LMFDB - Embedded newform 232.5.j.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,5,Mod(17,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("232.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	232.j (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:	$23.9818314355$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	232.17
Dual form			232.5.j.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.45823 + 9.45823i) q^{3} -40.7263i q^{5} -7.09414 q^{7} -97.9163i q^{9} +O(q^{10})$	\(q+(-9.45823 + 9.45823i) q^{3} -40.7263i q^{5} -7.09414 q^{7} -97.9163i q^{9} +(127.843 - 127.843i) q^{11} +129.421i q^{13} +(385.199 + 385.199i) q^{15} +(-375.293 + 375.293i) q^{17} +(49.5930 - 49.5930i) q^{19} +(67.0980 - 67.0980i) q^{21} +490.923 q^{23} -1033.63 q^{25} +(159.998 + 159.998i) q^{27} +(-541.690 - 643.314i) q^{29} +(154.628 - 154.628i) q^{31} +2418.34i q^{33} +288.918i q^{35} +(409.322 + 409.322i) q^{37} +(-1224.09 - 1224.09i) q^{39} +(-1509.38 - 1509.38i) q^{41} +(-2266.20 + 2266.20i) q^{43} -3987.77 q^{45} +(120.559 + 120.559i) q^{47} -2350.67 q^{49} -7099.22i q^{51} +871.941 q^{53} +(-5206.57 - 5206.57i) q^{55} +938.124i q^{57} +43.7251 q^{59} +(-3300.32 + 3300.32i) q^{61} +694.632i q^{63} +5270.83 q^{65} +7321.19i q^{67} +(-4643.26 + 4643.26i) q^{69} +6686.16i q^{71} +(-2411.68 - 2411.68i) q^{73} +(9776.34 - 9776.34i) q^{75} +(-906.935 + 906.935i) q^{77} +(-7494.79 + 7494.79i) q^{79} +4904.62 q^{81} -296.718 q^{83} +(15284.3 + 15284.3i) q^{85} +(11208.0 + 961.185i) q^{87} +(412.162 - 412.162i) q^{89} -918.129i q^{91} +2925.02i q^{93} +(-2019.74 - 2019.74i) q^{95} +(-4463.03 - 4463.03i) q^{97} +(-12517.9 - 12517.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 16 q^{3} + 96 q^{7}+O(q^{10}) $ 30 * q - 16 * q^3 + 96 * q^7	$ 30 q - 16 q^{3} + 96 q^{7} - 240 q^{15} - 338 q^{17} - 936 q^{19} + 1400 q^{21} - 352 q^{23} - 2154 q^{25} + 2648 q^{27} + 500 q^{29} - 1896 q^{31} - 1862 q^{37} + 1088 q^{39} + 2854 q^{41} - 800 q^{43} + 4552 q^{45} - 696 q^{47} + 9698 q^{49} + 4584 q^{53} - 8560 q^{55} + 7144 q^{59} - 1070 q^{61} + 8672 q^{65} - 19352 q^{69} - 7942 q^{73} + 11072 q^{75} - 3048 q^{77} + 3560 q^{79} - 10398 q^{81} - 9848 q^{83} + 11968 q^{85} - 13704 q^{87} - 9634 q^{89} - 33160 q^{95} - 27582 q^{97} + 16480 q^{99}+O(q^{100}) $ 30 * q - 16 * q^3 + 96 * q^7 - 240 * q^15 - 338 * q^17 - 936 * q^19 + 1400 * q^21 - 352 * q^23 - 2154 * q^25 + 2648 * q^27 + 500 * q^29 - 1896 * q^31 - 1862 * q^37 + 1088 * q^39 + 2854 * q^41 - 800 * q^43 + 4552 * q^45 - 696 * q^47 + 9698 * q^49 + 4584 * q^53 - 8560 * q^55 + 7144 * q^59 - 1070 * q^61 + 8672 * q^65 - 19352 * q^69 - 7942 * q^73 + 11072 * q^75 - 3048 * q^77 + 3560 * q^79 - 10398 * q^81 - 9848 * q^83 + 11968 * q^85 - 13704 * q^87 - 9634 * q^89 - 33160 * q^95 - 27582 * q^97 + 16480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−9.45823	+	9.45823i	−1.05091	+	1.05091i	−0.0522823	+	0.998632i	$0.516650\pi$
$3$	−9.45823	+	9.45823i	−1.05091	+	1.05091i	−0.998632	+	0.0522823i	$0.983350\pi$
$4$		0			0
$5$		−	40.7263i		−	1.62905i	−0.580127	−	0.814526i	$-0.696997\pi$
$5$		−	40.7263i		−	1.62905i	0.580127	−	0.814526i	$-0.303003\pi$
$6$		0			0
$7$	−7.09414			−0.144778			−0.0723892	−	0.997376i	$-0.523062\pi$
$7$	−7.09414			−0.144778			−0.0723892	+	0.997376i	$0.523062\pi$
$8$		0			0
$9$		−	97.9163i		−	1.20884i
$10$		0			0
$11$	127.843	−	127.843i	1.05655	−	1.05655i	0.0582509	−	0.998302i	$-0.481448\pi$
$11$	127.843	−	127.843i	1.05655	−	1.05655i	0.998302	−	0.0582509i	$-0.0185523\pi$
$12$		0			0
$13$			129.421i			0.765803i	0.923789	+	0.382902i	$0.125075\pi$
$13$			129.421i			0.765803i	−0.923789	+	0.382902i	$0.874925\pi$
$14$		0			0
$15$	385.199	+	385.199i	1.71200	+	1.71200i
$16$		0			0
$17$	−375.293	+	375.293i	−1.29859	+	1.29859i	−0.369269	+	0.929323i	$0.620392\pi$
$17$	−375.293	+	375.293i	−1.29859	+	1.29859i	−0.929323	+	0.369269i	$0.879608\pi$
