8.29867i	−0.460622	−	0.386507i	0.382738	−	0.923857i	$-0.374981\pi$
$461$	−9.88996	−	8.29867i	−0.460622	−	0.386507i	−0.843360	+	0.537349i	$0.819426\pi$
$462$		0			0
$463$	−0.261444	−	1.48273i	−0.0121504	−	0.0689081i	0.978130	−	0.207996i	$-0.0666941\pi$
$463$	−0.261444	−	1.48273i	−0.0121504	−	0.0689081i	−0.990280	+	0.139088i	$0.955583\pi$
$464$		0			0
$465$	2.60560	−	6.82688i	0.120832	−	0.316589i
$466$		0			0
$467$	8.72235	−	15.1076i	0.403622	−	0.699094i	−0.590538	−	0.807010i	$-0.701084\pi$
$467$	8.72235	−	15.1076i	0.403622	−	0.699094i	0.994160	+	0.107916i	$0.0344177\pi$
$468$		0			0
$469$	2.13820	+	3.70347i	0.0987328	+	0.171010i
$470$		0			0
$471$	23.9716	+	14.3411i	1.10455	+	0.660805i
$472$		0			0
$473$	−20.3869	+	17.1066i	−0.937390	+	0.786563i
$474$		0			0
$475$	12.4293	−	4.52389i	0.570295	−	0.207570i
$476$		0			0
$477$	−24.9165	−	9.95607i	−1.14085	−	0.455857i
$478$		0			0
$479$	1.46375	−	8.30136i	0.0668806	−	0.379299i	−0.932934	−	0.360047i	$-0.882761\pi$
$479$	1.46375	−	8.30136i	0.0668806	−	0.379299i	0.999815	−	0.0192516i	$-0.00612834\pi$
$480$		0			0
$481$	−31.1663	−	11.3436i	−1.42106	−	0.517223i
$482$		0			0
$483$	5.43884	+	1.04640i	0.247476	+	0.0476127i
$484$		0			0
$485$	−24.4823			−1.11168
$486$		0			0
$487$	−6.07460			−0.275266			−0.137633	−	0.990483i	$-0.543949\pi$
$487$	−6.07460			−0.275266			−0.137633	+	0.990483i	$0.543949\pi$
$488$		0			0
$489$	10.8854	+	2.09427i	0.492254	+	0.0947063i
$490$		0			0
$491$	20.2071	+	7.35479i	0.911934	+	0.331917i	0.755025	−	0.655696i	$-0.227625\pi$
$491$	20.2071	+	7.35479i	0.911934	+	0.331917i	0.156909	+	0.987613i	$0.449847\pi$
$492$		0			0
$493$	−1.45977	+	8.27879i	−0.0657449	+	0.372858i
$494$		0			0
$495$	−10.9194	−	4.36313i	−0.490790	−	0.196108i
$496$		0			0
$497$	−7.94294	+	2.89099i	−0.356290	+	0.129679i
$498$		0			0
$499$	10.4617	−	8.77845i	0.468332	−	0.392977i	−0.377854	−	0.925865i	$-0.623338\pi$
$499$	10.4617	−	8.77845i	0.468332	−	0.392977i	0.846186	+	0.532888i	$0.178893\pi$
$500$		0			0
$501$	24.6842	+	14.7675i	1.10281	+	0.659761i
$502$		0			0
$503$	8.78795	+	15.2212i	0.391835	+	0.678679i	0.992692	−	0.120678i	$-0.0385070\pi$
$503$	8.78795	+	15.2212i	0.391835	+	0.678679i	−0.600856	+	0.799357i	$0.705174\pi$
$504$		0			0
$505$	8.10037	−	14.0303i	0.360462	−	0.624338i
$506$		0			0
$507$	5.00949	−	13.1252i	0.222479	−	0.582913i
$508$		0			0
$509$	−4.90270	−	27.8046i	−0.217309	−	1.23242i	−0.876855	−	0.480754i	$-0.840363\pi$
$509$	−4.90270	−	27.8046i	−0.217309	−	1.23242i	0.659547	−	0.751663i	$-0.270748\pi$
$510$		0			0
$511$	1.97943	+	1.66094i	0.0875647	+	0.0734755i
$512$		0			0
$513$	−20.7836	+	10.7407i	−0.917620	+	0.474212i
$514$		0			0
$515$	−6.71230	−	5.63229i	−0.295779	−	0.248188i
$516$		0			0
$517$	−1.04518	−	5.92750i	−0.0459669	−	0.260691i
$518$		0			0
$519$	19.3488	−	3.10255i	0.849317	−	0.136187i
$520$		0			0
$521$	−4.70302	+	8.14587i	−0.206043	+	0.356877i	−0.950465	−	0.310833i	$-0.899392\pi$
$521$	−4.70302	+	8.14587i	−0.206043	+	0.356877i	0.744422	+	0.667710i	$0.232725\pi$
$522$		0			0
$523$	−5.11801	−	8.86465i	−0.223795	−	0.387624i	0.732162	−	0.681130i	$-0.238511\pi$
$523$	−5.11801	−	8.86465i	−0.223795	−	0.387624i	−0.955957	+	0.293506i	$0.905178\pi$
$524$		0			0
$525$	2.84246	−	1.58272i	0.124055	−	0.0690757i
$526$		0			0
$527$	6.18868	−	5.19292i	0.269583	−	0.226207i
$528$		0			0
$529$	−1.89169	+	0.688520i	−0.0822476	+	0.0299357i
$530$		0			0
$531$	−26.6383	−	23.8011i	−1.15600	−	1.03288i
$532$		0			0
$533$	−8.66213	+	49.1254i	−0.375199	+	2.12786i
