LMFDB - Embedded newform 1148.2.k.b.337.15

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			337.15
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65216 + 1.65216i) q^{3} +2.95400i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.45924i q^{9} +O(q^{10})$	\(q+(1.65216 + 1.65216i) q^{3} +2.95400i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.45924i q^{9} +(0.583260 + 0.583260i) q^{11} +(-0.304108 - 0.304108i) q^{13} +(-4.88047 + 4.88047i) q^{15} +(-4.59921 + 4.59921i) q^{17} +(-2.24427 + 2.24427i) q^{19} -2.33650i q^{21} -2.62025 q^{23} -3.72611 q^{25} +(0.893418 - 0.893418i) q^{27} +(3.12871 + 3.12871i) q^{29} +3.25380 q^{31} +1.92727i q^{33} +(2.08879 - 2.08879i) q^{35} +9.55376 q^{37} -1.00487i q^{39} +(-6.24482 - 1.41499i) q^{41} -4.05599i q^{43} -7.26460 q^{45} +(-7.44566 + 7.44566i) q^{47} +1.00000i q^{49} -15.1972 q^{51} +(0.577050 + 0.577050i) q^{53} +(-1.72295 + 1.72295i) q^{55} -7.41578 q^{57} +5.94695 q^{59} +5.32768i q^{61} +(1.73895 - 1.73895i) q^{63} +(0.898336 - 0.898336i) q^{65} +(6.10945 - 6.10945i) q^{67} +(-4.32906 - 4.32906i) q^{69} +(-7.75761 - 7.75761i) q^{71} -5.39839i q^{73} +(-6.15612 - 6.15612i) q^{75} -0.824855i q^{77} +(3.82764 + 3.82764i) q^{79} +10.3299 q^{81} +4.27367 q^{83} +(-13.5861 - 13.5861i) q^{85} +10.3382i q^{87} +(1.40401 + 1.40401i) q^{89} +0.430074i q^{91} +(5.37579 + 5.37579i) q^{93} +(-6.62958 - 6.62958i) q^{95} +(5.46950 - 5.46950i) q^{97} +(-1.43438 + 1.43438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.65216	+	1.65216i	0.953873	+	0.953873i	0.998982	−	0.0451092i	$-0.0143636\pi$
$3$	1.65216	+	1.65216i	0.953873	+	0.953873i	−0.0451092	+	0.998982i	$0.514364\pi$
$4$		0			0
$5$			2.95400i			1.32107i	0.750796	+	0.660534i	$0.229670\pi$
$5$			2.95400i			1.32107i	−0.750796	+	0.660534i	$0.770330\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$			2.45924i			0.819747i
$10$		0			0
$11$	0.583260	+	0.583260i	0.175860	+	0.175860i	0.789548	−	0.613689i	$-0.210315\pi$
$11$	0.583260	+	0.583260i	0.175860	+	0.175860i	−0.613689	+	0.789548i	$0.710315\pi$
$12$		0			0
$13$	−0.304108	−	0.304108i	−0.0843445	−	0.0843445i	0.663676	−	0.748020i	$-0.268995\pi$
$13$	−0.304108	−	0.304108i	−0.0843445	−	0.0843445i	−0.748020	+	0.663676i	$0.768995\pi$
$14$		0			0
$15$	−4.88047	+	4.88047i	−1.26013	+	1.26013i
$16$		0			0
$17$	−4.59921	+	4.59921i	−1.11547	+	1.11547i	−0.123076	+	0.992397i	$0.539276\pi$
$17$	−4.59921	+	4.59921i	−1.11547	+	1.11547i	−0.992397	+	0.123076i	$0.960724\pi$
$18$		0			0
$19$	−2.24427	+	2.24427i	−0.514872	+	0.514872i	−0.916015	−	0.401144i	$-0.868613\pi$
$19$	−2.24427	+	2.24427i	−0.514872	+	0.514872i	0.401144	+	0.916015i	$0.368613\pi$
$20$		0			0
$21$		−	2.33650i		−	0.509867i
$22$		0			0
$23$	−2.62025			−0.546359			−0.273180	−	0.961963i	$-0.588075\pi$
$23$	−2.62025			−0.546359			−0.273180	+	0.961963i	$0.588075\pi$
$24$		0			0
$25$	−3.72611			−0.745223
$26$		0			0
$27$	0.893418	−	0.893418i	0.171938	−	0.171938i
$28$		0			0
$29$	3.12871	+	3.12871i	0.580987	+	0.580987i	0.935174	−	0.354188i	$-0.115243\pi$
$29$	3.12871	+	3.12871i	0.580987	+	0.580987i	−0.354188	+	0.935174i	$0.615243\pi$
$30$		0			0
$31$	3.25380			0.584400			0.292200	−	0.956357i	$-0.405613\pi$
$31$	3.25380			0.584400			0.292200	+	0.956357i	$0.405613\pi$
$32$		0			0
$33$			1.92727i			0.335495i
$34$		0			0
$35$	2.08879	−	2.08879i	0.353070	−	0.353070i
$36$		0			0
$37$	9.55376			1.57063			0.785314	−	0.619098i	$-0.212501\pi$
$37$	9.55376			1.57063			0.785314	+	0.619098i	$0.212501\pi$
$38$		0			0
$39$		−	1.00487i		−	0.160908i
$40$		0			0
$41$	−6.24482	−	1.41499i	−0.975277	−	0.220984i
$41$	−6.24482	−	1.41499i	−0.975277	−	0.220984i
$42$		0			0
$43$		−	4.05599i		−	0.618533i	−0.950975	−	0.309266i	$-0.899917\pi$
$43$		−	4.05599i		−	0.618533i	0.950975	−	0.309266i	$-0.100083\pi$
$44$		0			0
$45$	−7.26460			−1.08294
$46$		0			0
$47$	−7.44566	+	7.44566i	−1.08606	+	1.08606i	−0.0901312	+	0.995930i	$0.528729\pi$
$47$	−7.44566	+	7.44566i	−1.08606	+	1.08606i	−0.995930	+	0.0901312i	$0.971271\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−15.1972			−2.12804
$52$		0			0
$53$	0.577050	+	0.577050i	0.0792639	+	0.0792639i	0.745627	−	0.666363i	$-0.232150\pi$
$53$	0.577050	+	0.577050i	0.0792639	+	0.0792639i	−0.666363	+	0.745627i	$0.732150\pi$
$54$		0			0
$55$	−1.72295	+	1.72295i	−0.232323	+	0.232323i
$56$		0			0
$57$	−7.41578			−0.982244
$58$		0			0
$59$	5.94695			0.774227			0.387113	−	0.922032i	$-0.373472\pi$
$59$	5.94695			0.774227			0.387113	+	0.922032i	$0.373472\pi$
$60$		0			0
$61$			5.32768i			0.682140i	0.940038	+	0.341070i	$0.110789\pi$
$61$			5.32768i			0.682140i	−0.940038	+	0.341070i	$0.889211\pi$
$62$		0			0
$63$	1.73895	−	1.73895i	0.219087	−	0.219087i
$64$		0			0
$65$	0.898336	−	0.898336i	0.111425	−	0.111425i
$66$		0			0
$67$	6.10945	−	6.10945i	0.746388	−	0.746388i	−0.227411	−	0.973799i	$-0.573026\pi$
$67$	6.10945	−	6.10945i	0.746388	−	0.746388i	0.973799	+	0.227411i	$0.0730260\pi$
$68$		0			0
$69$	−4.32906	−	4.32906i	−0.521157	−	0.521157i
$70$		0			0
$71$	−7.75761	−	7.75761i	−0.920658	−	0.920658i	0.0764175	−	0.997076i	$-0.475652\pi$
$71$	−7.75761	−	7.75761i	−0.920658	−	0.920658i	−0.997076	+	0.0764175i	$0.975652\pi$
$72$		0			0
$73$		−	5.39839i		−	0.631834i	−0.948787	−	0.315917i	$-0.897688\pi$
$73$		−	5.39839i		−	0.631834i	0.948787	−	0.315917i	$-0.102312\pi$
$74$		0			0
$75$	−6.15612	−	6.15612i	−0.710848	−	0.710848i
$76$		0			0
$77$		−	0.824855i		−	0.0940009i
$78$		0			0
$79$	3.82764	+	3.82764i	0.430643	+	0.430643i	0.888847	−	0.458204i	$-0.151507\pi$
$79$	3.82764	+	3.82764i	0.430643	+	0.430643i	−0.458204	+	0.888847i	$0.651507\pi$
$80$		0			0
$81$	10.3299			1.14776
$82$		0			0
$83$	4.27367			0.469097			0.234548	−	0.972104i	$-0.424639\pi$
$83$	4.27367			0.469097			0.234548	+	0.972104i	$0.424639\pi$
$84$		0			0
$85$	−13.5861	−	13.5861i	−1.47362	−	1.47362i
$86$		0			0
$87$			10.3382i			1.10837i
$88$		0			0