$18$		0			0
$19$	49.5930	−	49.5930i	0.137377	−	0.137377i	−0.635074	−	0.772451i	$-0.719031\pi$
$19$	49.5930	−	49.5930i	0.137377	−	0.137377i	0.772451	+	0.635074i	$0.219031\pi$
$20$		0			0
$21$	67.0980	−	67.0980i	0.152150	−	0.152150i
$22$		0			0
$23$	490.923			0.928021			0.464010	−	0.885830i	$-0.346410\pi$
$23$	490.923			0.928021			0.464010	+	0.885830i	$0.346410\pi$
$24$		0			0
$25$	−1033.63			−1.65381
$26$		0			0
$27$	159.998	+	159.998i	0.219476	+	0.219476i
$28$		0			0
$29$	−541.690	−	643.314i	−0.644102	−	0.764939i
$29$	−541.690	−	643.314i	−0.644102	−	0.764939i
$30$		0			0
$31$	154.628	−	154.628i	0.160904	−	0.160904i	−0.622063	−	0.782967i	$-0.713705\pi$
$31$	154.628	−	154.628i	0.160904	−	0.160904i	0.782967	+	0.622063i	$0.213705\pi$
$32$		0			0
$33$			2418.34i			2.22069i
$34$		0			0
$35$			288.918i			0.235852i
$36$		0			0
$37$	409.322	+	409.322i	0.298993	+	0.298993i	0.840619	−	0.541626i	$-0.182191\pi$
$37$	409.322	+	409.322i	0.298993	+	0.298993i	−0.541626	+	0.840619i	$0.682191\pi$
$38$		0			0
$39$	−1224.09	−	1224.09i	−0.804794	−	0.804794i
$40$		0			0
$41$	−1509.38	−	1509.38i	−0.897908	−	0.897908i	0.0973426	−	0.995251i	$-0.468966\pi$
$41$	−1509.38	−	1509.38i	−0.897908	−	0.897908i	−0.995251	+	0.0973426i	$0.968966\pi$
$42$		0			0
$43$	−2266.20	+	2266.20i	−1.22564	+	1.22564i	−0.260038	+	0.965598i	$0.583735\pi$
$43$	−2266.20	+	2266.20i	−1.22564	+	1.22564i	−0.965598	+	0.260038i	$0.916265\pi$
$44$		0			0
$45$	−3987.77			−1.96927
$46$		0			0
$47$	120.559	+	120.559i	0.0545761	+	0.0545761i	0.733868	−	0.679292i	$-0.237713\pi$
$47$	120.559	+	120.559i	0.0545761	+	0.0545761i	−0.679292	+	0.733868i	$0.737713\pi$
$48$		0			0
$49$	−2350.67			−0.979039
$50$		0			0
$51$		−	7099.22i		−	2.72942i
$52$		0			0
$53$	871.941			0.310410			0.155205	−	0.987882i	$-0.450396\pi$
$53$	871.941			0.310410			0.155205	+	0.987882i	$0.450396\pi$
$54$		0			0
$55$	−5206.57	−	5206.57i	−1.72118	−	1.72118i
$56$		0			0
$57$			938.124i			0.288742i
$58$		0			0
$59$	43.7251			0.0125611			0.00628054	−	0.999980i	$-0.498001\pi$
$59$	43.7251			0.0125611			0.00628054	+	0.999980i	$0.498001\pi$
$60$		0			0
$61$	−3300.32	+	3300.32i	−0.886945	+	0.886945i	−0.994229	−	0.107283i	$-0.965785\pi$
$61$	−3300.32	+	3300.32i	−0.886945	+	0.886945i	0.107283	+	0.994229i	$0.465785\pi$
$62$		0			0
$63$			694.632i			0.175014i
$64$		0			0
$65$	5270.83			1.24753
$66$		0			0
$67$			7321.19i			1.63092i	0.578815	+	0.815459i	$0.303515\pi$
$67$			7321.19i			1.63092i	−0.578815	+	0.815459i	$0.696485\pi$
$68$		0			0
$69$	−4643.26	+	4643.26i	−0.975270	+	0.975270i
$70$		0			0
$71$			6686.16i			1.32636i	0.748462	+	0.663178i	$0.230793\pi$
$71$			6686.16i			1.32636i	−0.748462	+	0.663178i	$0.769207\pi$
$72$		0			0
$73$	−2411.68	−	2411.68i	−0.452557	−	0.452557i	0.443645	−	0.896202i	$-0.353685\pi$
$73$	−2411.68	−	2411.68i	−0.452557	−	0.452557i	−0.896202	+	0.443645i	$0.853685\pi$
$74$		0			0
$75$	9776.34	−	9776.34i	1.73802	−	1.73802i
$76$		0			0
$77$	−906.935	+	906.935i	−0.152966	+	0.152966i
$78$		0			0
$79$	−7494.79	+	7494.79i	−1.20090	+	1.20090i	−0.227001	+	0.973895i	$0.572892\pi$
$79$	−7494.79	+	7494.79i	−1.20090	+	1.20090i	−0.973895	+	0.227001i	$0.927108\pi$
$80$		0			0
$81$	4904.62			0.747542
$82$		0			0
$83$	−296.718			−0.0430713			−0.0215356	−	0.999768i	$-0.506856\pi$
$83$	−296.718			−0.0430713			−0.0215356	+	0.999768i	$0.506856\pi$
$84$		0			0
$85$	15284.3	+	15284.3i	2.11547	+	2.11547i
$86$		0			0
$87$	11208.0	+	961.185i	1.48078	+	0.126990i
$88$		0			0
$89$	412.162	−	412.162i	0.0520341	−	0.0520341i	−0.680611	−	0.732645i	$-0.738286\pi$
$89$	412.162	−	412.162i	0.0520341	−	0.0520341i	0.732645	+	0.680611i	$0.238286\pi$
$90$		0			0
$91$		−	918.129i		−	0.110872i
$92$		0			0
$93$			2925.02i			0.338192i
$94$		0			0
$95$	−2019.74	−	2019.74i	−0.223794	−	0.223794i
$96$		0			0
$97$	−4463.03	−	4463.03i	−0.474336	−	0.474336i	0.428978	−	0.903315i	$-0.358874\pi$