$534$		0			0
$535$	4.11559	+	1.49795i	0.177932	+	0.0647621i
$536$		0			0
$537$	1.55261	+	4.48121i	0.0670002	+	0.193379i
$538$		0			0
$539$	−17.9904			−0.774902
$540$		0			0
$541$	−23.4018			−1.00612			−0.503062	−	0.864250i	$-0.667793\pi$
$541$	−23.4018			−1.00612			−0.503062	+	0.864250i	$0.667793\pi$
$542$		0			0
$543$	−27.7851	+	32.0870i	−1.19237	+	1.37699i
$544$		0			0
$545$	−2.58238	−	0.939911i	−0.110617	−	0.0402614i
$546$		0			0
$547$	−1.02195	+	5.79579i	−0.0436956	+	0.247810i	−0.998830	−	0.0483633i	$-0.984599\pi$
$547$	−1.02195	+	5.79579i	−0.0436956	+	0.247810i	0.955134	+	0.296173i	$0.0957106\pi$
$548$		0			0
$549$	14.8308	−	23.9378i	0.632962	−	1.02164i
$550$		0			0
$551$	−12.9337	+	4.70747i	−0.550993	+	0.200545i
$552$		0			0
$553$	6.70922	−	5.62970i	0.285305	−	0.239399i
$554$		0			0
$555$	0.278959	−	17.9522i	0.0118412	−	0.762029i
$556$		0			0
$557$	−6.44436	−	11.1620i	−0.273056	−	0.472947i	0.696587	−	0.717473i	$-0.254701\pi$
$557$	−6.44436	−	11.1620i	−0.273056	−	0.472947i	−0.969643	+	0.244525i	$0.921368\pi$
$558$		0			0
$559$	22.3998	−	38.7977i	0.947412	−	1.64097i
$560$		0			0
$561$	−8.20074	−	10.0875i	−0.346236	−	0.425895i
$562$		0			0
$563$	4.65833	+	26.4187i	0.196325	+	1.11341i	0.910519	+	0.413467i	$0.135682\pi$
$563$	4.65833	+	26.4187i	0.196325	+	1.11341i	−0.714194	+	0.699948i	$0.753207\pi$
$564$		0			0
$565$	−6.57069	−	5.51346i	−0.276431	−	0.231953i
$566$		0			0
$567$	−4.62932	+	3.41790i	−0.194413	+	0.143538i
$568$		0			0
$569$	−25.8068	−	21.6545i	−1.08188	−	0.907803i	−0.0858026	−	0.996312i	$-0.527345\pi$
$569$	−25.8068	−	21.6545i	−1.08188	−	0.907803i	−0.996075	+	0.0885088i	$0.971790\pi$
$570$		0			0
$571$	−4.35069	−	24.6740i	−0.182071	−	1.03258i	−0.929661	−	0.368415i	$-0.879900\pi$
$571$	−4.35069	−	24.6740i	−0.182071	−	1.03258i	0.747590	−	0.664160i	$-0.231211\pi$
$572$		0			0
$573$	20.5770	+	25.3112i	0.859616	+	1.05739i
$574$		0			0
$575$	−7.34641	+	12.7244i	−0.306366	+	0.530642i
$576$		0			0
$577$	10.7965	+	18.7002i	0.449466	+	0.778498i	0.998351	−	0.0573995i	$-0.0182809\pi$
$577$	10.7965	+	18.7002i	0.449466	+	0.778498i	−0.548885	+	0.835898i	$0.684948\pi$
$578$		0			0
$579$	−0.218646	+	14.0708i	−0.00908660	+	0.584762i
$580$		0			0
$581$	1.90807	−	1.60106i	0.0791602	−	0.0664233i
$582$		0			0
$583$	22.9401	−	8.34950i	0.950081	−	0.345801i
$584$		0			0
$585$	19.7848	+	0.615020i	0.818002	+	0.0254280i
$586$		0			0
$587$	−7.47193	+	42.3754i	−0.308399	+	1.74902i	0.298657	+	0.954361i	$0.403461\pi$
$587$	−7.47193	+	42.3754i	−0.308399	+	1.74902i	−0.607056	+	0.794659i	$0.707650\pi$
$588$		0			0
$589$	12.4294	+	4.52393i	0.512145	+	0.186405i
$590$		0			0
$591$	−12.1175	+	13.9937i	−0.498449	+	0.575623i
$592$		0			0
$593$	29.7818			1.22299			0.611496	−	0.791248i	$-0.290568\pi$
$593$	29.7818			1.22299			0.611496	+	0.791248i	$0.290568\pi$
$594$		0			0
$595$	−2.52487			−0.103510
$596$		0			0
$597$	0.409280	+	1.18128i	0.0167507	+	0.0483466i
$598$		0			0
$599$	10.8521	+	3.94983i	0.443404	+	0.161386i	0.554067	−	0.832472i	$-0.313075\pi$
$599$	10.8521	+	3.94983i	0.443404	+	0.161386i	−0.110663	+	0.993858i	$0.535297\pi$
$600$		0			0
$601$	−5.10637	+	28.9596i	−0.208293	+	1.18129i	0.683880	+	0.729595i	$0.260291\pi$
$601$	−5.10637	+	28.9596i	−0.208293	+	1.18129i	−0.892173	+	0.451694i	$0.850820\pi$
$602$		0			0
$603$	19.0593	−	6.27357i	0.776154	−	0.255479i
$604$		0			0
$605$	−4.79056	+	1.74362i	−0.194764	+	0.0708882i
$606$		0			0
