LMFDB - Embedded newform 1148.2.k.b.337.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.17
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +O(q^{10})$	\(q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +(2.99130 + 2.99130i) q^{11} +(0.619012 + 0.619012i) q^{13} +(5.52326 - 5.52326i) q^{15} +(1.08301 - 1.08301i) q^{17} +(-1.93662 + 1.93662i) q^{19} +2.63662i q^{21} -1.66835 q^{23} -3.77657 q^{25} +(-1.77446 + 1.77446i) q^{27} +(-2.85131 - 2.85131i) q^{29} +10.4509 q^{31} +11.1538i q^{33} +(2.09482 - 2.09482i) q^{35} +5.67577 q^{37} +2.30814i q^{39} +(-2.65185 + 5.82818i) q^{41} +0.246878i q^{43} +11.7072 q^{45} +(1.86462 - 1.86462i) q^{47} +1.00000i q^{49} +4.03826 q^{51} +(-2.37754 - 2.37754i) q^{53} +(8.86182 - 8.86182i) q^{55} -7.22118 q^{57} +12.0601 q^{59} +2.07952i q^{61} +(-2.79432 + 2.79432i) q^{63} +(1.83384 - 1.83384i) q^{65} +(-3.35588 + 3.35588i) q^{67} +(-3.11043 - 3.11043i) q^{69} +(-7.87049 - 7.87049i) q^{71} +2.12655i q^{73} +(-7.04094 - 7.04094i) q^{75} +4.23034i q^{77} +(-3.02140 - 3.02140i) q^{79} +5.23882 q^{81} -2.75282 q^{83} +(-3.20844 - 3.20844i) q^{85} -10.6318i q^{87} +(-9.71983 - 9.71983i) q^{89} +0.875415i q^{91} +(19.4843 + 19.4843i) q^{93} +(5.73730 + 5.73730i) q^{95} +(-11.1964 + 11.1964i) q^{97} +(-11.8210 + 11.8210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.86437	+	1.86437i	1.07640	+	1.07640i	0.996830	+	0.0795665i	$0.0253536\pi$
$3$	1.86437	+	1.86437i	1.07640	+	1.07640i	0.0795665	+	0.996830i	$0.474646\pi$
$4$		0			0
$5$		−	2.96253i		−	1.32488i	−0.749114	−	0.662441i	$-0.769520\pi$
$5$		−	2.96253i		−	1.32488i	0.749114	−	0.662441i	$-0.230480\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$			3.95177i			1.31726i
$10$		0			0
$11$	2.99130	+	2.99130i	0.901912	+	0.901912i	0.995601	−	0.0936893i	$-0.0298660\pi$
$11$	2.99130	+	2.99130i	0.901912	+	0.901912i	−0.0936893	+	0.995601i	$0.529866\pi$
$12$		0			0
$13$	0.619012	+	0.619012i	0.171683	+	0.171683i	0.787718	−	0.616035i	$-0.211262\pi$
$13$	0.619012	+	0.619012i	0.171683	+	0.171683i	−0.616035	+	0.787718i	$0.711262\pi$
$14$		0			0
$15$	5.52326	−	5.52326i	1.42610	−	1.42610i
$16$		0			0
$17$	1.08301	−	1.08301i	0.262668	−	0.262668i	−0.563469	−	0.826137i	$-0.690534\pi$
$17$	1.08301	−	1.08301i	0.262668	−	0.262668i	0.826137	+	0.563469i	$0.190534\pi$
$18$		0			0
$19$	−1.93662	+	1.93662i	−0.444292	+	0.444292i	−0.893452	−	0.449160i	$-0.851723\pi$
$19$	−1.93662	+	1.93662i	−0.444292	+	0.444292i	0.449160	+	0.893452i	$0.351723\pi$
$20$		0			0
$21$			2.63662i			0.575358i
$22$		0			0
$23$	−1.66835			−0.347875			−0.173938	−	0.984757i	$-0.555649\pi$
$23$	−1.66835			−0.347875			−0.173938	+	0.984757i	$0.555649\pi$
$24$		0			0
$25$	−3.77657			−0.755314
$26$		0			0
$27$	−1.77446	+	1.77446i	−0.341494	+	0.341494i
$28$		0			0
$29$	−2.85131	−	2.85131i	−0.529475	−	0.529475i	0.390941	−	0.920416i	$-0.372150\pi$
$29$	−2.85131	−	2.85131i	−0.529475	−	0.529475i	−0.920416	+	0.390941i	$0.872150\pi$
$30$		0			0
$31$	10.4509			1.87703			0.938515	−	0.345238i	$-0.112202\pi$
$31$	10.4509			1.87703			0.938515	+	0.345238i	$0.112202\pi$
$32$		0			0
$33$			11.1538i			1.94163i
$34$		0			0
$35$	2.09482	−	2.09482i	0.354090	−	0.354090i
$36$		0			0
$37$	5.67577			0.933090			0.466545	−	0.884497i	$-0.345499\pi$
$37$	5.67577			0.933090			0.466545	+	0.884497i	$0.345499\pi$
$38$		0			0
$39$			2.30814i			0.369598i
$40$		0			0
$41$	−2.65185	+	5.82818i	−0.414150	+	0.910209i
$41$	−2.65185	+	5.82818i	−0.414150	+	0.910209i
$42$		0			0
$43$			0.246878i			0.0376486i	0.999823	+	0.0188243i	$0.00599231\pi$
$43$			0.246878i			0.0376486i	−0.999823	+	0.0188243i	$0.994008\pi$
$44$		0			0
$45$	11.7072			1.74521
$46$		0			0
$47$	1.86462	−	1.86462i	0.271983	−	0.271983i	−0.557915	−	0.829898i	$-0.688399\pi$
$47$	1.86462	−	1.86462i	0.271983	−	0.271983i	0.829898	+	0.557915i	$0.188399\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	4.03826			0.565470
$52$		0			0
$53$	−2.37754	−	2.37754i	−0.326581	−	0.326581i	0.524704	−	0.851285i	$-0.324176\pi$
$53$	−2.37754	−	2.37754i	−0.326581	−	0.326581i	−0.851285	+	0.524704i	$0.824176\pi$
$54$		0			0
$55$	8.86182	−	8.86182i	1.19493	−	1.19493i
$56$		0			0
$57$	−7.22118			−0.956468
$58$		0			0
$59$	12.0601			1.57010			0.785048	−	0.619436i	$-0.212638\pi$
$59$	12.0601			1.57010			0.785048	+	0.619436i	$0.212638\pi$
$60$		0			0
$61$			2.07952i			0.266255i	0.991099	+	0.133128i	$0.0425020\pi$
$61$			2.07952i			0.266255i	−0.991099	+	0.133128i	$0.957498\pi$
$62$		0			0
$63$	−2.79432	+	2.79432i	−0.352052	+	0.352052i
$64$		0			0
$65$	1.83384	−	1.83384i	0.227460	−	0.227460i
$66$		0			0
$67$	−3.35588	+	3.35588i	−0.409986	+	0.409986i	−0.881734	−	0.471748i	$-0.843623\pi$
$67$	−3.35588	+	3.35588i	−0.409986	+	0.409986i	0.471748	+	0.881734i	$0.343623\pi$
$68$		0			0
$69$	−3.11043	−	3.11043i	−0.374452	−	0.374452i
$70$		0			0
$71$	−7.87049	−	7.87049i	−0.934055	−	0.934055i	0.0639014	−	0.997956i	$-0.479646\pi$
$71$	−7.87049	−	7.87049i	−0.934055	−	0.934055i	−0.997956	+	0.0639014i	$0.979646\pi$
$72$		0			0
$73$			2.12655i			0.248894i	0.992226	+	0.124447i	$0.0397156\pi$
$73$			2.12655i			0.248894i	−0.992226	+	0.124447i	$0.960284\pi$
$74$		0			0
$75$	−7.04094	−	7.04094i	−0.813017	−	0.813017i
$76$		0			0
$77$			4.23034i			0.482092i
$78$		0			0
$79$	−3.02140	−	3.02140i	−0.339934	−	0.339934i	0.516408	−	0.856342i	$-0.327269\pi$
$79$	−3.02140	−	3.02140i	−0.339934	−	0.339934i	−0.856342	+	0.516408i	$0.827269\pi$
$80$		0			0
$81$	5.23882			0.582091
$82$		0			0
$83$	−2.75282			−0.302162			−0.151081	−	0.988521i	$-0.548275\pi$
$83$	−2.75282			−0.302162			−0.151081	+	0.988521i	$0.548275\pi$
$84$		0			0
$85$	−3.20844	−	3.20844i	−0.348004	−	0.348004i
$86$		0			0
$87$		−	10.6318i		−	1.13985i
$88$		0			0
$89$	−9.71983	−	9.71983i	−1.03030	−	1.03030i	−0.999526	−	0.0307731i	$-0.990203\pi$
$89$	−9.71983	−	9.71983i	−1.03030	−	1.03030i	−0.0307731	−	0.999526i	$-0.509797\pi$