$97$	−4463.03	−	4463.03i	−0.474336	−	0.474336i	−0.903315	+	0.428978i	$0.858874\pi$
$98$		0			0
$99$	−12517.9	−	12517.9i	−1.27721	−	1.27721i
$100$		0			0
$101$	−2165.71	+	2165.71i	−0.212304	+	0.212304i	−0.805245	−	0.592942i	$-0.797966\pi$
$101$	−2165.71	+	2165.71i	−0.212304	+	0.212304i	0.592942	+	0.805245i	$0.297966\pi$
$102$		0			0
$103$	102.720			0.00968230			0.00484115	−	0.999988i	$-0.498459\pi$
$103$	102.720			0.00968230			0.00484115	+	0.999988i	$0.498459\pi$
$104$		0			0
$105$	−2732.66	−	2732.66i	−0.247860	−	0.247860i
$106$		0			0
$107$	17072.5			1.49117			0.745587	−	0.666408i	$-0.232169\pi$
$107$	17072.5			1.49117			0.745587	+	0.666408i	$0.232169\pi$
$108$		0			0
$109$		−	1220.10i		−	0.102693i	−0.998681	−	0.0513466i	$-0.983649\pi$
$109$		−	1220.10i		−	0.102693i	0.998681	−	0.0513466i	$-0.0163513\pi$
$110$		0			0
$111$	−7742.92			−0.628433
$112$		0			0
$113$	−6473.89	−	6473.89i	−0.507000	−	0.507000i	0.406604	−	0.913604i	$-0.366713\pi$
$113$	−6473.89	−	6473.89i	−0.507000	−	0.507000i	−0.913604	+	0.406604i	$0.866713\pi$
$114$		0			0
$115$		−	19993.5i		−	1.51179i
$116$		0			0
$117$	12672.4			0.925736
$118$		0			0
$119$	2662.38	−	2662.38i	0.188008	−	0.188008i
$120$		0			0
$121$		−	18046.6i		−	1.23261i
$122$		0			0
$123$	28552.2			1.88725
$124$		0			0
$125$			16642.1i			1.06510i
$126$		0			0
$127$	−10713.8	+	10713.8i	−0.664254	+	0.664254i	−0.956380	−	0.292126i	$-0.905638\pi$
$127$	−10713.8	+	10713.8i	−0.664254	+	0.664254i	0.292126	+	0.956380i	$0.405638\pi$
$128$		0			0
$129$		−	42868.5i		−	2.57608i
$130$		0			0
$131$	−4061.23	−	4061.23i	−0.236655	−	0.236655i	0.578809	−	0.815463i	$-0.303518\pi$
$131$	−4061.23	−	4061.23i	−0.236655	−	0.236655i	−0.815463	+	0.578809i	$0.803518\pi$
$132$		0			0
$133$	−351.820	+	351.820i	−0.0198892	+	0.0198892i
$134$		0			0
$135$	6516.14	−	6516.14i	0.357538	−	0.357538i
$136$		0			0
$137$	−24908.6	+	24908.6i	−1.32711	+	1.32711i	−0.419237	+	0.907877i	$0.637702\pi$
$137$	−24908.6	+	24908.6i	−1.32711	+	1.32711i	−0.907877	+	0.419237i	$0.862298\pi$
$138$		0			0
$139$	978.274			0.0506327			0.0253164	−	0.999679i	$-0.491941\pi$
$139$	978.274			0.0506327			0.0253164	+	0.999679i	$0.491941\pi$
$140$		0			0
$141$	−2280.54			−0.114710
$142$		0			0
$143$	16545.5	+	16545.5i	0.809112	+	0.809112i
$144$		0			0
$145$	−26199.8	+	22061.0i	−1.24613	+	1.04928i
$146$		0			0
$147$	22233.2	−	22233.2i	1.02889	−	1.02889i
$148$		0			0
$149$			35641.8i			1.60542i	0.596373	+	0.802708i	$0.296608\pi$
$149$			35641.8i			1.60542i	−0.596373	+	0.802708i	$0.703392\pi$
$150$		0			0
$151$		−	31500.6i		−	1.38155i	−0.723072	−	0.690773i	$-0.757270\pi$
$151$		−	31500.6i		−	1.38155i	0.723072	−	0.690773i	$-0.242730\pi$
$152$		0			0
$153$	36747.3	+	36747.3i	1.56979	+	1.56979i
$154$		0			0
$155$	−6297.45	−	6297.45i	−0.262121	−	0.262121i
$156$		0			0
$157$	−32944.9	−	32944.9i	−1.33656	−	1.33656i	−0.899369	−	0.437191i	$-0.855974\pi$
$157$	−32944.9	−	32944.9i	−1.33656	−	1.33656i	−0.437191	−	0.899369i	$-0.644026\pi$
$158$		0			0
$159$	−8247.02	+	8247.02i	−0.326214	+	0.326214i
$160$		0			0
$161$	−3482.68			−0.134357
$162$		0			0
$163$	23341.5	+	23341.5i	0.878525	+	0.878525i	0.993382	−	0.114857i	$-0.0366410\pi$
$163$	23341.5	+	23341.5i	0.878525	+	0.878525i	−0.114857	+	0.993382i	$0.536641\pi$
$164$		0			0
$165$	98489.9			3.61763
$166$		0			0
$167$		−	35118.9i		−	1.25924i	−0.776904	−	0.629619i	$-0.783211\pi$
$167$		−	35118.9i		−	1.25924i	0.776904	−	0.629619i	$-0.216789\pi$
$168$		0			0
$169$	11811.3			0.413545
$170$		0			0
$171$	−4855.96	−	4855.96i	−0.166067	−	0.166067i
$172$		0			0
$173$			44917.1i			1.50079i	0.660991	+	0.750394i	$0.270136\pi$
$173$			44917.1i			1.50079i	−0.660991	+	0.750394i	$0.729864\pi$
$174$		0			0
$175$	7332.74			0.239436
$176$		0			0
$177$	−413.563	+	413.563i	−0.0132006	+	0.0132006i
$178$		0			0
$179$			81.2940i			0.00253719i	0.999999	+	0.00126859i	$0.000403806\pi$
