LMFDB - Embedded newform 192.2.j.a.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(49,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("192.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.j (of order $4$, degree $2$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			145.4
Root			$0.500000 - 1.44392i$ of defining polynomial
Character	$\chi$	$=$	192.145
Dual form			192.2.j.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +1.00000i q^{9} +(-0.473626 + 0.473626i) q^{11} +(2.88784 + 2.88784i) q^{13} +2.47363 q^{15} -6.44549 q^{17} +(4.55765 + 4.55765i) q^{19} +(1.80853 - 1.80853i) q^{21} -2.82843i q^{23} -1.11882i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-3.07931 - 3.07931i) q^{29} -6.55765 q^{31} -0.669808 q^{33} +(-4.47363 - 4.47363i) q^{35} +(-2.72922 + 2.72922i) q^{37} +4.08402i q^{39} +0.788632i q^{41} +(0.389604 - 0.389604i) q^{43} +(1.74912 + 1.74912i) q^{45} -2.82843 q^{47} +0.458440 q^{49} +(-4.55765 - 4.55765i) q^{51} +(-2.57754 + 2.57754i) q^{53} +1.65685i q^{55} +6.44549i q^{57} +(-4.00000 + 4.00000i) q^{59} +(-4.38607 - 4.38607i) q^{61} +2.55765 q^{63} +10.1023 q^{65} +(2.11882 + 2.11882i) q^{67} +(2.00000 - 2.00000i) q^{69} +5.11529i q^{71} -14.7721i q^{73} +(0.791128 - 0.791128i) q^{75} +(1.21137 + 1.21137i) q^{77} +6.32000 q^{79} -1.00000 q^{81} +(-0.641669 - 0.641669i) q^{83} +(-11.2739 + 11.2739i) q^{85} -4.35480i q^{87} +6.31724i q^{89} +(7.38607 - 7.38607i) q^{91} +(-4.63696 - 4.63696i) q^{93} +15.9437 q^{95} +12.6533 q^{97} +(-0.473626 - 0.473626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{43} - 8 q^{49} - 8 q^{51} + 16 q^{53} - 32 q^{59} + 16 q^{61} - 8 q^{63} - 16 q^{65} + 16 q^{67} + 16 q^{69} - 16 q^{75}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^43 - 8 * q^49 - 8 * q^51 + 16 * q^53 - 32 * q^59 + 16 * q^61 - 8 * q^63 - 16 * q^65 + 16 * q^67 + 16 * q^69 - 16 * q^75 + 16 * q^77 + 24 * q^79 - 8 * q^81 + 40 * q^83 - 16 * q^85 + 8 * q^91 + 48 * q^95 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	1.74912	−	1.74912i	0.782229	−	0.782229i	−0.197977	−	0.980207i	$-0.563437\pi$
$5$	1.74912	−	1.74912i	0.782229	−	0.782229i	0.980207	+	0.197977i	$0.0634373\pi$
$6$		0			0
$7$		−	2.55765i		−	0.966700i	−0.875427	−	0.483350i	$-0.839420\pi$
$7$		−	2.55765i		−	0.966700i	0.875427	−	0.483350i	$-0.160580\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.473626	+	0.473626i	−0.142804	+	0.142804i	−0.774894	−	0.632091i	$-0.782197\pi$
$11$	−0.473626	+	0.473626i	−0.142804	+	0.142804i	0.632091	+	0.774894i	$0.282197\pi$
$12$		0			0
$13$	2.88784	+	2.88784i	0.800943	+	0.800943i	0.983243	−	0.182300i	$-0.0583543\pi$
$13$	2.88784	+	2.88784i	0.800943	+	0.800943i	−0.182300	+	0.983243i	$0.558354\pi$
$14$		0			0
$15$	2.47363			0.638687
$16$		0			0
$17$	−6.44549			−1.56326			−0.781630	−	0.623742i	$-0.785611\pi$
$17$	−6.44549			−1.56326			−0.781630	+	0.623742i	$0.785611\pi$
$18$		0			0
$19$	4.55765	+	4.55765i	1.04560	+	1.04560i	0.998910	+	0.0466864i	$0.0148661\pi$
$19$	4.55765	+	4.55765i	1.04560	+	1.04560i	0.0466864	+	0.998910i	$0.485134\pi$
$20$		0			0
$21$	1.80853	−	1.80853i	0.394654	−	0.394654i
$22$		0			0
$23$		−	2.82843i		−	0.589768i	−0.955533	−	0.294884i	$-0.904719\pi$
$23$		−	2.82843i		−	0.589768i	0.955533	−	0.294884i	$-0.0952810\pi$
$24$		0			0
$25$		−	1.11882i		−	0.223765i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−3.07931	−	3.07931i	−0.571813	−	0.571813i	0.360821	−	0.932635i	$-0.382496\pi$
$29$	−3.07931	−	3.07931i	−0.571813	−	0.571813i	−0.932635	+	0.360821i	$0.882496\pi$
$30$		0			0
$31$	−6.55765			−1.17779			−0.588894	−	0.808210i	$-0.700437\pi$
$31$	−6.55765			−1.17779			−0.588894	+	0.808210i	$0.700437\pi$
$32$		0			0
$33$	−0.669808			−0.116599
$34$		0			0
$35$	−4.47363	−	4.47363i	−0.756181	−	0.756181i
$36$		0			0
$37$	−2.72922	+	2.72922i	−0.448681	+	0.448681i	−0.894916	−	0.446235i	$-0.852765\pi$
$37$	−2.72922	+	2.72922i	−0.448681	+	0.448681i	0.446235	+	0.894916i	$0.352765\pi$
$38$		0			0
$39$			4.08402i			0.653967i
$40$		0			0
$41$			0.788632i			0.123164i	0.998102	+	0.0615818i	$0.0196145\pi$
$41$			0.788632i			0.123164i	−0.998102	+	0.0615818i	$0.980385\pi$
$42$		0			0
$43$	0.389604	−	0.389604i	0.0594141	−	0.0594141i	−0.676775	−	0.736190i	$-0.736623\pi$
$43$	0.389604	−	0.389604i	0.0594141	−	0.0594141i	0.736190	+	0.676775i	$0.236623\pi$
$44$		0			0
$45$	1.74912	+	1.74912i	0.260743	+	0.260743i
$46$		0			0
$47$	−2.82843			−0.412568			−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843			−0.412568			−0.206284	+	0.978492i	$0.566137\pi$
$48$		0			0
$49$	0.458440			0.0654915
$50$		0			0
$51$	−4.55765	−	4.55765i	−0.638198	−	0.638198i
$52$		0			0
$53$	−2.57754	+	2.57754i	−0.354053	+	0.354053i	−0.861615	−	0.507562i	$-0.830547\pi$
$53$	−2.57754	+	2.57754i	−0.354053	+	0.354053i	0.507562	+	0.861615i	$0.330547\pi$
$54$		0			0
$55$			1.65685i			0.223410i
$56$		0			0
$57$			6.44549i			0.853726i
$58$		0			0
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	−0.917800	−	0.397044i	$-0.870036\pi$
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	0.397044	+	0.917800i	$0.370036\pi$
$60$		0			0
$61$	−4.38607	−	4.38607i	−0.561579	−	0.561579i	0.368177	−	0.929756i	$-0.379982\pi$
$61$	−4.38607	−	4.38607i	−0.561579	−	0.561579i	−0.929756	+	0.368177i	$0.879982\pi$
$62$		0			0
$63$	2.55765			0.322233
$64$		0			0
$65$	10.1023			1.25304
$66$		0			0
$67$	2.11882	+	2.11882i	0.258856	+	0.258856i	0.824589	−	0.565733i	$-0.191407\pi$
$67$	2.11882	+	2.11882i	0.258856	+	0.258856i	−0.565733	+	0.824589i	$0.691407\pi$
$68$		0			0
$69$	2.00000	−	2.00000i	0.240772	−	0.240772i
$70$		0			0
$71$			5.11529i			0.607074i	0.952820	+	0.303537i	$0.0981676\pi$
$71$			5.11529i			0.607074i	−0.952820	+	0.303537i	$0.901832\pi$
$72$		0			0
$73$		−	14.7721i		−	1.72895i	−0.502676	−	0.864475i	$-0.667651\pi$
$73$		−	14.7721i		−	1.72895i	0.502676	−	0.864475i	$-0.332349\pi$
$74$		0			0
$75$	0.791128	−	0.791128i	0.0913516	−	0.0913516i
$76$		0			0
$77$	1.21137	+	1.21137i	0.138048	+	0.138048i
$78$		0			0
$79$	6.32000			0.711055			0.355528	−	0.934666i	$-0.384301\pi$
$79$	6.32000			0.711055			0.355528	+	0.934666i	$0.384301\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−0.641669	−	0.641669i	−0.0704323	−	0.0704323i	0.671013	−	0.741445i	$-0.265859\pi$