$607$	−18.4853	+	15.5110i	−0.750297	+	0.629574i	−0.935581	−	0.353111i	$-0.885124\pi$
$607$	−18.4853	+	15.5110i	−0.750297	+	0.629574i	0.185285	+	0.982685i	$0.440679\pi$
$608$		0			0
$609$	−2.95780	+	1.64695i	−0.119856	+	0.0667378i
$610$		0			0
$611$	5.06604	+	8.77464i	0.204950	+	0.354984i
$612$		0			0
$613$	12.7421	−	22.0700i	0.514649	−	0.891398i	−0.485207	−	0.874399i	$-0.661256\pi$
$613$	12.7421	−	22.0700i	0.514649	−	0.891398i	0.999856	−	0.0169983i	$-0.00541098\pi$
$614$		0			0
$615$	−26.6633	+	4.27542i	−1.07517	+	0.172402i
$616$		0			0
$617$	3.65022	+	20.7014i	0.146952	+	0.833409i	0.965779	+	0.259367i	$0.0835140\pi$
$617$	3.65022	+	20.7014i	0.146952	+	0.833409i	−0.818826	+	0.574041i	$0.805375\pi$
$618$		0			0
$619$	−0.689621	−	0.578661i	−0.0277182	−	0.0232583i	0.628823	−	0.777548i	$-0.283537\pi$
$619$	−0.689621	−	0.578661i	−0.0277182	−	0.0232583i	−0.656542	+	0.754290i	$0.727981\pi$
$620$		0			0
$621$	10.0165	−	23.9796i	0.401949	−	0.962270i
$622$		0			0
$623$	−3.86009	−	3.23900i	−0.154651	−	0.129768i
$624$		0			0
$625$	−0.291798	−	1.65487i	−0.0116719	−	0.0661947i
$626$		0			0
$627$	7.58984	−	19.8860i	0.303109	−	0.794169i
$628$		0			0
$629$	9.92505	−	17.1907i	0.395738	−	0.685438i
$630$		0			0
$631$	−2.60884	−	4.51865i	−0.103856	−	0.179885i	0.809414	−	0.587238i	$-0.199785\pi$
$631$	−2.60884	−	4.51865i	−0.103856	−	0.179885i	−0.913270	+	0.407354i	$0.866452\pi$
$632$		0			0
$633$	42.7898	+	25.5993i	1.70074	+	1.01748i
$634$		0			0
$635$	−15.1373	+	12.7017i	−0.600704	+	0.504051i
$636$		0			0
$637$	28.4581	−	10.3579i	1.12755	−	0.410394i
$638$		0			0
$639$	5.67015	+	39.2534i	0.224308	+	1.55284i
$640$		0			0
$641$	8.61846	−	48.8777i	0.340409	−	1.93055i	−0.0249562	−	0.999689i	$-0.507945\pi$
$641$	8.61846	−	48.8777i	0.340409	−	1.93055i	0.365365	−	0.930864i	$-0.380944\pi$
$642$		0			0
$643$	−12.5048	−	4.55138i	−0.493142	−	0.179489i	0.0834649	−	0.996511i	$-0.473401\pi$
$643$	−12.5048	−	4.55138i	−0.493142	−	0.179489i	−0.576607	+	0.817022i	$0.695624\pi$
$644$		0			0
$645$	23.8152	+	4.58188i	0.937722	+	0.180411i
$646$		0			0
$647$	10.8976			0.428429			0.214215	−	0.976787i	$-0.431281\pi$
$647$	10.8976			0.428429			0.214215	+	0.976787i	$0.431281\pi$
$648$		0			0
$649$	32.5009			1.27577
$650$		0			0
$651$	3.19483	+	0.614663i	0.125215	+	0.0240906i
$652$		0			0
$653$	22.7736	+	8.28893i	0.891202	+	0.324371i	0.746722	−	0.665137i	$-0.231627\pi$
$653$	22.7736	+	8.28893i	0.891202	+	0.324371i	0.144480	+	0.989508i	$0.453849\pi$
$654$		0			0
$655$	2.95254	−	16.7447i	0.115365	−	0.654268i
$656$		0			0
$657$	9.52532	−	7.50094i	0.371618	−	0.292639i
$658$		0			0
$659$	1.77619	−	0.646482i	0.0691907	−	0.0251833i	−0.307193	−	0.951647i	$-0.599390\pi$
$659$	1.77619	−	0.646482i	0.0691907	−	0.0251833i	0.376384	+	0.926464i	$0.377167\pi$
$660$		0			0
$661$	−8.02397	+	6.73291i	−0.312096	+	0.261880i	−0.785358	−	0.619042i	$-0.787521\pi$
$661$	−8.02397	+	6.73291i	−0.312096	+	0.261880i	0.473261	+	0.880922i	$0.343077\pi$
$662$		0			0
$663$	18.7801	+	11.2353i	0.729360	+	0.436344i
$664$		0			0
$665$	−2.06695	−	3.58006i	−0.0801529	−	0.138829i
$666$		0			0
$667$	7.64452	−	13.2407i	0.295997	−	0.512682i
$668$		0			0
$669$	−8.07039	+	21.1451i	−0.312019	+	0.817515i
$670$		0			0
$671$	4.44891	+	25.2310i	0.171748	+	0.974034i
$672$		0			0
$673$	17.8712	+	14.9957i	0.688883	+	0.578041i	0.918587	−	0.395219i	$-0.129331\pi$
$673$	17.8712	+	14.9957i	0.688883	+	0.578041i	−0.229704	+	0.973261i	$0.573776\pi$
$674$		0			0
$675$	−4.54694	−	14.5723i	−0.175012	−	0.560889i
$676$		0			0