$179$			81.2940i			0.00253719i	−0.999999	+	0.00126859i	$0.999596\pi$
$180$		0			0
$181$	−1340.50			−0.0409177			−0.0204588	−	0.999791i	$-0.506513\pi$
$181$	−1340.50			−0.0409177			−0.0204588	+	0.999791i	$0.506513\pi$
$182$		0			0
$183$		−	62430.4i		−	1.86421i
$184$		0			0
$185$	16670.2	−	16670.2i	0.487076	−	0.487076i
$186$		0			0
$187$			95957.1i			2.74406i
$188$		0			0
$189$	−1135.05	−	1135.05i	−0.0317754	−	0.0317754i
$190$		0			0
$191$	31040.6	−	31040.6i	0.850870	−	0.850870i	−0.139370	−	0.990240i	$-0.544508\pi$
$191$	31040.6	−	31040.6i	0.850870	−	0.850870i	0.990240	+	0.139370i	$0.0445078\pi$
$192$		0			0
$193$	44020.7	−	44020.7i	1.18180	−	1.18180i	0.202517	−	0.979279i	$-0.435088\pi$
$193$	44020.7	−	44020.7i	1.18180	−	1.18180i	0.979279	−	0.202517i	$-0.0649121\pi$
$194$		0			0
$195$	−49852.7	+	49852.7i	−1.31105	+	1.31105i
$196$		0			0
$197$	−20207.4			−0.520688			−0.260344	−	0.965516i	$-0.583836\pi$
$197$	−20207.4			−0.520688			−0.260344	+	0.965516i	$0.583836\pi$
$198$		0			0
$199$	−18474.7			−0.466520			−0.233260	−	0.972414i	$-0.574939\pi$
$199$	−18474.7			−0.466520			−0.233260	+	0.972414i	$0.574939\pi$
$200$		0			0
$201$	−69245.5	−	69245.5i	−1.71396	−	1.71396i
$202$		0			0
$203$	3842.82	+	4563.76i	0.0932521	+	0.110747i
$204$		0			0
$205$	−61471.7	+	61471.7i	−1.46274	+	1.46274i
$206$		0			0
$207$		−	48069.3i		−	1.12183i
$208$		0			0
$209$		−	12680.2i		−	0.290292i
$210$		0			0
$211$	33395.8	+	33395.8i	0.750113	+	0.750113i	0.974500	−	0.224387i	$-0.0720380\pi$
$211$	33395.8	+	33395.8i	0.750113	+	0.750113i	−0.224387	+	0.974500i	$0.572038\pi$
$212$		0			0
$213$	−63239.3	−	63239.3i	−1.39389	−	1.39389i
$214$		0			0
$215$	92294.1	+	92294.1i	1.99663	+	1.99663i
$216$		0			0
$217$	−1096.96	+	1096.96i	−0.0232954	+	0.0232954i
$218$		0			0
$219$	45620.4			0.951198
$220$		0			0
$221$	−48570.7	−	48570.7i	−0.994466	−	0.994466i
$222$		0			0
$223$	−37362.6			−0.751324			−0.375662	−	0.926757i	$-0.622585\pi$
$223$	−37362.6			−0.751324			−0.375662	+	0.926757i	$0.622585\pi$
$224$		0			0
$225$			101210.i			1.99920i
$226$		0			0
$227$	−50545.2			−0.980908			−0.490454	−	0.871467i	$-0.663169\pi$
$227$	−50545.2			−0.980908			−0.490454	+	0.871467i	$0.663169\pi$
$228$		0			0
$229$	40586.2	+	40586.2i	0.773940	+	0.773940i	0.978793	−	0.204853i	$-0.0656717\pi$
$229$	40586.2	+	40586.2i	0.773940	+	0.773940i	−0.204853	+	0.978793i	$0.565672\pi$
$230$		0			0
$231$		−	17156.0i		−	0.321508i
$232$		0			0
$233$	60054.0			1.10619			0.553095	−	0.833118i	$-0.313446\pi$
$233$	60054.0			1.10619			0.553095	+	0.833118i	$0.313446\pi$
$234$		0			0
$235$	4909.91	−	4909.91i	0.0889074	−	0.0889074i
$236$		0			0
$237$		−	141775.i		−	2.52408i
$238$		0			0
$239$	−47752.4			−0.835986			−0.417993	−	0.908450i	$-0.637266\pi$
$239$	−47752.4			−0.835986			−0.417993	+	0.908450i	$0.637266\pi$
$240$		0			0
$241$		−	21146.1i		−	0.364079i	−0.983291	−	0.182040i	$-0.941730\pi$
$241$		−	21146.1i		−	0.364079i	0.983291	−	0.182040i	$-0.0582699\pi$
$242$		0			0
$243$	−59348.9	+	59348.9i	−1.00508	+	1.00508i
$244$		0			0
$245$			95734.3i			1.59491i
$246$		0			0
$247$	6418.36	+	6418.36i	0.105204	+	0.105204i
$248$		0			0
$249$	2806.43	−	2806.43i	0.0452642	−	0.0452642i
$250$		0			0
$251$	−3327.03	+	3327.03i	−0.0528092	+	0.0528092i	−0.733018	−	0.680209i	$-0.761889\pi$
$251$	−3327.03	+	3327.03i	−0.0528092	+	0.0528092i	0.680209	+	0.733018i	$0.261889\pi$
$252$		0			0
$253$	62761.0	−	62761.0i	0.980503	−	0.980503i
$254$		0			0
$255$	−289125.			−4.44637
$256$		0			0
$257$	−120640.			−1.82652			−0.913259	−	0.407379i	$-0.866443\pi$
$257$	−120640.			−1.82652			−0.913259	+	0.407379i	$0.866443\pi$
$258$		0			0
$259$	−2903.78	−	2903.78i	−0.0432877	−	0.0432877i
$260$		0			0
$261$	−62990.9	+	53040.3i	−0.924692	+	0.778618i
$262$		0			0
$263$	−53908.3	+	53908.3i	−0.779371	+	0.779371i	−0.979724	−	0.200353i	$-0.935791\pi$