$89$	1.40401	+	1.40401i	0.148825	+	0.148825i	0.777593	−	0.628768i	$-0.216441\pi$
$89$	1.40401	+	1.40401i	0.148825	+	0.148825i	−0.628768	+	0.777593i	$0.716441\pi$
$90$		0			0
$91$			0.430074i			0.0450840i
$92$		0			0
$93$	5.37579	+	5.37579i	0.557443	+	0.557443i
$94$		0			0
$95$	−6.62958	−	6.62958i	−0.680181	−	0.680181i
$96$		0			0
$97$	5.46950	−	5.46950i	0.555343	−	0.555343i	−0.372635	−	0.927978i	$-0.621546\pi$
$97$	5.46950	−	5.46950i	0.555343	−	0.555343i	0.927978	+	0.372635i	$0.121546\pi$
$98$		0			0
$99$	−1.43438	+	1.43438i	−0.144160	+	0.144160i
$100$		0			0
$101$	−10.8247	+	10.8247i	−1.07710	+	1.07710i	−0.0803306	+	0.996768i	$0.525598\pi$
$101$	−10.8247	+	10.8247i	−1.07710	+	1.07710i	−0.996768	+	0.0803306i	$0.974402\pi$
$102$		0			0
$103$			5.20778i			0.513138i	0.966526	+	0.256569i	$0.0825921\pi$
$103$			5.20778i			0.513138i	−0.966526	+	0.256569i	$0.917408\pi$
$104$		0			0
$105$	6.90203			0.673569
$106$		0			0
$107$	19.6992			1.90440			0.952199	−	0.305478i	$-0.0988164\pi$
$107$	19.6992			1.90440			0.952199	+	0.305478i	$0.0988164\pi$
$108$		0			0
$109$	−0.590425	+	0.590425i	−0.0565525	+	0.0565525i	−0.734817	−	0.678265i	$-0.762732\pi$
$109$	−0.590425	+	0.590425i	−0.0565525	+	0.0565525i	0.678265	+	0.734817i	$0.262732\pi$
$110$		0			0
$111$	15.7843	+	15.7843i	1.49818	+	1.49818i
$112$		0			0
$113$	−0.357625			−0.0336425			−0.0168213	−	0.999859i	$-0.505355\pi$
$113$	−0.357625			−0.0336425			−0.0168213	+	0.999859i	$0.505355\pi$
$114$		0			0
$115$		−	7.74021i		−	0.721778i
$116$		0			0
$117$	0.747876	−	0.747876i	0.0691412	−	0.0691412i
$118$		0			0
$119$	6.50427			0.596246
$120$		0			0
$121$		−	10.3196i		−	0.938147i
$122$		0			0
$123$	−7.97964	−	12.6552i	−0.719500	−	1.14108i
$124$		0			0
$125$			3.76306i			0.336578i
$126$		0			0
$127$	−2.66971			−0.236899			−0.118449	−	0.992960i	$-0.537792\pi$
$127$	−2.66971			−0.236899			−0.118449	+	0.992960i	$0.537792\pi$
$128$		0			0
$129$	6.70113	−	6.70113i	0.590001	−	0.590001i
$130$		0			0
$131$			10.8716i			0.949855i	0.880025	+	0.474928i	$0.157526\pi$
$131$			10.8716i			0.949855i	−0.880025	+	0.474928i	$0.842474\pi$
$132$		0			0
$133$	3.17388			0.275210
$134$		0			0
$135$	2.63916	+	2.63916i	0.227142	+	0.227142i
$136$		0			0
$137$	−1.62969	+	1.62969i	−0.139234	+	0.139234i	−0.773288	−	0.634054i	$-0.781389\pi$
$137$	−1.62969	+	1.62969i	−0.139234	+	0.139234i	0.634054	+	0.773288i	$0.281389\pi$
$138$		0			0
$139$	11.1845			0.948655			0.474328	−	0.880348i	$-0.342691\pi$
$139$	11.1845			0.948655			0.474328	+	0.880348i	$0.342691\pi$
$140$		0			0
$141$	−24.6028			−2.07193
$142$		0			0
$143$		−	0.354749i		−	0.0296656i
$144$		0			0
$145$	−9.24220	+	9.24220i	−0.767523	+	0.767523i
$146$		0			0
$147$	−1.65216	+	1.65216i	−0.136268	+	0.136268i
$148$		0			0
$149$	−3.73283	+	3.73283i	−0.305805	+	0.305805i	−0.843280	−	0.537475i	$-0.819378\pi$
$149$	−3.73283	+	3.73283i	−0.305805	+	0.305805i	0.537475	+	0.843280i	$0.319378\pi$
$150$		0			0
$151$	5.68611	+	5.68611i	0.462729	+	0.462729i	0.899549	−	0.436820i	$-0.143895\pi$
$151$	5.68611	+	5.68611i	0.462729	+	0.462729i	−0.436820	+	0.899549i	$0.643895\pi$
$152$		0			0
$153$	−11.3106	−	11.3106i	−0.914406	−	0.914406i
$154$		0			0
$155$			9.61172i			0.772032i
$156$		0			0
$157$	−4.12315	−	4.12315i	−0.329064	−	0.329064i	0.523167	−	0.852230i	$-0.324750\pi$
$157$	−4.12315	−	4.12315i	−0.329064	−	0.329064i	−0.852230	+	0.523167i	$0.824750\pi$
$158$		0			0
$159$			1.90675i			0.151215i
$160$		0			0
$161$	1.85279	+	1.85279i	0.146021	+	0.146021i
$162$		0			0
$163$	11.8690			0.929651			0.464826	−	0.885402i	$-0.346117\pi$
$163$	11.8690			0.929651			0.464826	+	0.885402i	$0.346117\pi$
$164$		0			0
$165$	−5.69317			−0.443213
$166$		0			0
$167$	6.18373	+	6.18373i	0.478512	+	0.478512i	0.904655	−	0.426144i	$-0.140128\pi$
$167$	6.18373	+	6.18373i	0.478512	+	0.478512i	−0.426144	+	0.904655i	$0.640128\pi$
$168$		0			0
$169$		−	12.8150i		−	0.985772i
$170$		0			0
$171$	−5.51921	−	5.51921i	−0.422064	−	0.422064i
$172$		0			0
$173$		−	9.85989i		−	0.749634i	−0.927099	−	0.374817i	$-0.877706\pi$
$173$		−	9.85989i		−	0.749634i	0.927099	−	0.374817i	$-0.122294\pi$
$174$		0			0
$175$	2.63476	+	2.63476i	0.199169	+	0.199169i
$176$		0			0
$177$	9.82529	+	9.82529i	0.738514	+	0.738514i
$178$		0			0
$179$	17.7789	−	17.7789i	1.32885	−	1.32885i	0.422483	−	0.906371i	$-0.361159\pi$
$179$	17.7789	−	17.7789i	1.32885	−	1.32885i	0.906371	−	0.422483i	$-0.138841\pi$
$180$		0			0
$181$	−12.3686	+	12.3686i	−0.919351	+	0.919351i	−0.996982	−	0.0776310i	$-0.975264\pi$
$181$	−12.3686	+	12.3686i	−0.919351	+	0.919351i	0.0776310	+	0.996982i	$0.475264\pi$
$182$		0			0
$183$	−8.80216	+	8.80216i	−0.650674	+	0.650674i
$184$		0			0
$185$			28.2218i			2.07491i
$186$		0			0
$187$	−5.36508			−0.392333
$188$		0			0
$189$	−1.26348			−0.0919049
$190$		0			0
$191$	9.54514	−	9.54514i	0.690662	−	0.690662i	−0.271716	−	0.962378i	$-0.587591\pi$
$191$	9.54514	−	9.54514i	0.690662	−	0.690662i	0.962378	+	0.271716i	$0.0875910\pi$
$192$		0			0
$193$	12.5298	+	12.5298i	0.901917	+	0.901917i	0.995602	−	0.0936851i	$-0.0298647\pi$
$193$	12.5298	+	12.5298i	0.901917	+	0.901917i	−0.0936851	+	0.995602i	$0.529865\pi$
$194$		0			0
$195$	2.96838			0.212570
$196$		0			0
$197$			15.5518i			1.10802i	0.832510	+	0.554010i	$0.186903\pi$
$197$			15.5518i			1.10802i	−0.832510	+	0.554010i	$0.813097\pi$
$198$		0			0
$199$	−3.71168	+	3.71168i	−0.263114	+	0.263114i	−0.826318	−	0.563204i	$-0.809569\pi$
$199$	−3.71168	+	3.71168i	−0.263114	+	0.263114i	0.563204	+	0.826318i	$0.309569\pi$
$200$		0			0
$201$	20.1875			1.42392
$202$		0			0
$203$		−	4.42466i		−	0.310550i
$204$		0			0
$205$	4.17987	−	18.4472i	0.291935	−	1.28841i
$206$		0			0
$207$		−	6.44382i		−	0.447876i
$208$		0			0
$209$	−2.61799			−0.181090
$210$		0			0
$211$	−8.78315	+	8.78315i	−0.604657	+	0.604657i	−0.941545	−	0.336888i	$-0.890626\pi$
$211$	−8.78315	+	8.78315i	−0.604657	+	0.604657i	0.336888	+	0.941545i	$0.390626\pi$
$212$		0			0
$213$		−	25.6336i		−	1.75638i
