LMFDB - Embedded newform 1386.2.ba.a.1187.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1187.8
Character	$\chi$	$=$	1386.1187
Dual form			1386.2.ba.a.989.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.346303 + 0.199938i) q^{5} +(1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.346303 + 0.199938i) q^{5} +(1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +(0.346303 + 0.199938i) q^{10} +(3.01389 + 1.38437i) q^{11} +0.164753i q^{13} +(1.58739 - 2.11664i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.906908 - 1.57081i) q^{17} +(-5.41372 + 3.12561i) q^{19} -0.399877i q^{20} +(-0.308042 - 3.30229i) q^{22} +(3.76546 - 2.17399i) q^{23} +(-2.42005 + 4.19165i) q^{25} +(0.142681 - 0.0823767i) q^{26} +(-2.62676 - 0.316401i) q^{28} -4.12269 q^{29} +(-0.141785 + 0.245579i) q^{31} +(-0.500000 + 0.866025i) q^{32} -1.81382 q^{34} +(-0.846396 - 0.634761i) q^{35} +(2.40479 + 4.16521i) q^{37} +(5.41372 + 3.12561i) q^{38} +(-0.346303 + 0.199938i) q^{40} -9.23554 q^{41} +2.07944i q^{43} +(-2.70584 + 1.91792i) q^{44} +(-3.76546 - 2.17399i) q^{46} +(0.367808 - 0.212354i) q^{47} +(-4.83941 + 5.05767i) q^{49} +4.84010 q^{50} +(-0.142681 - 0.0823767i) q^{52} +(7.71343 + 4.45335i) q^{53} +(-1.32051 + 0.123179i) q^{55} +(1.03937 + 2.43304i) q^{56} +(2.06135 + 3.57036i) q^{58} +(6.92731 + 3.99948i) q^{59} +(-6.10939 + 3.52726i) q^{61} +0.283570 q^{62} +1.00000 q^{64} +(-0.0329405 - 0.0570546i) q^{65} +(0.0327874 - 0.0567894i) q^{67} +(0.906908 + 1.57081i) q^{68} +(-0.126521 + 1.05038i) q^{70} +6.43763i q^{71} +(7.21457 + 4.16533i) q^{73} +(2.40479 - 4.16521i) q^{74} -6.25122i q^{76} +(-0.235692 + 8.77180i) q^{77} +(0.531141 - 0.306654i) q^{79} +(0.346303 + 0.199938i) q^{80} +(4.61777 + 7.99822i) q^{82} +1.91649 q^{83} +0.725302i q^{85} +(1.80085 - 1.03972i) q^{86} +(3.01389 + 1.38437i) q^{88} +(8.89851 - 5.13756i) q^{89} +(-0.400852 + 0.171240i) q^{91} +4.34798i q^{92} +(-0.367808 - 0.212354i) q^{94} +(1.24986 - 2.16482i) q^{95} -15.3888 q^{97} +(6.79978 + 1.66222i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.346303	+	0.199938i	−0.154872	+	0.0894151i	−0.575433	−	0.817849i	$-0.695166\pi$
$5$	−0.346303	+	0.199938i	−0.154872	+	0.0894151i	0.420561	+	0.907264i	$0.361833\pi$
$6$		0			0
$7$	1.03937	+	2.43304i	0.392845	+	0.919605i
$7$	1.03937	+	2.43304i	0.392845	+	0.919605i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.346303	+	0.199938i	0.109511	+	0.0632260i
$11$	3.01389	+	1.38437i	0.908721	+	0.417404i
$11$	3.01389	+	1.38437i	0.908721	+	0.417404i
$12$		0			0
$13$			0.164753i			0.0456944i	0.999739	+	0.0228472i	$0.00727312\pi$
$13$			0.164753i			0.0456944i	−0.999739	+	0.0228472i	$0.992727\pi$
$14$	1.58739	−	2.11664i	0.424249	−	0.565697i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.906908	−	1.57081i	0.219957	−	0.380977i	−0.734837	−	0.678243i	$-0.762742\pi$
$17$	0.906908	−	1.57081i	0.219957	−	0.380977i	0.954795	+	0.297266i	$0.0960748\pi$
$18$		0			0
$19$	−5.41372	+	3.12561i	−1.24199	+	0.717065i	−0.969499	−	0.245093i	$-0.921181\pi$
$19$	−5.41372	+	3.12561i	−1.24199	+	0.717065i	−0.272493	+	0.962158i	$0.587848\pi$
$20$		−	0.399877i		−	0.0894151i
$21$		0			0
$22$	−0.308042	−	3.30229i	−0.0656748	−	0.704050i
$23$	3.76546	−	2.17399i	0.785153	−	0.453309i	−0.0531002	−	0.998589i	$-0.516910\pi$
$23$	3.76546	−	2.17399i	0.785153	−	0.453309i	0.838254	+	0.545281i	$0.183577\pi$
$24$		0			0
$25$	−2.42005	+	4.19165i	−0.484010	+	0.838330i
$26$	0.142681	−	0.0823767i	0.0279820	−	0.0161554i
$27$		0			0
$28$	−2.62676	−	0.316401i	−0.496412	−	0.0597941i
$29$	−4.12269			−0.765565			−0.382782	−	0.923839i	$-0.625034\pi$
$29$	−4.12269			−0.765565			−0.382782	+	0.923839i	$0.625034\pi$
$30$		0			0
$31$	−0.141785	+	0.245579i	−0.0254653	+	0.0441072i	−0.878477	−	0.477784i	$-0.841440\pi$
$31$	−0.141785	+	0.245579i	−0.0254653	+	0.0441072i	0.853012	+	0.521891i	$0.174773\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.81382			−0.311067
$35$	−0.846396	−	0.634761i	−0.143067	−	0.107294i
$36$		0			0
$37$	2.40479	+	4.16521i	0.395344	+	0.684756i	0.993145	−	0.116888i	$-0.0372919\pi$
$37$	2.40479	+	4.16521i	0.395344	+	0.684756i	−0.597801	+	0.801645i	$0.703959\pi$
$38$	5.41372	+	3.12561i	0.878221	+	0.507041i
$39$		0			0
$40$	−0.346303	+	0.199938i	−0.0547554	+	0.0316130i
$41$	−9.23554			−1.44235			−0.721175	−	0.692753i	$-0.756398\pi$
$41$	−9.23554			−1.44235			−0.721175	+	0.692753i	$0.756398\pi$
$42$		0			0
$43$			2.07944i			0.317112i	0.987350	+	0.158556i	$0.0506839\pi$
$43$			2.07944i			0.317112i	−0.987350	+	0.158556i	$0.949316\pi$
$44$	−2.70584	+	1.91792i	−0.407921	+	0.289137i
$45$		0			0
$46$	−3.76546	−	2.17399i	−0.555187	−	0.320538i
$47$	0.367808	−	0.212354i	0.0536503	−	0.0309750i	−0.472935	−	0.881097i	$-0.656805\pi$
$47$	0.367808	−	0.212354i	0.0536503	−	0.0309750i	0.526585	+	0.850122i	$0.323472\pi$
$48$		0			0
$49$	−4.83941	+	5.05767i	−0.691345	+	0.722525i
$50$	4.84010			0.684493
$51$		0			0
$52$	−0.142681	−	0.0823767i	−0.0197862	−	0.0114236i
$53$	7.71343	+	4.45335i	1.05952	+	0.611714i	0.925300	−	0.379237i	$-0.123813\pi$
$53$	7.71343	+	4.45335i	1.05952	+	0.611714i	0.134221	+	0.990951i	$0.457147\pi$
$54$		0			0
$55$	−1.32051	+	0.123179i	−0.178057	+	0.0166094i
$56$	1.03937	+	2.43304i	0.138892	+	0.325129i
$57$		0			0
$58$	2.06135	+	3.57036i	0.270668	+	0.468811i
$59$	6.92731	+	3.99948i	0.901858	+	0.520688i	0.877803	−	0.479022i	$-0.159009\pi$
$59$	6.92731	+	3.99948i	0.901858	+	0.520688i	0.0240557	+	0.999711i	$0.492342\pi$
$60$		0			0
$61$	−6.10939	+	3.52726i	−0.782227	+	0.451619i	−0.837219	−	0.546868i	$-0.815820\pi$
$61$	−6.10939	+	3.52726i	−0.782227	+	0.451619i	0.0549920	+	0.998487i	$0.482487\pi$
$62$	0.283570			0.0360134
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.0329405	−	0.0570546i	−0.00408577	−	0.00707676i
$66$		0			0
$67$	0.0327874	−	0.0567894i	0.00400562	−	0.00693793i	−0.864016	−	0.503465i	$-0.832058\pi$
$67$	0.0327874	−	0.0567894i	0.00400562	−	0.00693793i	0.868021	+	0.496527i	$0.165392\pi$
$68$	0.906908	+	1.57081i	0.109979	+	0.190489i
$69$		0			0
$70$	−0.126521	+	1.05038i	−0.0151222	+	0.125545i
$71$			6.43763i			0.764006i	0.924161	+	0.382003i	$0.124766\pi$
$71$			6.43763i			0.764006i	−0.924161	+	0.382003i	$0.875234\pi$
$72$		0			0
$73$	7.21457	+	4.16533i	0.844402	+	0.487515i	0.858758	−	0.512381i	$-0.171237\pi$
$73$	7.21457	+	4.16533i	0.844402	+	0.487515i	−0.0143564	+	0.999897i	$0.504570\pi$
$74$	2.40479	−	4.16521i	0.279551	−	0.484196i
$75$		0			0
$76$		−	6.25122i		−	0.717065i
$77$	−0.235692	+	8.77180i	−0.0268596	+	0.999639i
$78$		0			0
$79$	0.531141	−	0.306654i	0.0597580	−	0.0345013i	−0.469823	−	0.882760i	$-0.655682\pi$
$79$	0.531141	−	0.306654i	0.0597580	−	0.0345013i	0.529581	+	0.848259i	$0.322349\pi$
$80$	0.346303	+	0.199938i	0.0387179	+	0.0223538i
$81$		0			0
$82$	4.61777	+	7.99822i	0.509948	+	0.883255i
$83$	1.91649			0.210362			0.105181	−	0.994453i	$-0.466458\pi$
$83$	1.91649			0.210362			0.105181	+	0.994453i	$0.466458\pi$
$84$		0			0
$85$			0.725302i			0.0786701i
$86$	1.80085	−	1.03972i	0.194191	−	0.112116i
$87$		0			0
$88$	3.01389	+	1.38437i	0.321281	+	0.147575i