$90$		0			0
$91$			0.875415i			0.0917684i
$92$		0			0
$93$	19.4843	+	19.4843i	2.02043	+	2.02043i
$94$		0			0
$95$	5.73730	+	5.73730i	0.588635	+	0.588635i
$96$		0			0
$97$	−11.1964	+	11.1964i	−1.13682	+	1.13682i	−0.147806	+	0.989016i	$0.547221\pi$
$97$	−11.1964	+	11.1964i	−1.13682	+	1.13682i	−0.989016	+	0.147806i	$0.952779\pi$
$98$		0			0
$99$	−11.8210	+	11.8210i	−1.18805	+	1.18805i
$100$		0			0
$101$	−11.9754	+	11.9754i	−1.19160	+	1.19160i	−0.214977	+	0.976619i	$0.568968\pi$
$101$	−11.9754	+	11.9754i	−1.19160	+	1.19160i	−0.976619	+	0.214977i	$0.931032\pi$
$102$		0			0
$103$		−	4.53596i		−	0.446941i	−0.974711	−	0.223470i	$-0.928261\pi$
$103$		−	4.53596i		−	0.446941i	0.974711	−	0.223470i	$-0.0717386\pi$
$104$		0			0
$105$	7.81106			0.762282
$106$		0			0
$107$	−5.03676			−0.486922			−0.243461	−	0.969911i	$-0.578283\pi$
$107$	−5.03676			−0.486922			−0.243461	+	0.969911i	$0.578283\pi$
$108$		0			0
$109$	−7.55793	+	7.55793i	−0.723918	+	0.723918i	−0.969401	−	0.245483i	$-0.921054\pi$
$109$	−7.55793	+	7.55793i	−0.723918	+	0.723918i	0.245483	+	0.969401i	$0.421054\pi$
$110$		0			0
$111$	10.5817	+	10.5817i	1.00437	+	1.00437i
$112$		0			0
$113$	−15.4571			−1.45408			−0.727041	−	0.686594i	$-0.759105\pi$
$113$	−15.4571			−1.45408			−0.727041	+	0.686594i	$0.759105\pi$
$114$		0			0
$115$			4.94254i			0.460894i
$116$		0			0
$117$	−2.44619	+	2.44619i	−0.226151	+	0.226151i
$118$		0			0
$119$	1.53160			0.140402
$120$		0			0
$121$			6.89580i			0.626891i
$122$		0			0
$123$	−15.8099	+	5.92185i	−1.42553	+	0.533956i
$124$		0			0
$125$		−	3.62444i		−	0.324180i
$126$		0			0
$127$	3.48488			0.309233			0.154616	−	0.987975i	$-0.450586\pi$
$127$	3.48488			0.309233			0.154616	+	0.987975i	$0.450586\pi$
$128$		0			0
$129$	−0.460273	+	0.460273i	−0.0405248	+	0.0405248i
$130$		0			0
$131$		−	8.94915i		−	0.781891i	−0.920414	−	0.390946i	$-0.872148\pi$
$131$		−	8.94915i		−	0.781891i	0.920414	−	0.390946i	$-0.127852\pi$
$132$		0			0
$133$	−2.73880			−0.237484
$134$		0			0
$135$	5.25688	+	5.25688i	0.452440	+	0.452440i
$136$		0			0
$137$	9.10060	−	9.10060i	0.777517	−	0.777517i	−0.201891	−	0.979408i	$-0.564709\pi$
$137$	9.10060	−	9.10060i	0.777517	−	0.777517i	0.979408	+	0.201891i	$0.0647088\pi$
$138$		0			0
$139$	−22.6023			−1.91710			−0.958552	−	0.284919i	$-0.908033\pi$
$139$	−22.6023			−1.91710			−0.958552	+	0.284919i	$0.908033\pi$
$140$		0			0
$141$	6.95269			0.585522
$142$		0			0
$143$			3.70330i			0.309686i
$144$		0			0
$145$	−8.44708	+	8.44708i	−0.701492	+	0.701492i
$146$		0			0
$147$	−1.86437	+	1.86437i	−0.153771	+	0.153771i
$148$		0			0
$149$	17.0991	−	17.0991i	1.40081	−	1.40081i	0.603292	−	0.797520i	$-0.293855\pi$
$149$	17.0991	−	17.0991i	1.40081	−	1.40081i	0.797520	−	0.603292i	$-0.206145\pi$
$150$		0			0
$151$	3.55269	+	3.55269i	0.289114	+	0.289114i	0.836730	−	0.547616i	$-0.184464\pi$
$151$	3.55269	+	3.55269i	0.289114	+	0.289114i	−0.547616	+	0.836730i	$0.684464\pi$
$152$		0			0
$153$	4.27980	+	4.27980i	0.346001	+	0.346001i
$154$		0			0
$155$		−	30.9610i		−	2.48684i
$156$		0			0
$157$	−3.45235	−	3.45235i	−0.275527	−	0.275527i	0.555793	−	0.831321i	$-0.312415\pi$
$157$	−3.45235	−	3.45235i	−0.275527	−	0.275527i	−0.831321	+	0.555793i	$0.812415\pi$
$158$		0			0
$159$		−	8.86526i		−	0.703061i
$160$		0			0
$161$	−1.17970	−	1.17970i	−0.0929736	−	0.0929736i
$162$		0			0
$163$	−12.9288			−1.01266			−0.506332	−	0.862339i	$-0.668999\pi$
$163$	−12.9288			−1.01266			−0.506332	+	0.862339i	$0.668999\pi$
$164$		0			0
$165$	33.0435			2.57243
$166$		0			0
$167$	6.02429	+	6.02429i	0.466173	+	0.466173i	0.900672	−	0.434499i	$-0.143075\pi$
$167$	6.02429	+	6.02429i	0.466173	+	0.466173i	−0.434499	+	0.900672i	$0.643075\pi$
$168$		0			0
$169$		−	12.2336i		−	0.941050i
$170$		0			0
$171$	−7.65309	−	7.65309i	−0.585247	−	0.585247i
$172$		0			0
$173$		−	10.8343i		−	0.823714i	−0.911249	−	0.411857i	$-0.864880\pi$
$173$		−	10.8343i		−	0.823714i	0.911249	−	0.411857i	$-0.135120\pi$
$174$		0			0
$175$	−2.67044	−	2.67044i	−0.201866	−	0.201866i
$176$		0			0
$177$	22.4846	+	22.4846i	1.69004	+	1.69004i
$178$		0			0
$179$	11.4482	−	11.4482i	0.855679	−	0.855679i	−0.135147	−	0.990826i	$-0.543151\pi$
$179$	11.4482	−	11.4482i	0.855679	−	0.855679i	0.990826	+	0.135147i	$0.0431506\pi$
$180$		0			0
$181$	13.7929	−	13.7929i	1.02521	−	1.02521i	0.0255409	−	0.999674i	$-0.491869\pi$
$181$	13.7929	−	13.7929i	1.02521	−	1.02521i	0.999674	−	0.0255409i	$-0.00813081\pi$
$182$		0			0
$183$	−3.87700	+	3.87700i	−0.286596	+	0.286596i
$184$		0			0
$185$		−	16.8146i		−	1.23623i
$186$		0			0
$187$	6.47921			0.473807
$188$		0			0
$189$	−2.50946			−0.182536
$190$		0			0
$191$	−11.9361	+	11.9361i	−0.863665	+	0.863665i	−0.991762	−	0.128097i	$-0.959113\pi$
$191$	−11.9361	+	11.9361i	−0.863665	+	0.863665i	0.128097	+	0.991762i	$0.459113\pi$
$192$		0			0
$193$	0.740264	+	0.740264i	0.0532854	+	0.0532854i	0.733247	−	0.679962i	$-0.238004\pi$
$193$	0.740264	+	0.740264i	0.0532854	+	0.0532854i	−0.679962	+	0.733247i	$0.738004\pi$
$194$		0			0
$195$	6.83792			0.489674
$196$		0			0
$197$		−	10.4556i		−	0.744933i	−0.928046	−	0.372466i	$-0.878512\pi$
$197$		−	10.4556i		−	0.744933i	0.928046	−	0.372466i	$-0.121488\pi$
$198$		0			0
$199$	4.72768	−	4.72768i	0.335137	−	0.335137i	−0.519397	−	0.854533i	$-0.673843\pi$
$199$	4.72768	−	4.72768i	0.335137	−	0.335137i	0.854533	+	0.519397i	$0.173843\pi$
$200$		0			0
$201$	−12.5132			−0.882615
$202$		0			0
$203$		−	4.03236i		−	0.283016i
$204$		0			0
$205$	17.2661	+	7.85619i	1.20592	+	0.548700i
$206$		0			0
$207$		−	6.59295i		−	0.458241i
$208$		0			0
$209$	−11.5861			−0.801424
$210$		0			0
$211$	−1.37936	+	1.37936i	−0.0949588	+	0.0949588i	−0.752990	−	0.658032i	$-0.771389\pi$
$211$	−1.37936	+	1.37936i	−0.0949588	+	0.0949588i	0.658032	+	0.752990i	$0.271389\pi$
$212$		0			0
$213$		−	29.3470i		−	2.01083i
$214$		0			0
$215$	0.731384			0.0498800
$216$		0			0