$214$		0			0
$215$	11.9814			0.817124
$216$		0			0
$217$	−2.30078	−	2.30078i	−0.156187	−	0.156187i
$218$		0			0
$219$	8.91899	−	8.91899i	0.602690	−	0.602690i
$220$		0			0
$221$	2.79732			0.188168
$222$		0			0
$223$	14.9853			1.00349			0.501743	−	0.865016i	$-0.332692\pi$
$223$	14.9853			1.00349			0.501743	+	0.865016i	$0.332692\pi$
$224$		0			0
$225$		−	9.16341i		−	0.610894i
$226$		0			0
$227$	−4.68712	+	4.68712i	−0.311095	+	0.311095i	−0.845334	−	0.534239i	$-0.820598\pi$
$227$	−4.68712	+	4.68712i	−0.311095	+	0.311095i	0.534239	+	0.845334i	$0.320598\pi$
$228$		0			0
$229$	4.91562	−	4.91562i	0.324833	−	0.324833i	−0.525785	−	0.850618i	$-0.676228\pi$
$229$	4.91562	−	4.91562i	0.324833	−	0.324833i	0.850618	+	0.525785i	$0.176228\pi$
$230$		0			0
$231$	1.36279	−	1.36279i	0.0896649	−	0.0896649i
$232$		0			0
$233$	−5.61073	−	5.61073i	−0.367571	−	0.367571i	0.499020	−	0.866591i	$-0.333694\pi$
$233$	−5.61073	−	5.61073i	−0.367571	−	0.367571i	−0.866591	+	0.499020i	$0.833694\pi$
$234$		0			0
$235$	−21.9945	−	21.9945i	−1.43476	−	1.43476i
$236$		0			0
$237$			12.6477i			0.821557i
$238$		0			0
$239$	2.26725	+	2.26725i	0.146656	+	0.146656i	0.776622	−	0.629966i	$-0.216931\pi$
$239$	2.26725	+	2.26725i	0.146656	+	0.146656i	−0.629966	+	0.776622i	$0.716931\pi$
$240$		0			0
$241$			15.7463i			1.01431i	0.861855	+	0.507155i	$0.169303\pi$
$241$			15.7463i			1.01431i	−0.861855	+	0.507155i	$0.830697\pi$
$242$		0			0
$243$	14.3863	+	14.3863i	0.922880	+	0.922880i
$244$		0			0
$245$	−2.95400			−0.188724
$246$		0			0
$247$	1.36500			0.0868532
$248$		0			0
$249$	7.06078	+	7.06078i	0.447459	+	0.447459i
$250$		0			0
$251$		−	24.9768i		−	1.57652i	−0.615340	−	0.788262i	$-0.710981\pi$
$251$		−	24.9768i		−	1.57652i	0.615340	−	0.788262i	$-0.289019\pi$
$252$		0			0
$253$	−1.52829	−	1.52829i	−0.0960825	−	0.0960825i
$254$		0			0
$255$		−	44.8926i		−	2.81129i
$256$		0			0
$257$	7.98241	+	7.98241i	0.497929	+	0.497929i	0.910793	−	0.412864i	$-0.135471\pi$
$257$	7.98241	+	7.98241i	0.497929	+	0.497929i	−0.412864	+	0.910793i	$0.635471\pi$
$258$		0			0
$259$	−6.75553	−	6.75553i	−0.419768	−	0.419768i
$260$		0			0
$261$	−7.69425	+	7.69425i	−0.476262	+	0.476262i
$262$		0			0
$263$	8.44004	−	8.44004i	0.520435	−	0.520435i	−0.397268	−	0.917703i	$-0.630042\pi$
$263$	8.44004	−	8.44004i	0.520435	−	0.520435i	0.917703	+	0.397268i	$0.130042\pi$
$264$		0			0
$265$	−1.70460	+	1.70460i	−0.104713	+	0.104713i
$266$		0			0
$267$			4.63928i			0.283920i
$268$		0			0
$269$	−12.1960			−0.743603			−0.371802	−	0.928312i	$-0.621260\pi$
$269$	−12.1960			−0.743603			−0.371802	+	0.928312i	$0.621260\pi$
$270$		0			0
$271$	0.702973			0.0427025			0.0213513	−	0.999772i	$-0.493203\pi$
$271$	0.702973			0.0427025			0.0213513	+	0.999772i	$0.493203\pi$
$272$		0			0
$273$	−0.710550	+	0.710550i	−0.0430044	+	0.0430044i
$274$		0			0
$275$	−2.17329	−	2.17329i	−0.131055	−	0.131055i
$276$		0			0
$277$	−27.0584			−1.62578			−0.812891	−	0.582416i	$-0.802107\pi$
$277$	−27.0584			−1.62578			−0.812891	+	0.582416i	$0.802107\pi$
$278$		0			0
$279$			8.00188i			0.479060i
$280$		0			0
$281$	2.09997	−	2.09997i	0.125274	−	0.125274i	−0.641690	−	0.766964i	$-0.721766\pi$
$281$	2.09997	−	2.09997i	0.125274	−	0.125274i	0.766964	+	0.641690i	$0.221766\pi$
$282$		0			0
$283$	21.9796			1.30655			0.653275	−	0.757120i	$-0.273394\pi$
$283$	21.9796			1.30655			0.653275	+	0.757120i	$0.273394\pi$
$284$		0			0
$285$		−	21.9062i		−	1.29761i
$286$		0			0
$287$	3.41521	+	5.41630i	0.201593	+	0.319714i
$288$		0			0
$289$		−	25.3055i		−	1.48856i
$290$		0			0
$291$	18.0729			1.05945
$292$		0			0
$293$	2.14640	−	2.14640i	0.125394	−	0.125394i	−0.641625	−	0.767019i	$-0.721739\pi$
$293$	2.14640	−	2.14640i	0.125394	−	0.125394i	0.767019	+	0.641625i	$0.221739\pi$
$294$		0			0
$295$			17.5673i			1.02281i
$296$		0			0
$297$	1.04219			0.0604740
$298$		0			0
$299$	0.796839	+	0.796839i	0.0460824	+	0.0460824i
$300$		0			0
$301$	−2.86802	+	2.86802i	−0.165310	+	0.165310i
$302$		0			0
$303$	−35.7682			−2.05483
$304$		0			0
$305$	−15.7380			−0.901153
$306$		0			0
$307$		−	25.7136i		−	1.46755i	−0.679392	−	0.733776i	$-0.737756\pi$
$307$		−	25.7136i		−	1.46755i	0.679392	−	0.733776i	$-0.262244\pi$
$308$		0			0
$309$	−8.60407	+	8.60407i	−0.489469	+	0.489469i
$310$		0			0
$311$	18.5145	−	18.5145i	1.04986	−	1.04986i	0.0511688	−	0.998690i	$-0.483705\pi$
$311$	18.5145	−	18.5145i	1.04986	−	1.04986i	0.998690	−	0.0511688i	$-0.0162947\pi$
$312$		0			0
$313$	7.51282	−	7.51282i	0.424650	−	0.424650i	−0.462151	−	0.886801i	$-0.652922\pi$
$313$	7.51282	−	7.51282i	0.424650	−	0.424650i	0.886801	+	0.462151i	$0.152922\pi$
$314$		0			0
$315$	5.13685	+	5.13685i	0.289428	+	0.289428i
$316$		0			0
$317$	23.3975	+	23.3975i	1.31414	+	1.31414i	0.918338	+	0.395798i	$0.129532\pi$
$317$	23.3975	+	23.3975i	1.31414	+	1.31414i	0.395798	+	0.918338i	$0.370468\pi$
$318$		0			0
$319$			3.64970i			0.204344i
$320$		0			0
$321$	32.5462	+	32.5462i	1.81655	+	1.81655i
$322$		0			0
$323$		−	20.6438i		−	1.14865i
$324$		0			0
$325$	1.13314	+	1.13314i	0.0628554	+	0.0628554i
$326$		0			0
$327$	−1.95095			−0.107888
$328$		0			0
$329$	10.5298			0.580524
$330$		0			0
$331$	−19.8680	−	19.8680i	−1.09204	−	1.09204i	−0.995310	−	0.0967336i	$-0.969161\pi$
$331$	−19.8680	−	19.8680i	−1.09204	−	1.09204i	−0.0967336	−	0.995310i	$-0.530839\pi$
$332$		0			0
$333$			23.4950i			1.28752i
$334$		0			0
$335$	18.0473	+	18.0473i	0.986030	+	0.986030i
$336$		0			0
$337$			5.40369i			0.294358i	0.989110	+	0.147179i	$0.0470193\pi$
$337$			5.40369i			0.294358i	−0.989110	+	0.147179i	$0.952981\pi$
$338$		0			0
$339$	−0.590852	−	0.590852i	−0.0320907	−	0.0320907i
$340$		0			0
$341$	1.89781	+	1.89781i	0.102772	+	0.102772i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	12.7880	−	12.7880i	0.688485	−	0.688485i
$346$		0			0
$347$	−15.3749	+	15.3749i	−0.825368	+	0.825368i	−0.986872	−	0.161504i	$-0.948366\pi$
$347$	−15.3749	+	15.3749i	−0.825368	+	0.825368i	0.161504	+	0.986872i	$0.448366\pi$