$677$	11.5795	+	9.71637i	0.445037	+	0.373430i	0.837590	−	0.546299i	$-0.183964\pi$
$677$	11.5795	+	9.71637i	0.445037	+	0.373430i	−0.392553	+	0.919729i	$0.628408\pi$
$678$		0			0
$679$	−1.89283	−	10.7348i	−0.0726400	−	0.411962i
$680$		0			0
$681$	40.2303	−	6.45088i	1.54163	−	0.247198i
$682$		0			0
$683$	−5.83323	+	10.1034i	−0.223202	+	0.386597i	−0.955779	−	0.294087i	$-0.904984\pi$
$683$	−5.83323	+	10.1034i	−0.223202	+	0.386597i	0.732576	+	0.680685i	$0.238318\pi$
$684$		0			0
$685$	−3.09994	−	5.36926i	−0.118443	−	0.205149i
$686$		0			0
$687$	16.8061	−	9.35790i	0.641193	−	0.357026i
$688$		0			0
$689$	−31.4805	+	26.4152i	−1.19931	+	1.00634i
$690$		0			0
$691$	4.85816	−	1.76823i	0.184813	−	0.0672665i	−0.247956	−	0.968771i	$-0.579759\pi$
$691$	4.85816	−	1.76823i	0.184813	−	0.0672665i	0.432769	+	0.901505i	$0.357537\pi$
$692$		0			0
$693$	1.06888	−	5.12516i	0.0406034	−	0.194689i
$694$		0			0
$695$	2.21579	−	12.5664i	0.0840497	−	0.476669i
$696$		0			0
$697$	−28.0546	−	10.2110i	−1.06264	−	0.386771i
$698$		0			0
$699$	13.0857	+	37.7683i	0.494945	+	1.42853i
$700$		0			0
$701$	−18.9800			−0.716864			−0.358432	−	0.933556i	$-0.616688\pi$
$701$	−18.9800			−0.716864			−0.358432	+	0.933556i	$0.616688\pi$
$702$		0			0
$703$	32.5000			1.22576
$704$		0			0
$705$	−3.59050	+	4.14641i	−0.135226	+	0.156163i
$706$		0			0
$707$	6.77812	+	2.46704i	0.254918	+	0.0927824i
$708$		0			0
$709$	6.13074	−	34.7692i	0.230245	−	1.30578i	−0.622156	−	0.782894i	$-0.713743\pi$
$709$	6.13074	−	34.7692i	0.230245	−	1.30578i	0.852400	−	0.522890i	$-0.175146\pi$
$710$		0			0
$711$	−19.4316	−	36.2102i	−0.728742	−	1.35799i
$712$		0			0
$713$	−13.8069	+	5.02528i	−0.517071	+	0.188198i
$714$		0			0
$715$	−13.7960	+	11.5762i	−0.515939	+	0.432924i
$716$		0			0
$717$	0.330031	−	21.2389i	0.0123252	−	0.793182i
$718$		0			0
$719$	−22.9792	−	39.8011i	−0.856979	−	1.48433i	−0.874797	−	0.484490i	$-0.839005\pi$
$719$	−22.9792	−	39.8011i	−0.856979	−	1.48433i	0.0178181	−	0.999841i	$-0.494328\pi$
$720$		0			0
$721$	1.95063	−	3.37860i	0.0726454	−	0.125826i
$722$		0			0
$723$	25.6268	+	31.5227i	0.953069	+	1.17234i
$724$		0			0
$725$	−1.55951	−	8.84442i	−0.0579188	−	0.328474i
$726$		0			0
$727$	9.17453	+	7.69834i	0.340264	+	0.285516i	0.796867	−	0.604155i	$-0.206489\pi$
$727$	9.17453	+	7.69834i	0.340264	+	0.285516i	−0.456602	+	0.889671i	$0.650934\pi$
$728$		0			0
$729$	11.2647	+	24.5379i	0.417209	+	0.908810i
$730$		0			0
$731$	20.5396	+	17.2348i	0.759686	+	0.637452i
$732$		0			0
$733$	6.15108	+	34.8845i	0.227195	+	1.28849i	0.858444	+	0.512907i	$0.171432\pi$
$733$	6.15108	+	34.8845i	0.227195	+	1.28849i	−0.631249	+	0.775580i	$0.717457\pi$
$734$		0			0
$735$	10.3416	+	12.7209i	0.381456	+	0.469219i
$736$		0			0
$737$	−9.12788	+	15.8100i	−0.336230	+	0.582367i
$738$		0			0
$739$	−6.40053	−	11.0860i	−0.235447	−	0.407806i	0.723955	−	0.689847i	$-0.242322\pi$
$739$	−6.40053	−	11.0860i	−0.235447	−	0.407806i	−0.959403	+	0.282040i	$0.908989\pi$
$740$		0			0
$741$	−0.556704	+	35.8263i	−0.0204510	+	1.31611i
$742$		0			0
$743$	15.0241	−	12.6067i	0.551180	−	0.462495i	−0.324160	−	0.946002i	$-0.605082\pi$
$743$	15.0241	−	12.6067i	0.551180	−	0.462495i	0.875341	+	0.483507i	$0.160637\pi$
$744$		0			0
$745$	−8.15078	+	2.96664i	−0.298622	+	0.108689i
$746$		0			0
$747$	−5.52627	−	10.2980i	−0.202195	−	0.376785i
$748$		0			0
$749$	−0.338614	+	1.92038i	−0.0123727	+	0.0701690i
$750$		0			0
$751$	−0.834905	−	0.303880i	−0.0304661	−	0.0110888i	0.326742	−	0.945114i	$-0.394049\pi$