$217$	7.38987	+	7.38987i	0.501657	+	0.501657i
$218$		0			0
$219$	−3.96468	+	3.96468i	−0.267908	+	0.267908i
$220$		0			0
$221$	1.34079			0.0901912
$222$		0			0
$223$	−3.79309			−0.254004			−0.127002	−	0.991902i	$-0.540535\pi$
$223$	−3.79309			−0.254004			−0.127002	+	0.991902i	$0.540535\pi$
$224$		0			0
$225$		−	14.9241i		−	0.994943i
$226$		0			0
$227$	−13.0020	+	13.0020i	−0.862975	+	0.862975i	−0.991683	−	0.128707i	$-0.958917\pi$
$227$	−13.0020	+	13.0020i	−0.862975	+	0.862975i	0.128707	+	0.991683i	$0.458917\pi$
$228$		0			0
$229$	−10.9076	+	10.9076i	−0.720797	+	0.720797i	−0.968768	−	0.247970i	$-0.920236\pi$
$229$	−10.9076	+	10.9076i	−0.720797	+	0.720797i	0.247970	+	0.968768i	$0.420236\pi$
$230$		0			0
$231$	−7.88694	+	7.88694i	−0.518922	+	0.518922i
$232$		0			0
$233$	−8.61461	−	8.61461i	−0.564362	−	0.564362i	0.366181	−	0.930543i	$-0.380665\pi$
$233$	−8.61461	−	8.61461i	−0.564362	−	0.564362i	−0.930543	+	0.366181i	$0.880665\pi$
$234$		0			0
$235$	−5.52399	−	5.52399i	−0.360345	−	0.360345i
$236$		0			0
$237$		−	11.2660i		−	0.731807i
$238$		0			0
$239$	4.44216	+	4.44216i	0.287340	+	0.287340i	0.836027	−	0.548688i	$-0.184872\pi$
$239$	4.44216	+	4.44216i	0.287340	+	0.287340i	−0.548688	+	0.836027i	$0.684872\pi$
$240$		0			0
$241$			8.60928i			0.554573i	0.960787	+	0.277286i	$0.0894350\pi$
$241$			8.60928i			0.554573i	−0.960787	+	0.277286i	$0.910565\pi$
$242$		0			0
$243$	15.0905	+	15.0905i	0.968055	+	0.968055i
$244$		0			0
$245$	2.96253			0.189269
$246$		0			0
$247$	−2.39759			−0.152555
$248$		0			0
$249$	−5.13229	−	5.13229i	−0.325246	−	0.325246i
$250$		0			0
$251$			6.75004i			0.426059i	0.977046	+	0.213029i	$0.0683330\pi$
$251$			6.75004i			0.426059i	−0.977046	+	0.213029i	$0.931667\pi$
$252$		0			0
$253$	−4.99055	−	4.99055i	−0.313753	−	0.313753i
$254$		0			0
$255$		−	11.9635i		−	0.749181i
$256$		0			0
$257$	9.70135	+	9.70135i	0.605154	+	0.605154i	0.941676	−	0.336522i	$-0.109251\pi$
$257$	9.70135	+	9.70135i	0.605154	+	0.605154i	−0.336522	+	0.941676i	$0.609251\pi$
$258$		0			0
$259$	4.01337	+	4.01337i	0.249379	+	0.249379i
$260$		0			0
$261$	11.2677	−	11.2677i	0.697454	−	0.697454i
$262$		0			0
$263$	17.8681	−	17.8681i	1.10179	−	1.10179i	0.107601	−	0.994194i	$-0.465683\pi$
$263$	17.8681	−	17.8681i	1.10179	−	1.10179i	0.994194	−	0.107601i	$-0.0343168\pi$
$264$		0			0
$265$	−7.04354	+	7.04354i	−0.432681	+	0.432681i
$266$		0			0
$267$		−	36.2428i		−	2.21802i
$268$		0			0
$269$	6.55438			0.399628			0.199814	−	0.979834i	$-0.435966\pi$
$269$	6.55438			0.399628			0.199814	+	0.979834i	$0.435966\pi$
$270$		0			0
$271$	−13.8236			−0.839724			−0.419862	−	0.907588i	$-0.637922\pi$
$271$	−13.8236			−0.839724			−0.419862	+	0.907588i	$0.637922\pi$
$272$		0			0
$273$	−1.63210	+	1.63210i	−0.0987792	+	0.0987792i
$274$		0			0
$275$	−11.2969	−	11.2969i	−0.681227	−	0.681227i
$276$		0			0
$277$	11.2742			0.677403			0.338701	−	0.940894i	$-0.390012\pi$
$277$	11.2742			0.677403			0.338701	+	0.940894i	$0.390012\pi$
$278$		0			0
$279$			41.2994i			2.47253i
$280$		0			0
$281$	15.9759	−	15.9759i	0.953043	−	0.953043i	−0.0459031	−	0.998946i	$-0.514617\pi$
$281$	15.9759	−	15.9759i	0.953043	−	0.953043i	0.998946	+	0.0459031i	$0.0146165\pi$
$282$		0			0
$283$	−12.9982			−0.772663			−0.386332	−	0.922360i	$-0.626258\pi$
$283$	−12.9982			−0.772663			−0.386332	+	0.922360i	$0.626258\pi$
$284$		0			0
$285$			21.3929i			1.26721i
$286$		0			0
$287$	−5.99629	+	2.24600i	−0.353950	+	0.132577i
$288$		0			0
$289$			14.6542i			0.862011i
$290$		0			0
$291$	−41.7485			−2.44734
$292$		0			0
$293$	−14.9236	+	14.9236i	−0.871843	+	0.871843i	−0.992673	−	0.120830i	$-0.961444\pi$
$293$	−14.9236	+	14.9236i	−0.871843	+	0.871843i	0.120830	+	0.992673i	$0.461444\pi$
$294$		0			0
$295$		−	35.7285i		−	2.08019i
$296$		0			0
$297$	−10.6159			−0.615996
$298$		0			0
$299$	−1.03273	−	1.03273i	−0.0597243	−	0.0597243i
$300$		0			0
$301$	−0.174569	+	0.174569i	−0.0100620	+	0.0100620i
$302$		0			0
$303$	−44.6532			−2.56526
$304$		0			0
$305$	6.16064			0.352757
$306$		0			0
$307$		−	23.2534i		−	1.32714i	−0.748113	−	0.663571i	$-0.769040\pi$
$307$		−	23.2534i		−	1.32714i	0.748113	−	0.663571i	$-0.230960\pi$
$308$		0			0
$309$	8.45671	−	8.45671i	0.481085	−	0.481085i
$310$		0			0
$311$	−9.99104	+	9.99104i	−0.566540	+	0.566540i	−0.931157	−	0.364618i	$-0.881200\pi$
$311$	−9.99104	+	9.99104i	−0.566540	+	0.566540i	0.364618	+	0.931157i	$0.381200\pi$
$312$		0			0
$313$	6.24374	−	6.24374i	0.352917	−	0.352917i	−0.508277	−	0.861194i	$-0.669717\pi$
$313$	6.24374	−	6.24374i	0.352917	−	0.352917i	0.861194	+	0.508277i	$0.169717\pi$
$314$		0			0
$315$	8.27826	+	8.27826i	0.466427	+	0.466427i
$316$		0			0
$317$	−6.18228	−	6.18228i	−0.347231	−	0.347231i	0.511846	−	0.859077i	$-0.328962\pi$
$317$	−6.18228	−	6.18228i	−0.347231	−	0.347231i	−0.859077	+	0.511846i	$0.828962\pi$
$318$		0			0
$319$		−	17.0583i		−	0.955079i
$320$		0			0
$321$	−9.39040	−	9.39040i	−0.524121	−	0.524121i
$322$		0			0
$323$			4.19476i			0.233402i
$324$		0			0
$325$	−2.33774	−	2.33774i	−0.129675	−	0.129675i
$326$		0			0
$327$	−28.1816			−1.55845
$328$		0			0
$329$	2.63697			0.145381
$330$		0			0
$331$	1.41693	+	1.41693i	0.0778817	+	0.0778817i	0.744975	−	0.667093i	$-0.232462\pi$
$331$	1.41693	+	1.41693i	0.0778817	+	0.0778817i	−0.667093	+	0.744975i	$0.732462\pi$
$332$		0			0
$333$			22.4293i			1.22912i
$334$		0			0
$335$	9.94189	+	9.94189i	0.543183	+	0.543183i
$336$		0			0
$337$			20.9764i			1.14266i	0.820721	+	0.571329i	$0.193572\pi$
$337$			20.9764i			1.14266i	−0.820721	+	0.571329i	$0.806428\pi$
$338$		0			0
$339$	−28.8178	−	28.8178i	−1.56517	−	1.56517i
$340$		0			0
$341$	31.2617	+	31.2617i	1.69292	+	1.69292i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	−9.21474	+	9.21474i	−0.496105	+	0.496105i
$346$		0			0
$347$	10.4052	−	10.4052i	0.558578	−	0.558578i	−0.370325	−	0.928902i	$-0.620754\pi$
$347$	10.4052	−	10.4052i	0.558578	−	0.558578i	0.928902	+	0.370325i	$0.120754\pi$