$89$	8.89851	−	5.13756i	0.943241	−	0.544580i	0.0522659	−	0.998633i	$-0.483356\pi$
$89$	8.89851	−	5.13756i	0.943241	−	0.544580i	0.890975	+	0.454053i	$0.150022\pi$
$90$		0			0
$91$	−0.400852	+	0.171240i	−0.0420207	+	0.0179508i
$92$			4.34798i			0.453309i
$93$		0			0
$94$	−0.367808	−	0.212354i	−0.0379365	−	0.0219027i
$95$	1.24986	−	2.16482i	0.128233	−	0.222106i
$96$		0			0
$97$	−15.3888			−1.56249			−0.781246	−	0.624223i	$-0.785416\pi$
$97$	−15.3888			−1.56249			−0.781246	+	0.624223i	$0.785416\pi$
$98$	6.79978	+	1.66222i	0.686882	+	0.167909i
$99$		0			0
$100$	−2.42005	−	4.19165i	−0.242005	−	0.419165i
$101$	−1.20313	+	2.08388i	−0.119716	+	0.207354i	−0.919655	−	0.392727i	$-0.871532\pi$
$101$	−1.20313	+	2.08388i	−0.119716	+	0.207354i	0.799939	+	0.600081i	$0.204865\pi$
$102$		0			0
$103$	2.10989	+	3.65443i	0.207893	+	0.360082i	0.951051	−	0.309035i	$-0.100006\pi$
$103$	2.10989	+	3.65443i	0.207893	+	0.360082i	−0.743157	+	0.669117i	$0.766673\pi$
$104$			0.164753i			0.0161554i
$105$		0			0
$106$		−	8.90670i		−	0.865095i
$107$	−6.05913	−	10.4947i	−0.585758	−	1.01456i	−0.994780	−	0.102039i	$-0.967463\pi$
$107$	−6.05913	−	10.4947i	−0.585758	−	1.01456i	0.409022	−	0.912524i	$-0.365870\pi$
$108$		0			0
$109$	14.5861	+	8.42128i	1.39709	+	0.806613i	0.994087	−	0.108584i	$-0.0346317\pi$
$109$	14.5861	+	8.42128i	1.39709	+	0.806613i	0.403007	+	0.915197i	$0.367965\pi$
$110$	0.766930	+	1.08200i	0.0731239	+	0.103165i
$111$		0			0
$112$	1.58739	−	2.11664i	0.149995	−	0.200004i
$113$			3.04275i			0.286238i	0.989705	+	0.143119i	$0.0457131\pi$
$113$			3.04275i			0.286238i	−0.989705	+	0.143119i	$0.954287\pi$
$114$		0			0
$115$	−0.869328	+	1.50572i	−0.0810653	+	0.140409i
$116$	2.06135	−	3.57036i	0.191391	−	0.331499i
$117$		0			0
$118$		−	7.99896i		−	0.736364i
$119$	4.76446	+	0.573892i	0.436758	+	0.0526086i
$120$		0			0
$121$	7.16703	+	8.34468i	0.651548	+	0.758607i
$122$	6.10939	+	3.52726i	0.553118	+	0.319343i
$123$		0			0
$124$	−0.141785	−	0.245579i	−0.0127327	−	0.0220536i
$125$		−	3.93482i		−	0.351941i
$126$		0			0
$127$			10.8250i			0.960561i	0.877115	+	0.480281i	$0.159465\pi$
$127$			10.8250i			0.960561i	−0.877115	+	0.480281i	$0.840535\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.0329405	+	0.0570546i	−0.00288907	+	0.00500402i
$131$	7.68882	+	13.3174i	0.671775	+	1.16355i	0.977400	+	0.211396i	$0.0678011\pi$
$131$	7.68882	+	13.3174i	0.671775	+	1.16355i	−0.305625	+	0.952152i	$0.598866\pi$
$132$		0			0
$133$	−13.2316	−	9.92315i	−1.14733	−	0.860446i
$134$	−0.0655748			−0.00566480
$135$		0			0
$136$	0.906908	−	1.57081i	0.0777667	−	0.134696i
$137$	−14.9235	−	8.61608i	−1.27500	−	0.736121i	−0.299075	−	0.954230i	$-0.596678\pi$
$137$	−14.9235	−	8.61608i	−1.27500	−	0.736121i	−0.975924	+	0.218109i	$0.930011\pi$
$138$		0			0
$139$		−	7.87238i		−	0.667726i	−0.942622	−	0.333863i	$-0.891648\pi$
$139$		−	7.87238i		−	0.667726i	0.942622	−	0.333863i	$-0.108352\pi$
$140$	0.972918	−	0.415620i	0.0822265	−	0.0351263i
$141$		0			0
$142$	5.57515	−	3.21881i	0.467856	−	0.270117i
$143$	−0.228080	+	0.496548i	−0.0190730	+	0.0415234i
$144$		0			0
$145$	1.42770	−	0.824284i	0.118564	−	0.0684531i
$146$		−	8.33067i		−	0.689451i
$147$		0			0
$148$	−4.80957			−0.395344
$149$	0.346336	+	0.599872i	0.0283730	+	0.0491435i	0.879863	−	0.475227i	$-0.157634\pi$
$149$	0.346336	+	0.599872i	0.0283730	+	0.0491435i	−0.851490	+	0.524370i	$0.824301\pi$
$150$		0			0
$151$	−7.27714	−	4.20146i	−0.592205	−	0.341910i	0.173764	−	0.984787i	$-0.444407\pi$
$151$	−7.27714	−	4.20146i	−0.592205	−	0.341910i	−0.765969	+	0.642877i	$0.777740\pi$
$152$	−5.41372	+	3.12561i	−0.439111	+	0.253521i
$153$		0			0
$154$	7.71445	−	4.18178i	0.621648	−	0.336978i
$155$		−	0.113393i		−	0.00910794i
$156$		0			0
$157$	1.21224	−	2.09967i	0.0967477	−	0.167572i	−0.813589	−	0.581440i	$-0.802489\pi$
$157$	1.21224	−	2.09967i	0.0967477	−	0.167572i	0.910337	+	0.413869i	$0.135823\pi$
$158$	−0.531141	−	0.306654i	−0.0422553	−	0.0243961i
$159$		0			0
$160$		−	0.399877i		−	0.0316130i
$161$	9.20313	+	6.90196i	0.725308	+	0.543950i
$162$		0			0
$163$	5.60153	+	9.70213i	0.438746	+	0.759930i	0.997593	−	0.0693409i	$-0.0220896\pi$
$163$	5.60153	+	9.70213i	0.438746	+	0.759930i	−0.558848	+	0.829270i	$0.688756\pi$
$164$	4.61777	−	7.99822i	0.360587	−	0.624556i
$165$		0			0
$166$	−0.958245	−	1.65973i	−0.0743742	−	0.128820i
$167$	−17.7532			−1.37378			−0.686892	−	0.726760i	$-0.741025\pi$
$167$	−17.7532			−1.37378			−0.686892	+	0.726760i	$0.741025\pi$
$168$		0			0
$169$	12.9729			0.997912
$170$	0.628130	−	0.362651i	0.0481754	−	0.0278141i
$171$		0			0
$172$	−1.80085	−	1.03972i	−0.137314	−	0.0792781i
$173$	7.75760	+	13.4366i	0.589799	+	1.02156i	0.994258	+	0.107006i	$0.0341265\pi$
$173$	7.75760	+	13.4366i	0.589799	+	1.02156i	−0.404459	+	0.914556i	$0.632540\pi$
$174$		0			0
$175$	−12.7138	−	1.53141i	−0.961073	−	0.115764i
$176$	−0.308042	−	3.30229i	−0.0232195	−	0.248919i
$177$		0			0
$178$	−8.89851	−	5.13756i	−0.666972	−	0.385076i
$179$	1.11782	+	0.645375i	0.0835500	+	0.0482376i	0.541193	−	0.840898i	$-0.317973\pi$
$179$	1.11782	+	0.645375i	0.0835500	+	0.0482376i	−0.457643	+	0.889136i	$0.651306\pi$
$180$		0			0
$181$	20.0823			1.49271			0.746354	−	0.665549i	$-0.231803\pi$
$181$	20.0823			1.49271			0.746354	+	0.665549i	$0.231803\pi$
$182$	0.348724	+	0.261528i	0.0258492	+	0.0193858i
$183$		0			0
$184$	3.76546	−	2.17399i	0.277594	−	0.160269i
$185$	−1.66557	−	0.961617i	−0.122455	−	0.0706995i
$186$		0			0
$187$	4.90790	−	3.47875i	0.358901	−	0.254391i
$188$			0.424708i			0.0309750i
$189$		0			0
$190$	−2.49972			−0.181349
$191$	−12.4810	+	7.20591i	−0.903094	+	0.521402i	−0.878203	−	0.478289i	$-0.841257\pi$
$191$	−12.4810	+	7.20591i	−0.903094	+	0.521402i	−0.0248912	+	0.999690i	$0.507924\pi$
$192$		0			0
$193$	15.7143	+	9.07265i	1.13114	+	0.653064i	0.944221	−	0.329312i	$-0.106817\pi$
$193$	15.7143	+	9.07265i	1.13114	+	0.653064i	0.186918	+	0.982376i	$0.440150\pi$
$194$	7.69438	+	13.3271i	0.552424	+	0.956827i
$195$		0			0
$196$	−1.96037	−	6.71989i	−0.140026	−	0.479992i
$197$	−3.45410			−0.246095			−0.123047	−	0.992401i	$-0.539267\pi$
$197$	−3.45410			−0.246095			−0.123047	+	0.992401i	$0.539267\pi$
$198$		0			0
$199$	12.7513	−	22.0860i	0.903918	−	1.56563i	0.0815547	−	0.996669i	$-0.474011\pi$
$199$	12.7513	−	22.0860i	0.903918	−	1.56563i	0.822363	−	0.568963i	$-0.192655\pi$
$200$	−2.42005	+	4.19165i	−0.171123	+	0.296394i
$201$		0			0
$202$	2.40626			0.169304
$203$	−4.28501	−	10.0307i	−0.300749	−	0.704017i
$204$		0			0
$205$	3.19830	−	1.84654i	0.223379	−	0.128968i
$206$	2.10989	−	3.65443i	0.147003	−	0.254616i
$207$		0			0
$208$	0.142681	−	0.0823767i	0.00989312	−	0.00571180i
$209$	−20.6433	+	1.92564i	−1.42793	+	0.133199i
$210$		0			0
$211$		−	4.16072i		−	0.286436i	−0.989691	−	0.143218i	$-0.954255\pi$
$211$		−	4.16072i		−	0.286436i	0.989691	−	0.143218i	$-0.0457450\pi$
$212$	−7.71343	+	4.45335i	−0.529760	+	0.305857i
$213$		0			0
$214$	−6.05913	+	10.4947i	−0.414194	+	0.717404i
$215$	−0.415761	−	0.720119i	−0.0283546	−	0.0491117i
$216$		0			0
$217$	−0.744871	−	0.0897216i	−0.0505651	−	0.00609070i
$218$		−	16.8426i		−	1.14072i
$219$		0			0
$220$	0.553578	−	1.20518i	0.0373222	−	0.0812534i