$263$	−53908.3	+	53908.3i	−0.779371	+	0.779371i	0.200353	+	0.979724i	$0.435791\pi$
$264$		0			0
$265$		−	35510.9i		−	0.505674i
$266$		0			0
$267$			7796.66i			0.109367i
$268$		0			0
$269$	−2654.79	−	2654.79i	−0.0366882	−	0.0366882i	0.688525	−	0.725213i	$-0.258259\pi$
$269$	−2654.79	−	2654.79i	−0.0366882	−	0.0366882i	−0.725213	+	0.688525i	$0.758259\pi$
$270$		0			0
$271$	−20233.1	−	20233.1i	−0.275501	−	0.275501i	0.555809	−	0.831310i	$-0.312409\pi$
$271$	−20233.1	−	20233.1i	−0.275501	−	0.275501i	−0.831310	+	0.555809i	$0.812409\pi$
$272$		0			0
$273$	8683.88	+	8683.88i	0.116517	+	0.116517i
$274$		0			0
$275$	−132143.	+	132143.i	−1.74734	+	1.74734i
$276$		0			0
$277$	128929.			1.68031			0.840157	−	0.542343i	$-0.182463\pi$
$277$	128929.			1.68031			0.840157	+	0.542343i	$0.182463\pi$
$278$		0			0
$279$	−15140.6	−	15140.6i	−0.194507	−	0.194507i
$280$		0			0
$281$	10319.2			0.130687			0.0653436	−	0.997863i	$-0.479186\pi$
$281$	10319.2			0.130687			0.0653436	+	0.997863i	$0.479186\pi$
$282$		0			0
$283$		−	76103.8i		−	0.950240i	−0.879921	−	0.475120i	$-0.842405\pi$
$283$		−	76103.8i		−	0.950240i	0.879921	−	0.475120i	$-0.157595\pi$
$284$		0			0
$285$	38206.3			0.470377
$286$		0			0
$287$	10707.8	+	10707.8i	0.129998	+	0.129998i
$288$		0			0
$289$		−	198169.i		−	2.37268i
$290$		0			0
$291$	84424.7			0.996974
$292$		0			0
$293$	20822.9	−	20822.9i	0.242553	−	0.242553i	−0.575353	−	0.817905i	$-0.695135\pi$
$293$	20822.9	−	20822.9i	0.242553	−	0.242553i	0.817905	+	0.575353i	$0.195135\pi$
$294$		0			0
$295$		−	1780.76i		−	0.0204627i
$296$		0			0
$297$	40909.3			0.463776
$298$		0			0
$299$			63535.6i			0.710681i
$300$		0			0
$301$	16076.8	−	16076.8i	0.177446	−	0.177446i
$302$		0			0
$303$		−	40967.5i		−	0.446226i
$304$		0			0
$305$	134410.	+	134410.i	1.44488	+	1.44488i
$306$		0			0
$307$	−17004.9	+	17004.9i	−0.180426	+	0.180426i	−0.791541	−	0.611116i	$-0.790721\pi$
$307$	−17004.9	+	17004.9i	−0.180426	+	0.180426i	0.611116	+	0.791541i	$0.290721\pi$
$308$		0			0
$309$	−971.545	+	971.545i	−0.0101753	+	0.0101753i
$310$		0			0
$311$	−3650.36	+	3650.36i	−0.0377411	+	0.0377411i	−0.725725	−	0.687984i	$-0.758496\pi$
$311$	−3650.36	+	3650.36i	−0.0377411	+	0.0377411i	0.687984	+	0.725725i	$0.258496\pi$
$312$		0			0
$313$	75535.1			0.771010			0.385505	−	0.922706i	$-0.374027\pi$
$313$	75535.1			0.771010			0.385505	+	0.922706i	$0.374027\pi$
$314$		0			0
$315$	28289.8			0.285108
$316$		0			0
$317$	−49235.3	−	49235.3i	−0.489957	−	0.489957i	0.418336	−	0.908292i	$-0.362614\pi$
$317$	−49235.3	−	49235.3i	−0.489957	−	0.489957i	−0.908292	+	0.418336i	$0.862614\pi$
$318$		0			0
$319$	−151494.	−	12991.9i	−1.48873	−	0.127671i
$320$		0			0
$321$	−161475.	+	161475.i	−1.56710	+	1.56710i
$322$		0			0
$323$			37223.8i			0.356793i
$324$		0			0
$325$		−	133774.i		−	1.26650i
$326$		0			0
$327$	11540.0	+	11540.0i	0.107922	+	0.107922i
$328$		0			0
$329$	−855.260	−	855.260i	−0.00790144	−	0.00790144i
$330$		0			0
$331$	−72078.4	−	72078.4i	−0.657884	−	0.657884i	0.296995	−	0.954879i	$-0.404015\pi$
$331$	−72078.4	−	72078.4i	−0.657884	−	0.657884i	−0.954879	+	0.296995i	$0.904015\pi$
$332$		0			0
$333$	40079.3	−	40079.3i	0.361436	−	0.361436i
$334$		0			0
$335$	298165.			2.65685
$336$		0			0
$337$	−100550.	−	100550.i	−0.885369	−	0.885369i	0.108705	−	0.994074i	$-0.465330\pi$
$337$	−100550.	−	100550.i	−0.885369	−	0.885369i	−0.994074	+	0.108705i	$0.965330\pi$
$338$		0			0
$339$	122463.			1.06563
$340$		0			0
$341$		−	39536.3i		−	0.340007i
$342$		0			0
$343$	33709.0			0.286522
$344$		0			0
$345$	189103.	+	189103.i	1.58877	+	1.58877i
$346$		0			0
$347$		−	152683.i		−	1.26803i	−0.773319	−	0.634017i	$-0.781405\pi$
$347$		−	152683.i		−	1.26803i	0.773319	−	0.634017i	$-0.218595\pi$
$348$		0			0
$349$	169599.			1.39242			0.696212	−	0.717836i	$-0.254867\pi$
$349$	169599.			1.39242			0.696212	+	0.717836i	$0.254867\pi$
$350$		0			0