$348$		0			0
$349$		−	4.66785i		−	0.249864i	−0.992165	−	0.124932i	$-0.960129\pi$
$349$		−	4.66785i		−	0.249864i	0.992165	−	0.124932i	$-0.0398713\pi$
$350$		0			0
$351$	−2.19682			−0.117258
$352$		0			0
$353$	−0.537690			−0.0286184			−0.0143092	−	0.999898i	$-0.504555\pi$
$353$	−0.537690			−0.0286184			−0.0143092	+	0.999898i	$0.504555\pi$
$354$		0			0
$355$	−23.3165	+	23.3165i	−1.23751	+	1.23751i
$356$		0			0
$357$	2.85548	+	2.85548i	0.151128	+	0.151128i
$358$		0			0
$359$	−21.2692			−1.12255			−0.561273	−	0.827631i	$-0.689688\pi$
$359$	−21.2692			−1.12255			−0.561273	+	0.827631i	$0.689688\pi$
$360$		0			0
$361$			11.4990i			0.605209i
$362$		0			0
$363$	−12.8563	+	12.8563i	−0.674783	+	0.674783i
$364$		0			0
$365$	6.29996			0.329755
$366$		0			0
$367$			4.93875i			0.257801i	0.991658	+	0.128900i	$0.0411447\pi$
$367$			4.93875i			0.257801i	−0.991658	+	0.128900i	$0.958855\pi$
$368$		0			0
$369$	−23.0316	−	10.4795i	−1.19898	−	0.545542i
$370$		0			0
$371$		−	3.36236i		−	0.174565i
$372$		0			0
$373$	−28.1009			−1.45501			−0.727506	−	0.686102i	$-0.759320\pi$
$373$	−28.1009			−1.45501			−0.727506	+	0.686102i	$0.759320\pi$
$374$		0			0
$375$	6.75731	−	6.75731i	0.348946	−	0.348946i
$376$		0			0
$377$		−	3.52999i		−	0.181804i
$378$		0			0
$379$	−0.0435824			−0.00223868			−0.00111934	−	0.999999i	$-0.500356\pi$
$379$	−0.0435824			−0.00223868			−0.00111934	+	0.999999i	$0.500356\pi$
$380$		0			0
$381$	6.49711	+	6.49711i	0.332857	+	0.332857i
$382$		0			0
$383$	2.20923	−	2.20923i	0.112886	−	0.112886i	−0.648407	−	0.761294i	$-0.724565\pi$
$383$	2.20923	−	2.20923i	0.112886	−	0.112886i	0.761294	+	0.648407i	$0.224565\pi$
$384$		0			0
$385$	12.5325			0.638716
$386$		0			0
$387$	−0.975607			−0.0495929
$388$		0			0
$389$			12.5762i			0.637638i	0.947816	+	0.318819i	$0.103286\pi$
$389$			12.5762i			0.637638i	−0.947816	+	0.318819i	$0.896714\pi$
$390$		0			0
$391$	−1.80684	+	1.80684i	−0.0913757	+	0.0913757i
$392$		0			0
$393$	16.6846	−	16.6846i	0.841625	−	0.841625i
$394$		0			0
$395$	−8.95098	+	8.95098i	−0.450373	+	0.450373i
$396$		0			0
$397$	6.83348	+	6.83348i	0.342962	+	0.342962i	0.857480	−	0.514517i	$-0.172029\pi$
$397$	6.83348	+	6.83348i	0.342962	+	0.342962i	−0.514517	+	0.857480i	$0.672029\pi$
$398$		0			0
$399$	−5.10614	−	5.10614i	−0.255627	−	0.255627i
$400$		0			0
$401$		−	18.3776i		−	0.917732i	−0.888505	−	0.458866i	$-0.848256\pi$
$401$		−	18.3776i		−	0.917732i	0.888505	−	0.458866i	$-0.151744\pi$
$402$		0			0
$403$	6.46921	+	6.46921i	0.322254	+	0.322254i
$404$		0			0
$405$		−	15.5201i		−	0.771202i
$406$		0			0
$407$	16.9779	+	16.9779i	0.841565	+	0.841565i
$408$		0			0
$409$	−32.3286			−1.59855			−0.799273	−	0.600968i	$-0.794782\pi$
$409$	−32.3286			−1.59855			−0.799273	+	0.600968i	$0.794782\pi$
$410$		0			0
$411$	33.9338			1.67383
$412$		0			0
$413$	8.52780	+	8.52780i	0.419626	+	0.419626i
$414$		0			0
$415$			8.15532i			0.400329i
$416$		0			0
$417$	−42.1391	−	42.1391i	−2.06356	−	2.06356i
$418$		0			0
$419$			30.0922i			1.47010i	0.678014	+	0.735049i	$0.262841\pi$
$419$			30.0922i			1.47010i	−0.678014	+	0.735049i	$0.737159\pi$
$420$		0			0
$421$	0.865599	+	0.865599i	0.0421867	+	0.0421867i	0.727885	−	0.685699i	$-0.240503\pi$
$421$	0.865599	+	0.865599i	0.0421867	+	0.0421867i	−0.685699	+	0.727885i	$0.740503\pi$
$422$		0			0
$423$	7.36855	+	7.36855i	0.358271	+	0.358271i
$424$		0			0
$425$	−4.09006	+	4.09006i	−0.198397	+	0.198397i
$426$		0			0
$427$	−1.47044	+	1.47044i	−0.0711598	+	0.0711598i
$428$		0			0
$429$	−6.90434	+	6.90434i	−0.333345	+	0.333345i
$430$		0			0
$431$		−	11.4284i		−	0.550488i	−0.961374	−	0.275244i	$-0.911241\pi$
$431$		−	11.4284i		−	0.550488i	0.961374	−	0.275244i	$-0.0887586\pi$
$432$		0			0
$433$	27.5678			1.32482			0.662412	−	0.749140i	$-0.269533\pi$
$433$	27.5678			1.32482			0.662412	+	0.749140i	$0.269533\pi$
$434$		0			0
$435$	−31.4970			−1.51017
$436$		0			0
$437$	3.23097	−	3.23097i	0.154558	−	0.154558i
$438$		0			0
$439$	−17.3450	−	17.3450i	−0.827829	−	0.827829i	0.159387	−	0.987216i	$-0.449048\pi$
$439$	−17.3450	−	17.3450i	−0.827829	−	0.827829i	−0.987216	+	0.159387i	$0.949048\pi$
$440$		0			0
$441$	−3.95177			−0.188180
$442$		0			0
$443$		−	35.3005i		−	1.67718i	−0.544763	−	0.838590i	$-0.683381\pi$
$443$		−	35.3005i		−	1.67718i	0.544763	−	0.838590i	$-0.316619\pi$
$444$		0			0
$445$	−28.7953	+	28.7953i	−1.36503	+	1.36503i
$446$		0			0
$447$	63.7582			3.01566
$448$		0			0
$449$		−	0.647504i		−	0.0305576i	−0.999883	−	0.0152788i	$-0.995136\pi$
$449$		−	0.647504i		−	0.0305576i	0.999883	−	0.0152788i	$-0.00486358\pi$
$450$		0			0
$451$	−25.3664	+	9.50136i	−1.19446	+	0.447401i
$452$		0			0
$453$			13.2471i			0.622402i
$454$		0			0
$455$	2.59344			0.121582
$456$		0			0
$457$	−12.1129	+	12.1129i	−0.566616	+	0.566616i	−0.931179	−	0.364563i	$-0.881218\pi$
$457$	−12.1129	+	12.1129i	−0.566616	+	0.566616i	0.364563	+	0.931179i	$0.381218\pi$
$458$		0			0
$459$			3.84350i			0.179399i
$460$		0			0
$461$	24.3612			1.13462			0.567308	−	0.823506i	$-0.307985\pi$
$461$	24.3612			1.13462			0.567308	+	0.823506i	$0.307985\pi$
$462$		0			0
$463$	−5.63968	−	5.63968i	−0.262098	−	0.262098i	0.563808	−	0.825906i	$-0.309336\pi$
$463$	−5.63968	−	5.63968i	−0.262098	−	0.262098i	−0.825906	+	0.563808i	$0.809336\pi$
$464$		0			0
$465$	57.7228	−	57.7228i	2.67683	−	2.67683i
$466$		0			0
$467$	33.0389			1.52886			0.764430	−	0.644707i	$-0.223021\pi$
$467$	33.0389			1.52886			0.764430	+	0.644707i	$0.223021\pi$
$468$		0			0
$469$	−4.74593			−0.219147
$470$		0			0
$471$		−	12.8729i		−	0.593153i
$472$		0			0
$473$	−0.738488	+	0.738488i	−0.0339557	+	0.0339557i
$474$		0			0
$475$	7.31380	−	7.31380i	0.335580	−	0.335580i
$476$		0			0
$477$	9.39551	−	9.39551i	0.430191	−	0.430191i
$478$		0			0
$479$	10.6584	+	10.6584i	0.486993	+	0.486993i	0.907356	−	0.420363i	$-0.138097\pi$