$221$	0.258796	+	0.149416i	0.0174085	+	0.0100508i
$222$		0			0
$223$	−10.8608			−0.727292			−0.363646	−	0.931537i	$-0.618468\pi$
$223$	−10.8608			−0.727292			−0.363646	+	0.931537i	$0.618468\pi$
$224$	−2.62676	−	0.316401i	−0.175508	−	0.0211404i
$225$		0			0
$226$	2.63510	−	1.52138i	0.175284	−	0.101200i
$227$	6.56574	−	11.3722i	0.435783	−	0.754799i	−0.561576	−	0.827425i	$-0.689805\pi$
$227$	6.56574	−	11.3722i	0.435783	−	0.754799i	0.997359	+	0.0726263i	$0.0231380\pi$
$228$		0			0
$229$	−12.7878	−	22.1491i	−0.845040	−	1.46365i	−0.885586	−	0.464475i	$-0.846243\pi$
$229$	−12.7878	−	22.1491i	−0.845040	−	1.46365i	0.0405465	−	0.999178i	$-0.487090\pi$
$230$	1.73866			0.114644
$231$		0			0
$232$	−4.12269			−0.270668
$233$	−5.30687	−	9.19177i	−0.347664	−	0.602173i	0.638170	−	0.769896i	$-0.279692\pi$
$233$	−5.30687	−	9.19177i	−0.347664	−	0.602173i	−0.985834	+	0.167723i	$0.946359\pi$
$234$		0			0
$235$	−0.0849155	+	0.147078i	−0.00553927	+	0.00959430i
$236$	−6.92731	+	3.99948i	−0.450929	+	0.260344i
$237$		0			0
$238$	−1.88523	−	4.41309i	−0.122201	−	0.286058i
$239$	−6.19484			−0.400711			−0.200355	−	0.979723i	$-0.564210\pi$
$239$	−6.19484			−0.400711			−0.200355	+	0.979723i	$0.564210\pi$
$240$		0			0
$241$	8.85163	+	5.11049i	0.570183	+	0.329196i	0.757223	−	0.653157i	$-0.226556\pi$
$241$	8.85163	+	5.11049i	0.570183	+	0.329196i	−0.187039	+	0.982352i	$0.559889\pi$
$242$	3.64319	−	10.3792i	0.234193	−	0.667198i
$243$		0			0
$244$		−	7.05451i		−	0.451619i
$245$	0.664683	−	2.71907i	0.0424650	−	0.173715i
$246$		0			0
$247$	−0.514955	−	0.891928i	−0.0327658	−	0.0567520i
$248$	−0.141785	+	0.245579i	−0.00900335	+	0.0155943i
$249$		0			0
$250$	−3.40766	+	1.96741i	−0.215519	+	0.124430i
$251$		−	12.9208i		−	0.815556i	−0.913081	−	0.407778i	$-0.866304\pi$
$251$		−	12.9208i		−	0.815556i	0.913081	−	0.407778i	$-0.133696\pi$
$252$		0			0
$253$	14.3583	−	1.33936i	0.902698	−	0.0842049i
$254$	9.37471	−	5.41249i	0.588221	−	0.339610i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−23.0048	+	13.2818i	−1.43500	+	0.828498i	−0.997496	−	0.0707192i	$-0.977471\pi$
$257$	−23.0048	+	13.2818i	−1.43500	+	0.828498i	−0.437504	+	0.899217i	$0.644137\pi$
$258$		0			0
$259$	−7.63468	+	10.1802i	−0.474396	+	0.632564i
$260$	0.0658810			0.00408577
$261$		0			0
$262$	7.68882	−	13.3174i	0.475017	−	0.822753i
$263$	8.38615	−	14.5252i	0.517112	−	0.895664i	−0.482690	−	0.875791i	$-0.660340\pi$
$263$	8.38615	−	14.5252i	0.517112	−	0.895664i	0.999803	−	0.0198733i	$-0.00632629\pi$
$264$		0			0
$265$	−3.56158			−0.218786
$266$	−1.97789	+	16.4205i	−0.121272	+	1.00680i
$267$		0			0
$268$	0.0327874	+	0.0567894i	0.00200281	+	0.00346897i
$269$	−0.0333496	−	0.0192544i	−0.00203336	−	0.00117396i	0.498983	−	0.866612i	$-0.333707\pi$
$269$	−0.0333496	−	0.0192544i	−0.00203336	−	0.00117396i	−0.501016	+	0.865438i	$0.667040\pi$
$270$		0			0
$271$	−10.9630	+	6.32950i	−0.665956	+	0.384490i	−0.794543	−	0.607208i	$-0.792289\pi$
$271$	−10.9630	+	6.32950i	−0.665956	+	0.384490i	0.128587	+	0.991698i	$0.458956\pi$
$272$	−1.81382			−0.109979
$273$		0			0
$274$			17.2322i			1.04103i
$275$	−13.0966	+	9.28291i	−0.789752	+	0.559780i
$276$		0			0
$277$	15.7022	+	9.06569i	0.943456	+	0.544705i	0.891042	−	0.453921i	$-0.149975\pi$
$277$	15.7022	+	9.06569i	0.943456	+	0.544705i	0.0524139	+	0.998625i	$0.483308\pi$
$278$	−6.81768	+	3.93619i	−0.408897	+	0.236077i
$279$		0			0
$280$	−0.846396	−	0.634761i	−0.0505819	−	0.0379342i
$281$	29.7454			1.77446			0.887231	−	0.461326i	$-0.152626\pi$
$281$	29.7454			1.77446			0.887231	+	0.461326i	$0.152626\pi$
$282$		0			0
$283$	4.03054	+	2.32703i	0.239591	+	0.138328i	0.614989	−	0.788536i	$-0.289161\pi$
$283$	4.03054	+	2.32703i	0.239591	+	0.138328i	−0.375398	+	0.926864i	$0.622494\pi$
$284$	−5.57515	−	3.21881i	−0.330824	−	0.191001i
$285$		0			0
$286$	0.544063	−	0.0507510i	0.0321711	−	0.00300097i
$287$	−9.59916	−	22.4705i	−0.566620	−	1.32639i
$288$		0			0
$289$	6.85504	+	11.8733i	0.403238	+	0.698428i
$290$	−1.42770	−	0.824284i	−0.0838375	−	0.0484036i
$291$		0			0
$292$	−7.21457	+	4.16533i	−0.422201	+	0.243758i
$293$	−18.1852			−1.06239			−0.531197	−	0.847249i	$-0.678257\pi$
$293$	−18.1852			−1.06239			−0.531197	+	0.847249i	$0.678257\pi$
$294$		0			0
$295$	−3.19860			−0.186230
$296$	2.40479	+	4.16521i	0.139775	+	0.242098i
$297$		0			0
$298$	0.346336	−	0.599872i	0.0200627	−	0.0347497i
$299$	0.358172	+	0.620373i	0.0207136	+	0.0358771i
$300$		0			0
$301$	−5.05938	+	2.16132i	−0.291618	+	0.124576i
$302$			8.40292i			0.483534i
$303$		0			0
$304$	5.41372	+	3.12561i	0.310498	+	0.179266i
$305$	1.41047	−	2.44300i	0.0807631	−	0.139886i
$306$		0			0
$307$		−	11.6702i		−	0.666051i	−0.942918	−	0.333025i	$-0.891931\pi$
$307$		−	11.6702i		−	0.666051i	0.942918	−	0.333025i	$-0.108069\pi$
$308$	−7.47875	−	4.59001i	−0.426142	−	0.261540i
$309$		0			0
$310$	−0.0982011	+	0.0566965i	−0.00557745	+	0.00322014i
$311$	−21.3421	−	12.3218i	−1.21020	−	0.698708i	−0.247395	−	0.968915i	$-0.579575\pi$
$311$	−21.3421	−	12.3218i	−1.21020	−	0.698708i	−0.962802	+	0.270207i	$0.912908\pi$
$312$		0			0
$313$	0.450517	+	0.780318i	0.0254647	+	0.0441062i	0.878477	−	0.477785i	$-0.158560\pi$
$313$	0.450517	+	0.780318i	0.0254647	+	0.0441062i	−0.853012	+	0.521891i	$0.825227\pi$
$314$	−2.42449			−0.136822
$315$		0			0
$316$			0.613309i			0.0345013i
$317$	−4.22112	+	2.43707i	−0.237082	+	0.136879i	−0.613835	−	0.789435i	$-0.710374\pi$
$317$	−4.22112	+	2.43707i	−0.237082	+	0.136879i	0.376753	+	0.926314i	$0.377041\pi$
$318$		0			0
$319$	−12.4253	−	5.70734i	−0.695685	−	0.319550i
$320$	−0.346303	+	0.199938i	−0.0193589	+	0.0111769i
$321$		0			0
$322$	1.37570	−	11.4211i	0.0766650	−	0.636474i
$323$			11.3386i			0.630895i
$324$		0			0
$325$	−0.690588	−	0.398711i	−0.0383069	−	0.0221165i
$326$	5.60153	−	9.70213i	0.310240	−	0.537351i
$327$		0			0
$328$	−9.23554			−0.509948
$329$	0.898956	+	0.674179i	0.0495611	+	0.0371687i
$330$		0			0
$331$	−16.9428	−	29.3457i	−0.931259	−	1.61299i	−0.781173	−	0.624314i	$-0.785379\pi$
$331$	−16.9428	−	29.3457i	−0.931259	−	1.61299i	−0.150085	−	0.988673i	$-0.547955\pi$
$332$	−0.958245	+	1.65973i	−0.0525905	+	0.0910894i
$333$		0			0
$334$	8.87660	+	15.3747i	0.485706	+	0.841267i
$335$			0.0262218i			0.00143265i
$336$		0			0
$337$			25.0659i			1.36542i	0.730687	+	0.682712i	$0.239200\pi$
$337$			25.0659i			1.36542i	−0.730687	+	0.682712i	$0.760800\pi$
$338$	−6.48643	−	11.2348i	−0.352815	−	0.611094i
$339$		0			0
$340$	−0.628130	−	0.362651i	−0.0340651	−	0.0196675i
$341$	−0.767296	+	0.543863i	−0.0415514	+	0.0294518i
$342$		0			0
$343$	−17.3355	−	6.51771i	−0.936029	−	0.351923i
$344$			2.07944i			0.112116i
$345$		0			0
$346$	7.75760	−	13.4366i	0.417051	−	0.722354i
$347$	11.0467	−	19.1335i	0.593021	−	1.02714i	−0.400802	−	0.916165i	$-0.631269\pi$
$347$	11.0467	−	19.1335i	0.593021	−	1.02714i	0.993823	−	0.110977i	$-0.0353981\pi$
$348$		0			0
$349$		−	12.3244i		−	0.659709i	−0.944032	−	0.329854i	$-0.893000\pi$
$349$		−	12.3244i		−	0.659709i	0.944032	−	0.329854i	$-0.107000\pi$
$350$	5.03066	+	11.7762i	0.268900	+	0.629463i
$351$		0			0
$352$	−2.70584	+	1.91792i	−0.144222	+	0.102225i