$351$	−20707.1	+	20707.1i	−0.168076	+	0.168076i
$352$		0			0
$353$		−	97996.9i		−	0.786435i	−0.919445	−	0.393218i	$-0.871362\pi$
$353$		−	97996.9i		−	0.786435i	0.919445	−	0.393218i	$-0.128638\pi$
$354$		0			0
$355$	272303.			2.16070
$356$		0			0
$357$			50362.8i			0.395161i
$358$		0			0
$359$	−96368.6	+	96368.6i	−0.747733	+	0.747733i	−0.974053	−	0.226320i	$-0.927330\pi$
$359$	−96368.6	+	96368.6i	−0.747733	+	0.747733i	0.226320	+	0.974053i	$0.427330\pi$
$360$		0			0
$361$			125402.i			0.962255i
$362$		0			0
$363$	170689.	+	170689.i	1.29537	+	1.29537i
$364$		0			0
$365$	−98218.7	+	98218.7i	−0.737239	+	0.737239i
$366$		0			0
$367$	−29088.3	+	29088.3i	−0.215966	+	0.215966i	−0.806796	−	0.590830i	$-0.798800\pi$
$367$	−29088.3	+	29088.3i	−0.215966	+	0.215966i	0.590830	+	0.806796i	$0.298800\pi$
$368$		0			0
$369$	−147793.	+	147793.i	−1.08543	+	1.08543i
$370$		0			0
$371$	−6185.67			−0.0449406
$372$		0			0
$373$	−69556.5			−0.499942			−0.249971	−	0.968253i	$-0.580421\pi$
$373$	−69556.5			−0.499942			−0.249971	+	0.968253i	$0.580421\pi$
$374$		0			0
$375$	−157405.	−	157405.i	−1.11932	−	1.11932i
$376$		0			0
$377$	83258.2	−	70105.9i	0.585793	−	0.493256i
$378$		0			0
$379$	189492.	−	189492.i	1.31920	−	1.31920i	0.404800	−	0.914405i	$-0.367341\pi$
$379$	189492.	−	189492.i	1.31920	−	1.31920i	0.914405	−	0.404800i	$-0.132659\pi$
$380$		0			0
$381$		−	202666.i		−	1.39615i
$382$		0			0
$383$		−	17421.9i		−	0.118768i	−0.998235	−	0.0593839i	$-0.981086\pi$
$383$		−	17421.9i		−	0.118768i	0.998235	−	0.0593839i	$-0.0189136\pi$
$384$		0			0
$385$	36936.1	+	36936.1i	0.249190	+	0.249190i
$386$		0			0
$387$	221898.	+	221898.i	1.48160	+	1.48160i
$388$		0			0
$389$	−13862.8	−	13862.8i	−0.0916116	−	0.0916116i	0.659816	−	0.751427i	$-0.270634\pi$
$389$	−13862.8	−	13862.8i	−0.0916116	−	0.0916116i	−0.751427	+	0.659816i	$0.770634\pi$
$390$		0			0
$391$	−184240.	+	184240.i	−1.20512	+	1.20512i
$392$		0			0
$393$	76824.1			0.497408
$394$		0			0
$395$	305235.	+	305235.i	1.95632	+	1.95632i
$396$		0			0
$397$	−232731.			−1.47664			−0.738318	−	0.674453i	$-0.764380\pi$
$397$	−232731.			−1.47664			−0.738318	+	0.674453i	$0.764380\pi$
$398$		0			0
$399$		−	6655.18i		−	0.0418037i
$400$		0			0
$401$	33759.5			0.209946			0.104973	−	0.994475i	$-0.466524\pi$
$401$	33759.5			0.209946			0.104973	+	0.994475i	$0.466524\pi$
$402$		0			0
$403$	20012.1	+	20012.1i	0.123221	+	0.123221i
$404$		0			0
$405$		−	199747.i		−	1.21778i
$406$		0			0
$407$	104658.			0.631804
$408$		0			0
$409$	−191407.	+	191407.i	−1.14422	+	1.14422i	−0.156554	+	0.987669i	$0.550038\pi$
$409$	−191407.	+	191407.i	−1.14422	+	1.14422i	−0.987669	+	0.156554i	$0.949962\pi$
$410$		0			0
$411$		−	471183.i		−	2.78937i
$412$		0			0
$413$	−310.192			−0.00181857
$414$		0			0
$415$			12084.2i			0.0701654i
$416$		0			0
$417$	−9252.75	+	9252.75i	−0.0532106	+	0.0532106i
$418$		0			0
$419$		−	86465.1i		−	0.492507i	−0.969205	−	0.246254i	$-0.920800\pi$
$419$		−	86465.1i		−	0.492507i	0.969205	−	0.246254i	$-0.0791996\pi$
$420$		0			0
$421$	−198891.	−	198891.i	−1.12215	−	1.12215i	−0.991417	−	0.130734i	$-0.958267\pi$
$421$	−198891.	−	198891.i	−1.12215	−	1.12215i	−0.130734	−	0.991417i	$-0.541733\pi$
$422$		0			0
$423$	11804.7	−	11804.7i	0.0659740	−	0.0659740i
$424$		0			0
$425$	387915.	−	387915.i	2.14763	−	2.14763i
$426$		0			0
$427$	23413.0	−	23413.0i	0.128410	−	0.128410i
$428$		0			0
$429$	−312983.			−1.70061
$430$		0			0
$431$	−153604.			−0.826892			−0.413446	−	0.910529i	$-0.635675\pi$
$431$	−153604.			−0.826892			−0.413446	+	0.910529i	$0.635675\pi$
$432$		0			0
$433$	38181.3	+	38181.3i	0.203646	+	0.203646i	0.801560	−	0.597914i	$-0.204004\pi$
$433$	38181.3	+	38181.3i	0.203646	+	0.203646i	−0.597914	+	0.801560i	$0.704004\pi$
$434$		0			0
$435$	39145.5	−	456462.i	0.206873	−	2.41227i
$436$		0			0
$437$	24346.3	−	24346.3i	0.127488	−	0.127488i
$438$		0			0