$751$	−0.834905	−	0.303880i	−0.0304661	−	0.0110888i	−0.357208	+	0.934025i	$0.616271\pi$
$752$		0			0
$753$	−5.23180	+	6.04183i	−0.190657	+	0.220177i
$754$		0			0
$755$	19.1467			0.696821
$756$		0			0
$757$	7.82668			0.284466			0.142233	−	0.989833i	$-0.454572\pi$
$757$	7.82668			0.284466			0.142233	+	0.989833i	$0.454572\pi$
$758$		0			0
$759$	7.74055	+	22.3411i	0.280964	+	0.810929i
$760$		0			0
$761$	13.5553	+	4.93374i	0.491381	+	0.178848i	0.575813	−	0.817581i	$-0.304685\pi$
$761$	13.5553	+	4.93374i	0.491381	+	0.178848i	−0.0844324	+	0.996429i	$0.526908\pi$
$762$		0			0
$763$	0.212468	−	1.20497i	0.00769186	−	0.0436227i
$764$		0			0
$765$	−2.41870	+	11.5974i	−0.0874484	+	0.419305i
$766$		0			0
$767$	−51.4114	+	18.7122i	−1.85636	+	0.675660i
$768$		0			0
$769$	−17.2184	+	14.4479i	−0.620910	+	0.521005i	−0.898090	−	0.439813i	$-0.855045\pi$
$769$	−17.2184	+	14.4479i	−0.620910	+	0.521005i	0.277179	+	0.960818i	$0.410600\pi$
$770$		0			0
$771$	−4.90138	+	2.72916i	−0.176519	+	0.0982885i
$772$		0			0
$773$	−23.8250	−	41.2662i	−0.856927	−	1.48424i	−0.874846	−	0.484401i	$-0.839037\pi$
$773$	−23.8250	−	41.2662i	−0.856927	−	1.48424i	0.0179190	−	0.999839i	$-0.494296\pi$
$774$		0			0
$775$	−4.31536	+	7.47441i	−0.155012	+	0.268489i
$776$		0			0
$777$	7.89308	−	1.26564i	0.283163	−	0.0454048i
$778$		0			0
$779$	−8.48808	−	48.1383i	−0.304117	−	1.72473i
$780$		0			0
$781$	−27.6421	−	23.1945i	−0.989113	−	0.829965i
$782$		0			0
$783$	4.73145	+	15.1637i	0.169088	+	0.541905i
$784$		0			0
$785$	17.7415	+	14.8869i	0.633223	+	0.531337i
$786$		0			0
$787$	−1.24247	−	7.04642i	−0.0442894	−	0.251178i	0.954622	−	0.297819i	$-0.0962593\pi$
$787$	−1.24247	−	7.04642i	−0.0442894	−	0.251178i	−0.998912	+	0.0466414i	$0.985148\pi$
$788$		0			0
$789$	7.99259	−	20.9412i	0.284544	−	0.745527i
$790$		0			0
$791$	1.90948	−	3.30732i	0.0678933	−	0.117595i
$792$		0			0
$793$	−21.5641	−	37.3502i	−0.765764	−	1.32634i
$794$		0			0
$795$	−19.0908	−	11.4212i	−0.677080	−	0.405067i
$796$		0			0
$797$	24.1053	−	20.2267i	0.853853	−	0.716467i	−0.106782	−	0.994282i	$-0.534055\pi$
$797$	24.1053	−	20.2267i	0.853853	−	0.716467i	0.960635	+	0.277815i	$0.0896103\pi$
$798$		0			0
$799$	−5.69834	+	2.07403i	−0.201593	+	0.0733737i
$800$		0			0
$801$	−18.5753	+	14.6276i	−0.656328	+	0.516841i
$802$		0			0
$803$	−1.91548	+	10.8632i	−0.0675959	+	0.383355i
$804$		0			0
$805$	4.31509	+	1.57057i	0.152087	+	0.0553552i
$806$		0			0
$807$	26.3767	+	5.07469i	0.928502	+	0.178637i
$808$		0			0
$809$	−55.1927			−1.94047			−0.970237	−	0.242159i	$-0.922144\pi$
$809$	−55.1927			−1.94047			−0.970237	+	0.242159i	$0.922144\pi$
$810$		0			0
$811$	25.3913			0.891609			0.445804	−	0.895130i	$-0.352918\pi$
$811$	25.3913			0.891609			0.445804	+	0.895130i	$0.352918\pi$
$812$		0			0
$813$	−19.8305	−	3.81525i	−0.695486	−	0.133807i
$814$		0			0
$815$	8.63630	+	3.14335i	0.302516	+	0.110107i
$816$		0			0
$817$	−7.62306	+	43.2325i	−0.266697	+	1.51252i
$818$		0			0
$819$	1.25998	+	8.72261i	0.0440272	+	0.304793i
$820$		0			0
$821$	−30.2228	+	11.0002i	−1.05478	+	0.383909i	−0.810465	−	0.585787i	$-0.800786\pi$
$821$	−30.2228	+	11.0002i	−1.05478	+	0.383909i	−0.244316	+	0.969696i	$0.578563\pi$
$822$		0			0
$823$	13.9272	−	11.6863i	0.485472	−	0.407360i	−0.366928	−	0.930249i	$-0.619590\pi$
$823$	13.9272	−	11.6863i	0.485472	−	0.407360i	0.852400	+	0.522890i	$0.175146\pi$
$824$		0			0
$825$	11.9185	+	7.13034i	0.414950	+	0.248247i
$826$		0			0
$827$	−2.50483	−	4.33849i	−0.0871014	−	0.150864i	0.819183	−	0.573532i	$-0.194427\pi$