$353$	10.9072	+	6.29726i	0.580531	+	0.335169i	0.761344	−	0.648348i	$-0.224540\pi$
$353$	10.9072	+	6.29726i	0.580531	+	0.335169i	−0.180814	+	0.983517i	$0.557873\pi$
$354$		0			0
$355$	−1.28713	−	2.22937i	−0.0683136	−	0.118323i
$356$			10.2751i			0.544580i
$357$		0			0
$358$		−	1.29075i		−	0.0682183i
$359$	−13.0266	−	22.5628i	−0.687520	−	1.19082i	−0.972638	−	0.232327i	$-0.925366\pi$
$359$	−13.0266	−	22.5628i	−0.687520	−	1.19082i	0.285118	−	0.958493i	$-0.407967\pi$
$360$		0			0
$361$	10.0389	−	17.3879i	0.528363	−	0.915152i
$362$	−10.0412	−	17.3918i	−0.527752	−	0.914093i
$363$		0			0
$364$	0.0521281	−	0.432768i	0.00273225	−	0.0226832i
$365$	−3.33124			−0.174365
$366$		0			0
$367$	−7.79109	+	13.4946i	−0.406692	+	0.704411i	−0.994517	−	0.104577i	$-0.966651\pi$
$367$	−7.79109	+	13.4946i	−0.406692	+	0.704411i	0.587825	+	0.808988i	$0.299984\pi$
$368$	−3.76546	−	2.17399i	−0.196288	−	0.113327i
$369$		0			0
$370$			1.92323i			0.0999842i
$371$	−2.81808	+	23.3958i	−0.146308	+	1.21465i
$372$		0			0
$373$	−10.9916	+	6.34599i	−0.569123	+	0.328583i	−0.756799	−	0.653648i	$-0.773238\pi$
$373$	−10.9916	+	6.34599i	−0.569123	+	0.328583i	0.187676	+	0.982231i	$0.439904\pi$
$374$	−5.46663	−	2.51099i	−0.282673	−	0.129840i
$375$		0			0
$376$	0.367808	−	0.212354i	0.0189683	−	0.0109513i
$377$		−	0.679227i		−	0.0349820i
$378$		0			0
$379$	22.9946			1.18115			0.590577	−	0.806981i	$-0.298900\pi$
$379$	22.9946			1.18115			0.590577	+	0.806981i	$0.298900\pi$
$380$	1.24986	+	2.16482i	0.0641164	+	0.111053i
$381$		0			0
$382$	12.4810	+	7.20591i	0.638584	+	0.368687i
$383$	21.6145	−	12.4791i	1.10445	−	0.637653i	0.167062	−	0.985946i	$-0.446572\pi$
$383$	21.6145	−	12.4791i	1.10445	−	0.637653i	0.937386	+	0.348293i	$0.113239\pi$
$384$		0			0
$385$	−1.67220	−	3.08483i	−0.0852231	−	0.157217i
$386$		−	18.1453i		−	0.923571i
$387$		0			0
$388$	7.69438	−	13.3271i	0.390623	−	0.676579i
$389$	−15.6436	−	9.03184i	−0.793162	−	0.457932i	0.0479125	−	0.998852i	$-0.484743\pi$
$389$	−15.6436	−	9.03184i	−0.793162	−	0.457932i	−0.841075	+	0.540919i	$0.818076\pi$
$390$		0			0
$391$		−	7.88644i		−	0.398834i
$392$	−4.83941	+	5.05767i	−0.244427	+	0.255451i
$393$		0			0
$394$	1.72705	+	2.99134i	0.0870075	+	0.150701i
$395$	−0.122624	+	0.212391i	−0.00616988	+	0.0106865i
$396$		0			0
$397$	−15.5641	−	26.9578i	−0.781138	−	1.35297i	−0.931279	−	0.364306i	$-0.881306\pi$
$397$	−15.5641	−	26.9578i	−0.781138	−	1.35297i	0.150141	−	0.988665i	$-0.452027\pi$
$398$	−25.5027			−1.27833
$399$		0			0
$400$	4.84010			0.242005
$401$	−10.9072	+	6.29726i	−0.544678	+	0.314470i	−0.746973	−	0.664854i	$-0.768494\pi$
$401$	−10.9072	+	6.29726i	−0.544678	+	0.314470i	0.202294	+	0.979325i	$0.435160\pi$
$402$		0			0
$403$	−0.0404599	−	0.0233595i	−0.00201545	−	0.00116362i
$404$	−1.20313	−	2.08388i	−0.0598580	−	0.103677i
$405$		0			0
$406$	−6.54433	+	8.72627i	−0.324790	+	0.433078i
$407$	1.48155	+	15.8826i	0.0734377	+	0.787271i
$408$		0			0
$409$	4.95999	+	2.86365i	0.245256	+	0.141598i	0.617590	−	0.786500i	$-0.288109\pi$
$409$	4.95999	+	2.86365i	0.245256	+	0.141598i	−0.372334	+	0.928099i	$0.621443\pi$
$410$	−3.19830	−	1.84654i	−0.157953	−	0.0911941i
$411$		0			0
$412$	−4.21977			−0.207893
$413$	−2.53088	+	21.0114i	−0.124536	+	1.03390i
$414$		0			0
$415$	−0.663687	+	0.383180i	−0.0325791	+	0.0188095i
$416$	−0.142681	−	0.0823767i	−0.00699549	−	0.00403885i
$417$		0			0
$418$	11.9893	+	16.9148i	0.586417	+	0.827332i
$419$		−	16.5405i		−	0.808055i	−0.914747	−	0.404027i	$-0.867610\pi$
$419$		−	16.5405i		−	0.808055i	0.914747	−	0.404027i	$-0.132390\pi$
$420$		0			0
$421$	−9.41277			−0.458751			−0.229375	−	0.973338i	$-0.573668\pi$
$421$	−9.41277			−0.458751			−0.229375	+	0.973338i	$0.573668\pi$
$422$	−3.60329	+	2.08036i	−0.175405	+	0.101270i
$423$		0			0
$424$	7.71343	+	4.45335i	0.374597	+	0.216274i
$425$	4.38952	+	7.60287i	0.212923	+	0.368794i
$426$		0			0
$427$	−14.9319	−	11.1983i	−0.722605	−	0.541923i
$428$	12.1183			0.585758
$429$		0			0
$430$	−0.415761	+	0.720119i	−0.0200498	+	0.0347272i
$431$	17.0304	−	29.4975i	0.820326	−	1.42085i	−0.0851140	−	0.996371i	$-0.527125\pi$
$431$	17.0304	−	29.4975i	0.820326	−	1.42085i	0.905440	−	0.424475i	$-0.139541\pi$
$432$		0			0
$433$	30.8495			1.48253			0.741266	−	0.671211i	$-0.234226\pi$
$433$	30.8495			1.48253			0.741266	+	0.671211i	$0.234226\pi$
$434$	0.294734	+	0.689938i	0.0141477	+	0.0331181i
$435$		0			0
$436$	−14.5861	+	8.42128i	−0.698547	+	0.403306i
$437$	−13.5901	+	23.5388i	−0.650103	+	1.12601i
$438$		0			0
$439$	−31.6900	+	18.2962i	−1.51248	+	0.873232i	−0.512588	+	0.858635i	$0.671313\pi$
$439$	−31.6900	+	18.2962i	−1.51248	+	0.873232i	−0.999893	+	0.0145970i	$0.995353\pi$
$440$	−1.32051	+	0.123179i	−0.0629527	+	0.00587232i
$441$		0			0
$442$		−	0.298832i		−	0.0142140i
$443$	4.85111	−	2.80079i	0.230483	−	0.133070i	−0.380312	−	0.924858i	$-0.624183\pi$
$443$	4.85111	−	2.80079i	0.230483	−	0.133070i	0.610795	+	0.791789i	$0.290850\pi$
$444$		0			0
$445$	−2.05439	+	3.55831i	−0.0973874	+	0.168680i
$446$	5.43039	+	9.40572i	0.257137	+	0.445374i
$447$		0			0
$448$	1.03937	+	2.43304i	0.0491057	+	0.114951i
$449$		−	6.07297i		−	0.286601i	−0.989679	−	0.143301i	$-0.954228\pi$
$449$		−	6.07297i		−	0.286601i	0.989679	−	0.143301i	$-0.0457716\pi$
$450$		0			0
$451$	−27.8349	−	12.7854i	−1.31069	−	0.602042i
$452$	−2.63510	−	1.52138i	−0.123945	−	0.0715595i
$453$		0			0
$454$	−13.1315			−0.616291
$455$	0.104579	−	0.139447i	0.00490274	−	0.00653736i
$456$		0			0
$457$	21.4636	−	12.3920i	1.00402	−	0.579674i	0.0945879	−	0.995517i	$-0.469847\pi$
$457$	21.4636	−	12.3920i	1.00402	−	0.579674i	0.909437	+	0.415843i	$0.136513\pi$
$458$	−12.7878	+	22.1491i	−0.597534	+	1.03496i
$459$		0			0
$460$	−0.869328	−	1.50572i	−0.0405326	−	0.0702046i
$461$	1.67869			0.0781842			0.0390921	−	0.999236i	$-0.487553\pi$
$461$	1.67869			0.0781842			0.0390921	+	0.999236i	$0.487553\pi$
$462$		0			0
$463$	−13.3190			−0.618987			−0.309494	−	0.950902i	$-0.600160\pi$
$463$	−13.3190			−0.618987			−0.309494	+	0.950902i	$0.600160\pi$
$464$	2.06135	+	3.57036i	0.0956956	+	0.165750i
$465$		0			0
$466$	−5.30687	+	9.19177i	−0.245836	+	0.425800i
$467$	−20.9573	+	12.0997i	−0.969787	+	0.559907i	−0.899171	−	0.437597i	$-0.855830\pi$
$467$	−20.9573	+	12.0997i	−0.969787	+	0.559907i	−0.0706157	+	0.997504i	$0.522496\pi$
$468$		0			0
$469$	0.172250	+	0.0207479i	0.00795374	+	0.000958049i
$470$	0.169831			0.00783372
$471$		0			0
$472$	6.92731	+	3.99948i	0.318855	+	0.184091i
$473$	−2.87873	+	6.26721i	−0.132364	+	0.288167i
$474$		0			0
$475$		−	30.2565i		−	1.38827i
$476$	−2.87924	+	3.83920i	−0.131970	+	0.175970i
$477$		0			0
$478$	3.09742	+	5.36489i	0.141673	+	0.245384i
$479$	13.3087	−	23.0514i	0.608092	−	1.05325i	−0.383462	−	0.923556i	$-0.625268\pi$
$479$	13.3087	−	23.0514i	0.608092	−	1.05325i	0.991555	−	0.129690i	$-0.0413982\pi$
$480$		0			0
$481$	−0.686233	+	0.396197i	−0.0312895	+	0.0180650i
$482$		−	10.2210i		−	0.465553i
$483$		0			0
$484$	−10.8102	+	2.03449i	−0.491374	+	0.0924767i
$485$	5.32918	−	3.07680i	0.241986	−	0.139710i
$486$		0			0
$487$	10.7456	−	18.6119i	0.486929	−	0.843387i	−0.512958	−	0.858414i	$-0.671450\pi$