$348$		0			0
$349$		−	10.6437i		−	0.569743i	−0.958566	−	0.284872i	$-0.908049\pi$
$349$		−	10.6437i		−	0.569743i	0.958566	−	0.284872i	$-0.0919509\pi$
$350$		0			0
$351$	−0.543392			−0.0290041
$352$		0			0
$353$	6.85305			0.364751			0.182375	−	0.983229i	$-0.441621\pi$
$353$	6.85305			0.364751			0.182375	+	0.983229i	$0.441621\pi$
$354$		0			0
$355$	22.9160	−	22.9160i	1.21625	−	1.21625i
$356$		0			0
$357$	10.7461	+	10.7461i	0.568742	+	0.568742i
$358$		0			0
$359$	27.9264			1.47390			0.736948	−	0.675949i	$-0.236266\pi$
$359$	27.9264			1.47390			0.736948	+	0.675949i	$0.236266\pi$
$360$		0			0
$361$			8.92648i			0.469815i
$362$		0			0
$363$	17.0496	−	17.0496i	0.894873	−	0.894873i
$364$		0			0
$365$	15.9469			0.834697
$366$		0			0
$367$		−	22.4127i		−	1.16993i	−0.811057	−	0.584966i	$-0.801108\pi$
$367$		−	22.4127i		−	1.16993i	0.811057	−	0.584966i	$-0.198892\pi$
$368$		0			0
$369$	3.47980	−	15.3575i	0.181151	−	0.799481i
$370$		0			0
$371$		−	0.816072i		−	0.0423683i
$372$		0			0
$373$	−8.45165			−0.437610			−0.218805	−	0.975769i	$-0.570216\pi$
$373$	−8.45165			−0.437610			−0.218805	+	0.975769i	$0.570216\pi$
$374$		0			0
$375$	−6.21716	+	6.21716i	−0.321053	+	0.321053i
$376$		0			0
$377$		−	1.90293i		−	0.0980060i
$378$		0			0
$379$	−20.7183			−1.06423			−0.532113	−	0.846673i	$-0.678602\pi$
$379$	−20.7183			−1.06423			−0.532113	+	0.846673i	$0.678602\pi$
$380$		0			0
$381$	−4.41078	−	4.41078i	−0.225971	−	0.225971i
$382$		0			0
$383$	−1.22706	+	1.22706i	−0.0626996	+	0.0626996i	−0.737761	−	0.675062i	$-0.764117\pi$
$383$	−1.22706	+	1.22706i	−0.0626996	+	0.0626996i	0.675062	+	0.737761i	$0.264117\pi$
$384$		0			0
$385$	2.43662			0.124182
$386$		0			0
$387$	9.97465			0.507040
$388$		0			0
$389$		−	7.77430i		−	0.394172i	−0.980386	−	0.197086i	$-0.936852\pi$
$389$		−	7.77430i		−	0.394172i	0.980386	−	0.197086i	$-0.0631479\pi$
$390$		0			0
$391$	12.0511	−	12.0511i	0.609449	−	0.609449i
$392$		0			0
$393$	−17.9616	+	17.9616i	−0.906041	+	0.906041i
$394$		0			0
$395$	−11.3068	+	11.3068i	−0.568909	+	0.568909i
$396$		0			0
$397$	−13.3035	−	13.3035i	−0.667681	−	0.667681i	0.289498	−	0.957179i	$-0.406512\pi$
$397$	−13.3035	−	13.3035i	−0.667681	−	0.667681i	−0.957179	+	0.289498i	$0.906512\pi$
$398$		0			0
$399$	5.24375	+	5.24375i	0.262516	+	0.262516i
$400$		0			0
$401$			19.7275i			0.985144i	0.870272	+	0.492572i	$0.163943\pi$
$401$			19.7275i			0.985144i	−0.870272	+	0.492572i	$0.836057\pi$
$402$		0			0
$403$	−0.989508	−	0.989508i	−0.0492909	−	0.0492909i
$404$		0			0
$405$			30.5144i			1.51627i
$406$		0			0
$407$	5.57233	+	5.57233i	0.276210	+	0.276210i
$408$		0			0
$409$	−30.4183			−1.50409			−0.752044	−	0.659113i	$-0.770932\pi$
$409$	−30.4183			−1.50409			−0.752044	+	0.659113i	$0.770932\pi$
$410$		0			0
$411$	−5.38501			−0.265623
$412$		0			0
$413$	−4.20513	−	4.20513i	−0.206921	−	0.206921i
$414$		0			0
$415$			12.6244i			0.619709i
$416$		0			0
$417$	18.4785	+	18.4785i	0.904896	+	0.904896i
$418$		0			0
$419$		−	33.8189i		−	1.65216i	−0.563553	−	0.826080i	$-0.690566\pi$
$419$		−	33.8189i		−	1.65216i	0.563553	−	0.826080i	$-0.309434\pi$
$420$		0			0
$421$	−2.40237	−	2.40237i	−0.117084	−	0.117084i	0.646137	−	0.763221i	$-0.276383\pi$
$421$	−2.40237	−	2.40237i	−0.117084	−	0.117084i	−0.763221	+	0.646137i	$0.776383\pi$
$422$		0			0
$423$	−18.3107	−	18.3107i	−0.890295	−	0.890295i
$424$		0			0
$425$	17.1372	−	17.1372i	0.831276	−	0.831276i
$426$		0			0
$427$	3.76724	−	3.76724i	0.182309	−	0.182309i
$428$		0			0
$429$	0.586100	−	0.586100i	0.0282972	−	0.0282972i
$430$		0			0
$431$			8.60222i			0.414354i	0.978303	+	0.207177i	$0.0664277\pi$
$431$			8.60222i			0.414354i	−0.978303	+	0.207177i	$0.933572\pi$
$432$		0			0
$433$	−22.6257			−1.08732			−0.543661	−	0.839305i	$-0.682962\pi$
$433$	−22.6257			−1.08732			−0.543661	+	0.839305i	$0.682962\pi$
$434$		0			0
$435$	−30.5391			−1.46424
$436$		0			0
$437$	5.88055	−	5.88055i	0.281305	−	0.281305i
$438$		0			0
$439$	7.12568	+	7.12568i	0.340090	+	0.340090i	0.856401	−	0.516311i	$-0.172695\pi$
$439$	7.12568	+	7.12568i	0.340090	+	0.340090i	−0.516311	+	0.856401i	$0.672695\pi$
$440$		0			0
$441$	−2.45924			−0.117107
$442$		0			0
$443$			13.4557i			0.639298i	0.947536	+	0.319649i	$0.103565\pi$
$443$			13.4557i			0.639298i	−0.947536	+	0.319649i	$0.896435\pi$
$444$		0			0
$445$	−4.14744	+	4.14744i	−0.196608	+	0.196608i
$446$		0			0
$447$	−12.3344			−0.583398
$448$		0			0
$449$		−	31.9547i		−	1.50803i	−0.656855	−	0.754017i	$-0.728113\pi$
$449$		−	31.9547i		−	1.50803i	0.656855	−	0.754017i	$-0.271887\pi$
$450$		0			0
$451$	−2.81705	−	4.46766i	−0.132650	−	0.210374i
$452$		0			0
$453$			18.7887i			0.882769i
$454$		0			0
$455$	−1.27044			−0.0595591
$456$		0			0
$457$	8.80331	−	8.80331i	0.411801	−	0.411801i	−0.470564	−	0.882366i	$-0.655950\pi$
$457$	8.80331	−	8.80331i	0.411801	−	0.411801i	0.882366	+	0.470564i	$0.155950\pi$
$458$		0			0
$459$			8.21804i			0.383585i
$460$		0			0
$461$	−32.9461			−1.53445			−0.767226	−	0.641377i	$-0.778364\pi$
$461$	−32.9461			−1.53445			−0.767226	+	0.641377i	$0.778364\pi$
$462$		0			0
$463$	−22.6636	−	22.6636i	−1.05327	−	1.05327i	−0.998499	−	0.0547672i	$-0.982558\pi$
$463$	−22.6636	−	22.6636i	−1.05327	−	1.05327i	−0.0547672	−	0.998499i	$-0.517442\pi$
$464$		0			0
$465$	−15.8801	+	15.8801i	−0.736421	+	0.736421i
$466$		0			0
$467$	22.5274			1.04244			0.521221	−	0.853422i	$-0.325477\pi$
$467$	22.5274			1.04244			0.521221	+	0.853422i	$0.325477\pi$
$468$		0			0
$469$	−8.64007			−0.398961
$470$		0			0
$471$		−	13.6242i		−	0.627770i
$472$		0			0
$473$	2.36570	−	2.36570i	0.108775	−	0.108775i
$474$		0			0
$475$	8.36242	−	8.36242i	0.383694	−	0.383694i
$476$		0			0
$477$	−1.41910	+	1.41910i	−0.0649763	+	0.0649763i
$478$		0			0
$479$	−24.9383	−	24.9383i	−1.13946	−	1.13946i	−0.988547	−	0.150915i	$-0.951778\pi$
$479$	−24.9383	−	24.9383i	−1.13946	−	1.13946i	−0.150915	−	0.988547i	$-0.548222\pi$
$480$		0			0