$827$	−2.50483	−	4.33849i	−0.0871014	−	0.150864i	−0.906285	+	0.422668i	$0.861094\pi$
$828$		0			0
$829$	18.4883	−	32.0227i	0.642127	−	1.11220i	−0.342830	−	0.939397i	$-0.611386\pi$
$829$	18.4883	−	32.0227i	0.642127	−	1.11220i	0.984957	−	0.172799i	$-0.0552810\pi$
$830$		0			0
$831$	18.9751	−	49.7164i	0.658240	−	1.72464i
$832$		0			0
$833$	3.14741	+	17.8499i	0.109051	+	0.618461i
$834$		0			0
$835$	18.2689	+	15.3295i	0.632223	+	0.530498i
$836$		0			0
$837$	5.88380	−	14.0859i	0.203374	−	0.486879i
$838$		0			0
$839$	−19.6074	−	16.4526i	−0.676923	−	0.568006i	0.238182	−	0.971220i	$-0.423448\pi$
$839$	−19.6074	−	16.4526i	−0.676923	−	0.568006i	−0.915105	+	0.403215i	$0.867893\pi$
$840$		0			0
$841$	−3.41300	−	19.3561i	−0.117690	−	0.667452i
$842$		0			0
$843$	22.6084	−	3.62522i	0.778674	−	0.124859i
$844$		0			0
$845$	5.82389	−	10.0873i	0.200348	−	0.347012i
$846$		0			0
$847$	−1.13490	−	1.96571i	−0.0389957	−	0.0675426i
$848$		0			0
$849$	−17.9349	+	9.98646i	−0.615525	+	0.342734i
$850$		0			0
$851$	−27.6555	+	23.2057i	−0.948019	+	0.795482i
$852$		0			0
$853$	−25.1605	+	9.15766i	−0.861478	+	0.313552i	−0.734711	−	0.678380i	$-0.762682\pi$
$853$	−25.1605	+	9.15766i	−0.861478	+	0.313552i	−0.126767	+	0.991933i	$0.540460\pi$
$854$		0			0
$855$	−18.4242	+	6.06452i	−0.630095	+	0.207402i
$856$		0			0
$857$	−5.63415	+	31.9528i	−0.192459	+	1.09149i	0.723532	+	0.690290i	$0.242517\pi$
$857$	−5.63415	+	31.9528i	−0.192459	+	1.09149i	−0.915991	+	0.401198i	$0.868594\pi$
$858$		0			0
$859$	−39.6782	−	14.4417i	−1.35380	−	0.492744i	−0.439671	−	0.898159i	$-0.644905\pi$
$859$	−39.6782	−	14.4417i	−1.35380	−	0.492744i	−0.914133	+	0.405415i	$0.867127\pi$
$860$		0			0
$861$	−3.93609	−	11.3605i	−0.134142	−	0.387165i
$862$		0			0
$863$	−5.61985			−0.191302			−0.0956509	−	0.995415i	$-0.530493\pi$
$863$	−5.61985			−0.191302			−0.0956509	+	0.995415i	$0.530493\pi$
$864$		0			0
$865$	16.2469			0.552413
$866$		0			0
$867$	10.7010	−	12.3578i	0.363425	−	0.419693i
$868$		0			0
$869$	35.1339	+	12.7877i	1.19183	+	0.433792i
$870$		0			0
$871$	5.33640	−	30.2642i	0.180817	−	1.02546i
$872$		0			0
$873$	−51.1208	−	1.58911i	−1.73018	−	0.0537833i
$874$		0			0
$875$	6.84867	−	2.49271i	0.231527	−	0.0842691i
$876$		0			0
$877$	7.15193	−	6.00118i	0.241504	−	0.202646i	−0.514000	−	0.857790i	$-0.671837\pi$
$877$	7.15193	−	6.00118i	0.241504	−	0.202646i	0.755503	+	0.655145i	$0.227392\pi$
$878$		0			0
$879$	0.334803	−	21.5460i	0.0112926	−	0.726729i
$880$		0			0
$881$	0.248845	+	0.431012i	0.00838379	+	0.0145211i	0.870187	−	0.492722i	$-0.163998\pi$
$881$	0.248845	+	0.431012i	0.00838379	+	0.0145211i	−0.861803	+	0.507243i	$0.830665\pi$
$882$		0			0
$883$	−27.7879	+	48.1301i	−0.935139	+	1.61971i	−0.160753	+	0.986995i	$0.551392\pi$
$883$	−27.7879	+	48.1301i	−0.935139	+	1.61971i	−0.774386	+	0.632714i	$0.781941\pi$
$884$		0			0
$885$	−18.6828	−	22.9812i	−0.628017	−	0.772506i
$886$		0			0
$887$	−4.54374	−	25.7688i	−0.152564	−	0.865232i	−0.960979	−	0.276620i	$-0.910786\pi$
$887$	−4.54374	−	25.7688i	−0.152564	−	0.865232i	0.808416	−	0.588612i	$-0.200325\pi$
$888$		0			0
$889$	−6.73963	−	5.65522i	−0.226040	−	0.189670i
$890$		0			0
$891$	−22.5173	−	9.81930i	−0.754357	−	0.328959i
$892$		0			0
$893$	−7.60566	−	6.38191i	−0.254514	−	0.213562i
$894$		0			0
$895$	0.682792	+	3.87230i	0.0228232	+	0.129437i
$896$		0			0
$897$	−25.1071	−	30.8835i	−0.838301	−	1.03117i
$898$		0			0
$899$	4.49047	−	7.77772i	0.149766	−	0.259402i