$487$	10.7456	−	18.6119i	0.486929	−	0.843387i	0.999887	+	0.0150274i	$0.00478355\pi$
$488$	−6.10939	+	3.52726i	−0.276559	+	0.159671i
$489$		0			0
$490$	−2.68713	+	0.783905i	−0.121392	+	0.0354132i
$491$	27.9035			1.25927			0.629633	−	0.776893i	$-0.283205\pi$
$491$	27.9035			1.25927			0.629633	+	0.776893i	$0.283205\pi$
$492$		0			0
$493$	−3.73890	+	6.47597i	−0.168392	+	0.291663i
$494$	−0.514955	+	0.891928i	−0.0231689	+	0.0401298i
$495$		0			0
$496$	0.283570			0.0127327
$497$	−15.6630	+	6.69108i	−0.702583	+	0.300136i
$498$		0			0
$499$	18.4160	+	31.8975i	0.824415	+	1.42793i	0.902366	+	0.430971i	$0.141829\pi$
$499$	18.4160	+	31.8975i	0.824415	+	1.42793i	−0.0779511	+	0.996957i	$0.524838\pi$
$500$	3.40766	+	1.96741i	0.152395	+	0.0879854i
$501$		0			0
$502$	−11.1898	+	6.46042i	−0.499424	+	0.288342i
$503$	−7.07546			−0.315479			−0.157740	−	0.987481i	$-0.550421\pi$
$503$	−7.07546			−0.315479			−0.157740	+	0.987481i	$0.550421\pi$
$504$		0			0
$505$		−	0.962208i		−	0.0428177i
$506$	−8.33907	−	11.7650i	−0.370717	−	0.523017i
$507$		0			0
$508$	−9.37471	−	5.41249i	−0.415935	−	0.240140i
$509$	33.9365	−	19.5933i	1.50421	−	0.868456i	0.504222	−	0.863574i	$-0.331779\pi$
$509$	33.9365	−	19.5933i	1.50421	−	0.868456i	0.999988	−	0.00488238i	$-0.00155412\pi$
$510$		0			0
$511$	−2.63583	+	21.8827i	−0.116602	+	0.968034i
$512$	1.00000			0.0441942
$513$		0			0
$514$	23.0048	+	13.2818i	1.01470	+	0.585836i
$515$	−1.46132	−	0.843694i	−0.0643935	−	0.0371776i
$516$		0			0
$517$	1.40251	−	0.130828i	0.0616823	−	0.00575381i
$518$	12.6336	+	1.52175i	0.555089	+	0.0668619i
$519$		0			0
$520$	−0.0329405	−	0.0570546i	−0.00144454	−	0.00250201i
$521$	−1.11383	−	0.643068i	−0.0487976	−	0.0281733i	0.475403	−	0.879768i	$-0.342302\pi$
$521$	−1.11383	−	0.643068i	−0.0487976	−	0.0281733i	−0.524200	+	0.851595i	$0.675636\pi$
$522$		0			0
$523$	19.0077	−	10.9741i	0.831150	−	0.479865i	−0.0230963	−	0.999733i	$-0.507352\pi$
$523$	19.0077	−	10.9741i	0.831150	−	0.479865i	0.854246	+	0.519869i	$0.174019\pi$
$524$	−15.3776			−0.671775
$525$		0			0
$526$	−16.7723			−0.731307
$527$	0.257172	+	0.445434i	0.0112026	+	0.0194034i
$528$		0			0
$529$	−2.04752	+	3.54642i	−0.0890228	+	0.154192i
$530$	1.78079	+	3.08442i	0.0773526	+	0.133979i
$531$		0			0
$532$	15.2095	−	6.49734i	0.659416	−	0.281695i
$533$		−	1.52159i		−	0.0659073i
$534$		0			0
$535$	4.19659	+	2.42290i	0.181435	+	0.104751i
$536$	0.0327874	−	0.0567894i	0.00141620	−	0.00245293i
$537$		0			0
$538$			0.0385088i			0.00166023i
$539$	−21.5872	+	8.54371i	−0.929824	+	0.368003i
$540$		0			0
$541$	37.6161	−	21.7177i	1.61724	−	0.933716i	0.629615	−	0.776907i	$-0.283213\pi$
$541$	37.6161	−	21.7177i	1.61724	−	0.933716i	0.987629	−	0.156809i	$-0.0501207\pi$
$542$	10.9630	+	6.32950i	0.470902	+	0.271875i
$543$		0			0
$544$	0.906908	+	1.57081i	0.0388833	+	0.0673479i
$545$	−6.73495			−0.288493
$546$		0			0
$547$		−	15.0701i		−	0.644351i	−0.946680	−	0.322176i	$-0.895586\pi$
$547$		−	15.0701i		−	0.644351i	0.946680	−	0.322176i	$-0.104414\pi$
$548$	14.9235	−	8.61608i	0.637500	−	0.368061i
$549$		0			0
$550$	14.5875	+	6.70050i	0.622014	+	0.285710i
$551$	22.3191	−	12.8859i	0.950825	−	0.548959i
$552$		0			0
$553$	1.29816	+	0.973562i	0.0552032	+	0.0414001i
$554$		−	18.1314i		−	0.770328i
$555$		0			0
$556$	6.81768	+	3.93619i	0.289134	+	0.166932i
$557$	16.9504	−	29.3590i	0.718213	−	1.24398i	−0.243494	−	0.969902i	$-0.578294\pi$
$557$	16.9504	−	29.3590i	0.718213	−	1.24398i	0.961707	−	0.274080i	$-0.0883732\pi$
$558$		0			0
$559$	−0.342596			−0.0144902
$560$	−0.126521	+	1.05038i	−0.00534649	+	0.0443867i
$561$		0			0
$562$	−14.8727	−	25.7603i	−0.627367	−	1.08663i
$563$	7.23496	−	12.5313i	0.304917	−	0.528132i	−0.672326	−	0.740256i	$-0.734705\pi$
$563$	7.23496	−	12.5313i	0.304917	−	0.528132i	0.977243	+	0.212123i	$0.0680379\pi$
$564$		0			0
$565$	−0.608362	−	1.05371i	−0.0255940	−	0.0443301i
$566$		−	4.65407i		−	0.195625i
$567$		0			0
$568$			6.43763i			0.270117i
$569$	12.8626	+	22.2787i	0.539229	+	0.933973i	0.998946	+	0.0459069i	$0.0146178\pi$
$569$	12.8626	+	22.2787i	0.539229	+	0.933973i	−0.459716	+	0.888066i	$0.652049\pi$
$570$		0			0
$571$	12.6298	+	7.29182i	0.528541	+	0.305153i	0.740422	−	0.672142i	$-0.234626\pi$
$571$	12.6298	+	7.29182i	0.528541	+	0.305153i	−0.211881	+	0.977295i	$0.567959\pi$
$572$	−0.315983	−	0.445797i	−0.0132119	−	0.0186397i
$573$		0			0
$574$	−14.6604	+	19.5484i	−0.611915	+	0.815933i
$575$			21.0447i			0.877623i
$576$		0			0
$577$	−6.12595	+	10.6104i	−0.255026	+	0.441719i	−0.964903	−	0.262608i	$-0.915418\pi$
$577$	−6.12595	+	10.6104i	−0.255026	+	0.441719i	0.709876	+	0.704326i	$0.248751\pi$
$578$	6.85504	−	11.8733i	0.285132	−	0.493863i
$579$		0			0
$580$			1.64857i			0.0684531i
$581$	1.99194	+	4.66291i	0.0826398	+	0.193450i
$582$		0			0
$583$	17.0823	+	24.1001i	0.707477	+	0.998126i
$584$	7.21457	+	4.16533i	0.298541	+	0.172363i
$585$		0			0
$586$	9.09262	+	15.7489i	0.375613	+	0.650580i
$587$			11.4407i			0.472207i	0.971728	+	0.236104i	$0.0758705\pi$
$587$			11.4407i			0.472207i	−0.971728	+	0.236104i	$0.924129\pi$
$588$		0			0
$589$		−	1.77266i		−	0.0730411i
$590$	1.59930	+	2.77007i	0.0658421	+	0.114042i
$591$		0			0
$592$	2.40479	−	4.16521i	0.0988361	−	0.171189i
$593$	4.71698	+	8.17005i	0.193703	+	0.335504i	0.946475	−	0.322778i	$-0.104617\pi$
$593$	4.71698	+	8.17005i	0.193703	+	0.335504i	−0.752771	+	0.658282i	$0.771283\pi$
$594$		0			0
$595$	−1.76469	+	0.753858i	−0.0723453	+	0.0309052i
$596$	−0.692673			−0.0283730
$597$		0			0
$598$	0.358172	−	0.620373i	0.0146468	−	0.0253689i
$599$	29.3273	+	16.9321i	1.19828	+	0.691827i	0.960171	−	0.279411i	$-0.0901393\pi$
$599$	29.3273	+	16.9321i	1.19828	+	0.691827i	0.238108	+	0.971239i	$0.423473\pi$
$600$		0			0
$601$		−	26.4610i		−	1.07937i	−0.841868	−	0.539683i	$-0.818544\pi$
$601$		−	26.4610i		−	1.07937i	0.841868	−	0.539683i	$-0.181456\pi$
$602$	4.40145	+	3.30090i	0.179390	+	0.134534i
$603$		0			0
$604$	7.27714	−	4.20146i	0.296103	−	0.170955i
$605$	−4.15039	−	1.45683i	−0.168737	−	0.0592284i
$606$		0			0
$607$	−9.68966	+	5.59433i	−0.393291	+	0.227067i	−0.683585	−	0.729871i	$-0.739580\pi$
$607$	−9.68966	+	5.59433i	−0.393291	+	0.227067i	0.290294	+	0.956938i	$0.406247\pi$
$608$		−	6.25122i		−	0.253521i
$609$		0			0
$610$	−2.82093			−0.114216
$611$	0.0349861	+	0.0605976i	0.00141538	+	0.00245152i
$612$		0			0
$613$	1.83466	+	1.05924i	0.0741014	+	0.0427824i	0.536593	−	0.843841i	$-0.319711\pi$
$613$	1.83466	+	1.05924i	0.0741014	+	0.0427824i	−0.462492	+	0.886624i	$0.653044\pi$
$614$	−10.1066	+	5.83508i	−0.407871	+	0.235485i
$615$		0			0
$616$	−0.235692	+	8.77180i	−0.00949630	+	0.353426i
$617$			15.0359i			0.605321i	0.953098	+	0.302660i	$0.0978748\pi$
$617$			15.0359i			0.605321i	−0.953098	+	0.302660i	$0.902125\pi$
$618$		0			0
$619$	−3.78009	+	6.54731i	−0.151935	+	0.263159i	−0.931939	−	0.362616i	$-0.881884\pi$
$619$	−3.78009	+	6.54731i	−0.151935	+	0.263159i	0.780004	+	0.625775i	$0.215217\pi$
$620$	0.0982011	+	0.0566965i	0.00394385	+	0.00227698i
$621$		0			0
$622$			24.6437i			0.988122i
$623$	21.7488	+	16.3107i	0.871346	+	0.653472i
$624$		0			0
$625$	−11.3135	−	19.5956i	−0.452541	−	0.783824i