$481$	−2.90538	−	2.90538i	−0.132474	−	0.132474i
$482$		0			0
$483$			6.12221i			0.278570i
$484$		0			0
$485$	16.1569	+	16.1569i	0.733647	+	0.733647i
$486$		0			0
$487$			14.7261i			0.667302i	0.942697	+	0.333651i	$0.108281\pi$
$487$			14.7261i			0.667302i	−0.942697	+	0.333651i	$0.891719\pi$
$488$		0			0
$489$	19.6094	+	19.6094i	0.886769	+	0.886769i
$490$		0			0
$491$	−18.4511			−0.832687			−0.416344	−	0.909207i	$-0.636689\pi$
$491$	−18.4511			−0.832687			−0.416344	+	0.909207i	$0.636689\pi$
$492$		0			0
$493$	−28.7792			−1.29615
$494$		0			0
$495$	−4.23715	−	4.23715i	−0.190446	−	0.190446i
$496$		0			0
$497$			10.9709i			0.492113i
$498$		0			0
$499$	3.86414	+	3.86414i	0.172982	+	0.172982i	0.788288	−	0.615306i	$-0.210968\pi$
$499$	3.86414	+	3.86414i	0.172982	+	0.172982i	−0.615306	+	0.788288i	$0.710968\pi$
$500$		0			0
$501$			20.4330i			0.912879i
$502$		0			0
$503$	14.9077	+	14.9077i	0.664701	+	0.664701i	0.956484	−	0.291784i	$-0.0942487\pi$
$503$	14.9077	+	14.9077i	0.664701	+	0.664701i	−0.291784	+	0.956484i	$0.594249\pi$
$504$		0			0
$505$	−31.9762	−	31.9762i	−1.42292	−	1.42292i
$506$		0			0
$507$	21.1724	−	21.1724i	0.940301	−	0.940301i
$508$		0			0
$509$	26.8720	−	26.8720i	1.19108	−	1.19108i	0.214318	−	0.976764i	$-0.431247\pi$
$509$	26.8720	−	26.8720i	1.19108	−	1.19108i	0.976764	−	0.214318i	$-0.0687530\pi$
$510$		0			0
$511$	−3.81724	+	3.81724i	−0.168865	+	0.168865i
$512$		0			0
$513$			4.01015i			0.177052i
$514$		0			0
$515$	−15.3838			−0.677891
$516$		0			0
$517$	−8.68552			−0.381989
$518$		0			0
$519$	16.2901	−	16.2901i	0.715055	−	0.715055i
$520$		0			0
$521$	−11.7175	−	11.7175i	−0.513354	−	0.513354i	0.402199	−	0.915552i	$-0.368246\pi$
$521$	−11.7175	−	11.7175i	−0.513354	−	0.513354i	−0.915552	+	0.402199i	$0.868246\pi$
$522$		0			0
$523$	15.1470			0.662331			0.331166	−	0.943573i	$-0.392558\pi$
$523$	15.1470			0.662331			0.331166	+	0.943573i	$0.392558\pi$
$524$		0			0
$525$			8.70607i			0.379964i
$526$		0			0
$527$	−14.9649	+	14.9649i	−0.651882	+	0.651882i
$528$		0			0
$529$	−16.1343			−0.701492
$530$		0			0
$531$			14.6250i			0.634670i
$532$		0			0
$533$	1.46879	+	2.32941i	0.0636205	+	0.100898i
$534$		0			0
$535$			58.1916i			2.51584i
$536$		0			0
$537$	58.7469			2.53512
$538$		0			0
$539$	−0.583260	+	0.583260i	−0.0251228	+	0.0251228i
$540$		0			0
$541$			22.3169i			0.959481i	0.877411	+	0.479740i	$0.159269\pi$
$541$			22.3169i			0.959481i	−0.877411	+	0.479740i	$0.840731\pi$
$542$		0			0
$543$	−40.8697			−1.75389
$544$		0			0
$545$	−1.74412	−	1.74412i	−0.0747097	−	0.0747097i
$546$		0			0
$547$	−16.8083	+	16.8083i	−0.718673	+	0.718673i	−0.968333	−	0.249660i	$-0.919681\pi$
$547$	−16.8083	+	16.8083i	−0.718673	+	0.718673i	0.249660	+	0.968333i	$0.419681\pi$
$548$		0			0
$549$	−13.1020			−0.559182
$550$		0			0
$551$	−14.0434			−0.598267
$552$		0			0
$553$		−	5.41310i		−	0.230188i
$554$		0			0
$555$	−46.6268	+	46.6268i	−1.97920	+	1.97920i
$556$		0			0
$557$	−22.3758	+	22.3758i	−0.948091	+	0.948091i	−0.998718	−	0.0506266i	$-0.983878\pi$
$557$	−22.3758	+	22.3758i	−0.948091	+	0.948091i	0.0506266	+	0.998718i	$0.483878\pi$
$558$		0			0
$559$	−1.23346	+	1.23346i	−0.0521698	+	0.0521698i
$560$		0			0
$561$	−8.86395	−	8.86395i	−0.374236	−	0.374236i
$562$		0			0
$563$	−5.34204	−	5.34204i	−0.225140	−	0.225140i	0.585519	−	0.810659i	$-0.300891\pi$
$563$	−5.34204	−	5.34204i	−0.225140	−	0.225140i	−0.810659	+	0.585519i	$0.800891\pi$
$564$		0			0
$565$		−	1.05642i		−	0.0444441i
$566$		0			0
$567$	−7.30431	−	7.30431i	−0.306752	−	0.306752i
$568$		0			0
$569$		−	12.2047i		−	0.511650i	−0.966723	−	0.255825i	$-0.917653\pi$
$569$		−	12.2047i		−	0.511650i	0.966723	−	0.255825i	$-0.0823470\pi$
$570$		0			0
$571$	−0.427220	−	0.427220i	−0.0178786	−	0.0178786i	0.698111	−	0.715990i	$-0.254024\pi$
$571$	−0.427220	−	0.427220i	−0.0178786	−	0.0178786i	−0.715990	+	0.698111i	$0.754024\pi$
$572$		0			0
$573$	31.5401			1.31761
$574$		0			0
$575$	9.76334			0.407159
$576$		0			0
$577$	13.5326	+	13.5326i	0.563371	+	0.563371i	0.930263	−	0.366893i	$-0.119578\pi$
$577$	13.5326	+	13.5326i	0.563371	+	0.563371i	−0.366893	+	0.930263i	$0.619578\pi$
$578$		0			0
$579$			41.4025i			1.72063i
$580$		0			0
$581$	−3.02194	−	3.02194i	−0.125371	−	0.125371i
$582$		0			0
$583$			0.673140i			0.0278786i
$584$		0			0
$585$	2.20923	+	2.20923i	0.0913402	+	0.0913402i
$586$		0			0
$587$	−4.29502	−	4.29502i	−0.177275	−	0.177275i	0.612892	−	0.790167i	$-0.290006\pi$
$587$	−4.29502	−	4.29502i	−0.177275	−	0.177275i	−0.790167	+	0.612892i	$0.790006\pi$
$588$		0			0
$589$	−7.30242	+	7.30242i	−0.300891	+	0.300891i
$590$		0			0
$591$	−25.6940	+	25.6940i	−1.05691	+	1.05691i
$592$		0			0
$593$	−7.52938	+	7.52938i	−0.309194	+	0.309194i	−0.844597	−	0.535403i	$-0.820160\pi$
$593$	−7.52938	+	7.52938i	−0.309194	+	0.309194i	0.535403	+	0.844597i	$0.320160\pi$
$594$		0			0
$595$			19.2136i			0.787681i
$596$		0			0
$597$	−12.2646			−0.501955
$598$		0			0
$599$	−12.9937			−0.530908			−0.265454	−	0.964123i	$-0.585522\pi$
$599$	−12.9937			−0.530908			−0.265454	+	0.964123i	$0.585522\pi$
$600$		0			0
$601$	17.3582	−	17.3582i	0.708056	−	0.708056i	−0.258070	−	0.966126i	$-0.583087\pi$
$601$	17.3582	−	17.3582i	0.708056	−	0.708056i	0.966126	+	0.258070i	$0.0830866\pi$
$602$		0			0
$603$	15.0246	+	15.0246i	0.611850	+	0.611850i
$604$		0			0
$605$	30.4841			1.23936
$606$		0			0
$607$			35.1559i			1.42693i	0.700689	+	0.713467i	$0.252876\pi$
$607$			35.1559i			1.42693i	−0.700689	+	0.713467i	$0.747124\pi$
$608$		0			0
$609$	7.31023	−	7.31023i	0.296226	−	0.296226i
$610$		0			0
$611$	4.52858			0.183207
$612$		0			0
$613$		−	39.5795i		−	1.59860i	−0.600933	−	0.799300i	$-0.705204\pi$
$613$		−	39.5795i		−	1.59860i	0.600933	−	0.799300i	$-0.294796\pi$
$614$		0			0
$615$	37.3835	−	23.5719i	1.50745	−	0.950509i
$616$		0			0
$617$		−	21.9755i		−	0.884701i	−0.896842	−	0.442351i	$-0.854145\pi$
$617$		−	21.9755i		−	0.884701i	0.896842	−	0.442351i	$-0.145855\pi$
$618$		0			0