$83$	−0.641669	−	0.641669i	−0.0704323	−	0.0704323i	−0.741445	+	0.671013i	$0.765859\pi$
$84$		0			0
$85$	−11.2739	+	11.2739i	−1.22283	+	1.22283i
$86$		0			0
$87$		−	4.35480i		−	0.466884i
$88$		0			0
$89$			6.31724i			0.669626i	0.942285	+	0.334813i	$0.108673\pi$
$89$			6.31724i			0.669626i	−0.942285	+	0.334813i	$0.891327\pi$
$90$		0			0
$91$	7.38607	−	7.38607i	0.774271	−	0.774271i
$92$		0			0
$93$	−4.63696	−	4.63696i	−0.480830	−	0.480830i
$94$		0			0
$95$	15.9437			1.63579
$96$		0			0
$97$	12.6533			1.28475			0.642375	−	0.766390i	$-0.277949\pi$
$97$	12.6533			1.28475			0.642375	+	0.766390i	$0.277949\pi$
$98$		0			0
$99$	−0.473626	−	0.473626i	−0.0476012	−	0.0476012i
$100$		0			0
$101$	7.52480	−	7.52480i	0.748745	−	0.748745i	−0.225498	−	0.974244i	$-0.572401\pi$
$101$	7.52480	−	7.52480i	0.748745	−	0.748745i	0.974244	+	0.225498i	$0.0724010\pi$
$102$		0			0
$103$			3.33686i			0.328790i	0.986395	+	0.164395i	$0.0525672\pi$
$103$			3.33686i			0.328790i	−0.986395	+	0.164395i	$0.947433\pi$
$104$		0			0
$105$		−	6.32666i		−	0.617419i
$106$		0			0
$107$	14.0625	−	14.0625i	1.35948	−	1.35948i	0.484918	−	0.874560i	$-0.338849\pi$
$107$	14.0625	−	14.0625i	1.35948	−	1.35948i	0.874560	−	0.484918i	$-0.161151\pi$
$108$		0			0
$109$	2.76901	+	2.76901i	0.265224	+	0.265224i	0.827172	−	0.561949i	$-0.189948\pi$
$109$	2.76901	+	2.76901i	0.265224	+	0.265224i	−0.561949	+	0.827172i	$0.689948\pi$
$110$		0			0
$111$	−3.85970			−0.366347
$112$		0			0
$113$	2.23765			0.210500			0.105250	−	0.994446i	$-0.466436\pi$
$113$	2.23765			0.210500			0.105250	+	0.994446i	$0.466436\pi$
$114$		0			0
$115$	−4.94725	−	4.94725i	−0.461334	−	0.461334i
$116$		0			0
$117$	−2.88784	+	2.88784i	−0.266981	+	0.266981i
$118$		0			0
$119$			16.4853i			1.51120i
$120$		0			0
$121$			10.5514i			0.959214i
$122$		0			0
$123$	−0.557647	+	0.557647i	−0.0502814	+	0.0502814i
$124$		0			0
$125$	6.78863	+	6.78863i	0.607194	+	0.607194i
$126$		0			0
$127$	−12.2145			−1.08386			−0.541931	−	0.840423i	$-0.682307\pi$
$127$	−12.2145			−1.08386			−0.541931	+	0.840423i	$0.682307\pi$
$128$		0			0
$129$	0.550984			0.0485114
$130$		0			0
$131$	3.77568	+	3.77568i	0.329883	+	0.329883i	0.852542	−	0.522659i	$-0.175060\pi$
$131$	3.77568	+	3.77568i	0.329883	+	0.329883i	−0.522659	+	0.852542i	$0.675060\pi$
$132$		0			0
$133$	11.6569	−	11.6569i	1.01078	−	1.01078i
$134$		0			0
$135$			2.47363i			0.212896i
$136$		0			0
$137$		−	5.10587i		−	0.436224i	−0.975924	−	0.218112i	$-0.930010\pi$
$137$		−	5.10587i		−	0.436224i	0.975924	−	0.218112i	$-0.0699898\pi$
$138$		0			0
$139$	−11.7757	+	11.7757i	−0.998800	+	0.998800i	−0.999999	−	0.00119925i	$-0.999618\pi$
$139$	−11.7757	+	11.7757i	−0.998800	+	0.998800i	0.00119925	+	0.999999i	$0.499618\pi$
$140$		0			0
$141$	−2.00000	−	2.00000i	−0.168430	−	0.168430i
$142$		0			0
$143$	−2.73551			−0.228755
$144$		0			0
$145$	−10.7721			−0.894578
$146$		0			0
$147$	0.324166	+	0.324166i	0.0267368	+	0.0267368i
$148$		0			0
$149$	−7.90774	+	7.90774i	−0.647827	+	0.647827i	−0.952467	−	0.304640i	$-0.901464\pi$
$149$	−7.90774	+	7.90774i	−0.647827	+	0.647827i	0.304640	+	0.952467i	$0.401464\pi$
$150$		0			0
$151$		−	14.6506i		−	1.19225i	−0.802893	−	0.596123i	$-0.796707\pi$
$151$		−	14.6506i		−	1.19225i	0.802893	−	0.596123i	$-0.203293\pi$
$152$		0			0
$153$		−	6.44549i		−	0.521087i
$154$		0			0
$155$	−11.4701	+	11.4701i	−0.921300	+	0.921300i
$156$		0			0
$157$	−3.15196	−	3.15196i	−0.251553	−	0.251553i	0.570054	−	0.821607i	$-0.306922\pi$
$157$	−3.15196	−	3.15196i	−0.251553	−	0.251553i	−0.821607	+	0.570054i	$0.806922\pi$
$158$		0			0
$159$	−3.64520			−0.289083
$160$		0			0
$161$	−7.23412			−0.570128
$162$		0			0
$163$	−5.50490	−	5.50490i	−0.431177	−	0.431177i	0.457852	−	0.889029i	$-0.348619\pi$
$163$	−5.50490	−	5.50490i	−0.431177	−	0.431177i	−0.889029	+	0.457852i	$0.848619\pi$
$164$		0			0
$165$	−1.17157	+	1.17157i	−0.0912068	+	0.0912068i
$166$		0			0
$167$		−	20.1814i		−	1.56168i	−0.624730	−	0.780841i	$-0.714791\pi$
$167$		−	20.1814i		−	1.56168i	0.624730	−	0.780841i	$-0.285209\pi$
$168$		0			0
$169$			3.67923i			0.283018i
$170$		0			0
$171$	−4.55765	+	4.55765i	−0.348532	+	0.348532i
$172$		0			0
$173$	4.35322	+	4.35322i	0.330969	+	0.330969i	0.852955	−	0.521985i	$-0.174808\pi$
$173$	4.35322	+	4.35322i	0.330969	+	0.330969i	−0.521985	+	0.852955i	$0.674808\pi$
$174$		0			0
$175$	−2.86156			−0.216313
$176$		0			0
$177$	−5.65685			−0.425195
$178$		0			0
$179$	13.2833	+	13.2833i	0.992843	+	0.992843i	0.999975	−	0.00713130i	$-0.00226998\pi$
$179$	13.2833	+	13.2833i	0.992843	+	0.992843i	−0.00713130	+	0.999975i	$0.502270\pi$
$180$		0			0
$181$	6.34628	−	6.34628i	0.471715	−	0.471715i	−0.430754	−	0.902469i	$-0.641752\pi$
$181$	6.34628	−	6.34628i	0.471715	−	0.471715i	0.902469	+	0.430754i	$0.141752\pi$
$182$		0			0
$183$		−	6.20285i		−	0.458528i
$184$		0			0
$185$			9.54745i			0.701943i
$186$		0			0
$187$	3.05275	−	3.05275i	0.223239	−	0.223239i
$188$		0			0
$189$	1.80853	+	1.80853i	0.131551	+	0.131551i
$190$		0			0
$191$	−5.60058			−0.405243			−0.202622	−	0.979257i	$-0.564946\pi$
$191$	−5.60058			−0.405243			−0.202622	+	0.979257i	$0.564946\pi$
$192$		0			0
$193$	−19.4514			−1.40014			−0.700071	−	0.714074i	$-0.746848\pi$
$193$	−19.4514			−1.40014			−0.700071	+	0.714074i	$0.746848\pi$
$194$		0			0
$195$	7.14343	+	7.14343i	0.511552	+	0.511552i
$196$		0			0
$197$	1.23793	−	1.23793i	0.0881988	−	0.0881988i	−0.661631	−	0.749830i	$-0.730135\pi$
$197$	1.23793	−	1.23793i	0.0881988	−	0.0881988i	0.749830	+	0.661631i	$0.230135\pi$
$198$		0			0
$199$		−	0.993710i		−	0.0704422i	−0.999380	−	0.0352211i	$-0.988786\pi$
$199$		−	0.993710i		−	0.0704422i	0.999380	−	0.0352211i	$-0.0112135\pi$
$200$		0			0
$201$			2.99647i			0.211355i
$202$		0			0
$203$	−7.87579	+	7.87579i	−0.552772	+	0.552772i
$204$		0			0
$205$	1.37941	+	1.37941i	0.0963422	+	0.0963422i
$206$		0			0
$207$	2.82843			0.196589
$208$		0			0
$209$	−4.31724			−0.298630
$210$		0			0
$211$	−4.22432	−	4.22432i	−0.290814	−	0.290814i	0.546588	−	0.837402i	$-0.315927\pi$
$211$	−4.22432	−	4.22432i	−0.290814	−	0.290814i	−0.837402	+	0.546588i	$0.815927\pi$
$212$		0			0
$213$	−3.61706	+	3.61706i	−0.247837	+	0.247837i
$214$		0			0