$479$	10.6584	+	10.6584i	0.486993	+	0.486993i	−0.420363	+	0.907356i	$0.638097\pi$
$480$		0			0
$481$	3.51337	+	3.51337i	0.160196	+	0.160196i
$482$		0			0
$483$		−	4.39881i		−	0.200153i
$484$		0			0
$485$	33.1696	+	33.1696i	1.50616	+	1.50616i
$486$		0			0
$487$		−	30.6853i		−	1.39048i	−0.718776	−	0.695242i	$-0.755297\pi$
$487$		−	30.6853i		−	1.39048i	0.718776	−	0.695242i	$-0.244703\pi$
$488$		0			0
$489$	−24.1041	−	24.1041i	−1.09003	−	1.09003i
$490$		0			0
$491$	−3.89308			−0.175692			−0.0878461	−	0.996134i	$-0.527998\pi$
$491$	−3.89308			−0.175692			−0.0878461	+	0.996134i	$0.527998\pi$
$492$		0			0
$493$	−6.17598			−0.278152
$494$		0			0
$495$	35.0199	+	35.0199i	1.57403	+	1.57403i
$496$		0			0
$497$		−	11.1305i		−	0.499273i
$498$		0			0
$499$	3.34648	+	3.34648i	0.149809	+	0.149809i	0.778033	−	0.628224i	$-0.216218\pi$
$499$	3.34648	+	3.34648i	0.149809	+	0.149809i	−0.628224	+	0.778033i	$0.716218\pi$
$500$		0			0
$501$			22.4630i			1.00357i
$502$		0			0
$503$	−16.0237	−	16.0237i	−0.714460	−	0.714460i	0.253005	−	0.967465i	$-0.418581\pi$
$503$	−16.0237	−	16.0237i	−0.714460	−	0.714460i	−0.967465	+	0.253005i	$0.918581\pi$
$504$		0			0
$505$	35.4774	+	35.4774i	1.57873	+	1.57873i
$506$		0			0
$507$	22.8081	−	22.8081i	1.01294	−	1.01294i
$508$		0			0
$509$	−20.4686	+	20.4686i	−0.907257	+	0.907257i	−0.996050	−	0.0887935i	$-0.971699\pi$
$509$	−20.4686	+	20.4686i	−0.907257	+	0.907257i	0.0887935	+	0.996050i	$0.471699\pi$
$510$		0			0
$511$	−1.50370	+	1.50370i	−0.0665196	+	0.0665196i
$512$		0			0
$513$		−	6.87291i		−	0.303446i
$514$		0			0
$515$	−13.4379			−0.592144
$516$		0			0
$517$	11.1553			0.490609
$518$		0			0
$519$	20.1991	−	20.1991i	0.886642	−	0.886642i
$520$		0			0
$521$	−3.70892	−	3.70892i	−0.162491	−	0.162491i	0.621179	−	0.783669i	$-0.286654\pi$
$521$	−3.70892	−	3.70892i	−0.162491	−	0.162491i	−0.783669	+	0.621179i	$0.786654\pi$
$522$		0			0
$523$	31.5018			1.37748			0.688738	−	0.725010i	$-0.258165\pi$
$523$	31.5018			1.37748			0.688738	+	0.725010i	$0.258165\pi$
$524$		0			0
$525$		−	9.95739i		−	0.434576i
$526$		0			0
$527$	11.3184	−	11.3184i	0.493036	−	0.493036i
$528$		0			0
$529$	−20.2166			−0.878983
$530$		0			0
$531$			47.6589i			2.06822i
$532$		0			0
$533$	−5.24924	+	1.96618i	−0.227370	+	0.0851648i
$534$		0			0
$535$			14.9215i			0.645114i
$536$		0			0
$537$	42.6874			1.84210
$538$		0			0
$539$	−2.99130	+	2.99130i	−0.128845	+	0.128845i
$540$		0			0
$541$			19.6275i			0.843852i	0.906630	+	0.421926i	$0.138646\pi$
$541$			19.6275i			0.843852i	−0.906630	+	0.421926i	$0.861354\pi$
$542$		0			0
$543$	51.4300			2.20707
$544$		0			0
$545$	22.3906	+	22.3906i	0.959107	+	0.959107i
$546$		0			0
$547$	−13.7488	+	13.7488i	−0.587858	+	0.587858i	−0.937051	−	0.349193i	$-0.886456\pi$
$547$	−13.7488	+	13.7488i	−0.587858	+	0.587858i	0.349193	+	0.937051i	$0.386456\pi$
$548$		0			0
$549$	−8.21779			−0.350727
$550$		0			0
$551$	11.0438			0.470483
$552$		0			0
$553$		−	4.27290i		−	0.181702i
$554$		0			0
$555$	31.3487	−	31.3487i	1.33068	−	1.33068i
$556$		0			0
$557$	−0.950248	+	0.950248i	−0.0402633	+	0.0402633i	−0.726952	−	0.686688i	$-0.759064\pi$
$557$	−0.950248	+	0.950248i	−0.0402633	+	0.0402633i	0.686688	+	0.726952i	$0.259064\pi$
$558$		0			0
$559$	−0.152821	+	0.152821i	−0.00646362	+	0.00646362i
$560$		0			0
$561$	12.0797	+	12.0797i	0.510004	+	0.510004i
$562$		0			0
$563$	29.8627	+	29.8627i	1.25856	+	1.25856i	0.951780	+	0.306781i	$0.0992520\pi$
$563$	29.8627	+	29.8627i	1.25856	+	1.25856i	0.306781	+	0.951780i	$0.400748\pi$
$564$		0			0
$565$			45.7921i			1.92649i
$566$		0			0
$567$	3.70440	+	3.70440i	0.155570	+	0.155570i
$568$		0			0
$569$			30.1543i			1.26413i	0.774914	+	0.632067i	$0.217793\pi$
$569$			30.1543i			1.26413i	−0.774914	+	0.632067i	$0.782207\pi$
$570$		0			0
$571$	−0.0634064	−	0.0634064i	−0.00265348	−	0.00265348i	0.705779	−	0.708432i	$-0.250597\pi$
$571$	−0.0634064	−	0.0634064i	−0.00265348	−	0.00265348i	−0.708432	+	0.705779i	$0.750597\pi$
$572$		0			0
$573$	−44.5066			−1.85929
$574$		0			0
$575$	6.30065			0.262755
$576$		0			0
$577$	−25.1147	−	25.1147i	−1.04554	−	1.04554i	−0.998912	−	0.0466249i	$-0.985153\pi$
$577$	−25.1147	−	25.1147i	−1.04554	−	1.04554i	−0.0466249	−	0.998912i	$-0.514847\pi$
$578$		0			0
$579$			2.76026i			0.114712i
$580$		0			0
$581$	−1.94654	−	1.94654i	−0.0807561	−	0.0807561i
$582$		0			0
$583$		−	14.2239i		−	0.589094i
$584$		0			0
$585$	7.24691	+	7.24691i	0.299623	+	0.299623i
$586$		0			0
$587$	27.8322	+	27.8322i	1.14876	+	1.14876i	0.986797	+	0.161961i	$0.0517817\pi$
$587$	27.8322	+	27.8322i	1.14876	+	1.14876i	0.161961	+	0.986797i	$0.448218\pi$
$588$		0			0
$589$	−20.2394	+	20.2394i	−0.833949	+	0.833949i
$590$		0			0
$591$	19.4932	−	19.4932i	0.801842	−	0.801842i
$592$		0			0
$593$	8.79150	−	8.79150i	0.361023	−	0.361023i	−0.503166	−	0.864190i	$-0.667832\pi$
$593$	8.79150	−	8.79150i	0.361023	−	0.361023i	0.864190	+	0.503166i	$0.167832\pi$
$594$		0			0
$595$		−	4.53742i		−	0.186016i
$596$		0			0
$597$	17.6283			0.721480
$598$		0			0
$599$	−32.6899			−1.33567			−0.667837	−	0.744308i	$-0.732780\pi$
$599$	−32.6899			−1.33567			−0.667837	+	0.744308i	$0.732780\pi$
$600$		0			0
$601$	28.8995	−	28.8995i	1.17883	−	1.17883i	0.198792	−	0.980042i	$-0.436298\pi$
$601$	28.8995	−	28.8995i	1.17883	−	1.17883i	0.980042	−	0.198792i	$-0.0637020\pi$
$602$		0			0
$603$	−13.2617	−	13.2617i	−0.540057	−	0.540057i
$604$		0			0
$605$	20.4290			0.830557
$606$		0			0
$607$			1.35383i			0.0549502i	0.999622	+	0.0274751i	$0.00874670\pi$
$607$			1.35383i			0.0549502i	−0.999622	+	0.0274751i	$0.991253\pi$
$608$		0			0
$609$	7.51782	−	7.51782i	0.304637	−	0.304637i
$610$		0			0
$611$	2.30844			0.0933896
$612$		0			0
$613$		−	43.1444i		−	1.74259i	−0.490764	−	0.871293i	$-0.663282\pi$
$613$		−	43.1444i		−	1.74259i	0.490764	−	0.871293i	$-0.336718\pi$
$614$		0			0
$615$	17.5437	+	46.8374i	0.707429	+	1.88867i
$616$		0			0