$619$	17.1165			0.687970			0.343985	−	0.938975i	$-0.388223\pi$
$619$	17.1165			0.687970			0.343985	+	0.938975i	$0.388223\pi$
$620$		0			0
$621$	−2.34098	+	2.34098i	−0.0939401	+	0.0939401i
$622$		0			0
$623$		−	1.98557i		−	0.0795501i
$624$		0			0
$625$	−29.7466			−1.18987
$626$		0			0
$627$	−4.32533	−	4.32533i	−0.172737	−	0.172737i
$628$		0			0
$629$	−43.9398	+	43.9398i	−1.75199	+	1.75199i
$630$		0			0
$631$	−1.15821			−0.0461075			−0.0230537	−	0.999734i	$-0.507339\pi$
$631$	−1.15821			−0.0461075			−0.0230537	+	0.999734i	$0.507339\pi$
$632$		0			0
$633$	−29.0223			−1.15353
$634$		0			0
$635$		−	7.88633i		−	0.312959i
$636$		0			0
$637$	0.304108	−	0.304108i	0.0120492	−	0.0120492i
$638$		0			0
$639$	19.0778	−	19.0778i	0.754707	−	0.754707i
$640$		0			0
$641$	−31.2194	+	31.2194i	−1.23309	+	1.23309i	−0.270320	+	0.962771i	$0.587129\pi$
$641$	−31.2194	+	31.2194i	−1.23309	+	1.23309i	−0.962771	+	0.270320i	$0.912871\pi$
$642$		0			0
$643$	27.6878	+	27.6878i	1.09190	+	1.09190i	0.995326	+	0.0965746i	$0.0307886\pi$
$643$	27.6878	+	27.6878i	1.09190	+	1.09190i	0.0965746	+	0.995326i	$0.469211\pi$
$644$		0			0
$645$	19.7951	+	19.7951i	0.779432	+	0.779432i
$646$		0			0
$647$			19.4427i			0.764371i	0.924086	+	0.382185i	$0.124828\pi$
$647$			19.4427i			0.764371i	−0.924086	+	0.382185i	$0.875172\pi$
$648$		0			0
$649$	3.46862	+	3.46862i	0.136155	+	0.136155i
$650$		0			0
$651$		−	7.60251i		−	0.297966i
$652$		0			0
$653$	17.3031	+	17.3031i	0.677122	+	0.677122i	0.959348	−	0.282226i	$-0.0910728\pi$
$653$	17.3031	+	17.3031i	0.677122	+	0.677122i	−0.282226	+	0.959348i	$0.591073\pi$
$654$		0			0
$655$	−32.1147			−1.25482
$656$		0			0
$657$	13.2760			0.517944
$658$		0			0
$659$	2.94442	+	2.94442i	0.114698	+	0.114698i	0.762126	−	0.647428i	$-0.224155\pi$
$659$	2.94442	+	2.94442i	0.114698	+	0.114698i	−0.647428	+	0.762126i	$0.724155\pi$
$660$		0			0
$661$			48.4460i			1.88433i	0.335150	+	0.942165i	$0.391213\pi$
$661$			48.4460i			1.88433i	−0.335150	+	0.942165i	$0.608787\pi$
$662$		0			0
$663$	4.62161	+	4.62161i	0.179488	+	0.179488i
$664$		0			0
$665$			9.37565i			0.363572i
$666$		0			0
$667$	−8.19799	−	8.19799i	−0.317427	−	0.317427i
$668$		0			0
$669$	24.7580	+	24.7580i	0.957199	+	0.957199i
$670$		0			0
$671$	−3.10742	+	3.10742i	−0.119961	+	0.119961i
$672$		0			0
$673$	22.1467	−	22.1467i	0.853691	−	0.853691i	−0.136894	−	0.990586i	$-0.543712\pi$
$673$	22.1467	−	22.1467i	0.853691	−	0.853691i	0.990586	+	0.136894i	$0.0437120\pi$
$674$		0			0
$675$	−3.32898	+	3.32898i	−0.128132	+	0.128132i
$676$		0			0
$677$			15.2820i			0.587333i	0.955908	+	0.293667i	$0.0948755\pi$
$677$			15.2820i			0.587333i	−0.955908	+	0.293667i	$0.905124\pi$
$678$		0			0
$679$	−7.73504			−0.296844
$680$		0			0
$681$	−15.4877			−0.593490
$682$		0			0
$683$	9.64237	−	9.64237i	0.368955	−	0.368955i	−0.498141	−	0.867096i	$-0.665984\pi$
$683$	9.64237	−	9.64237i	0.368955	−	0.368955i	0.867096	+	0.498141i	$0.165984\pi$
$684$		0			0
$685$	−4.81411	−	4.81411i	−0.183938	−	0.183938i
$686$		0			0
$687$	16.2427			0.619699
$688$		0			0
$689$		−	0.350971i		−	0.0133709i
$690$		0			0
$691$	−25.9580	+	25.9580i	−0.987489	+	0.987489i	−0.999923	−	0.0124342i	$-0.996042\pi$
$691$	−25.9580	+	25.9580i	−0.987489	+	0.987489i	0.0124342	+	0.999923i	$0.496042\pi$
$692$		0			0
$693$	2.02852			0.0770570
$694$		0			0
$695$			33.0389i			1.25324i
$696$		0			0
$697$	35.2291	−	22.2134i	1.33440	−	0.841394i
$698$		0			0
$699$		−	18.5396i		−	0.701232i
$700$		0			0
$701$	−22.5048			−0.849993			−0.424996	−	0.905195i	$-0.639725\pi$
$701$	−22.5048			−0.849993			−0.424996	+	0.905195i	$0.639725\pi$
$702$		0			0
$703$	−21.4412	+	21.4412i	−0.808672	+	0.808672i
$704$		0			0
$705$		−	72.6766i		−	2.73716i
$706$		0			0
$707$	15.3085			0.575734
$708$		0			0
$709$	−5.36395	−	5.36395i	−0.201447	−	0.201447i	0.599173	−	0.800620i	$-0.295496\pi$
$709$	−5.36395	−	5.36395i	−0.201447	−	0.201447i	−0.800620	+	0.599173i	$0.795496\pi$
$710$		0			0
$711$	−9.41309	+	9.41309i	−0.353018	+	0.353018i
$712$		0			0
$713$	−8.52576			−0.319292
$714$		0			0
$715$	1.04793			0.0391903
$716$		0			0
$717$			7.49169i			0.279782i
$718$		0			0
$719$	17.1389	−	17.1389i	0.639174	−	0.639174i	−0.311178	−	0.950352i	$-0.600723\pi$
$719$	17.1389	−	17.1389i	0.639174	−	0.639174i	0.950352	+	0.311178i	$0.100723\pi$
$720$		0			0
$721$	3.68246	−	3.68246i	0.137142	−	0.137142i
$722$		0			0
$723$	−26.0154	+	26.0154i	−0.967523	+	0.967523i
$724$		0			0
$725$	−11.6579	−	11.6579i	−0.432964	−	0.432964i
$726$		0			0
$727$	−22.6030	−	22.6030i	−0.838298	−	0.838298i	0.150337	−	0.988635i	$-0.451964\pi$
$727$	−22.6030	−	22.6030i	−0.838298	−	0.838298i	−0.988635	+	0.150337i	$0.951964\pi$
$728$		0			0
$729$			16.5472i			0.612860i
$730$		0			0
$731$	18.6544	+	18.6544i	0.689956	+	0.689956i
$732$		0			0
$733$		−	12.9847i		−	0.479600i	−0.970822	−	0.239800i	$-0.922918\pi$
$733$		−	12.9847i		−	0.479600i	0.970822	−	0.239800i	$-0.0770818\pi$
$734$		0			0
$735$	−4.88047	−	4.88047i	−0.180019	−	0.180019i
$736$		0			0
$737$	7.12680			0.262519
$738$		0			0
$739$	−20.7989			−0.765099			−0.382550	−	0.923935i	$-0.624954\pi$
$739$	−20.7989			−0.765099			−0.382550	+	0.923935i	$0.624954\pi$
$740$		0			0
$741$	2.25520	+	2.25520i	0.0828469	+	0.0828469i
$742$		0			0
$743$			42.9275i			1.57486i	0.616406	+	0.787429i	$0.288588\pi$
$743$			42.9275i			1.57486i	−0.616406	+	0.787429i	$0.711412\pi$
$744$		0			0
$745$	−11.0268	−	11.0268i	−0.403990	−	0.403990i
$746$		0			0
$747$			10.5100i			0.384541i
$748$		0			0
$749$	−13.9295	−	13.9295i	−0.508972	−	0.508972i
$750$		0			0
$751$	−27.1730	−	27.1730i	−0.991555	−	0.991555i	0.00840929	−	0.999965i	$-0.497323\pi$
$751$	−27.1730	−	27.1730i	−0.991555	−	0.991555i	−0.999965	+	0.00840929i	$0.997323\pi$
$752$		0			0
$753$	41.2656	−	41.2656i	1.50380	−	1.50380i
$754$		0			0
$755$	−16.7968	+	16.7968i	−0.611297	+	0.611297i
$756$		0			0
$757$	8.44327	−	8.44327i	0.306876	−	0.306876i	−0.536821	−	0.843696i	$-0.680375\pi$