$215$		−	1.36293i		−	0.0929509i
$216$		0			0
$217$			16.7721i			1.13857i
$218$		0			0
$219$	10.4455	−	10.4455i	0.705841	−	0.705841i
$220$		0			0
$221$	−18.6135	−	18.6135i	−1.25208	−	1.25208i
$222$		0			0
$223$	23.7659			1.59148			0.795740	−	0.605639i	$-0.207082\pi$
$223$	23.7659			1.59148			0.795740	+	0.605639i	$0.207082\pi$
$224$		0			0
$225$	1.11882			0.0745883
$226$		0			0
$227$	0.641669	+	0.641669i	0.0425891	+	0.0425891i	0.728081	−	0.685492i	$-0.240413\pi$
$227$	0.641669	+	0.641669i	0.0425891	+	0.0425891i	−0.685492	+	0.728081i	$0.740413\pi$
$228$		0			0
$229$	5.34275	−	5.34275i	0.353059	−	0.353059i	−0.508188	−	0.861246i	$-0.669684\pi$
$229$	5.34275	−	5.34275i	0.353059	−	0.353059i	0.861246	+	0.508188i	$0.169684\pi$
$230$		0			0
$231$			1.71313i			0.112716i
$232$		0			0
$233$		−	23.2271i		−	1.52166i	−0.648954	−	0.760828i	$-0.724793\pi$
$233$		−	23.2271i		−	1.52166i	0.648954	−	0.760828i	$-0.275207\pi$
$234$		0			0
$235$	−4.94725	+	4.94725i	−0.322723	+	0.322723i
$236$		0			0
$237$	4.46891	+	4.46891i	0.290287	+	0.290287i
$238$		0			0
$239$	−26.9213			−1.74140			−0.870698	−	0.491817i	$-0.836333\pi$
$239$	−26.9213			−1.74140			−0.870698	+	0.491817i	$0.836333\pi$
$240$		0			0
$241$	−10.3494			−0.666664			−0.333332	−	0.942809i	$-0.608173\pi$
$241$	−10.3494			−0.666664			−0.333332	+	0.942809i	$0.608173\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	0.801866	−	0.801866i	0.0512293	−	0.0512293i
$246$		0			0
$247$			26.3235i			1.67492i
$248$		0			0
$249$		−	0.907457i		−	0.0575077i
$250$		0			0
$251$	9.75696	−	9.75696i	0.615854	−	0.615854i	−0.328611	−	0.944465i	$-0.606581\pi$
$251$	9.75696	−	9.75696i	0.615854	−	0.615854i	0.944465	+	0.328611i	$0.106581\pi$
$252$		0			0
$253$	1.33962	+	1.33962i	0.0842209	+	0.0842209i
$254$		0			0
$255$	−15.9437			−0.998435
$256$		0			0
$257$	16.9965			1.06021			0.530105	−	0.847932i	$-0.322152\pi$
$257$	16.9965			1.06021			0.530105	+	0.847932i	$0.322152\pi$
$258$		0			0
$259$	6.98038	+	6.98038i	0.433740	+	0.433740i
$260$		0			0
$261$	3.07931	−	3.07931i	0.190604	−	0.190604i
$262$		0			0
$263$		−	29.9929i		−	1.84944i	−0.380643	−	0.924722i	$-0.624297\pi$
$263$		−	29.9929i		−	1.84944i	0.380643	−	0.924722i	$-0.375703\pi$
$264$		0			0
$265$			9.01686i			0.553901i
$266$		0			0
$267$	−4.46696	+	4.46696i	−0.273374	+	0.273374i
$268$		0			0
$269$	20.6003	+	20.6003i	1.25602	+	1.25602i	0.952976	+	0.303046i	$0.0980037\pi$
$269$	20.6003	+	20.6003i	1.25602	+	1.25602i	0.303046	+	0.952976i	$0.401996\pi$
$270$		0			0
$271$	26.6506			1.61891			0.809453	−	0.587184i	$-0.199764\pi$
$271$	26.6506			1.61891			0.809453	+	0.587184i	$0.199764\pi$
$272$		0			0
$273$	10.4455			0.632190
$274$		0			0
$275$	0.529904	+	0.529904i	0.0319544	+	0.0319544i
$276$		0			0
$277$	12.1220	−	12.1220i	0.728338	−	0.728338i	−0.241951	−	0.970289i	$-0.577787\pi$
$277$	12.1220	−	12.1220i	0.728338	−	0.728338i	0.970289	+	0.241951i	$0.0777872\pi$
$278$		0			0
$279$		−	6.55765i		−	0.392596i
$280$		0			0
$281$		−	2.76588i		−	0.164999i	−0.996591	−	0.0824993i	$-0.973710\pi$
$281$		−	2.76588i		−	0.164999i	0.996591	−	0.0824993i	$-0.0262902\pi$
$282$		0			0
$283$	−4.48528	+	4.48528i	−0.266622	+	0.266622i	−0.827738	−	0.561115i	$-0.810372\pi$
$283$	−4.48528	+	4.48528i	−0.266622	+	0.266622i	0.561115	+	0.827738i	$0.310372\pi$
$284$		0			0
$285$	11.2739	+	11.2739i	0.667809	+	0.667809i
$286$		0			0
$287$	2.01704			0.119062
$288$		0			0
$289$	24.5443			1.44378
$290$		0			0
$291$	8.94725	+	8.94725i	0.524497	+	0.524497i
$292$		0			0
$293$	−8.20793	+	8.20793i	−0.479512	+	0.479512i	−0.904976	−	0.425463i	$-0.860111\pi$
$293$	−8.20793	+	8.20793i	−0.479512	+	0.479512i	0.425463	+	0.904976i	$0.360111\pi$
$294$		0			0
$295$			13.9929i			0.814700i
$296$		0			0
$297$		−	0.669808i		−	0.0388662i
$298$		0			0
$299$	8.16804	−	8.16804i	0.472370	−	0.472370i
$300$		0			0
$301$	−0.996470	−	0.996470i	−0.0574356	−	0.0574356i
$302$		0			0
$303$	10.6417			0.611348
$304$		0			0
$305$	−15.3435			−0.878567
$306$		0			0
$307$	−10.4549	−	10.4549i	−0.596693	−	0.596693i	0.342738	−	0.939431i	$-0.388646\pi$
$307$	−10.4549	−	10.4549i	−0.596693	−	0.596693i	−0.939431	+	0.342738i	$0.888646\pi$
$308$		0			0
$309$	−2.35951	+	2.35951i	−0.134228	+	0.134228i
$310$		0			0
$311$			15.0761i			0.854885i	0.904043	+	0.427442i	$0.140585\pi$
$311$			15.0761i			0.854885i	−0.904043	+	0.427442i	$0.859415\pi$
$312$		0			0
$313$		−	23.0027i		−	1.30019i	−0.759852	−	0.650096i	$-0.774729\pi$
$313$		−	23.0027i		−	1.30019i	0.759852	−	0.650096i	$-0.225271\pi$
$314$		0			0
$315$	4.47363	−	4.47363i	0.252060	−	0.252060i
$316$		0			0
$317$	−6.75892	−	6.75892i	−0.379618	−	0.379618i	0.491346	−	0.870964i	$-0.336505\pi$
$317$	−6.75892	−	6.75892i	−0.379618	−	0.379618i	−0.870964	+	0.491346i	$0.836505\pi$
$318$		0			0
$319$	2.91688			0.163314
$320$		0			0
$321$	19.8874			1.11001
$322$		0			0
$323$	−29.3763	−	29.3763i	−1.63454	−	1.63454i
$324$		0			0
$325$	3.23099	−	3.23099i	0.179223	−	0.179223i
$326$		0			0
$327$			3.91598i			0.216554i
$328$		0			0
$329$			7.23412i			0.398830i
$330$		0			0
$331$	19.6631	−	19.6631i	1.08078	−	1.08078i	0.0843464	−	0.996436i	$-0.473120\pi$
$331$	19.6631	−	19.6631i	1.08078	−	1.08078i	0.996436	−	0.0843464i	$-0.0268802\pi$
$332$		0			0
$333$	−2.72922	−	2.72922i	−0.149560	−	0.149560i
$334$		0			0
$335$	7.41215			0.404969
$336$		0			0
$337$	3.00980			0.163954			0.0819771	−	0.996634i	$-0.473877\pi$
$337$	3.00980			0.163954			0.0819771	+	0.996634i	$0.473877\pi$
$338$		0			0
$339$	1.58226	+	1.58226i	0.0859364	+	0.0859364i
$340$		0			0
$341$	3.10587	−	3.10587i	0.168192	−	0.168192i
$342$		0			0
$343$		−	19.0761i		−	1.03001i
$344$		0			0
$345$		−	6.99647i		−	0.376677i
$346$		0			0
$347$	−6.27521	+	6.27521i	−0.336871	+	0.336871i	−0.855188	−	0.518317i	$-0.826559\pi$
$347$	−6.27521	+	6.27521i	−0.336871	+	0.336871i	0.518317	+	0.855188i	$0.326559\pi$
$348$		0			0
$349$	−4.74255	−	4.74255i	−0.253863	−	0.253863i	0.568690	−	0.822552i	$-0.307451\pi$
$349$	−4.74255	−	4.74255i	−0.253863	−	0.253863i	−0.822552	+	0.568690i	$0.807451\pi$
$350$		0			0
$351$	−4.08402			−0.217989
$352$		0			0
$353$	−8.75882			−0.466185			−0.233093	−	0.972455i	$-0.574884\pi$
$353$	−8.75882			−0.466185			−0.233093	+	0.972455i	$0.574884\pi$