$617$		−	39.3454i		−	1.58399i	−0.610529	−	0.791994i	$-0.709043\pi$
$617$		−	39.3454i		−	1.58399i	0.610529	−	0.791994i	$-0.290957\pi$
$618$		0			0
$619$	−37.3816			−1.50249			−0.751246	−	0.660022i	$-0.770547\pi$
$619$	−37.3816			−1.50249			−0.751246	+	0.660022i	$0.770547\pi$
$620$		0			0
$621$	2.96042	−	2.96042i	0.118798	−	0.118798i
$622$		0			0
$623$		−	13.7459i		−	0.550718i
$624$		0			0
$625$	−29.6204			−1.18481
$626$		0			0
$627$	−21.6007	−	21.6007i	−0.862650	−	0.862650i
$628$		0			0
$629$	6.14690	−	6.14690i	0.245093	−	0.245093i
$630$		0			0
$631$	27.9832			1.11399			0.556997	−	0.830515i	$-0.311954\pi$
$631$	27.9832			1.11399			0.556997	+	0.830515i	$0.311954\pi$
$632$		0			0
$633$	−5.14327			−0.204426
$634$		0			0
$635$		−	10.3240i		−	0.409697i
$636$		0			0
$637$	−0.619012	+	0.619012i	−0.0245261	+	0.0245261i
$638$		0			0
$639$	31.1024	−	31.1024i	1.23039	−	1.23039i
$640$		0			0
$641$	4.77628	−	4.77628i	0.188652	−	0.188652i	−0.606461	−	0.795113i	$-0.707411\pi$
$641$	4.77628	−	4.77628i	0.188652	−	0.188652i	0.795113	+	0.606461i	$0.207411\pi$
$642$		0			0
$643$	35.3684	+	35.3684i	1.39480	+	1.39480i	0.814173	+	0.580622i	$0.197191\pi$
$643$	35.3684	+	35.3684i	1.39480	+	1.39480i	0.580622	+	0.814173i	$0.302809\pi$
$644$		0			0
$645$	1.36357	+	1.36357i	0.0536906	+	0.0536906i
$646$		0			0
$647$		−	12.9182i		−	0.507868i	−0.967221	−	0.253934i	$-0.918275\pi$
$647$		−	12.9182i		−	0.507868i	0.967221	−	0.253934i	$-0.0817247\pi$
$648$		0			0
$649$	36.0755	+	36.0755i	1.41609	+	1.41609i
$650$		0			0
$651$			27.5550i			1.07996i
$652$		0			0
$653$	−12.7030	−	12.7030i	−0.497109	−	0.497109i	0.413428	−	0.910537i	$-0.364331\pi$
$653$	−12.7030	−	12.7030i	−0.497109	−	0.497109i	−0.910537	+	0.413428i	$0.864331\pi$
$654$		0			0
$655$	−26.5121			−1.03591
$656$		0			0
$657$	−8.40363			−0.327857
$658$		0			0
$659$	22.0826	+	22.0826i	0.860216	+	0.860216i	0.991363	−	0.131147i	$-0.0418659\pi$
$659$	22.0826	+	22.0826i	0.860216	+	0.860216i	−0.131147	+	0.991363i	$0.541866\pi$
$660$		0			0
$661$			43.6695i			1.69855i	0.527953	+	0.849274i	$0.322960\pi$
$661$			43.6695i			1.69855i	−0.527953	+	0.849274i	$0.677040\pi$
$662$		0			0
$663$	2.49973	+	2.49973i	0.0970815	+	0.0970815i
$664$		0			0
$665$			8.11377i			0.314638i
$666$		0			0
$667$	4.75699	+	4.75699i	0.184191	+	0.184191i
$668$		0			0
$669$	−7.07174	−	7.07174i	−0.273409	−	0.273409i
$670$		0			0
$671$	−6.22048	+	6.22048i	−0.240139	+	0.240139i
$672$		0			0
$673$	11.6853	−	11.6853i	0.450437	−	0.450437i	−0.445063	−	0.895499i	$-0.646819\pi$
$673$	11.6853	−	11.6853i	0.450437	−	0.450437i	0.895499	+	0.445063i	$0.146819\pi$
$674$		0			0
$675$	6.70136	−	6.70136i	0.257936	−	0.257936i
$676$		0			0
$677$			10.4067i			0.399963i	0.979800	+	0.199981i	$0.0640882\pi$
$677$			10.4067i			0.399963i	−0.979800	+	0.199981i	$0.935912\pi$
$678$		0			0
$679$	−15.8341			−0.607657
$680$		0			0
$681$	−48.4813			−1.85781
$682$		0			0
$683$	−5.00945	+	5.00945i	−0.191681	+	0.191681i	−0.796422	−	0.604741i	$-0.793277\pi$
$683$	−5.00945	+	5.00945i	−0.191681	+	0.191681i	0.604741	+	0.796422i	$0.293277\pi$
$684$		0			0
$685$	−26.9608	−	26.9608i	−1.03012	−	1.03012i
$686$		0			0
$687$	−40.6718			−1.55173
$688$		0			0
$689$		−	2.94346i		−	0.112137i
$690$		0			0
$691$	−9.29478	+	9.29478i	−0.353590	+	0.353590i	−0.861444	−	0.507853i	$-0.830439\pi$
$691$	−9.29478	+	9.29478i	−0.353590	+	0.353590i	0.507853	+	0.861444i	$0.330439\pi$
$692$		0			0
$693$	−16.7173			−0.635040
$694$		0			0
$695$			66.9600i			2.53994i
$696$		0			0
$697$	3.43998	+	9.18394i	0.130299	+	0.347867i
$698$		0			0
$699$		−	32.1217i		−	1.21495i
$700$		0			0
$701$	21.6512			0.817755			0.408878	−	0.912589i	$-0.365920\pi$
$701$	21.6512			0.817755			0.408878	+	0.912589i	$0.365920\pi$
$702$		0			0
$703$	−10.9918	+	10.9918i	−0.414564	+	0.414564i
$704$		0			0
$705$		−	20.5975i		−	0.775748i
$706$		0			0
$707$	−16.9358			−0.636935
$708$		0			0
$709$	23.2112	+	23.2112i	0.871717	+	0.871717i	0.992659	−	0.120943i	$-0.0385918\pi$
$709$	23.2112	+	23.2112i	0.871717	+	0.871717i	−0.120943	+	0.992659i	$0.538592\pi$
$710$		0			0
$711$	11.9399	−	11.9399i	0.447780	−	0.447780i
$712$		0			0
$713$	−17.4357			−0.652973
$714$		0			0
$715$	10.9711			0.410297
$716$		0			0
$717$			16.5637i			0.618582i
$718$		0			0
$719$	1.30997	−	1.30997i	0.0488537	−	0.0488537i	−0.682258	−	0.731112i	$-0.739002\pi$
$719$	1.30997	−	1.30997i	0.0488537	−	0.0488537i	0.731112	+	0.682258i	$0.239002\pi$
$720$		0			0
$721$	3.20740	−	3.20740i	0.119450	−	0.119450i
$722$		0			0
$723$	−16.0509	+	16.0509i	−0.596940	+	0.596940i
$724$		0			0
$725$	10.7682	+	10.7682i	0.399920	+	0.399920i
$726$		0			0
$727$	25.9337	+	25.9337i	0.961828	+	0.961828i	0.999298	−	0.0374696i	$-0.0119297\pi$
$727$	25.9337	+	25.9337i	0.961828	+	0.961828i	−0.0374696	+	0.999298i	$0.511930\pi$
$728$		0			0
$729$			40.5521i			1.50193i
$730$		0			0
$731$	0.267371	+	0.267371i	0.00988908	+	0.00988908i
$732$		0			0
$733$			34.9903i			1.29240i	0.763170	+	0.646198i	$0.223642\pi$
$733$			34.9903i			1.29240i	−0.763170	+	0.646198i	$0.776358\pi$
$734$		0			0
$735$	5.52326	+	5.52326i	0.203728	+	0.203728i
$736$		0			0
$737$	−20.0769			−0.739543
$738$		0			0
$739$	51.9176			1.90982			0.954910	−	0.296895i	$-0.0959511\pi$
$739$	51.9176			1.90982			0.954910	+	0.296895i	$0.0959511\pi$
$740$		0			0
$741$	−4.46999	−	4.46999i	−0.164209	−	0.164209i
$742$		0			0
$743$		−	48.7958i		−	1.79015i	−0.445920	−	0.895073i	$-0.647123\pi$
$743$		−	48.7958i		−	1.79015i	0.445920	−	0.895073i	$-0.352877\pi$
$744$		0			0
$745$	−50.6565	−	50.6565i	−1.85591	−	1.85591i
$746$		0			0
$747$		−	10.8785i		−	0.398025i
$748$		0			0
$749$	−3.56153	−	3.56153i	−0.130135	−	0.130135i
$750$		0			0
$751$	25.3074	+	25.3074i	0.923478	+	0.923478i	0.997273	−	0.0737950i	$-0.0235110\pi$
$751$	25.3074	+	25.3074i	0.923478	+	0.923478i	−0.0737950	+	0.997273i	$0.523511\pi$
$752$		0			0
$753$	−12.5846	+	12.5846i	−0.458608	+	0.458608i
$754$		0			0