$757$	8.44327	−	8.44327i	0.306876	−	0.306876i	0.843696	+	0.536821i	$0.180375\pi$
$758$		0			0
$759$		−	5.04994i		−	0.183301i
$760$		0			0
$761$	39.3579			1.42672			0.713361	−	0.700796i	$-0.247172\pi$
$761$	39.3579			1.42672			0.713361	+	0.700796i	$0.247172\pi$
$762$		0			0
$763$	0.834987			0.0302286
$764$		0			0
$765$	33.4114	−	33.4114i	1.20799	−	1.20799i
$766$		0			0
$767$	−1.80852	−	1.80852i	−0.0653018	−	0.0653018i
$768$		0			0
$769$	−17.0701			−0.615563			−0.307781	−	0.951457i	$-0.599587\pi$
$769$	−17.0701			−0.615563			−0.307781	+	0.951457i	$0.599587\pi$
$770$		0			0
$771$			26.3764i			0.949922i
$772$		0			0
$773$	28.6315	−	28.6315i	1.02980	−	1.02980i	0.0302606	−	0.999542i	$-0.490366\pi$
$773$	28.6315	−	28.6315i	1.02980	−	1.02980i	0.999542	−	0.0302606i	$-0.00963372\pi$
$774$		0			0
$775$	−12.1240			−0.435508
$776$		0			0
$777$		−	22.3224i		−	0.800811i
$778$		0			0
$779$	17.1907	−	10.8395i	0.615921	−	0.388364i
$780$		0			0
$781$		−	9.04941i		−	0.323813i
$782$		0			0
$783$	5.59049			0.199788
$784$		0			0
$785$	12.1798	−	12.1798i	0.434716	−	0.434716i
$786$		0			0
$787$			34.1654i			1.21786i	0.793222	+	0.608932i	$0.208402\pi$
$787$			34.1654i			1.21786i	−0.793222	+	0.608932i	$0.791598\pi$
$788$		0			0
$789$	27.8885			0.992858
$790$		0			0
$791$	0.252879	+	0.252879i	0.00899134	+	0.00899134i
$792$		0			0
$793$	1.62019	−	1.62019i	0.0575347	−	0.0575347i
$794$		0			0
$795$	−5.63255			−0.199766
$796$		0			0
$797$	−22.8507			−0.809412			−0.404706	−	0.914447i	$-0.632626\pi$
$797$	−22.8507			−0.809412			−0.404706	+	0.914447i	$0.632626\pi$
$798$		0			0
$799$		−	68.4884i		−	2.42294i
$800$		0			0
$801$	−3.45280	+	3.45280i	−0.121999	+	0.121999i
$802$		0			0
$803$	3.14867	−	3.14867i	0.111114	−	0.111114i
$804$		0			0
$805$	−5.47315	+	5.47315i	−0.192903	+	0.192903i
$806$		0			0
$807$	−20.1497	−	20.1497i	−0.709303	−	0.709303i
$808$		0			0
$809$	−34.4015	−	34.4015i	−1.20949	−	1.20949i	−0.971191	−	0.238303i	$-0.923409\pi$
$809$	−34.4015	−	34.4015i	−1.20949	−	1.20949i	−0.238303	−	0.971191i	$-0.576591\pi$
$810$		0			0
$811$		−	36.8733i		−	1.29480i	−0.762152	−	0.647399i	$-0.775857\pi$
$811$		−	36.8733i		−	1.29480i	0.762152	−	0.647399i	$-0.224143\pi$
$812$		0			0
$813$	1.16142	+	1.16142i	0.0407328	+	0.0407328i
$814$		0			0
$815$			35.0610i			1.22813i
$816$		0			0
$817$	9.10275	+	9.10275i	0.318465	+	0.318465i
$818$		0			0
$819$	−1.05766			−0.0369575
$820$		0			0
$821$	7.59563			0.265089			0.132545	−	0.991177i	$-0.457685\pi$
$821$	7.59563			0.265089			0.132545	+	0.991177i	$0.457685\pi$
$822$		0			0
$823$	28.6146	+	28.6146i	0.997441	+	0.997441i	0.999997	−	0.00255532i	$-0.000813386\pi$
$823$	28.6146	+	28.6146i	0.997441	+	0.997441i	−0.00255532	+	0.999997i	$0.500813\pi$
$824$		0			0
$825$		−	7.18124i		−	0.250019i
$826$		0			0
$827$	10.2451	+	10.2451i	0.356256	+	0.356256i	0.862431	−	0.506175i	$-0.168941\pi$
$827$	10.2451	+	10.2451i	0.356256	+	0.356256i	−0.506175	+	0.862431i	$0.668941\pi$
$828$		0			0
$829$		−	25.5950i		−	0.888950i	−0.895791	−	0.444475i	$-0.853390\pi$
$829$		−	25.5950i		−	0.888950i	0.895791	−	0.444475i	$-0.146610\pi$
$830$		0			0
$831$	−44.7047	−	44.7047i	−1.55079	−	1.55079i
$832$		0			0
$833$	−4.59921	−	4.59921i	−0.159353	−	0.159353i
$834$		0			0
$835$	−18.2667	+	18.2667i	−0.632147	+	0.632147i
$836$		0			0
$837$	2.90700	−	2.90700i	0.100481	−	0.100481i
$838$		0			0
$839$	−13.2837	+	13.2837i	−0.458603	+	0.458603i	−0.898197	−	0.439594i	$-0.855122\pi$
$839$	−13.2837	+	13.2837i	−0.458603	+	0.458603i	0.439594	+	0.898197i	$0.355122\pi$
$840$		0			0
$841$		−	9.42237i		−	0.324909i
$842$		0			0
$843$	6.93896			0.238990
$844$		0			0
$845$	37.8556			1.30227
$846$		0			0
$847$	−7.29707	+	7.29707i	−0.250730	+	0.250730i
$848$		0			0
$849$	36.3137	+	36.3137i	1.24628	+	1.24628i
$850$		0			0
$851$	−25.0332			−0.858127
$852$		0			0
$853$		−	55.5073i		−	1.90053i	−0.311439	−	0.950266i	$-0.600811\pi$
$853$		−	55.5073i		−	1.90053i	0.311439	−	0.950266i	$-0.399189\pi$
$854$		0			0
$855$	16.3037	−	16.3037i	0.557576	−	0.557576i
$856$		0			0
$857$	−47.1421			−1.61034			−0.805171	−	0.593043i	$-0.797926\pi$
$857$	−47.1421			−1.61034			−0.805171	+	0.593043i	$0.797926\pi$
$858$		0			0
$859$		−	47.2175i		−	1.61104i	−0.592568	−	0.805521i	$-0.701886\pi$
$859$		−	47.2175i		−	1.61104i	0.592568	−	0.805521i	$-0.298114\pi$
$860$		0			0
$861$	−3.30612	+	14.5910i	−0.112672	+	0.497261i
$862$		0			0
$863$		−	4.40314i		−	0.149885i	−0.997188	−	0.0749424i	$-0.976123\pi$
$863$		−	4.40314i		−	0.149885i	0.997188	−	0.0749424i	$-0.0238773\pi$
$864$		0			0
$865$	29.1261			0.990318
$866$		0			0
$867$	41.8087	−	41.8087i	1.41990	−	1.41990i
$868$		0			0
$869$			4.46502i			0.151465i
$870$		0			0
$871$	−3.71587			−0.125907
$872$		0			0
$873$	13.4508	+	13.4508i	0.455241	+	0.455241i
$874$		0			0
$875$	2.66088	−	2.66088i	0.0899543	−	0.0899543i
$876$		0			0
$877$	−25.3584			−0.856291			−0.428145	−	0.903710i	$-0.640833\pi$
$877$	−25.3584			−0.856291			−0.428145	+	0.903710i	$0.640833\pi$
$878$		0			0
$879$	7.09238			0.239220
$880$		0			0
$881$		−	38.2849i		−	1.28985i	−0.764245	−	0.644926i	$-0.776888\pi$
$881$		−	38.2849i		−	1.28985i	0.764245	−	0.644926i	$-0.223112\pi$
$882$		0			0
$883$	−27.5057	+	27.5057i	−0.925639	+	0.925639i	−0.997420	−	0.0717814i	$-0.977132\pi$
$883$	−27.5057	+	27.5057i	−0.925639	+	0.925639i	0.0717814	+	0.997420i	$0.477132\pi$
$884$		0			0
$885$	−29.0239	+	29.0239i	−0.975627	+	0.975627i
$886$		0			0
$887$	−6.33407	+	6.33407i	−0.212677	+	0.212677i	−0.805404	−	0.592727i	$-0.798051\pi$
$887$	−6.33407	+	6.33407i	−0.212677	+	0.212677i	0.592727	+	0.805404i	$0.298051\pi$
$888$		0			0
$889$	1.88777	+	1.88777i	0.0633138	+	0.0633138i
$890$		0			0
$891$	6.02500	+	6.02500i	0.201845	+	0.201845i
$892$		0			0
$893$		−	33.4202i		−	1.11836i
$894$		0			0
$895$	52.5187	+	52.5187i	1.75551	+	1.75551i
$896$		0			0
$897$			2.63301i			0.0879135i
$898$		0			0
$899$	10.1802	+	10.1802i	0.339528	+	0.339528i
$900$		0			0