$900$		0			0
$901$	−12.2976	−	21.3001i	−0.409693	−	0.709609i
$902$		0			0
$903$	−0.167766	+	10.7965i	−0.00558292	+	0.359285i
$904$		0			0
$905$	−26.9580	+	22.6204i	−0.896114	+	0.751929i
$906$		0			0
$907$	−48.4172	+	17.6224i	−1.60767	+	0.585143i	−0.980977	−	0.194126i	$-0.937813\pi$
$907$	−48.4172	+	17.6224i	−1.60767	+	0.585143i	−0.626690	+	0.779269i	$0.715591\pi$
$908$		0			0
$909$	17.8249	−	28.7704i	0.591213	−	0.954254i
$910$		0			0
$911$	0.718666	−	4.07576i	0.0238105	−	0.135036i	−0.970585	−	0.240758i	$-0.922604\pi$
$911$	0.718666	−	4.07576i	0.0238105	−	0.135036i	0.994396	+	0.105722i	$0.0337152\pi$
$912$		0			0
$913$	9.99192	+	3.63676i	0.330684	+	0.120359i
$914$		0			0
$915$	15.2833	−	17.6496i	0.505251	−	0.583478i
$916$		0			0
$917$	7.57031			0.249994
$918$		0			0
$919$	−6.78452			−0.223801			−0.111900	−	0.993719i	$-0.535694\pi$
$919$	−6.78452			−0.223801			−0.111900	+	0.993719i	$0.535694\pi$
$920$		0			0
$921$	5.02590	+	14.5059i	0.165609	+	0.477987i
$922$		0			0
$923$	57.0797	+	20.7753i	1.87880	+	0.683827i
$924$		0			0
$925$	−3.68244	+	20.8841i	−0.121078	+	0.686666i
$926$		0			0
$927$	−13.6502	−	12.1963i	−0.448331	−	0.400579i
$928$		0			0
$929$	27.7215	−	10.0898i	0.909513	−	0.331036i	0.155455	−	0.987843i	$-0.450316\pi$
$929$	27.7215	−	10.0898i	0.909513	−	0.331036i	0.754058	+	0.656807i	$0.228094\pi$
$930$		0			0
$931$	−22.7331	+	19.0753i	−0.745046	+	0.625168i
$932$		0			0
$933$	−46.8839	+	26.1057i	−1.53491	+	0.854663i
$934$		0			0
$935$	−5.38929	−	9.33452i	−0.176249	−	0.305272i
$936$		0			0
$937$	7.87400	−	13.6382i	0.257232	−	0.445539i	−0.708267	−	0.705944i	$-0.750523\pi$
$937$	7.87400	−	13.6382i	0.257232	−	0.445539i	0.965499	+	0.260405i	$0.0838561\pi$
$938$		0			0
$939$	7.57001	−	1.21384i	0.247038	−	0.0396122i
$940$		0			0
$941$	4.06462	+	23.0516i	0.132503	+	0.751461i	0.976566	+	0.215217i	$0.0690460\pi$
$941$	4.06462	+	23.0516i	0.132503	+	0.751461i	−0.844063	+	0.536244i	$0.819843\pi$
$942$		0			0
$943$	41.5946	+	34.9021i	1.35451	+	1.13657i
$944$		0			0
$945$	−4.23841	+	2.19035i	−0.137875	+	0.0712520i
$946$		0			0
$947$	−45.2289	−	37.9515i	−1.46974	−	1.23326i	−0.916375	−	0.400321i	$-0.868899\pi$
$947$	−45.2289	−	37.9515i	−1.46974	−	1.23326i	−0.553366	−	0.832938i	$-0.686657\pi$
$948$		0			0
$949$	−3.22445	−	18.2868i	−0.104670	−	0.593614i
$950$		0			0
$951$	−15.0445	+	39.4178i	−0.487851	+	1.27821i
$952$		0			0
$953$	6.84271	−	11.8519i	0.221657	−	0.383921i	−0.733654	−	0.679523i	$-0.762187\pi$
$953$	6.84271	−	11.8519i	0.221657	−	0.383921i	0.955311	+	0.295602i	$0.0955201\pi$
$954$		0			0
$955$	13.5226	+	23.4218i	0.437581	+	0.757912i
$956$		0			0
$957$	−12.4022	−	7.41969i	−0.400906	−	0.239845i
$958$		0			0
$959$	2.11459	−	1.77435i	0.0682837	−	0.0572968i
$960$		0			0
$961$	21.0202	−	7.65072i	0.678070	−	0.246797i
$962$		0			0
$963$	8.49642	+	3.39497i	0.273793	+	0.109401i
$964$		0			0
$965$	−2.02603	+	11.4902i	−0.0652203	+	0.369883i
$966$		0			0
$967$	−30.2879	−	11.0239i	−0.973995	−	0.354505i	−0.194492	−	0.980904i	$-0.562306\pi$
$967$	−30.2879	−	11.0239i	−0.973995	−	0.354505i	−0.779503	+	0.626399i	$0.784528\pi$
$968$		0			0
$969$	−21.0584	−	4.05150i	−0.676494	−	0.130153i
$970$		0			0
$971$	28.2898			0.907864			0.453932	−	0.891036i	$-0.350021\pi$
$971$	28.2898			0.907864			0.453932	+	0.891036i	$0.350021\pi$
$972$		0			0
$973$	5.68129			0.182134
$974$		0			0
$975$	−22.9585	−	4.41706i	−0.735262	−	0.141459i
$976$		0			0
$977$	39.6488	+	14.4310i	1.26848	+	0.461688i	0.886605	−	0.462527i	$-0.153057\pi$