$755$	10.5249	−	10.5249i	0.383042	−	0.383042i
$756$		0			0
$757$	10.7127	−	10.7127i	0.389360	−	0.389360i	−0.485099	−	0.874459i	$-0.661217\pi$
$757$	10.7127	−	10.7127i	0.389360	−	0.389360i	0.874459	+	0.485099i	$0.161217\pi$
$758$		0			0
$759$		−	18.6085i		−	0.675445i
$760$		0			0
$761$	−37.3994			−1.35573			−0.677864	−	0.735187i	$-0.737094\pi$
$761$	−37.3994			−1.35573			−0.677864	+	0.735187i	$0.737094\pi$
$762$		0			0
$763$	−10.6885			−0.386951
$764$		0			0
$765$	12.6790	−	12.6790i	0.458411	−	0.458411i
$766$		0			0
$767$	7.46536	+	7.46536i	0.269559	+	0.269559i
$768$		0			0
$769$	−45.7162			−1.64857			−0.824283	−	0.566178i	$-0.808422\pi$
$769$	−45.7162			−1.64857			−0.824283	+	0.566178i	$0.808422\pi$
$770$		0			0
$771$			36.1739i			1.30277i
$772$		0			0
$773$	−4.26643	+	4.26643i	−0.153453	+	0.153453i	−0.779658	−	0.626205i	$-0.784607\pi$
$773$	−4.26643	+	4.26643i	−0.153453	+	0.153453i	0.626205	+	0.779658i	$0.284607\pi$
$774$		0			0
$775$	−39.4684			−1.41775
$776$		0			0
$777$			14.9648i			0.536861i
$778$		0			0
$779$	−6.15135	−	16.4226i	−0.220395	−	0.588402i
$780$		0			0
$781$		−	47.0860i		−	1.68487i
$782$		0			0
$783$	10.1190			0.361625
$784$		0			0
$785$	−10.2277	+	10.2277i	−0.365041	+	0.365041i
$786$		0			0
$787$			13.7853i			0.491394i	0.969347	+	0.245697i	$0.0790168\pi$
$787$			13.7853i			0.491394i	−0.969347	+	0.245697i	$0.920983\pi$
$788$		0			0
$789$	66.6256			2.37194
$790$		0			0
$791$	−10.9298	−	10.9298i	−0.388620	−	0.388620i
$792$		0			0
$793$	−1.28725	+	1.28725i	−0.0457115	+	0.0457115i
$794$		0			0
$795$	−26.2636			−0.931473
$796$		0			0
$797$	−40.6666			−1.44049			−0.720243	−	0.693722i	$-0.755970\pi$
$797$	−40.6666			−1.44049			−0.720243	+	0.693722i	$0.755970\pi$
$798$		0			0
$799$		−	4.03879i		−	0.142882i
$800$		0			0
$801$	38.4105	−	38.4105i	1.35717	−	1.35717i
$802$		0			0
$803$	−6.36115	+	6.36115i	−0.224480	+	0.224480i
$804$		0			0
$805$	−3.49490	+	3.49490i	−0.123179	+	0.123179i
$806$		0			0
$807$	12.2198	+	12.2198i	0.430158	+	0.430158i
$808$		0			0
$809$	19.5316	+	19.5316i	0.686694	+	0.686694i	0.961500	−	0.274806i	$-0.0886136\pi$
$809$	19.5316	+	19.5316i	0.686694	+	0.686694i	−0.274806	+	0.961500i	$0.588614\pi$
$810$		0			0
$811$			42.8058i			1.50311i	0.659668	+	0.751557i	$0.270697\pi$
$811$			42.8058i			1.50311i	−0.659668	+	0.751557i	$0.729303\pi$
$812$		0			0
$813$	−25.7724	−	25.7724i	−0.903876	−	0.903876i
$814$		0			0
$815$			38.3020i			1.34166i
$816$		0			0
$817$	−0.478110	−	0.478110i	−0.0167270	−	0.0167270i
$818$		0			0
$819$	−3.45944			−0.120883
$820$		0			0
$821$	26.0891			0.910517			0.455259	−	0.890359i	$-0.349547\pi$
$821$	26.0891			0.910517			0.455259	+	0.890359i	$0.349547\pi$
$822$		0			0
$823$	19.6628	+	19.6628i	0.685403	+	0.685403i	0.961212	−	0.275810i	$-0.0889459\pi$
$823$	19.6628	+	19.6628i	0.685403	+	0.685403i	−0.275810	+	0.961212i	$0.588946\pi$
$824$		0			0
$825$		−	42.1232i		−	1.46654i
$826$		0			0
$827$	−12.9153	−	12.9153i	−0.449110	−	0.449110i	0.445949	−	0.895058i	$-0.352866\pi$
$827$	−12.9153	−	12.9153i	−0.449110	−	0.449110i	−0.895058	+	0.445949i	$0.852866\pi$
$828$		0			0
$829$			30.6211i			1.06351i	0.846897	+	0.531757i	$0.178468\pi$
$829$			30.6211i			1.06351i	−0.846897	+	0.531757i	$0.821532\pi$
$830$		0			0
$831$	21.0194	+	21.0194i	0.729154	+	0.729154i
$832$		0			0
$833$	1.08301	+	1.08301i	0.0375240	+	0.0375240i
$834$		0			0
$835$	17.8471	−	17.8471i	0.617625	−	0.617625i
$836$		0			0
$837$	−18.5446	+	18.5446i	−0.640995	+	0.640995i
$838$		0			0
$839$	−13.0032	+	13.0032i	−0.448920	+	0.448920i	−0.894995	−	0.446076i	$-0.852821\pi$
$839$	−13.0032	+	13.0032i	−0.448920	+	0.448920i	0.446076	+	0.894995i	$0.352821\pi$
$840$		0			0
$841$		−	12.7401i		−	0.439313i
$842$		0			0
$843$	59.5701			2.05170
$844$		0			0
$845$	−36.2425			−1.24678
$846$		0			0
$847$	−4.87607	+	4.87607i	−0.167544	+	0.167544i
$848$		0			0
$849$	−24.2335	−	24.2335i	−0.831692	−	0.831692i
$850$		0			0
$851$	−9.46918			−0.324599
$852$		0			0
$853$			42.5303i			1.45621i	0.685466	+	0.728105i	$0.259599\pi$
$853$			42.5303i			1.45621i	−0.685466	+	0.728105i	$0.740401\pi$
$854$		0			0
$855$	−22.6725	+	22.6725i	−0.775383	+	0.775383i
$856$		0			0
$857$	−19.0333			−0.650165			−0.325082	−	0.945686i	$-0.605392\pi$
$857$	−19.0333			−0.650165			−0.325082	+	0.945686i	$0.605392\pi$
$858$		0			0
$859$		−	0.584577i		−	0.0199455i	−0.999950	−	0.00997276i	$-0.996826\pi$
$859$		−	0.584577i		−	0.0199455i	0.999950	−	0.00997276i	$-0.00317448\pi$
$860$		0			0
$861$	−15.3667	−	6.99193i	−0.523696	−	0.238284i
$862$		0			0
$863$		−	25.6794i		−	0.874137i	−0.899428	−	0.437069i	$-0.856017\pi$
$863$		−	25.6794i		−	0.874137i	0.899428	−	0.437069i	$-0.143983\pi$
$864$		0			0
$865$	−32.0968			−1.09132
$866$		0			0
$867$	−27.3209	+	27.3209i	−0.927865	+	0.927865i
$868$		0			0
$869$		−	18.0758i		−	0.613181i
$870$		0			0
$871$	−4.15466			−0.140775
$872$		0			0
$873$	−44.2456	−	44.2456i	−1.49749	−	1.49749i
$874$		0			0
$875$	2.56287	−	2.56287i	0.0866407	−	0.0866407i
$876$		0			0
$877$	33.0559			1.11622			0.558109	−	0.829768i	$-0.311527\pi$
$877$	33.0559			1.11622			0.558109	+	0.829768i	$0.311527\pi$
$878$		0			0
$879$	−55.6461			−1.87690
$880$		0			0
$881$			22.5032i			0.758152i	0.925365	+	0.379076i	$0.123758\pi$
$881$			22.5032i			0.758152i	−0.925365	+	0.379076i	$0.876242\pi$
$882$		0			0
$883$	8.25723	−	8.25723i	0.277878	−	0.277878i	−0.554383	−	0.832261i	$-0.687046\pi$
$883$	8.25723	−	8.25723i	0.277878	−	0.277878i	0.832261	+	0.554383i	$0.187046\pi$
$884$		0			0
$885$	66.6112	−	66.6112i	2.23911	−	2.23911i
$886$		0			0
$887$	40.3633	−	40.3633i	1.35527	−	1.35527i	0.475614	−	0.879654i	$-0.342226\pi$
$887$	40.3633	−	40.3633i	1.35527	−	1.35527i	0.879654	−	0.475614i	$-0.157774\pi$
$888$		0			0
$889$	2.46418	+	2.46418i	0.0826459	+	0.0826459i
$890$		0			0
$891$	15.6709	+	15.6709i	0.524995	+	0.524995i
$892$		0			0
$893$			7.22213i			0.241679i