$626$	0.450517	−	0.780318i	0.0180063	−	0.0311878i
$627$		0			0
$628$	1.21224	+	2.09967i	0.0483738	+	0.0837859i
$629$	8.72367			0.347836
$630$		0			0
$631$	47.5404			1.89255			0.946276	−	0.323359i	$-0.104812\pi$
$631$	47.5404			1.89255			0.946276	+	0.323359i	$0.104812\pi$
$632$	0.531141	−	0.306654i	0.0211277	−	0.0121981i
$633$		0			0
$634$	4.22112	+	2.43707i	0.167642	+	0.0967882i
$635$	−2.16433	−	3.74872i	−0.0858887	−	0.148764i
$636$		0			0
$637$	−0.833269	−	0.797310i	−0.0330153	−	0.0315906i
$638$	1.26996	+	13.6143i	0.0502783	+	0.538996i
$639$		0			0
$640$	0.346303	+	0.199938i	0.0136888	+	0.00790325i
$641$	24.4173	+	14.0974i	0.964427	+	0.556812i	0.897533	−	0.440948i	$-0.145358\pi$
$641$	24.4173	+	14.0974i	0.964427	+	0.556812i	0.0668942	+	0.997760i	$0.478691\pi$
$642$		0			0
$643$	−0.930892			−0.0367108			−0.0183554	−	0.999832i	$-0.505843\pi$
$643$	−0.930892			−0.0367108			−0.0183554	+	0.999832i	$0.505843\pi$
$644$	−10.5788	+	4.51917i	−0.416865	+	0.178080i
$645$		0			0
$646$	9.81948	−	5.66928i	0.386342	−	0.223055i
$647$	15.9156	+	9.18888i	0.625707	+	0.361252i	0.779088	−	0.626915i	$-0.215683\pi$
$647$	15.9156	+	9.18888i	0.625707	+	0.361252i	−0.153381	+	0.988167i	$0.549016\pi$
$648$		0			0
$649$	15.3413	+	21.6440i	0.602200	+	0.849599i
$650$			0.797423i			0.0312775i
$651$		0			0
$652$	−11.2031			−0.438746
$653$	−1.93226	+	1.11559i	−0.0756150	+	0.0436564i	−0.537331	−	0.843372i	$-0.680567\pi$
$653$	−1.93226	+	1.11559i	−0.0756150	+	0.0436564i	0.461716	+	0.887028i	$0.347234\pi$
$654$		0			0
$655$	−5.32532	−	3.07458i	−0.208078	−	0.120134i
$656$	4.61777	+	7.99822i	0.180294	+	0.312278i
$657$		0			0
$658$	0.134378	−	1.11561i	0.00523860	−	0.0434910i
$659$	24.8756			0.969015			0.484508	−	0.874787i	$-0.338999\pi$
$659$	24.8756			0.969015			0.484508	+	0.874787i	$0.338999\pi$
$660$		0			0
$661$	−16.4995	+	28.5780i	−0.641756	+	1.11155i	0.343284	+	0.939232i	$0.388461\pi$
$661$	−16.4995	+	28.5780i	−0.641756	+	1.11155i	−0.985041	+	0.172323i	$0.944873\pi$
$662$	−16.9428	+	29.3457i	−0.658499	+	1.14055i
$663$		0			0
$664$	1.91649			0.0743742
$665$	6.56617	+	0.790912i	0.254625	+	0.0306703i
$666$		0			0
$667$	−15.5238	+	8.96270i	−0.601086	+	0.347037i
$668$	8.87660	−	15.3747i	0.343446	−	0.594866i
$669$		0			0
$670$	0.0227088	−	0.0131109i	0.000877316	−	0.000506519i
$671$	−23.2960	+	2.17309i	−0.899334	+	0.0838911i
$672$		0			0
$673$			1.74912i			0.0674236i	0.999432	+	0.0337118i	$0.0107328\pi$
$673$			1.74912i			0.0674236i	−0.999432	+	0.0337118i	$0.989267\pi$
$674$	21.7077	−	12.5329i	0.836148	−	0.482750i
$675$		0			0
$676$	−6.48643	+	11.2348i	−0.249478	+	0.432109i
$677$	15.5773	+	26.9808i	0.598686	+	1.03695i	0.993015	+	0.117985i	$0.0376436\pi$
$677$	15.5773	+	26.9808i	0.598686	+	1.03695i	−0.394329	+	0.918969i	$0.629023\pi$
$678$		0			0
$679$	−15.9946	−	37.4416i	−0.613818	−	1.43687i
$680$			0.725302i			0.0278141i
$681$		0			0
$682$	0.854647	+	0.392566i	0.0327261	+	0.0150321i
$683$	37.1098	+	21.4253i	1.41997	+	0.819817i	0.996295	−	0.0859990i	$-0.0274082\pi$
$683$	37.1098	+	21.4253i	1.41997	+	0.819817i	0.423670	+	0.905816i	$0.360742\pi$
$684$		0			0
$685$	6.89073			0.263281
$686$	3.02324	+	18.2718i	0.115428	+	0.697622i
$687$		0			0
$688$	1.80085	−	1.03972i	0.0686568	−	0.0396390i
$689$	−0.733704	+	1.27081i	−0.0279519	+	0.0484141i
$690$		0			0
$691$	−12.9688	−	22.4626i	−0.493356	−	0.854518i	0.506615	−	0.862173i	$-0.330897\pi$
$691$	−12.9688	−	22.4626i	−0.493356	−	0.854518i	−0.999971	+	0.00765487i	$0.997563\pi$
$692$	−15.5152			−0.589799
$693$		0			0
$694$	−22.0935			−0.838658
$695$	1.57399	+	2.72623i	0.0597048	+	0.103412i
$696$		0			0
$697$	−8.37578	+	14.5073i	−0.317255	+	0.549503i
$698$	−10.6732	+	6.16219i	−0.403987	+	0.233242i
$699$		0			0
$700$	7.68314	−	10.2448i	0.290395	−	0.387216i
$701$	0.324170			0.0122437			0.00612186	−	0.999981i	$-0.498051\pi$
$701$	0.324170			0.0122437			0.00612186	+	0.999981i	$0.498051\pi$
$702$		0			0
$703$	−26.0377	−	15.0329i	−0.982029	−	0.566975i
$704$	3.01389	+	1.38437i	0.113590	+	0.0521755i
$705$		0			0
$706$		−	12.5945i		−	0.474001i
$707$	−6.32068	−	0.761343i	−0.237714	−	0.0286332i
$708$		0			0
$709$	8.36850	+	14.4947i	0.314285	+	0.544358i	0.979285	−	0.202485i	$-0.0649018\pi$
$709$	8.36850	+	14.4947i	0.314285	+	0.544358i	−0.665000	+	0.746843i	$0.731568\pi$
$710$	−1.28713	+	2.22937i	−0.0483050	+	0.0836668i
$711$		0			0
$712$	8.89851	−	5.13756i	0.333486	−	0.192538i
$713$			1.23296i			0.0461746i
$714$		0			0
$715$	−0.0202941	−	0.217558i	−0.000758957	−	0.00813621i
$716$	−1.11782	+	0.645375i	−0.0417750	+	0.0241188i
$717$		0			0
$718$	−13.0266	+	22.5628i	−0.486150	+	0.842037i
$719$	−3.90390	+	2.25392i	−0.145591	+	0.0840570i	−0.571026	−	0.820932i	$-0.693454\pi$
$719$	−3.90390	+	2.25392i	−0.145591	+	0.0840570i	0.425435	+	0.904989i	$0.360121\pi$
$720$		0			0
$721$	−6.69843	+	8.93175i	−0.249463	+	0.332636i
$722$	−20.0778			−0.747218
$723$		0			0
$724$	−10.0412	+	17.3918i	−0.373177	+	0.646362i
$725$	9.97712	−	17.2809i	0.370541	−	0.641796i
$726$		0			0
$727$	−38.4312			−1.42534			−0.712668	−	0.701502i	$-0.752513\pi$
$727$	−38.4312			−1.42534			−0.712668	+	0.701502i	$0.752513\pi$
$728$	−0.400852	+	0.171240i	−0.0148566	+	0.00634657i
$729$		0			0
$730$	1.66562	+	2.88494i	0.0616473	+	0.106776i
$731$	3.26641	+	1.88586i	0.120813	+	0.0697512i
$732$		0			0
$733$	42.5297	−	24.5546i	1.57087	−	0.906943i	0.574809	−	0.818287i	$-0.305076\pi$
$733$	42.5297	−	24.5546i	1.57087	−	0.906943i	0.996062	−	0.0886556i	$-0.0282571\pi$
$734$	15.5822			0.575149
$735$		0			0
$736$			4.34798i			0.160269i
$737$	0.177435	−	0.125767i	0.00653591	−	0.00463269i
$738$		0			0
$739$	28.4872	+	16.4471i	1.04792	+	0.605016i	0.922066	−	0.387033i	$-0.126500\pi$
$739$	28.4872	+	16.4471i	1.04792	+	0.605016i	0.125852	+	0.992049i	$0.459833\pi$
$740$	1.66557	−	0.961617i	0.0612276	−	0.0353498i
$741$		0			0
$742$	21.6704	−	9.25736i	0.795545	−	0.339849i
$743$	0.0301484			0.00110604			0.000553019	−	1.00000i	$-0.499824\pi$
$743$	0.0301484			0.00110604			0.000553019		1.00000i	$0.499824\pi$
$744$		0			0
$745$	−0.239875	−	0.138492i	−0.00878834	−	0.00507395i
$746$	10.9916	+	6.34599i	0.402430	+	0.232343i
$747$		0			0
$748$	0.558731	+	5.98974i	0.0204292	+	0.219007i
$749$	19.2364	−	25.6501i	0.702884	−	0.937232i
$750$		0			0
$751$	−21.1744	−	36.6752i	−0.772666	−	1.33830i	−0.936097	−	0.351741i	$-0.885590\pi$
$751$	−21.1744	−	36.6752i	−0.772666	−	1.33830i	0.163432	−	0.986555i	$-0.447744\pi$
$752$	−0.367808	−	0.212354i	−0.0134126	−	0.00774376i
$753$		0			0
$754$	−0.588228	+	0.339614i	−0.0214220	+	0.0123680i
$755$	3.36013			0.122288
$756$		0			0
$757$	4.32399			0.157158			0.0785790	−	0.996908i	$-0.474962\pi$
$757$	4.32399			0.157158			0.0785790	+	0.996908i	$0.474962\pi$
$758$	−11.4973	−	19.9139i	−0.417601	−	0.723307i
$759$		0			0
$760$	1.24986	−	2.16482i	0.0453371	−	0.0785262i
$761$	0.217251	+	0.376290i	0.00787535	+	0.0136405i	0.869936	−	0.493164i	$-0.164160\pi$
$761$	0.217251	+	0.376290i	0.00787535	+	0.0136405i	−0.862061	+	0.506805i	$0.830827\pi$
$762$		0			0
$763$	−5.32900	+	44.2415i	−0.192923	+	1.60165i
$764$		−	14.4118i		−	0.521402i
$765$		0			0
$766$	−21.6145	−	12.4791i	−0.780963	−	0.450889i