$354$		0			0
$355$	8.94725	+	8.94725i	0.474871	+	0.474871i
$356$		0			0
$357$	−11.6569	+	11.6569i	−0.616946	+	0.616946i
$358$		0			0
$359$			32.7917i			1.73068i	0.501184	+	0.865341i	$0.332898\pi$
$359$			32.7917i			1.73068i	−0.501184	+	0.865341i	$0.667102\pi$
$360$		0			0
$361$			22.5443i			1.18654i
$362$		0			0
$363$	−7.46094	+	7.46094i	−0.391598	+	0.391598i
$364$		0			0
$365$	−25.8382	−	25.8382i	−1.35243	−	1.35243i
$366$		0			0
$367$	−20.6435			−1.07758			−0.538791	−	0.842439i	$-0.681119\pi$
$367$	−20.6435			−1.07758			−0.538791	+	0.842439i	$0.681119\pi$
$368$		0			0
$369$	−0.788632			−0.0410546
$370$		0			0
$371$	6.59245	+	6.59245i	0.342263	+	0.342263i
$372$		0			0
$373$	−16.6167	+	16.6167i	−0.860378	+	0.860378i	−0.991382	−	0.131004i	$-0.958180\pi$
$373$	−16.6167	+	16.6167i	−0.860378	+	0.860378i	0.131004	+	0.991382i	$0.458180\pi$
$374$		0			0
$375$			9.60058i			0.495772i
$376$		0			0
$377$		−	17.7851i		−	0.915979i
$378$		0			0
$379$	−7.77844	+	7.77844i	−0.399552	+	0.399552i	−0.878075	−	0.478523i	$-0.841172\pi$
$379$	−7.77844	+	7.77844i	−0.399552	+	0.399552i	0.478523	+	0.878075i	$0.341172\pi$
$380$		0			0
$381$	−8.63696	−	8.63696i	−0.442485	−	0.442485i
$382$		0			0
$383$	17.2037			0.879070			0.439535	−	0.898225i	$-0.355143\pi$
$383$	17.2037			0.879070			0.439535	+	0.898225i	$0.355143\pi$
$384$		0			0
$385$	4.23765			0.215971
$386$		0			0
$387$	0.389604	+	0.389604i	0.0198047	+	0.0198047i
$388$		0			0
$389$	−23.8515	+	23.8515i	−1.20932	+	1.20932i	−0.238069	+	0.971248i	$0.576514\pi$
$389$	−23.8515	+	23.8515i	−1.20932	+	1.20932i	−0.971248	+	0.238069i	$0.923486\pi$
$390$		0			0
$391$			18.2306i			0.921961i
$392$		0			0
$393$			5.33962i			0.269348i
$394$		0			0
$395$	11.0544	−	11.0544i	0.556208	−	0.556208i
$396$		0			0
$397$	−10.2673	−	10.2673i	−0.515299	−	0.515299i	0.400847	−	0.916145i	$-0.368716\pi$
$397$	−10.2673	−	10.2673i	−0.515299	−	0.515299i	−0.916145	+	0.400847i	$0.868716\pi$
$398$		0			0
$399$	16.4853			0.825296
$400$		0			0
$401$	32.2274			1.60936			0.804681	−	0.593708i	$-0.202337\pi$
$401$	32.2274			1.60936			0.804681	+	0.593708i	$0.202337\pi$
$402$		0			0
$403$	−18.9374	−	18.9374i	−0.943341	−	0.943341i
$404$		0			0
$405$	−1.74912	+	1.74912i	−0.0869143	+	0.0869143i
$406$		0			0
$407$		−	2.58526i		−	0.128146i
$408$		0			0
$409$			11.5702i			0.572110i	0.958213	+	0.286055i	$0.0923440\pi$
$409$			11.5702i			0.572110i	−0.958213	+	0.286055i	$0.907656\pi$
$410$		0			0
$411$	3.61040	−	3.61040i	0.178088	−	0.178088i
$412$		0			0
$413$	10.2306	+	10.2306i	0.503414	+	0.503414i
$414$		0			0
$415$	−2.24471			−0.110188
$416$		0			0
$417$	−16.6533			−0.815517
$418$		0			0
$419$	−6.74717	−	6.74717i	−0.329621	−	0.329621i	0.522822	−	0.852442i	$-0.324879\pi$
$419$	−6.74717	−	6.74717i	−0.329621	−	0.329621i	−0.852442	+	0.522822i	$0.824879\pi$
$420$		0			0
$421$	−17.2239	+	17.2239i	−0.839443	+	0.839443i	−0.988785	−	0.149343i	$-0.952284\pi$
$421$	−17.2239	+	17.2239i	−0.839443	+	0.839443i	0.149343	+	0.988785i	$0.452284\pi$
$422$		0			0
$423$		−	2.82843i		−	0.137523i
$424$		0			0
$425$			7.21137i			0.349803i
$426$		0			0
$427$	−11.2180	+	11.2180i	−0.542879	+	0.542879i
$428$		0			0
$429$	−1.93430	−	1.93430i	−0.0933888	−	0.0933888i
$430$		0			0
$431$	−40.7088			−1.96087			−0.980437	−	0.196832i	$-0.936935\pi$
$431$	−40.7088			−1.96087			−0.980437	+	0.196832i	$0.936935\pi$
$432$		0			0
$433$	7.31371			0.351474			0.175737	−	0.984437i	$-0.443769\pi$
$433$	7.31371			0.351474			0.175737	+	0.984437i	$0.443769\pi$
$434$		0			0
$435$	−7.61706	−	7.61706i	−0.365210	−	0.365210i
$436$		0			0
$437$	12.8910	−	12.8910i	0.616659	−	0.616659i
$438$		0			0
$439$		−	17.7122i		−	0.845356i	−0.906280	−	0.422678i	$-0.861090\pi$
$439$		−	17.7122i		−	0.845356i	0.906280	−	0.422678i	$-0.138910\pi$
$440$		0			0
$441$			0.458440i			0.0218305i
$442$		0			0
$443$	−15.6944	+	15.6944i	−0.745664	+	0.745664i	−0.973662	−	0.227997i	$-0.926782\pi$
$443$	−15.6944	+	15.6944i	−0.745664	+	0.745664i	0.227997	+	0.973662i	$0.426782\pi$
$444$		0			0
$445$	11.0496	+	11.0496i	0.523801	+	0.523801i
$446$		0			0
$447$	−11.1832			−0.528949
$448$		0			0
$449$	−28.3400			−1.33745			−0.668723	−	0.743511i	$-0.733159\pi$
$449$	−28.3400			−1.33745			−0.668723	+	0.743511i	$0.733159\pi$
$450$		0			0
$451$	−0.373517	−	0.373517i	−0.0175882	−	0.0175882i
$452$		0			0
$453$	10.3595	−	10.3595i	0.486732	−	0.486732i
$454$		0			0
$455$		−	25.8382i		−	1.21131i
$456$		0			0
$457$		−	17.3396i		−	0.811113i	−0.914070	−	0.405557i	$-0.867078\pi$
$457$		−	17.3396i		−	0.811113i	0.914070	−	0.405557i	$-0.132922\pi$
$458$		0			0
$459$	4.55765	−	4.55765i	0.212733	−	0.212733i
$460$		0			0
$461$	−1.69284	−	1.69284i	−0.0788434	−	0.0788434i	0.666585	−	0.745429i	$-0.267755\pi$
$461$	−1.69284	−	1.69284i	−0.0788434	−	0.0788434i	−0.745429	+	0.666585i	$0.767755\pi$
$462$		0			0
$463$	−2.70238			−0.125590			−0.0627951	−	0.998026i	$-0.520001\pi$
$463$	−2.70238			−0.125590			−0.0627951	+	0.998026i	$0.520001\pi$
$464$		0			0
$465$	−16.2212			−0.752239
$466$		0			0
$467$	17.1136	+	17.1136i	0.791924	+	0.791924i	0.981807	−	0.189883i	$-0.0608108\pi$
$467$	17.1136	+	17.1136i	0.791924	+	0.791924i	−0.189883	+	0.981807i	$0.560811\pi$
$468$		0			0
$469$	5.41921	−	5.41921i	0.250236	−	0.250236i
$470$		0			0
$471$		−	4.45754i		−	0.205393i
$472$		0			0
$473$			0.369053i			0.0169691i
$474$		0			0
$475$	5.09921	−	5.09921i	0.233968	−	0.233968i
$476$		0			0
$477$	−2.57754	−	2.57754i	−0.118018	−	0.118018i
$478$		0			0
$479$	22.2251			1.01549			0.507745	−	0.861508i	$-0.330479\pi$
$479$	22.2251			1.01549			0.507745	+	0.861508i	$0.330479\pi$
$480$		0			0
$481$	−15.7631			−0.718735
$482$		0			0
$483$	−5.11529	−	5.11529i	−0.232754	−	0.232754i
$484$		0			0
$485$	22.1322	−	22.1322i	1.00497	−	1.00497i
$486$		0			0
$487$			13.9839i			0.633672i	0.948480	+	0.316836i	$0.102620\pi$
$487$			13.9839i			0.633672i	−0.948480	+	0.316836i	$0.897380\pi$
$488$		0			0
$489$		−	7.78510i		−	0.352055i
$490$		0			0
$491$	−7.23412	+	7.23412i	−0.326471	+	0.326471i	−0.851243	−	0.524772i	$-0.824151\pi$
$491$	−7.23412	+	7.23412i	−0.326471	+	0.326471i	0.524772	+	0.851243i	$0.324151\pi$
$492$		0			0
$493$	19.8476	+	19.8476i	0.893893	+	0.893893i
$494$		0			0