$894$		0			0
$895$	−33.9156	−	33.9156i	−1.13367	−	1.13367i
$896$		0			0
$897$		−	3.85079i		−	0.128574i
$898$		0			0
$899$	−29.7986	−	29.7986i	−0.993840	−	0.993840i
$900$		0			0
$901$	−5.14980			−0.171565
$902$		0			0
$903$	−0.650925			−0.0216614
$904$		0			0
$905$	−40.8617	−	40.8617i	−1.35829	−	1.35829i
$906$		0			0
$907$			2.08994i			0.0693952i	0.999398	+	0.0346976i	$0.0110468\pi$
$907$			2.08994i			0.0693952i	−0.999398	+	0.0346976i	$0.988953\pi$
$908$		0			0
$909$	−47.3240	−	47.3240i	−1.56964	−	1.56964i
$910$		0			0
$911$		−	15.5975i		−	0.516770i	−0.966042	−	0.258385i	$-0.916810\pi$
$911$		−	15.5975i		−	0.516770i	0.966042	−	0.258385i	$-0.0831903\pi$
$912$		0			0
$913$	−8.23453	−	8.23453i	−0.272523	−	0.272523i
$914$		0			0
$915$	11.4857	+	11.4857i	0.379706	+	0.379706i
$916$		0			0
$917$	6.32801	−	6.32801i	0.208969	−	0.208969i
$918$		0			0
$919$	−37.0984	+	37.0984i	−1.22376	+	1.22376i	−0.257480	+	0.966284i	$0.582892\pi$
$919$	−37.0984	+	37.0984i	−1.22376	+	1.22376i	−0.966284	+	0.257480i	$0.917108\pi$
$920$		0			0
$921$	43.3530	−	43.3530i	1.42853	−	1.42853i
$922$		0			0
$923$		−	9.74385i		−	0.320723i
$924$		0			0
$925$	−21.4349			−0.704776
$926$		0			0
$927$	17.9251			0.588736
$928$		0			0
$929$	16.8169	−	16.8169i	0.551744	−	0.551744i	−0.375200	−	0.926944i	$-0.622426\pi$
$929$	16.8169	−	16.8169i	0.551744	−	0.551744i	0.926944	+	0.375200i	$0.122426\pi$
$930$		0			0
$931$	−1.93662	−	1.93662i	−0.0634703	−	0.0634703i
$932$		0			0
$933$	−37.2540			−1.21964
$934$		0			0
$935$		−	19.1948i		−	0.627738i
$936$		0			0
$937$	−39.3030	+	39.3030i	−1.28397	+	1.28397i	−0.345588	+	0.938386i	$0.612320\pi$
$937$	−39.3030	+	39.3030i	−1.28397	+	1.28397i	−0.938386	+	0.345588i	$0.887680\pi$
$938$		0			0
$939$	23.2813			0.759757
$940$		0			0
$941$		−	28.1124i		−	0.916438i	−0.888839	−	0.458219i	$-0.848488\pi$
$941$		−	28.1124i		−	0.916438i	0.888839	−	0.458219i	$-0.151512\pi$
$942$		0			0
$943$	4.42423	−	9.72346i	0.144073	−	0.316639i
$944$		0			0
$945$			7.43435i			0.241839i
$946$		0			0
$947$	9.13257			0.296769			0.148384	−	0.988930i	$-0.452593\pi$
$947$	9.13257			0.296769			0.148384	+	0.988930i	$0.452593\pi$
$948$		0			0
$949$	−1.31636	+	1.31636i	−0.0427308	+	0.0427308i
$950$		0			0
$951$		−	23.0521i		−	0.747517i
$952$		0			0
$953$	−14.0482			−0.455067			−0.227533	−	0.973770i	$-0.573066\pi$
$953$	−14.0482			−0.455067			−0.227533	+	0.973770i	$0.573066\pi$
$954$		0			0
$955$	35.3610	+	35.3610i	1.14425	+	1.14425i
$956$		0			0
$957$	31.8030	−	31.8030i	1.02804	−	1.02804i
$958$		0			0
$959$	12.8702			0.415600
$960$		0			0
$961$	78.2205			2.52324
$962$		0			0
$963$		−	19.9041i		−	0.641401i
$964$		0			0
$965$	2.19305	−	2.19305i	0.0705969	−	0.0705969i
$966$		0			0
$967$	−13.5838	+	13.5838i	−0.436824	+	0.436824i	−0.890942	−	0.454118i	$-0.849955\pi$
$967$	−13.5838	+	13.5838i	−0.436824	+	0.436824i	0.454118	+	0.890942i	$0.349955\pi$
$968$		0			0
$969$	−7.82059	+	7.82059i	−0.251234	+	0.251234i
$970$		0			0
$971$	−2.00491	−	2.00491i	−0.0643406	−	0.0643406i	0.674204	−	0.738545i	$-0.264487\pi$
$971$	−2.00491	−	2.00491i	−0.0643406	−	0.0643406i	−0.738545	+	0.674204i	$0.764487\pi$
$972$		0			0
$973$	−15.9822	−	15.9822i	−0.512367	−	0.512367i
$974$		0			0
$975$		−	8.71684i		−	0.279162i
$976$		0			0
$977$	2.22498	+	2.22498i	0.0711835	+	0.0711835i	0.741802	−	0.670619i	$-0.233971\pi$
$977$	2.22498	+	2.22498i	0.0711835	+	0.0711835i	−0.670619	+	0.741802i	$0.733971\pi$
$978$		0			0
$979$		−	58.1499i		−	1.85848i
$980$		0			0
$981$	−29.8672	−	29.8672i	−0.953586	−	0.953586i
$982$		0			0
$983$	−2.38864			−0.0761859			−0.0380929	−	0.999274i	$-0.512128\pi$
$983$	−2.38864			−0.0761859			−0.0380929	+	0.999274i	$0.512128\pi$
$984$		0			0
$985$	−30.9751			−0.986948
$986$		0			0
$987$	4.91629	+	4.91629i	0.156487	+	0.156487i
$988$		0			0
$989$		−	0.411880i		−	0.0130970i
$990$		0			0
$991$	6.56538	+	6.56538i	0.208556	+	0.208556i	0.803654	−	0.595097i	$-0.202887\pi$
$991$	6.56538	+	6.56538i	0.208556	+	0.208556i	−0.595097	+	0.803654i	$0.702887\pi$
$992$		0			0
$993$			5.28339i			0.167663i
$994$		0			0
$995$	−14.0059	−	14.0059i	−0.444017	−	0.444017i
$996$		0			0
$997$	22.2458	+	22.2458i	0.704533	+	0.704533i	0.965380	−	0.260847i	$-0.0840019\pi$
$997$	22.2458	+	22.2458i	0.704533	+	0.704533i	−0.260847	+	0.965380i	$0.584002\pi$
$998$		0			0
$999$	−10.0714	+	10.0714i	−0.318645	+	0.318645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.17	✓	36
41.32	even	4	inner	1148.2.k.b.729.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.17	✓	36	1.1	even	1	trivial
1148.2.k.b.729.17	yes	36	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +O(q^{10})\)	\(q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +(2.99130 + 2.99130i) q^{11} +(0.619012 + 0.619012i) q^{13} +(5.52326 - 5.52326i) q^{15} +(1.08301 - 1.08301i) q^{17} +(-1.93662 + 1.93662i) q^{19} +2.63662i q^{21} -1.66835 q^{23} -3.77657 q^{25} +(-1.77446 + 1.77446i) q^{27} +(-2.85131 - 2.85131i) q^{29} +10.4509 q^{31} +11.1538i q^{33} +(2.09482 - 2.09482i) q^{35} +5.67577 q^{37} +2.30814i q^{39} +(-2.65185 + 5.82818i) q^{41} +0.246878i q^{43} +11.7072 q^{45} +(1.86462 - 1.86462i) q^{47} +1.00000i q^{49} +4.03826 q^{51} +(-2.37754 - 2.37754i) q^{53} +(8.86182 - 8.86182i) q^{55} -7.22118 q^{57} +12.0601 q^{59} +2.07952i q^{61} +(-2.79432 + 2.79432i) q^{63} +(1.83384 - 1.83384i) q^{65} +(-3.35588 + 3.35588i) q^{67} +(-3.11043 - 3.11043i) q^{69} +(-7.87049 - 7.87049i) q^{71} +2.12655i q^{73} +(-7.04094 - 7.04094i) q^{75} +4.23034i q^{77} +(-3.02140 - 3.02140i) q^{79} +5.23882 q^{81} -2.75282 q^{83} +(-3.20844 - 3.20844i) q^{85} -10.6318i q^{87} +(-9.71983 - 9.71983i) q^{89} +0.875415i q^{91} +(19.4843 + 19.4843i) q^{93} +(5.73730 + 5.73730i) q^{95} +(-11.1964 + 11.1964i) q^{97} +(-11.8210 + 11.8210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

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