$767$	−0.658928	+	1.14130i	−0.0237925	+	0.0412098i
$768$		0			0
$769$		−	33.3122i		−	1.20127i	−0.799524	−	0.600634i	$-0.794915\pi$
$769$		−	33.3122i		−	1.20127i	0.799524	−	0.600634i	$-0.205085\pi$
$770$	−1.83544	+	2.99058i	−0.0661446	+	0.107773i
$771$		0			0
$772$	−15.7143	+	9.07265i	−0.565570	+	0.326532i
$773$	−9.83462	−	5.67802i	−0.353727	−	0.204224i	0.312599	−	0.949885i	$-0.398801\pi$
$773$	−9.83462	−	5.67802i	−0.353727	−	0.204224i	−0.666325	+	0.745661i	$0.732134\pi$
$774$		0			0
$775$	−0.686253	−	1.18862i	−0.0246509	−	0.0426967i
$776$	−15.3888			−0.552424
$777$		0			0
$778$			18.0637i			0.647614i
$779$	49.9986	−	28.8667i	1.79139	−	1.03426i
$780$		0			0
$781$	−8.91207	+	19.4023i	−0.318899	+	0.694268i
$782$	−6.82985	+	3.94322i	−0.244235	+	0.141009i
$783$		0			0
$784$	6.79978	+	1.66222i	0.242849	+	0.0593650i
$785$			0.969497i			0.0346028i
$786$		0			0
$787$	−11.3772	−	6.56865i	−0.405555	−	0.234147i	0.283323	−	0.959024i	$-0.408563\pi$
$787$	−11.3772	−	6.56865i	−0.405555	−	0.234147i	−0.688878	+	0.724877i	$0.741896\pi$
$788$	1.72705	−	2.99134i	0.0615236	−	0.106562i
$789$		0			0
$790$	0.245248			0.00872553
$791$	−7.40315	+	3.16255i	−0.263226	+	0.112447i
$792$		0			0
$793$	−0.581127	−	1.00654i	−0.0206364	−	0.0357434i
$794$	−15.5641	+	26.9578i	−0.552348	+	0.956695i
$795$		0			0
$796$	12.7513	+	22.0860i	0.451959	+	0.782816i
$797$			47.2404i			1.67334i	0.547707	+	0.836670i	$0.315501\pi$
$797$			47.2404i			1.67334i	−0.547707	+	0.836670i	$0.684499\pi$
$798$		0			0
$799$		−	0.770342i		−	0.0272528i
$800$	−2.42005	−	4.19165i	−0.0855617	−	0.148197i
$801$		0			0
$802$	10.9072	+	6.29726i	0.385146	+	0.222364i
$803$	15.9775	+	22.5415i	0.563835	+	0.795472i
$804$		0			0
$805$	−4.56704	−	0.550112i	−0.160967	−	0.0193889i
$806$			0.0467191i			0.00164561i
$807$		0			0
$808$	−1.20313	+	2.08388i	−0.0423260	+	0.0733108i
$809$	−11.2285	+	19.4482i	−0.394771	+	0.683764i	−0.993072	−	0.117508i	$-0.962510\pi$
$809$	−11.2285	+	19.4482i	−0.394771	+	0.683764i	0.598301	+	0.801272i	$0.295843\pi$
$810$		0			0
$811$		−	32.4441i		−	1.13927i	−0.821899	−	0.569633i	$-0.807085\pi$
$811$		−	32.4441i		−	1.13927i	0.821899	−	0.569633i	$-0.192915\pi$
$812$	10.8293	+	1.30442i	0.380035	+	0.0457762i
$813$		0			0
$814$	13.0140	−	9.22436i	0.456139	−	0.323314i
$815$	−3.87965	−	2.23992i	−0.135898	−	0.0784610i
$816$		0			0
$817$	−6.49954	−	11.2575i	−0.227390	−	0.393851i
$818$		−	5.72730i		−	0.200250i
$819$		0			0
$820$			3.69308i			0.128968i
$821$	−10.8999	−	18.8792i	−0.380410	−	0.658890i	0.610710	−	0.791854i	$-0.290884\pi$
$821$	−10.8999	−	18.8792i	−0.380410	−	0.658890i	−0.991121	+	0.132964i	$0.957551\pi$
$822$		0			0
$823$	−0.981740	+	1.70042i	−0.0342213	+	0.0592730i	−0.882629	−	0.470071i	$-0.844228\pi$
$823$	−0.981740	+	1.70042i	−0.0342213	+	0.0592730i	0.848408	+	0.529344i	$0.177562\pi$
$824$	2.10989	+	3.65443i	0.0735013	+	0.127308i
$825$		0			0
$826$	19.4618	−	8.31389i	0.677164	−	0.289277i
$827$	1.67960			0.0584055			0.0292027	−	0.999574i	$-0.490703\pi$
$827$	1.67960			0.0584055			0.0292027	+	0.999574i	$0.490703\pi$
$828$		0			0
$829$	−17.3309	+	30.0180i	−0.601928	+	1.04257i	0.390601	+	0.920560i	$0.372267\pi$
$829$	−17.3309	+	30.0180i	−0.601928	+	1.04257i	−0.992529	+	0.122009i	$0.961066\pi$
$830$	0.663687	+	0.383180i	0.0230369	+	0.0133004i
$831$		0			0
$832$			0.164753i			0.00571180i
$833$	3.55574	+	12.1886i	0.123199	+	0.422311i
$834$		0			0
$835$	6.14799	−	3.54954i	0.212760	−	0.122837i
$836$	8.65402	−	18.8405i	0.299305	−	0.651612i
$837$		0			0
$838$	−14.3245	+	8.27023i	−0.494830	+	0.285690i
$839$			33.5627i			1.15871i	0.815074	+	0.579357i	$0.196696\pi$
$839$			33.5627i			1.15871i	−0.815074	+	0.579357i	$0.803304\pi$
$840$		0			0
$841$	−12.0034			−0.413911
$842$	4.70639	+	8.15170i	0.162193	+	0.280926i
$843$		0			0
$844$	3.60329	+	2.08036i	0.124030	+	0.0716089i
$845$	−4.49254	+	2.59377i	−0.154548	+	0.0892284i
$846$		0			0
$847$	−12.8538	+	26.1109i	−0.441661	+	0.897182i
$848$		−	8.90670i		−	0.305857i
$849$		0			0
$850$	4.38952	−	7.60287i	0.150559	−	0.260776i
$851$	18.1103	+	10.4560i	0.620812	+	0.358426i
$852$		0			0
$853$			46.9223i			1.60659i	0.595583	+	0.803294i	$0.296921\pi$
$853$			46.9223i			1.60659i	−0.595583	+	0.803294i	$0.703079\pi$
$854$	−2.23205	+	18.5305i	−0.0763792	+	0.634102i
$855$		0			0
$856$	−6.05913	−	10.4947i	−0.207097	−	0.358702i
$857$	−17.4824	+	30.2805i	−0.597189	+	1.03436i	0.396045	+	0.918231i	$0.370382\pi$
$857$	−17.4824	+	30.2805i	−0.597189	+	1.03436i	−0.993234	+	0.116131i	$0.962951\pi$
$858$		0			0
$859$	−10.3262	−	17.8856i	−0.352327	−	0.610248i	0.634330	−	0.773062i	$-0.281276\pi$
$859$	−10.3262	−	17.8856i	−0.352327	−	0.610248i	−0.986657	+	0.162815i	$0.947943\pi$
$860$	0.831521			0.0283546
$861$		0			0
$862$	−34.0608			−1.16012
$863$	0.203491	−	0.117486i	0.00692691	−	0.00399925i	−0.496533	−	0.868018i	$-0.665394\pi$
$863$	0.203491	−	0.117486i	0.00692691	−	0.00399925i	0.503459	+	0.864019i	$0.332060\pi$
$864$		0			0
$865$	−5.37296	−	3.10208i	−0.182686	−	0.105474i
$866$	−15.4247	−	26.7164i	−0.524154	−	0.907862i
$867$		0			0
$868$	0.450137	−	0.600216i	0.0152786	−	0.0203727i
$869$	2.02532	−	0.188925i	0.0687044	−	0.00640884i
$870$		0			0
$871$	0.00935625	+	0.00540183i	0.000317024	+	0.000183034i
$872$	14.5861	+	8.42128i	0.493947	+	0.285181i
$873$		0			0
$874$	27.1802			0.919384
$875$	9.57361	−	4.08974i	0.323647	−	0.138259i
$876$		0			0
$877$	−22.2696	+	12.8573i	−0.751990	+	0.434162i	−0.826413	−	0.563065i	$-0.809622\pi$
$877$	−22.2696	+	12.8573i	−0.751990	+	0.434162i	0.0744224	+	0.997227i	$0.476289\pi$
$878$	31.6900	+	18.2962i	1.06949	+	0.617468i
$879$		0			0
$880$	0.766930	+	1.08200i	0.0258532	+	0.0364743i
$881$		−	30.8712i		−	1.04008i	−0.854142	−	0.520039i	$-0.825917\pi$
$881$		−	30.8712i		−	1.04008i	0.854142	−	0.520039i	$-0.174083\pi$
$882$		0			0
$883$	18.4234			0.619998			0.309999	−	0.950737i	$-0.399671\pi$
$883$	18.4234			0.619998			0.309999	+	0.950737i	$0.399671\pi$
$884$	−0.258796	+	0.149416i	−0.00870426	+	0.00502541i
$885$		0			0
$886$	−4.85111	−	2.80079i	−0.162976	−	0.0940945i
$887$	−13.7593	−	23.8318i	−0.461993	−	0.800195i	0.537067	−	0.843539i	$-0.319532\pi$
$887$	−13.7593	−	23.8318i	−0.461993	−	0.800195i	−0.999060	+	0.0433442i	$0.986199\pi$
$888$		0			0
$889$	−26.3377	+	11.2512i	−0.883337	+	0.377352i
$890$	4.10878			0.137727
$891$		0			0
$892$	5.43039	−	9.40572i	0.181823	−	0.314927i
$893$	−1.32747	+	2.29925i	−0.0444222	+	0.0769415i
$894$		0			0
$895$	−0.516141			−0.0172527
$896$	1.58739	−	2.11664i	0.0530311	−	0.0707121i
$897$		0			0
$898$	−5.25935	+	3.03648i	−0.175507	+	0.101329i
$899$	0.584535	−	1.01245i	0.0194953	−	0.0337669i
$900$		0			0
$901$	13.9907	−	8.07755i	0.466099	−	0.269102i
$902$	2.84494	+	30.4984i	0.0947260	+	1.01549i
$903$		0			0
$904$			3.04275i			0.101200i
$905$	−6.95458	+	4.01523i	−0.231178	+	0.133471i
$906$		0			0
$907$	16.2361	−	28.1217i	0.539110	−	0.933767i	−0.459842	−	0.888001i	$-0.652094\pi$
$907$	16.2361	−	28.1217i	0.539110	−	0.933767i	0.998952	−	0.0457658i	$-0.0145728\pi$
$908$	6.56574	+	11.3722i	0.217892	+	0.377400i
$909$		0			0
$910$	−0.173054	−	0.0208448i	−0.00573668	−	0.000690998i