$495$	−1.65685			−0.0744701
$496$		0			0
$497$	13.0831			0.586858
$498$		0			0
$499$	−2.59078	−	2.59078i	−0.115979	−	0.115979i	0.646735	−	0.762715i	$-0.276134\pi$
$499$	−2.59078	−	2.59078i	−0.115979	−	0.115979i	−0.762715	+	0.646735i	$0.776134\pi$
$500$		0			0
$501$	14.2704	−	14.2704i	0.637554	−	0.637554i
$502$		0			0
$503$			39.6443i			1.76765i	0.467817	+	0.883825i	$0.345041\pi$
$503$			39.6443i			1.76765i	−0.467817	+	0.883825i	$0.654959\pi$
$504$		0			0
$505$		−	26.3235i		−	1.17138i
$506$		0			0
$507$	−2.60161	+	2.60161i	−0.115542	+	0.115542i
$508$		0			0
$509$	20.2875	+	20.2875i	0.899229	+	0.899229i	0.995368	−	0.0961393i	$-0.0306494\pi$
$509$	20.2875	+	20.2875i	0.899229	+	0.899229i	−0.0961393	+	0.995368i	$0.530649\pi$
$510$		0			0
$511$	−37.7819			−1.67137
$512$		0			0
$513$	−6.44549			−0.284575
$514$		0			0
$515$	5.83655	+	5.83655i	0.257189	+	0.257189i
$516$		0			0
$517$	1.33962	−	1.33962i	0.0589162	−	0.0589162i
$518$		0			0
$519$			6.15639i			0.270235i
$520$		0			0
$521$			23.1784i			1.01546i	0.861515	+	0.507732i	$0.169516\pi$
$521$			23.1784i			1.01546i	−0.861515	+	0.507732i	$0.830484\pi$
$522$		0			0
$523$	5.78550	−	5.78550i	0.252982	−	0.252982i	−0.569210	−	0.822192i	$-0.692751\pi$
$523$	5.78550	−	5.78550i	0.252982	−	0.252982i	0.822192	+	0.569210i	$0.192751\pi$
$524$		0			0
$525$	−2.02343	−	2.02343i	−0.0883096	−	0.0883096i
$526$		0			0
$527$	42.2672			1.84119
$528$		0			0
$529$	15.0000			0.652174
$530$		0			0
$531$	−4.00000	−	4.00000i	−0.173585	−	0.173585i
$532$		0			0
$533$	−2.27744	+	2.27744i	−0.0986470	+	0.0986470i
$534$		0			0
$535$		−	49.1941i		−	2.12685i
$536$		0			0
$537$			18.7855i			0.810653i
$538$		0			0
$539$	−0.217129	+	0.217129i	−0.00935241	+	0.00935241i
$540$		0			0
$541$	4.55175	+	4.55175i	0.195695	+	0.195695i	0.798152	−	0.602457i	$-0.205811\pi$
$541$	4.55175	+	4.55175i	0.195695	+	0.195695i	−0.602457	+	0.798152i	$0.705811\pi$
$542$		0			0
$543$	8.97499			0.385154
$544$		0			0
$545$	9.68667			0.414931
$546$		0			0
$547$	27.7355	+	27.7355i	1.18588	+	1.18588i	0.978195	+	0.207689i	$0.0665942\pi$
$547$	27.7355	+	27.7355i	1.18588	+	1.18588i	0.207689	+	0.978195i	$0.433406\pi$
$548$		0			0
$549$	4.38607	−	4.38607i	0.187193	−	0.187193i
$550$		0			0
$551$		−	28.0688i		−	1.19577i
$552$		0			0
$553$		−	16.1643i		−	0.687377i
$554$		0			0
$555$	−6.75107	+	6.75107i	−0.286567	+	0.286567i
$556$		0			0
$557$	−1.17538	−	1.17538i	−0.0498026	−	0.0498026i	0.681767	−	0.731569i	$-0.261212\pi$
$557$	−1.17538	−	1.17538i	−0.0498026	−	0.0498026i	−0.731569	+	0.681767i	$0.761212\pi$
$558$		0			0
$559$	2.25023			0.0951745
$560$		0			0
$561$	4.31724			0.182274
$562$		0			0
$563$	28.7346	+	28.7346i	1.21102	+	1.21102i	0.970692	+	0.240326i	$0.0772544\pi$
$563$	28.7346	+	28.7346i	1.21102	+	1.21102i	0.240326	+	0.970692i	$0.422746\pi$
$564$		0			0
$565$	3.91391	−	3.91391i	0.164659	−	0.164659i
$566$		0			0
$567$			2.55765i			0.107411i
$568$		0			0
$569$			27.0004i			1.13191i	0.824435	+	0.565957i	$0.191493\pi$
$569$			27.0004i			1.13191i	−0.824435	+	0.565957i	$0.808507\pi$
$570$		0			0
$571$	14.8284	−	14.8284i	0.620550	−	0.620550i	−0.325122	−	0.945672i	$-0.605405\pi$
$571$	14.8284	−	14.8284i	0.620550	−	0.620550i	0.945672	+	0.325122i	$0.105405\pi$
$572$		0			0
$573$	−3.96021	−	3.96021i	−0.165440	−	0.165440i
$574$		0			0
$575$	−3.16451			−0.131969
$576$		0			0
$577$	−37.6372			−1.56686			−0.783429	−	0.621481i	$-0.786531\pi$
$577$	−37.6372			−1.56686			−0.783429	+	0.621481i	$0.786531\pi$
$578$		0			0
$579$	−13.7542	−	13.7542i	−0.571605	−	0.571605i
$580$		0			0
$581$	−1.64116	+	1.64116i	−0.0680869	+	0.0680869i
$582$		0			0
$583$		−	2.44158i		−	0.101120i
$584$		0			0
$585$			10.1023i			0.417680i
$586$		0			0
$587$	31.2574	−	31.2574i	1.29013	−	1.29013i	0.355429	−	0.934703i	$-0.384335\pi$
$587$	31.2574	−	31.2574i	1.29013	−	1.29013i	0.934703	−	0.355429i	$-0.115665\pi$
$588$		0			0
$589$	−29.8874	−	29.8874i	−1.23149	−	1.23149i
$590$		0			0
$591$	1.75070			0.0720140
$592$		0			0
$593$	−3.59611			−0.147675			−0.0738373	−	0.997270i	$-0.523525\pi$
$593$	−3.59611			−0.147675			−0.0738373	+	0.997270i	$0.523525\pi$
$594$		0			0
$595$	28.8347	+	28.8347i	1.18211	+	1.18211i
$596$		0			0
$597$	0.702659	−	0.702659i	0.0287579	−	0.0287579i
$598$		0			0
$599$		−	22.0296i		−	0.900104i	−0.893002	−	0.450052i	$-0.851405\pi$
$599$		−	22.0296i		−	0.900104i	0.893002	−	0.450052i	$-0.148595\pi$
$600$		0			0
$601$		−	10.7721i		−	0.439405i	−0.975567	−	0.219703i	$-0.929491\pi$
$601$		−	10.7721i		−	0.439405i	0.975567	−	0.219703i	$-0.0705087\pi$
$602$		0			0
$603$	−2.11882	+	2.11882i	−0.0862852	+	0.0862852i
$604$		0			0
$605$	18.4556	+	18.4556i	0.750325	+	0.750325i
$606$		0			0
$607$	−5.47453			−0.222204			−0.111102	−	0.993809i	$-0.535438\pi$
$607$	−5.47453			−0.222204			−0.111102	+	0.993809i	$0.535438\pi$
$608$		0			0
$609$	−11.1380			−0.451336
$610$		0			0
$611$	−8.16804	−	8.16804i	−0.330444	−	0.330444i
$612$		0			0
$613$	−10.5049	+	10.5049i	−0.424289	+	0.424289i	−0.886677	−	0.462389i	$-0.846993\pi$
$613$	−10.5049	+	10.5049i	−0.424289	+	0.424289i	0.462389	+	0.886677i	$0.346993\pi$
$614$		0			0
$615$			1.95078i			0.0786631i
$616$		0			0
$617$			22.2235i			0.894686i	0.894363	+	0.447343i	$0.147630\pi$
$617$			22.2235i			0.894686i	−0.894363	+	0.447343i	$0.852370\pi$
$618$		0			0
$619$	−11.6398	+	11.6398i	−0.467843	+	0.467843i	−0.901215	−	0.433372i	$-0.857324\pi$
$619$	−11.6398	+	11.6398i	−0.467843	+	0.467843i	0.433372	+	0.901215i	$0.357324\pi$
$620$		0			0
$621$	2.00000	+	2.00000i	0.0802572	+	0.0802572i
$622$		0			0
$623$	16.1573			0.647327
$624$		0			0
$625$	29.3424			1.17369
$626$		0			0
$627$	−3.05275	−	3.05275i	−0.121915	−	0.121915i
$628$		0			0
$629$	17.5912	−	17.5912i	0.701405	−	0.701405i
$630$		0			0
$631$			4.06977i			0.162015i	0.996713	+	0.0810075i	$0.0258138\pi$
$631$			4.06977i			0.162015i	−0.996713	+	0.0810075i	$0.974186\pi$
$632$		0			0
$633$		−	5.97409i		−	0.237449i
$634$		0			0
$635$	−21.3646	+	21.3646i	−0.847828	+	0.847828i
$636$		0			0
$637$	1.32390	+	1.32390i	0.0524549	+	0.0524549i
$638$		0			0
$639$	−5.11529			−0.202358
$640$		0			0
$641$	−8.41958			−0.332553			−0.166277	−	0.986079i	$-0.553174\pi$
$641$	−8.41958			−0.332553			−0.166277	+	0.986079i	$0.553174\pi$