$439$		−	240456.i		−	1.24769i	−0.781549	−	0.623844i	$-0.785570\pi$
$439$		−	240456.i		−	1.24769i	0.781549	−	0.623844i	$-0.214430\pi$
$440$		0			0
$441$			230169.i			1.18350i
$442$		0			0
$443$	106757.	+	106757.i	0.543986	+	0.543986i	0.924695	−	0.380709i	$-0.124320\pi$
$443$	106757.	+	106757.i	0.543986	+	0.543986i	−0.380709	+	0.924695i	$0.624320\pi$
$444$		0			0
$445$	−16785.9	−	16785.9i	−0.0847664	−	0.0847664i
$446$		0			0
$447$	−337109.	−	337109.i	−1.68715	−	1.68715i
$448$		0			0
$449$	38020.7	−	38020.7i	0.188594	−	0.188594i	−0.606494	−	0.795088i	$-0.707425\pi$
$449$	38020.7	−	38020.7i	0.188594	−	0.188594i	0.795088	+	0.606494i	$0.207425\pi$
$450$		0			0
$451$	−385928.			−1.89738
$452$		0			0
$453$	297940.	+	297940.i	1.45189	+	1.45189i
$454$		0			0
$455$	−37392.0			−0.180616
$456$		0			0
$457$			14157.9i			0.0677899i	0.999425	+	0.0338950i	$0.0107912\pi$
$457$			14157.9i			0.0677899i	−0.999425	+	0.0338950i	$0.989209\pi$
$458$		0			0
$459$	−120092.			−0.570020
$460$		0			0
$461$	−135949.	−	135949.i	−0.639698	−	0.639698i	0.310783	−	0.950481i	$-0.399409\pi$
$461$	−135949.	−	135949.i	−0.639698	−	0.639698i	−0.950481	+	0.310783i	$0.899409\pi$
$462$		0			0
$463$		−	169569.i		−	0.791015i	−0.918463	−	0.395507i	$-0.870569\pi$
$463$		−	169569.i		−	0.791015i	0.918463	−	0.395507i	$-0.129431\pi$
$464$		0			0
$465$	119125.			0.550933
$466$		0			0
$467$	60089.7	−	60089.7i	0.275528	−	0.275528i	−0.555793	−	0.831321i	$-0.687585\pi$
$467$	60089.7	−	60089.7i	0.275528	−	0.275528i	0.831321	+	0.555793i	$0.187585\pi$
$468$		0			0
$469$		−	51937.5i		−	0.236122i
$470$		0			0
$471$	623200.			2.80922
$472$		0			0
$473$			579436.i			2.58990i
$474$		0			0
$475$	−51261.0	+	51261.0i	−0.227195	+	0.227195i
$476$		0			0
$477$		−	85377.2i		−	0.375237i
$478$		0			0
$479$	261533.	+	261533.i	1.13987	+	1.13987i	0.988473	+	0.151395i	$0.0483766\pi$
$479$	261533.	+	261533.i	1.13987	+	1.13987i	0.151395	+	0.988473i	$0.451623\pi$
$480$		0			0
$481$	−52974.7	+	52974.7i	−0.228970	+	0.228970i
$482$		0			0
$483$	32940.0	−	32940.0i	0.141198	−	0.141198i
$484$		0			0
$485$	−181763.	+	181763.i	−0.772719	+	0.772719i
$486$		0			0
$487$	−238103.			−1.00394			−0.501969	−	0.864886i	$-0.667391\pi$
$487$	−238103.			−1.00394			−0.501969	+	0.864886i	$0.667391\pi$
$488$		0			0
$489$	−441539.			−1.84651
$490$		0			0
$491$	264900.	+	264900.i	1.09880	+	1.09880i	0.994551	+	0.104248i	$0.0332435\pi$
$491$	264900.	+	264900.i	1.09880	+	1.09880i	0.104248	+	0.994551i	$0.466756\pi$
$492$		0			0
$493$	444724.	+	38138.8i	1.82977	+	0.156918i
$494$		0			0
$495$	−509808.	+	509808.i	−2.08064	+	2.08064i
$496$		0			0
$497$		−	47432.6i		−	0.192028i
$498$		0			0
$499$		−	11964.6i		−	0.0480505i	−0.999711	−	0.0240252i	$-0.992352\pi$
$499$		−	11964.6i		−	0.0480505i	0.999711	−	0.0240252i	$-0.00764821\pi$
$500$		0			0
$501$	332163.	+	332163.i	1.32335	+	1.32335i
$502$		0			0
$503$	242260.	+	242260.i	0.957514	+	0.957514i	0.999134	−	0.0416196i	$-0.0132518\pi$
$503$	242260.	+	242260.i	0.957514	+	0.957514i	−0.0416196	+	0.999134i	$0.513252\pi$
$504$		0			0
$505$	88201.3	+	88201.3i	0.345854	+	0.345854i
$506$		0			0
$507$	−111714.	+	111714.i	−0.434601	+	0.434601i
$508$		0			0
$509$	302988.			1.16947			0.584736	−	0.811224i	$-0.301198\pi$
$509$	302988.			1.16947			0.584736	+	0.811224i	$0.301198\pi$
$510$		0			0
$511$	17108.8	+	17108.8i	0.0655205	+	0.0655205i
$512$		0			0
$513$	15869.6			0.0603018
$514$		0			0
$515$		−	4183.39i		−	0.0157730i
$516$		0			0
$517$	30825.1			0.115325
$518$		0			0
$519$	−424836.	−	424836.i	−1.57720	−	1.57720i
$520$		0			0
$521$		−	120775.i		−	0.444939i	−0.974940	−	0.222469i	$-0.928588\pi$
$521$		−	120775.i		−	0.444939i	0.974940	−	0.222469i	$-0.0714118\pi$
$522$		0			0
$523$	540405.			1.97568			0.987838	−	0.155485i	$-0.0496940\pi$
$523$	540405.			1.97568			0.987838	+	0.155485i	$0.0496940\pi$
$524$		0			0
$525$	−69354.7	+	69354.7i	−0.251627	+	0.251627i