$977$	39.6488	+	14.4310i	1.26848	+	0.461688i	0.381872	+	0.924215i	$0.375280\pi$
$978$		0			0
$979$	3.73539	−	21.1844i	0.119383	−	0.677057i
$980$		0			0
$981$	−5.33119	−	2.13022i	−0.170212	−	0.0680127i
$982$		0			0
$983$	−50.4691	+	18.3693i	−1.60972	+	0.585888i	−0.981384	−	0.192057i	$-0.938484\pi$
$983$	−50.4691	+	18.3693i	−1.60972	+	0.585888i	−0.628331	+	0.777946i	$0.716262\pi$
$984$		0			0
$985$	−11.7568	+	9.86513i	−0.374603	+	0.314329i
$986$		0			0
$987$	−2.09567	−	1.25375i	−0.0667060	−	0.0399073i
$988$		0			0
$989$	−24.3822	−	42.2313i	−0.775310	−	1.34288i
$990$		0			0
$991$	11.1419	−	19.2983i	0.353934	−	0.613032i	−0.633001	−	0.774151i	$-0.718177\pi$
$991$	11.1419	−	19.2983i	0.353934	−	0.613032i	0.986935	+	0.161119i	$0.0515104\pi$
$992$		0			0
$993$	−15.2040	+	39.8357i	−0.482484	+	1.26415i
$994$		0			0
$995$	0.179989	+	1.02077i	0.00570603	+	0.0323605i
$996$		0			0
$997$	−11.6750	−	9.79646i	−0.369750	−	0.310257i	0.438913	−	0.898530i	$-0.355364\pi$
$997$	−11.6750	−	9.79646i	−0.369750	−	0.310257i	−0.808663	+	0.588273i	$0.799808\pi$
$998$		0			0
$999$	1.74774	−	37.4674i	0.0552961	−	1.18542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.97.5		30
4.3	odd	2		216.2.q.b.97.1	yes	30
12.11	even	2		648.2.q.b.289.3		30
27.22	even	9	inner	432.2.u.f.49.5		30
108.7	odd	18		5832.2.a.k.1.6		15
108.47	even	18		5832.2.a.l.1.10		15
108.59	even	18		648.2.q.b.361.3		30
108.103	odd	18		216.2.q.b.49.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.1	✓	30	108.103	odd	18
216.2.q.b.97.1	yes	30	4.3	odd	2
432.2.u.f.49.5		30	27.22	even	9	inner
432.2.u.f.97.5		30	1.1	even	1	trivial
648.2.q.b.289.3		30	12.11	even	2
648.2.q.b.361.3		30	108.59	even	18
5832.2.a.k.1.6		15	108.7	odd	18
5832.2.a.l.1.10		15	108.47	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70086 + 0.327233i) q^{3} +(1.34943 + 0.491154i) q^{5} +(-0.111026 + 0.629660i) q^{7} +(2.78584 + 1.11316i) q^{9} +O(q^{10})\)	\(q+(1.70086 + 0.327233i) q^{3} +(1.34943 + 0.491154i) q^{5} +(-0.111026 + 0.629660i) q^{7} +(2.78584 + 1.11316i) q^{9} +(-2.56485 + 0.933530i) q^{11} +(3.51973 - 2.95340i) q^{13} +(2.13447 + 1.27696i) q^{15} +(1.37496 + 2.38149i) q^{17} +(-2.25118 + 3.89915i) q^{19} +(-0.394885 + 1.03463i) q^{21} +(-0.868468 - 4.92533i) q^{23} +(-2.25048 - 1.88838i) q^{25} +(4.37405 + 2.80494i) q^{27} +(2.34180 + 1.96501i) q^{29} +(-0.510147 - 2.89319i) q^{31} +(-4.66793 + 0.748497i) q^{33} +(-0.459082 + 0.795154i) q^{35} +(-3.60922 - 6.25136i) q^{37} +(6.95301 - 3.87154i) q^{39} +(-8.31675 + 6.97858i) q^{41} +(9.16233 - 3.33481i) q^{43} +(3.21257 + 2.87040i) q^{45} +(-0.382925 + 2.17168i) q^{47} +(6.19370 + 2.25432i) q^{49} +(1.55930 + 4.50051i) q^{51} -8.94401 q^{53} -3.91961 q^{55} +(-5.10486 + 5.89524i) q^{57} +(-11.1894 - 4.07259i) q^{59} +(1.62996 - 9.24397i) q^{61} +(-1.01021 + 1.63054i) q^{63} +(6.20021 - 2.25669i) q^{65} +(5.12362 - 4.29923i) q^{67} +(0.134590 - 8.66148i) q^{69} +(6.61014 + 11.4491i) q^{71} +(2.02070 - 3.49995i) q^{73} +(-3.20981 - 3.94829i) q^{75} +(-0.303041 - 1.71863i) q^{77} +(-10.4934 - 8.80503i) q^{79} +(6.52177 + 6.20214i) q^{81} +(-2.98429 - 2.50411i) q^{83} +(0.685733 + 3.88898i) q^{85} +(3.34006 + 4.10852i) q^{87} +(-3.94057 + 6.82526i) q^{89} +(1.46886 + 2.54413i) q^{91} +(0.0790598 - 5.08784i) q^{93} +(-4.95290 + 4.15597i) q^{95} +(-16.0203 + 5.83093i) q^{97} +(-8.18443 - 0.254417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

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