$642$		0			0
$643$	7.37275	+	7.37275i	0.290753	+	0.290753i	0.837378	−	0.546625i	$-0.184088\pi$
$643$	7.37275	+	7.37275i	0.290753	+	0.290753i	−0.546625	+	0.837378i	$0.684088\pi$
$644$		0			0
$645$	0.963735	−	0.963735i	0.0379470	−	0.0379470i
$646$		0			0
$647$			11.6132i			0.456560i	0.973595	+	0.228280i	$0.0733102\pi$
$647$			11.6132i			0.456560i	−0.973595	+	0.228280i	$0.926690\pi$
$648$		0			0
$649$		−	3.78901i		−	0.148731i
$650$		0			0
$651$	−11.8597	+	11.8597i	−0.464818	+	0.464818i
$652$		0			0
$653$	−1.93049	−	1.93049i	−0.0755458	−	0.0755458i	0.668324	−	0.743870i	$-0.267012\pi$
$653$	−1.93049	−	1.93049i	−0.0755458	−	0.0755458i	−0.743870	+	0.668324i	$0.767012\pi$
$654$		0			0
$655$	13.2082			0.516088
$656$		0			0
$657$	14.7721			0.576316
$658$		0			0
$659$	−22.3102	−	22.3102i	−0.869081	−	0.869081i	0.123290	−	0.992371i	$-0.460656\pi$
$659$	−22.3102	−	22.3102i	−0.869081	−	0.869081i	−0.992371	+	0.123290i	$0.960656\pi$
$660$		0			0
$661$	10.7033	−	10.7033i	0.416311	−	0.416311i	−0.467619	−	0.883930i	$-0.654888\pi$
$661$	10.7033	−	10.7033i	0.416311	−	0.416311i	0.883930	+	0.467619i	$0.154888\pi$
$662$		0			0
$663$		−	26.3235i		−	1.02232i
$664$		0			0
$665$		−	40.7784i		−	1.58132i
$666$		0			0
$667$	−8.70960	+	8.70960i	−0.337237	+	0.337237i
$668$		0			0
$669$	16.8050	+	16.8050i	0.649719	+	0.649719i
$670$		0			0
$671$	4.15472			0.160391
$672$		0			0
$673$	−20.6345			−0.795401			−0.397700	−	0.917515i	$-0.630192\pi$
$673$	−20.6345			−0.795401			−0.397700	+	0.917515i	$0.630192\pi$
$674$		0			0
$675$	0.791128	+	0.791128i	0.0304505	+	0.0304505i
$676$		0			0
$677$	26.8246	−	26.8246i	1.03095	−	1.03095i	0.0314484	−	0.999505i	$-0.489988\pi$
$677$	26.8246	−	26.8246i	1.03095	−	1.03095i	0.999505	−	0.0314484i	$-0.0100120\pi$
$678$		0			0
$679$		−	32.3627i		−	1.24197i
$680$		0			0
$681$			0.907457i			0.0347738i
$682$		0			0
$683$	−12.9026	+	12.9026i	−0.493705	+	0.493705i	−0.909472	−	0.415766i	$-0.863513\pi$
$683$	−12.9026	+	12.9026i	−0.493705	+	0.493705i	0.415766	+	0.909472i	$0.363513\pi$
$684$		0			0
$685$	−8.93077	−	8.93077i	−0.341227	−	0.341227i
$686$		0			0
$687$	7.55579			0.288271
$688$		0			0
$689$	−14.8871			−0.567152
$690$		0			0
$691$	21.3923	+	21.3923i	0.813803	+	0.813803i	0.985202	−	0.171399i	$-0.0548286\pi$
$691$	21.3923	+	21.3923i	0.813803	+	0.813803i	−0.171399	+	0.985202i	$0.554829\pi$
$692$		0			0
$693$	−1.21137	+	1.21137i	−0.0460161	+	0.0460161i
$694$		0			0
$695$			41.1941i			1.56258i
$696$		0			0
$697$		−	5.08312i		−	0.192537i
$698$		0			0
$699$	16.4240	−	16.4240i	0.621213	−	0.621213i
$700$		0			0
$701$	14.2040	+	14.2040i	0.536479	+	0.536479i	0.922493	−	0.386014i	$-0.126148\pi$
$701$	14.2040	+	14.2040i	0.536479	+	0.536479i	−0.386014	+	0.922493i	$0.626148\pi$
$702$		0			0
$703$	−24.8776			−0.938278
$704$		0			0
$705$	−6.99647			−0.263502
$706$		0			0
$707$	−19.2458	−	19.2458i	−0.723812	−	0.723812i
$708$		0			0
$709$	−29.5474	+	29.5474i	−1.10968	+	1.10968i	−0.116485	+	0.993192i	$0.537163\pi$
$709$	−29.5474	+	29.5474i	−1.10968	+	1.10968i	−0.993192	+	0.116485i	$0.962837\pi$
$710$		0			0
$711$			6.32000i			0.237018i
$712$		0			0
$713$			18.5478i			0.694622i
$714$		0			0
$715$	−4.78473	+	4.78473i	−0.178939	+	0.178939i
$716$		0			0
$717$	−19.0363	−	19.0363i	−0.710922	−	0.710922i
$718$		0			0
$719$	−28.3683			−1.05796			−0.528979	−	0.848635i	$-0.677425\pi$
$719$	−28.3683			−1.05796			−0.528979	+	0.848635i	$0.677425\pi$
$720$		0			0
$721$	8.53450			0.317841
$722$		0			0
$723$	−7.31814	−	7.31814i	−0.272165	−	0.272165i
$724$		0			0
$725$	−3.44521	+	3.44521i	−0.127952	+	0.127952i
$726$		0			0
$727$			20.4843i			0.759722i	0.925044	+	0.379861i	$0.124028\pi$
$727$			20.4843i			0.759722i	−0.925044	+	0.379861i	$0.875972\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−2.51119	+	2.51119i	−0.0928797	+	0.0928797i
$732$		0			0
$733$	33.9961	+	33.9961i	1.25567	+	1.25567i	0.953138	+	0.302536i	$0.0978331\pi$
$733$	33.9961	+	33.9961i	1.25567	+	1.25567i	0.302536	+	0.953138i	$0.402167\pi$
$734$		0			0
$735$	1.13401			0.0418286
$736$		0			0
$737$	−2.00706			−0.0739310
$738$		0			0
$739$	−15.1645	−	15.1645i	−0.557836	−	0.557836i	0.370855	−	0.928691i	$-0.379065\pi$
$739$	−15.1645	−	15.1645i	−0.557836	−	0.557836i	−0.928691	+	0.370855i	$0.879065\pi$
$740$		0			0
$741$	−18.6135	+	18.6135i	−0.683785	+	0.683785i
$742$		0			0
$743$			2.17431i			0.0797677i	0.999204	+	0.0398839i	$0.0126988\pi$
$743$			2.17431i			0.0797677i	−0.999204	+	0.0398839i	$0.987301\pi$
$744$		0			0
$745$			27.6631i			1.01350i
$746$		0			0
$747$	0.641669	−	0.641669i	0.0234774	−	0.0234774i
$748$		0			0
$749$	−35.9670	−	35.9670i	−1.31421	−	1.31421i
$750$		0			0
$751$	−29.8980			−1.09099			−0.545497	−	0.838113i	$-0.683659\pi$
$751$	−29.8980			−1.09099			−0.545497	+	0.838113i	$0.683659\pi$
$752$		0			0
$753$	13.7984			0.502843
$754$		0			0
$755$	−25.6256	−	25.6256i	−0.932610	−	0.932610i
$756$		0			0
$757$	−15.3294	+	15.3294i	−0.557157	+	0.557157i	−0.928497	−	0.371340i	$-0.878899\pi$
$757$	−15.3294	+	15.3294i	−0.557157	+	0.557157i	0.371340	+	0.928497i	$0.378899\pi$
$758$		0			0
$759$			1.89450i			0.0687661i
$760$		0			0
$761$		−	4.29449i		−	0.155675i	−0.996966	−	0.0778375i	$-0.975198\pi$
$761$		−	4.29449i		−	0.155675i	0.996966	−	0.0778375i	$-0.0248015\pi$
$762$		0			0
$763$	7.08216	−	7.08216i	0.256392	−	0.256392i
$764$		0			0
$765$	−11.2739	−	11.2739i	−0.407609	−	0.407609i
$766$		0			0
$767$	−23.1027			−0.834191
$768$		0			0
$769$	33.8819			1.22181			0.610907	−	0.791703i	$-0.290805\pi$
$769$	33.8819			1.22181			0.610907	+	0.791703i	$0.290805\pi$
$770$		0			0
$771$	12.0183	+	12.0183i	0.432829	+	0.432829i
$772$		0			0
$773$	−35.0230	+	35.0230i	−1.25969	+	1.25969i	−0.308450	+	0.951240i	$0.599810\pi$
$773$	−35.0230	+	35.0230i	−1.25969	+	1.25969i	−0.951240	+	0.308450i	$0.900190\pi$
$774$		0			0
$775$			7.33686i			0.263548i
$776$		0			0
$777$			9.87175i			0.354147i
$778$		0			0
$779$	−3.59431	+	3.59431i	−0.128779	+	0.128779i
$780$		0			0
$781$	−2.42274	−	2.42274i	−0.0866923	−	0.0866923i
$782$		0			0
$783$	4.35480			0.155628
$784$		0			0
$785$	−11.0263			−0.393545
$786$		0			0
$787$	−24.1090	−	24.1090i	−0.859393	−	0.859393i	0.131873	−	0.991267i	$-0.457901\pi$