$911$		−	38.1349i		−	1.26347i	−0.775186	−	0.631733i	$-0.782344\pi$
$911$		−	38.1349i		−	1.26347i	0.775186	−	0.631733i	$-0.217656\pi$
$912$		0			0
$913$	5.77608	+	2.65313i	0.191160	+	0.0878059i
$914$	−21.4636	−	12.3920i	−0.709953	−	0.409891i
$915$		0			0
$916$	25.5756			0.845040
$917$	−24.4103	+	32.5490i	−0.806101	+	1.07486i
$918$		0			0
$919$	−15.1194	+	8.72919i	−0.498743	+	0.287949i	−0.728194	−	0.685371i	$-0.759640\pi$
$919$	−15.1194	+	8.72919i	−0.498743	+	0.287949i	0.229451	+	0.973320i	$0.426307\pi$
$920$	−0.869328	+	1.50572i	−0.0286609	+	0.0496421i
$921$		0			0
$922$	−0.839343	−	1.45378i	−0.0276423	−	0.0478778i
$923$	−1.06062			−0.0349107
$924$		0			0
$925$	−23.2788			−0.765402
$926$	6.65951	+	11.5346i	0.218845	+	0.379051i
$927$		0			0
$928$	2.06135	−	3.57036i	0.0676670	−	0.117203i
$929$	29.9636	−	17.2995i	0.983073	−	0.567577i	0.0798762	−	0.996805i	$-0.474547\pi$
$929$	29.9636	−	17.2995i	0.983073	−	0.567577i	0.903196	+	0.429228i	$0.141214\pi$
$930$		0			0
$931$	10.3909	−	42.5070i	0.340548	−	1.39311i
$932$	10.6137			0.347664
$933$		0			0
$934$	20.9573	+	12.0997i	0.685743	+	0.395914i
$935$	−1.00409	+	2.18598i	−0.0328372	+	0.0714891i
$936$		0			0
$937$			17.2978i			0.565095i	0.959253	+	0.282547i	$0.0911794\pi$
$937$			17.2978i			0.565095i	−0.959253	+	0.282547i	$0.908821\pi$
$938$	−0.0681566	−	0.159546i	−0.00222539	−	0.00520938i
$939$		0			0
$940$	−0.0849155	−	0.147078i	−0.00276964	−	0.00479715i
$941$	24.6790	−	42.7452i	0.804511	−	1.39345i	−0.112110	−	0.993696i	$-0.535761\pi$
$941$	24.6790	−	42.7452i	0.804511	−	1.39345i	0.916621	−	0.399758i	$-0.130906\pi$
$942$		0			0
$943$	−34.7761	+	20.0780i	−1.13247	+	0.653829i
$944$		−	7.99896i		−	0.260344i
$945$		0			0
$946$	6.86693	−	0.640557i	0.223263	−	0.0208263i
$947$	0.711757	−	0.410933i	0.0231290	−	0.0133535i	−0.488391	−	0.872625i	$-0.662416\pi$
$947$	0.711757	−	0.410933i	0.0231290	−	0.0133535i	0.511520	+	0.859271i	$0.329083\pi$
$948$		0			0
$949$	−0.686253	+	1.18862i	−0.0222767	+	0.0385844i
$950$	−26.2029	+	15.1283i	−0.850135	+	0.490826i
$951$		0			0
$952$	4.76446	+	0.573892i	0.154417	+	0.0185999i
$953$	−2.70180			−0.0875199			−0.0437600	−	0.999042i	$-0.513934\pi$
$953$	−2.70180			−0.0875199			−0.0437600	+	0.999042i	$0.513934\pi$
$954$		0			0
$955$	2.88148	−	4.99086i	0.0932424	−	0.161501i
$956$	3.09742	−	5.36489i	0.100178	−	0.173513i
$957$		0			0
$958$	−26.6175			−0.859972
$959$	5.45226	−	45.2648i	0.176063	−	1.46168i
$960$		0			0
$961$	15.4598	+	26.7771i	0.498703	+	0.863779i
$962$	0.686233	+	0.396197i	0.0221250	+	0.0127739i
$963$		0			0
$964$	−8.85163	+	5.11049i	−0.285092	+	0.164598i
$965$	−7.25588			−0.233575
$966$		0			0
$967$			20.9434i			0.673495i	0.941595	+	0.336748i	$0.109327\pi$
$967$			20.9434i			0.673495i	−0.941595	+	0.336748i	$0.890673\pi$
$968$	7.16703	+	8.34468i	0.230357	+	0.268208i
$969$		0			0
$970$	−5.32918	−	3.07680i	−0.171110	−	0.0987902i
$971$	19.9590	−	11.5233i	0.640514	−	0.369801i	−0.144299	−	0.989534i	$-0.546093\pi$
$971$	19.9590	−	11.5233i	0.640514	−	0.369801i	0.784812	+	0.619733i	$0.212759\pi$
$972$		0			0
$973$	19.1538	−	8.18232i	0.614044	−	0.262313i
$974$	−21.4912			−0.688622
$975$		0			0
$976$	6.10939	+	3.52726i	0.195557	+	0.112905i
$977$	−31.4396	−	18.1517i	−1.00584	−	0.580724i	−0.0958710	−	0.995394i	$-0.530564\pi$
$977$	−31.4396	−	18.1517i	−1.00584	−	0.580724i	−0.909972	+	0.414670i	$0.863897\pi$
$978$		0			0
$979$	33.9314	−	3.16517i	1.08445	−	0.101159i
$980$	2.02245	+	1.93517i	0.0646046	+	0.0618167i
$981$		0			0
$982$	−13.9517	−	24.1651i	−0.445218	−	0.771140i
$983$	−27.0902	−	15.6406i	−0.864045	−	0.498856i	0.00132008	−	0.999999i	$-0.499580\pi$
$983$	−27.0902	−	15.6406i	−0.864045	−	0.498856i	−0.865365	+	0.501143i	$0.832913\pi$
$984$		0			0
$985$	1.19617	−	0.690607i	0.0381130	−	0.0220046i
$986$	7.47780			0.238142
$987$		0			0
$988$	1.02991			0.0327658
$989$	4.52070	+	7.83007i	0.143750	+	0.248982i
$990$		0			0
$991$	14.4073	−	24.9542i	0.457664	−	0.792697i	−0.541173	−	0.840911i	$-0.682020\pi$
$991$	14.4073	−	24.9542i	0.457664	−	0.792697i	0.998837	+	0.0482144i	$0.0153531\pi$
$992$	−0.141785	−	0.245579i	−0.00450167	−	0.00779713i
$993$		0			0
$994$	13.6262	+	10.2190i	0.432196	+	0.324128i
$995$			10.1979i			0.323296i
$996$		0			0
$997$	49.8148	+	28.7606i	1.57765	+	0.910857i	0.995186	+	0.0980005i	$0.0312447\pi$
$997$	49.8148	+	28.7606i	1.57765	+	0.910857i	0.582464	+	0.812856i	$0.302089\pi$
$998$	18.4160	−	31.8975i	0.582949	−	1.00970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.a.1187.8	yes	32
3.2	odd	2		1386.2.ba.b.1187.9	yes	32
7.2	even	3	inner	1386.2.ba.a.989.9	yes	32
11.10	odd	2		1386.2.ba.b.1187.8	yes	32
21.2	odd	6		1386.2.ba.b.989.8	yes	32
33.32	even	2	inner	1386.2.ba.a.1187.9	yes	32
77.65	odd	6		1386.2.ba.b.989.9	yes	32
231.65	even	6	inner	1386.2.ba.a.989.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.8	✓	32	231.65	even	6	inner
1386.2.ba.a.989.9	yes	32	7.2	even	3	inner
1386.2.ba.a.1187.8	yes	32	1.1	even	1	trivial
1386.2.ba.a.1187.9	yes	32	33.32	even	2	inner
1386.2.ba.b.989.8	yes	32	21.2	odd	6
1386.2.ba.b.989.9	yes	32	77.65	odd	6
1386.2.ba.b.1187.8	yes	32	11.10	odd	2
1386.2.ba.b.1187.9	yes	32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.346303 + 0.199938i) q^{5} +(1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.346303 + 0.199938i) q^{5} +(1.03937 + 2.43304i) q^{7} +1.00000 q^{8} +(0.346303 + 0.199938i) q^{10} +(3.01389 + 1.38437i) q^{11} +0.164753i q^{13} +(1.58739 - 2.11664i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.906908 - 1.57081i) q^{17} +(-5.41372 + 3.12561i) q^{19} -0.399877i q^{20} +(-0.308042 - 3.30229i) q^{22} +(3.76546 - 2.17399i) q^{23} +(-2.42005 + 4.19165i) q^{25} +(0.142681 - 0.0823767i) q^{26} +(-2.62676 - 0.316401i) q^{28} -4.12269 q^{29} +(-0.141785 + 0.245579i) q^{31} +(-0.500000 + 0.866025i) q^{32} -1.81382 q^{34} +(-0.846396 - 0.634761i) q^{35} +(2.40479 + 4.16521i) q^{37} +(5.41372 + 3.12561i) q^{38} +(-0.346303 + 0.199938i) q^{40} -9.23554 q^{41} +2.07944i q^{43} +(-2.70584 + 1.91792i) q^{44} +(-3.76546 - 2.17399i) q^{46} +(0.367808 - 0.212354i) q^{47} +(-4.83941 + 5.05767i) q^{49} +4.84010 q^{50} +(-0.142681 - 0.0823767i) q^{52} +(7.71343 + 4.45335i) q^{53} +(-1.32051 + 0.123179i) q^{55} +(1.03937 + 2.43304i) q^{56} +(2.06135 + 3.57036i) q^{58} +(6.92731 + 3.99948i) q^{59} +(-6.10939 + 3.52726i) q^{61} +0.283570 q^{62} +1.00000 q^{64} +(-0.0329405 - 0.0570546i) q^{65} +(0.0327874 - 0.0567894i) q^{67} +(0.906908 + 1.57081i) q^{68} +(-0.126521 + 1.05038i) q^{70} +6.43763i q^{71} +(7.21457 + 4.16533i) q^{73} +(2.40479 - 4.16521i) q^{74} -6.25122i q^{76} +(-0.235692 + 8.77180i) q^{77} +(0.531141 - 0.306654i) q^{79} +(0.346303 + 0.199938i) q^{80} +(4.61777 + 7.99822i) q^{82} +1.91649 q^{83} +0.725302i q^{85} +(1.80085 - 1.03972i) q^{86} +(3.01389 + 1.38437i) q^{88} +(8.89851 - 5.13756i) q^{89} +(-0.400852 + 0.171240i) q^{91} +4.34798i q^{92} +(-0.367808 - 0.212354i) q^{94} +(1.24986 - 2.16482i) q^{95} -15.3888 q^{97} +(6.79978 + 1.66222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

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