$901$	−5.30795			−0.176833
$902$		0			0
$903$	−9.47683			−0.315369
$904$		0			0
$905$	−36.5369	−	36.5369i	−1.21453	−	1.21453i
$906$		0			0
$907$		−	44.7377i		−	1.48549i	−0.669574	−	0.742746i	$-0.733523\pi$
$907$		−	44.7377i		−	1.48549i	0.669574	−	0.742746i	$-0.266477\pi$
$908$		0			0
$909$	−26.6206	−	26.6206i	−0.882949	−	0.882949i
$910$		0			0
$911$		−	15.1168i		−	0.500844i	−0.968137	−	0.250422i	$-0.919431\pi$
$911$		−	15.1168i		−	0.500844i	0.968137	−	0.250422i	$-0.0805693\pi$
$912$		0			0
$913$	2.49266	+	2.49266i	0.0824952	+	0.0824952i
$914$		0			0
$915$	−26.0016	−	26.0016i	−0.859586	−	0.859586i
$916$		0			0
$917$	7.68737	−	7.68737i	0.253859	−	0.253859i
$918$		0			0
$919$	29.1273	−	29.1273i	0.960821	−	0.960821i	−0.0384403	−	0.999261i	$-0.512239\pi$
$919$	29.1273	−	29.1273i	0.960821	−	0.960821i	0.999261	+	0.0384403i	$0.0122389\pi$
$920$		0			0
$921$	42.4828	−	42.4828i	1.39986	−	1.39986i
$922$		0			0
$923$			4.71831i			0.155305i
$924$		0			0
$925$	−35.5984			−1.17047
$926$		0			0
$927$	−12.8072			−0.420643
$928$		0			0
$929$	−36.0955	+	36.0955i	−1.18425	+	1.18425i	−0.205624	+	0.978631i	$0.565922\pi$
$929$	−36.0955	+	36.0955i	−1.18425	+	1.18425i	−0.978631	+	0.205624i	$0.934078\pi$
$930$		0			0
$931$	−2.24427	−	2.24427i	−0.0735531	−	0.0735531i
$932$		0			0
$933$	61.1776			2.00286
$934$		0			0
$935$		−	15.8484i		−	0.518299i
$936$		0			0
$937$	22.1213	−	22.1213i	0.722673	−	0.722673i	−0.246476	−	0.969149i	$-0.579273\pi$
$937$	22.1213	−	22.1213i	0.722673	−	0.722673i	0.969149	+	0.246476i	$0.0792727\pi$
$938$		0			0
$939$	24.8247			0.810124
$940$		0			0
$941$		−	25.0697i		−	0.817250i	−0.912702	−	0.408625i	$-0.866008\pi$
$941$		−	25.0697i		−	0.817250i	0.912702	−	0.408625i	$-0.133992\pi$
$942$		0			0
$943$	16.3630	+	3.70762i	0.532852	+	0.120737i
$944$		0			0
$945$		−	3.73233i		−	0.121413i
$946$		0			0
$947$	−10.8063			−0.351157			−0.175579	−	0.984465i	$-0.556180\pi$
$947$	−10.8063			−0.351157			−0.175579	+	0.984465i	$0.556180\pi$
$948$		0			0
$949$	−1.64170	+	1.64170i	−0.0532917	+	0.0532917i
$950$		0			0
$951$			77.3127i			2.50704i
$952$		0			0
$953$	24.5945			0.796693			0.398347	−	0.917235i	$-0.369584\pi$
$953$	24.5945			0.796693			0.398347	+	0.917235i	$0.369584\pi$
$954$		0			0
$955$	28.1963	+	28.1963i	0.912412	+	0.912412i
$956$		0			0
$957$	−6.02988	+	6.02988i	−0.194918	+	0.194918i
$958$		0			0
$959$	2.30473			0.0744237
$960$		0			0
$961$	−20.4128			−0.658477
$962$		0			0
$963$			48.4452i			1.56112i
$964$		0			0
$965$	−37.0131	+	37.0131i	−1.19149	+	1.19149i
$966$		0			0
$967$	31.8690	−	31.8690i	1.02484	−	1.02484i	0.0251533	−	0.999684i	$-0.491993\pi$
$967$	31.8690	−	31.8690i	1.02484	−	1.02484i	0.999684	−	0.0251533i	$-0.00800740\pi$
$968$		0			0
$969$	34.1068	−	34.1068i	1.09567	−	1.09567i
$970$		0			0
$971$	−14.3767	−	14.3767i	−0.461372	−	0.461372i	0.437733	−	0.899105i	$-0.355781\pi$
$971$	−14.3767	−	14.3767i	−0.461372	−	0.461372i	−0.899105	+	0.437733i	$0.855781\pi$
$972$		0			0
$973$	−7.90862	−	7.90862i	−0.253539	−	0.253539i
$974$		0			0
$975$			3.74426i			0.119912i
$976$		0			0
$977$	−0.998581	−	0.998581i	−0.0319474	−	0.0319474i	0.690953	−	0.722900i	$-0.257191\pi$
$977$	−0.998581	−	0.998581i	−0.0319474	−	0.0319474i	−0.722900	+	0.690953i	$0.757191\pi$
$978$		0			0
$979$			1.63781i			0.0523445i
$980$		0			0
$981$	−1.45200	−	1.45200i	−0.0463587	−	0.0463587i
$982$		0			0
$983$	29.9652			0.955742			0.477871	−	0.878430i	$-0.341409\pi$
$983$	29.9652			0.955742			0.477871	+	0.878430i	$0.341409\pi$
$984$		0			0
$985$	−45.9401			−1.46377
$986$		0			0
$987$	17.3968	+	17.3968i	0.553746	+	0.553746i
$988$		0			0
$989$			10.6277i			0.337941i
$990$		0			0
$991$	1.86419	+	1.86419i	0.0592179	+	0.0592179i	0.736096	−	0.676878i	$-0.236667\pi$
$991$	1.86419	+	1.86419i	0.0592179	+	0.0592179i	−0.676878	+	0.736096i	$0.736667\pi$
$992$		0			0
$993$		−	65.6501i		−	2.08334i
$994$		0			0
$995$	−10.9643	−	10.9643i	−0.347592	−	0.347592i
$996$		0			0
$997$	−5.66855	−	5.66855i	−0.179525	−	0.179525i	0.611624	−	0.791149i	$-0.290517\pi$
$997$	−5.66855	−	5.66855i	−0.179525	−	0.179525i	−0.791149	+	0.611624i	$0.790517\pi$
$998$		0			0
$999$	8.53550	−	8.53550i	0.270051	−	0.270051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.15	✓	36
41.32	even	4	inner	1148.2.k.b.729.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.15	✓	36	1.1	even	1	trivial
1148.2.k.b.729.15	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)

\(f(q)\)	\(=\)	\(q+(1.65216 + 1.65216i) q^{3} +2.95400i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.45924i q^{9} +O(q^{10})\)	\(q+(1.65216 + 1.65216i) q^{3} +2.95400i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.45924i q^{9} +(0.583260 + 0.583260i) q^{11} +(-0.304108 - 0.304108i) q^{13} +(-4.88047 + 4.88047i) q^{15} +(-4.59921 + 4.59921i) q^{17} +(-2.24427 + 2.24427i) q^{19} -2.33650i q^{21} -2.62025 q^{23} -3.72611 q^{25} +(0.893418 - 0.893418i) q^{27} +(3.12871 + 3.12871i) q^{29} +3.25380 q^{31} +1.92727i q^{33} +(2.08879 - 2.08879i) q^{35} +9.55376 q^{37} -1.00487i q^{39} +(-6.24482 - 1.41499i) q^{41} -4.05599i q^{43} -7.26460 q^{45} +(-7.44566 + 7.44566i) q^{47} +1.00000i q^{49} -15.1972 q^{51} +(0.577050 + 0.577050i) q^{53} +(-1.72295 + 1.72295i) q^{55} -7.41578 q^{57} +5.94695 q^{59} +5.32768i q^{61} +(1.73895 - 1.73895i) q^{63} +(0.898336 - 0.898336i) q^{65} +(6.10945 - 6.10945i) q^{67} +(-4.32906 - 4.32906i) q^{69} +(-7.75761 - 7.75761i) q^{71} -5.39839i q^{73} +(-6.15612 - 6.15612i) q^{75} -0.824855i q^{77} +(3.82764 + 3.82764i) q^{79} +10.3299 q^{81} +4.27367 q^{83} +(-13.5861 - 13.5861i) q^{85} +10.3382i q^{87} +(1.40401 + 1.40401i) q^{89} +0.430074i q^{91} +(5.37579 + 5.37579i) q^{93} +(-6.62958 - 6.62958i) q^{95} +(5.46950 - 5.46950i) q^{97} +(-1.43438 + 1.43438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 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

L-functions

Modular forms

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