$787$	−24.1090	−	24.1090i	−0.859393	−	0.859393i	−0.991267	+	0.131873i	$0.957901\pi$
$788$		0			0
$789$	21.2082	−	21.2082i	0.755032	−	0.755032i
$790$		0			0
$791$		−	5.72312i		−	0.203491i
$792$		0			0
$793$		−	25.3326i		−	0.899585i
$794$		0			0
$795$	−6.37588	+	6.37588i	−0.226129	+	0.226129i
$796$		0			0
$797$	−28.7722	−	28.7722i	−1.01917	−	1.01917i	−0.999813	−	0.0193524i	$-0.993840\pi$
$797$	−28.7722	−	28.7722i	−1.01917	−	1.01917i	−0.0193524	−	0.999813i	$-0.506160\pi$
$798$		0			0
$799$	18.2306			0.644952
$800$		0			0
$801$	−6.31724			−0.223209
$802$		0			0
$803$	6.99647	+	6.99647i	0.246900	+	0.246900i
$804$		0			0
$805$	−12.6533	+	12.6533i	−0.445971	+	0.445971i
$806$		0			0
$807$			29.1332i			1.02554i
$808$		0			0
$809$		−	10.9926i		−	0.386478i	−0.981152	−	0.193239i	$-0.938101\pi$
$809$		−	10.9926i		−	0.386478i	0.981152	−	0.193239i	$-0.0618993\pi$
$810$		0			0
$811$	15.0259	−	15.0259i	0.527630	−	0.527630i	−0.392235	−	0.919865i	$-0.628298\pi$
$811$	15.0259	−	15.0259i	0.527630	−	0.527630i	0.919865	+	0.392235i	$0.128298\pi$
$812$		0			0
$813$	18.8448	+	18.8448i	0.660916	+	0.660916i
$814$		0			0
$815$	−19.2574			−0.674558
$816$		0			0
$817$	3.55136			0.124246
$818$		0			0
$819$	7.38607	+	7.38607i	0.258090	+	0.258090i
$820$		0			0
$821$	−21.2536	+	21.2536i	−0.741756	+	0.741756i	−0.972916	−	0.231159i	$-0.925748\pi$
$821$	−21.2536	+	21.2536i	−0.741756	+	0.741756i	0.231159	+	0.972916i	$0.425748\pi$
$822$		0			0
$823$			55.0851i			1.92015i	0.279751	+	0.960073i	$0.409748\pi$
$823$			55.0851i			1.92015i	−0.279751	+	0.960073i	$0.590252\pi$
$824$		0			0
$825$			0.749397i			0.0260907i
$826$		0			0
$827$	24.4290	−	24.4290i	0.849480	−	0.849480i	−0.140588	−	0.990068i	$-0.544899\pi$
$827$	24.4290	−	24.4290i	0.849480	−	0.849480i	0.990068	+	0.140588i	$0.0448994\pi$
$828$		0			0
$829$	−21.9235	−	21.9235i	−0.761436	−	0.761436i	0.215146	−	0.976582i	$-0.430977\pi$
$829$	−21.9235	−	21.9235i	−0.761436	−	0.761436i	−0.976582	+	0.215146i	$0.930977\pi$
$830$		0			0
$831$	17.1430			0.594685
$832$		0			0
$833$	−2.95487			−0.102380
$834$		0			0
$835$	−35.2996	−	35.2996i	−1.22159	−	1.22159i
$836$		0			0
$837$	4.63696	−	4.63696i	0.160277	−	0.160277i
$838$		0			0
$839$			5.14195i			0.177520i	0.996053	+	0.0887599i	$0.0282904\pi$
$839$			5.14195i			0.177520i	−0.996053	+	0.0887599i	$0.971710\pi$
$840$		0			0
$841$		−	10.0357i		−	0.346059i
$842$		0			0
$843$	1.95577	−	1.95577i	0.0673604	−	0.0673604i
$844$		0			0
$845$	6.43541	+	6.43541i	0.221385	+	0.221385i
$846$		0			0
$847$	26.9867			0.927272
$848$		0			0
$849$	−6.34315			−0.217696
$850$		0			0
$851$	7.71940	+	7.71940i	0.264618	+	0.264618i
$852$		0			0
$853$	13.0857	−	13.0857i	0.448046	−	0.448046i	−0.446659	−	0.894704i	$-0.647386\pi$
$853$	13.0857	−	13.0857i	0.448046	−	0.448046i	0.894704	+	0.446659i	$0.147386\pi$
$854$		0			0
$855$			15.9437i			0.545264i
$856$		0			0
$857$		−	22.8878i		−	0.781833i	−0.920426	−	0.390916i	$-0.872158\pi$
$857$		−	22.8878i		−	0.781833i	0.920426	−	0.390916i	$-0.127842\pi$
$858$		0			0
$859$	25.1225	−	25.1225i	0.857169	−	0.857169i	−0.133834	−	0.991004i	$-0.542729\pi$
$859$	25.1225	−	25.1225i	0.857169	−	0.857169i	0.991004	+	0.133834i	$0.0427290\pi$
$860$		0			0
$861$	1.42627	+	1.42627i	0.0486070	+	0.0486070i
$862$		0			0
$863$	43.9296			1.49538			0.747691	−	0.664047i	$-0.231163\pi$
$863$	43.9296			1.49538			0.747691	+	0.664047i	$0.231163\pi$
$864$		0			0
$865$	15.2286			0.517788
$866$		0			0
$867$	17.3554	+	17.3554i	0.589422	+	0.589422i
$868$		0			0
$869$	−2.99331	+	2.99331i	−0.101541	+	0.101541i
$870$		0			0
$871$			12.2376i			0.414657i
$872$		0			0
$873$			12.6533i			0.428250i
$874$		0			0
$875$	17.3629	−	17.3629i	0.586974	−	0.586974i
$876$		0			0
$877$	15.2575	+	15.2575i	0.515208	+	0.515208i	0.916117	−	0.400910i	$-0.131306\pi$
$877$	15.2575	+	15.2575i	0.515208	+	0.515208i	−0.400910	+	0.916117i	$0.631306\pi$
$878$		0			0
$879$	−11.6078			−0.391520
$880$		0			0
$881$	21.6686			0.730035			0.365018	−	0.931001i	$-0.381063\pi$
$881$	21.6686			0.730035			0.365018	+	0.931001i	$0.381063\pi$
$882$		0			0
$883$	0.0590385	+	0.0590385i	0.00198680	+	0.00198680i	0.708099	−	0.706113i	$-0.249553\pi$
$883$	0.0590385	+	0.0590385i	0.00198680	+	0.00198680i	−0.706113	+	0.708099i	$0.749553\pi$
$884$		0			0
$885$	−9.89450	+	9.89450i	−0.332600	+	0.332600i
$886$		0			0
$887$		−	30.8043i		−	1.03431i	−0.855892	−	0.517154i	$-0.826991\pi$
$887$		−	30.8043i		−	1.03431i	0.855892	−	0.517154i	$-0.173009\pi$
$888$		0			0
$889$			31.2404i			1.04777i
$890$		0			0
$891$	0.473626	−	0.473626i	0.0158671	−	0.0158671i
$892$		0			0
$893$	−12.8910	−	12.8910i	−0.431380	−	0.431380i
$894$		0			0
$895$	46.4682			1.55326
$896$		0			0
$897$	11.5514			0.385689
$898$		0			0
$899$	20.1930	+	20.1930i	0.673475	+	0.673475i
$900$		0			0
$901$	16.6135	−	16.6135i	0.553477	−	0.553477i
$902$		0			0
$903$		−	1.40922i		−	0.0468960i
$904$		0			0
$905$		−	22.2008i		−	0.737979i
$906$		0			0
$907$	−35.0170	+	35.0170i	−1.16272	+	1.16272i	−0.178844	+	0.983878i	$0.557236\pi$
$907$	−35.0170	+	35.0170i	−1.16272	+	1.16272i	−0.983878	+	0.178844i	$0.942764\pi$
$908$		0			0
$909$	7.52480	+	7.52480i	0.249582	+	0.249582i
$910$		0			0
$911$	−0.0829331			−0.00274770			−0.00137385	−	0.999999i	$-0.500437\pi$
$911$	−0.0829331			−0.00274770			−0.00137385	+	0.999999i	$0.500437\pi$
$912$		0			0
$913$	0.607822			0.0201160
$914$		0			0
$915$	−10.8495	−	10.8495i	−0.358674	−	0.358674i
$916$		0			0
$917$	9.65685	−	9.65685i	0.318897	−	0.318897i
$918$		0			0
$919$		−	20.1161i		−	0.663568i	−0.943355	−	0.331784i	$-0.892350\pi$
$919$		−	20.1161i		−	0.663568i	0.943355	−	0.331784i	$-0.107650\pi$
$920$		0			0
$921$		−	14.7855i		−	0.487198i
$922$		0			0
$923$	−14.7721	+	14.7721i	−0.486231	+	0.486231i
$924$		0			0
$925$	3.05352	+	3.05352i	0.100399	+	0.100399i
$926$		0			0
$927$	−3.33686			−0.109597
$928$		0			0
$929$	8.55098			0.280549			0.140274	−	0.990113i	$-0.455202\pi$
$929$	8.55098			0.280549			0.140274	+	0.990113i	$0.455202\pi$
$930$		0			0
$931$	2.08941	+	2.08941i	0.0684776	+	0.0684776i
$932$		0			0
$933$	−10.6604	+	10.6604i	−0.349005	+	0.349005i
$934$		0			0
$935$		−	10.6792i		−	0.349248i
$936$		0			0
$937$			33.5780i			1.09695i	0.836168	+	0.548473i	$0.184791\pi$
$937$			33.5780i			1.09695i	−0.836168	+	0.548473i	$0.815209\pi$
$938$		0			0
$939$	16.2654	−	16.2654i	0.530801	−	0.530801i
$940$		0			0
$941$	−8.48463	−	8.48463i	−0.276591	−	0.276591i	0.555156	−	0.831747i	$-0.312659\pi$
$941$	−8.48463	−	8.48463i	−0.276591	−	0.276591i	−0.831747	+	0.555156i	$0.812659\pi$
$942$		0			0
$943$	2.23059			0.0726380
$944$		0			0
$945$	6.32666			0.205806
$946$		0			0
$947$	−17.8571	−	17.8571i	−0.580277	−	0.580277i	0.354702	−	0.934979i	$-0.384582\pi$
$947$	−17.8571	−	17.8571i	−0.580277	−	0.580277i	−0.934979	+	0.354702i	$0.884582\pi$
$948$		0			0
$949$	42.6596	−	42.6596i	1.38479	−	1.38479i
$950$		0			0
$951$		−	9.55855i		−	0.309957i
$952$		0			0
$953$		−	3.86469i		−	0.125190i	−0.998039	−	0.0625948i	$-0.980062\pi$
$953$		−	3.86469i		−	0.125190i	0.998039	−	0.0625948i	$-0.0199376\pi$
$954$		0			0
$955$	−9.79607	+	9.79607i	−0.316993	+	0.316993i
$956$		0			0
$957$	2.06255	+	2.06255i	0.0666726	+	0.0666726i
$958$		0			0
$959$	−13.0590			−0.421698
$960$		0			0
$961$	12.0027			0.387185
$962$		0			0
$963$	14.0625	+	14.0625i	0.453159	+	0.453159i
$964$		0			0
$965$	−34.0228	+	34.0228i	−1.09523	+	1.09523i
$966$		0			0
$967$		−	37.8714i		−	1.21786i	−0.793224	−	0.608930i	$-0.791599\pi$
$967$		−	37.8714i		−	1.21786i	0.793224	−	0.608930i	$-0.208401\pi$
$968$		0			0
$969$		−	41.5443i		−	1.33460i
$970$		0			0
$971$	−2.64873	+	2.64873i	−0.0850017	+	0.0850017i	−0.748329	−	0.663327i	$-0.769144\pi$
$971$	−2.64873	+	2.64873i	−0.0850017	+	0.0850017i	0.663327	+	0.748329i	$0.269144\pi$
$972$		0			0
$973$	30.1180	+	30.1180i	0.965540	+	0.965540i
$974$		0			0
$975$	4.56930			0.146335
$976$		0			0
$977$	17.6530			0.564768			0.282384	−	0.959301i	$-0.408875\pi$
$977$	17.6530			0.564768			0.282384	+	0.959301i	$0.408875\pi$
$978$		0			0
$979$	−2.99201	−	2.99201i	−0.0956250	−	0.0956250i
$980$		0			0
$981$	−2.76901	+	2.76901i	−0.0884078	+	0.0884078i
$982$		0			0
$983$		−	22.3557i		−	0.713035i	−0.934289	−	0.356518i	$-0.883964\pi$
$983$		−	22.3557i		−	0.713035i	0.934289	−	0.356518i	$-0.116036\pi$
$984$		0			0
$985$		−	4.33057i		−	0.137983i
$986$		0			0
$987$	−5.11529	+	5.11529i	−0.162822	+	0.162822i
$988$		0			0
$989$	−1.10197	−	1.10197i	−0.0350405	−	0.0350405i
$990$		0			0
$991$	−17.8769			−0.567878			−0.283939	−	0.958842i	$-0.591641\pi$
$991$	−17.8769			−0.567878			−0.283939	+	0.958842i	$0.591641\pi$
$992$		0			0
$993$	27.8079			0.882456
$994$		0			0
$995$	−1.73812	−	1.73812i	−0.0551020	−	0.0551020i
$996$		0			0
$997$	4.28610	−	4.28610i	0.135742	−	0.135742i	−0.635971	−	0.771713i	$-0.719400\pi$
$997$	4.28610	−	4.28610i	0.135742	−	0.135742i	0.771713	+	0.635971i	$0.219400\pi$
$998$		0			0
$999$		−	3.85970i		−	0.122116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.j.a.145.4		8
3.2	odd	2		576.2.k.b.145.1		8
4.3	odd	2		48.2.j.a.13.2	✓	8
8.3	odd	2		384.2.j.b.289.3		8
8.5	even	2		384.2.j.a.289.1		8
12.11	even	2		144.2.k.b.109.3		8
16.3	odd	4		384.2.j.b.97.3		8
16.5	even	4	inner	192.2.j.a.49.4		8
16.11	odd	4		48.2.j.a.37.2	yes	8
16.13	even	4		384.2.j.a.97.1		8
24.5	odd	2		1152.2.k.f.289.4		8
24.11	even	2		1152.2.k.c.289.4		8
32.3	odd	8		3072.2.d.f.1537.3		8
32.5	even	8		3072.2.a.n.1.3		4
32.11	odd	8		3072.2.a.i.1.2		4
32.13	even	8		3072.2.d.i.1537.2		8
32.19	odd	8		3072.2.d.f.1537.6		8
32.21	even	8		3072.2.a.o.1.2		4
32.27	odd	8		3072.2.a.t.1.3		4
32.29	even	8		3072.2.d.i.1537.7		8
48.5	odd	4		576.2.k.b.433.1		8
48.11	even	4		144.2.k.b.37.3		8
48.29	odd	4		1152.2.k.f.865.4		8
48.35	even	4		1152.2.k.c.865.4		8
96.5	odd	8		9216.2.a.x.1.2		4
96.11	even	8		9216.2.a.bo.1.3		4
96.53	odd	8		9216.2.a.bn.1.3		4
96.59	even	8		9216.2.a.y.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.2	✓	8	4.3	odd	2
48.2.j.a.37.2	yes	8	16.11	odd	4
144.2.k.b.37.3		8	48.11	even	4
144.2.k.b.109.3		8	12.11	even	2
192.2.j.a.49.4		8	16.5	even	4	inner
192.2.j.a.145.4		8	1.1	even	1	trivial
384.2.j.a.97.1		8	16.13	even	4
384.2.j.a.289.1		8	8.5	even	2
384.2.j.b.97.3		8	16.3	odd	4
384.2.j.b.289.3		8	8.3	odd	2
576.2.k.b.145.1		8	3.2	odd	2
576.2.k.b.433.1		8	48.5	odd	4
1152.2.k.c.289.4		8	24.11	even	2
1152.2.k.c.865.4		8	48.35	even	4
1152.2.k.f.289.4		8	24.5	odd	2
1152.2.k.f.865.4		8	48.29	odd	4
3072.2.a.i.1.2		4	32.11	odd	8
3072.2.a.n.1.3		4	32.5	even	8
3072.2.a.o.1.2		4	32.21	even	8
3072.2.a.t.1.3		4	32.27	odd	8
3072.2.d.f.1537.3		8	32.3	odd	8
3072.2.d.f.1537.6		8	32.19	odd	8
3072.2.d.i.1537.2		8	32.13	even	8
3072.2.d.i.1537.7		8	32.29	even	8
9216.2.a.x.1.2		4	96.5	odd	8
9216.2.a.y.1.2		4	96.59	even	8
9216.2.a.bn.1.3		4	96.53	odd	8
9216.2.a.bo.1.3		4	96.11	even	8

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +1.00000i q^{9} +(-0.473626 + 0.473626i) q^{11} +(2.88784 + 2.88784i) q^{13} +2.47363 q^{15} -6.44549 q^{17} +(4.55765 + 4.55765i) q^{19} +(1.80853 - 1.80853i) q^{21} -2.82843i q^{23} -1.11882i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-3.07931 - 3.07931i) q^{29} -6.55765 q^{31} -0.669808 q^{33} +(-4.47363 - 4.47363i) q^{35} +(-2.72922 + 2.72922i) q^{37} +4.08402i q^{39} +0.788632i q^{41} +(0.389604 - 0.389604i) q^{43} +(1.74912 + 1.74912i) q^{45} -2.82843 q^{47} +0.458440 q^{49} +(-4.55765 - 4.55765i) q^{51} +(-2.57754 + 2.57754i) q^{53} +1.65685i q^{55} +6.44549i q^{57} +(-4.00000 + 4.00000i) q^{59} +(-4.38607 - 4.38607i) q^{61} +2.55765 q^{63} +10.1023 q^{65} +(2.11882 + 2.11882i) q^{67} +(2.00000 - 2.00000i) q^{69} +5.11529i q^{71} -14.7721i q^{73} +(0.791128 - 0.791128i) q^{75} +(1.21137 + 1.21137i) q^{77} +6.32000 q^{79} -1.00000 q^{81} +(-0.641669 - 0.641669i) q^{83} +(-11.2739 + 11.2739i) q^{85} -4.35480i q^{87} +6.31724i q^{89} +(7.38607 - 7.38607i) q^{91} +(-4.63696 - 4.63696i) q^{93} +15.9437 q^{95} +12.6533 q^{97} +(-0.473626 - 0.473626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{43} - 8 q^{49} - 8 q^{51} + 16 q^{53} - 32 q^{59} + 16 q^{61} - 8 q^{63} - 16 q^{65} + 16 q^{67} + 16 q^{69} - 16 q^{75}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^43 - 8 * q^49 - 8 * q^51 + 16 * q^53 - 32 * q^59 + 16 * q^61 - 8 * q^63 - 16 * q^65 + 16 * q^67 + 16 * q^69 - 16 * q^75 + 16 * q^77 + 24 * q^79 - 8 * q^81 + 40 * q^83 - 16 * q^85 + 8 * q^91 + 48 * q^95 + 8 * q^99

Introduction

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