$526$		0			0
$527$			116062.i			0.417896i
$528$		0			0
$529$	−38835.7			−0.138778
$530$		0			0
$531$		−	4281.40i		−	0.0151844i
$532$		0			0
$533$	195346.	−	195346.i	0.687621	−	0.687621i
$534$		0			0
$535$		−	695298.i		−	2.42920i
$536$		0			0
$537$	−768.897	−	768.897i	−0.00266637	−	0.00266637i
$538$		0			0
$539$	−300517.	+	300517.i	−1.03441	+	1.03441i
$540$		0			0
$541$	−200272.	+	200272.i	−0.684268	+	0.684268i	−0.960959	−	0.276691i	$-0.910762\pi$
$541$	−200272.	+	200272.i	−0.684268	+	0.684268i	0.276691	+	0.960959i	$0.410762\pi$
$542$		0			0
$543$	12678.8	−	12678.8i	0.0430010	−	0.0430010i
$544$		0			0
$545$	−49690.1			−0.167293
$546$		0			0
$547$	−405571.			−1.35548			−0.677738	−	0.735303i	$-0.737040\pi$
$547$	−405571.			−1.35548			−0.677738	+	0.735303i	$0.737040\pi$
$548$		0			0
$549$	323155.	+	323155.i	1.07218	+	1.07218i
$550$		0			0
$551$	−58767.9	−	5039.85i	−0.193570	−	0.0166002i
$552$		0			0
$553$	53169.1	−	53169.1i	0.173864	−	0.173864i
$554$		0			0
$555$			315341.i			1.02375i
$556$		0			0
$557$			214148.i			0.690245i	0.938558	+	0.345122i	$0.112163\pi$
$557$			214148.i			0.690245i	−0.938558	+	0.345122i	$0.887837\pi$
$558$		0			0
$559$	−293294.	−	293294.i	−0.938597	−	0.938597i
$560$		0			0
$561$	−907584.	−	907584.i	−2.88377	−	2.88377i
$562$		0			0
$563$	−431981.	−	431981.i	−1.36285	−	1.36285i	−0.870265	−	0.492583i	$-0.836053\pi$
$563$	−431981.	−	431981.i	−1.36285	−	1.36285i	−0.492583	−	0.870265i	$-0.663947\pi$
$564$		0			0
$565$	−263658.	+	263658.i	−0.825930	+	0.825930i
$566$		0			0
$567$	−34794.1			−0.108228
$568$		0			0
$569$	−25660.6	−	25660.6i	−0.0792579	−	0.0792579i	0.666366	−	0.745624i	$-0.267849\pi$
$569$	−25660.6	−	25660.6i	−0.0792579	−	0.0792579i	−0.745624	+	0.666366i	$0.767849\pi$
$570$		0			0
$571$	293162.			0.899156			0.449578	−	0.893241i	$-0.351574\pi$
$571$	293162.			0.899156			0.449578	+	0.893241i	$0.351574\pi$
$572$		0			0
$573$			587178.i			1.78838i
$574$		0			0
$575$	−507434.			−1.53477
$576$		0			0
$577$	262662.	+	262662.i	0.788944	+	0.788944i	0.981321	−	0.192377i	$-0.0616196\pi$
$577$	262662.	+	262662.i	0.788944	+	0.788944i	−0.192377	+	0.981321i	$0.561620\pi$
$578$		0			0
$579$			832716.i			2.48393i
$580$		0			0
$581$	2104.96			0.00623579
$582$		0			0
$583$	111471.	−	111471.i	0.327964	−	0.327964i
$584$		0			0
$585$		−	516100.i		−	1.50807i
$586$		0			0
$587$	−229034.			−0.664697			−0.332349	−	0.943157i	$-0.607841\pi$
$587$	−229034.			−0.664697			−0.332349	+	0.943157i	$0.607841\pi$
$588$		0			0
$589$		−	15337.0i		−	0.0442089i
$590$		0			0
$591$	191126.	−	191126.i	0.547199	−	0.547199i
$592$		0			0
$593$			530121.i			1.50753i	0.657145	+	0.753765i	$0.271764\pi$
$593$			530121.i			1.50753i	−0.657145	+	0.753765i	$0.728236\pi$
$594$		0			0
$595$	−108429.	−	108429.i	−0.306275	−	0.306275i
$596$		0			0
$597$	174738.	−	174738.i	0.490273	−	0.490273i
$598$		0			0
$599$	103657.	−	103657.i	0.288899	−	0.288899i	−0.547746	−	0.836645i	$-0.684514\pi$
$599$	103657.	−	103657.i	0.288899	−	0.288899i	0.836645	+	0.547746i	$0.184514\pi$
$600$		0			0
$601$	−81135.9	+	81135.9i	−0.224628	+	0.224628i	−0.810444	−	0.585816i	$-0.800774\pi$
$601$	−81135.9	+	81135.9i	−0.224628	+	0.224628i	0.585816	+	0.810444i	$0.300774\pi$
$602$		0			0
$603$	716864.			1.97152
$604$		0			0
$605$	−734972.			−2.00798
$606$		0			0
$607$	−127958.	−	127958.i	−0.347289	−	0.347289i	0.511810	−	0.859099i	$-0.328975\pi$
$607$	−127958.	−	127958.i	−0.347289	−	0.347289i	−0.859099	+	0.511810i	$0.828975\pi$
$608$		0			0
$609$	−79511.4	−	6818.78i	−0.214385	−	0.0183854i
$610$		0			0
$611$	−15602.8	+	15602.8i	−0.0417946	+	0.0417946i
$612$		0			0
$613$		−	395876.i		−	1.05351i	−0.850018	−	0.526754i	$-0.823409\pi$
$613$		−	395876.i		−	1.05351i	0.850018	−	0.526754i	$-0.176591\pi$
$614$		0			0
$615$		−	1.16283e6i		−	3.07443i
$616$		0			0
$617$	−293540.	−	293540.i	−0.771075	−	0.771075i	0.207219	−	0.978294i	$-0.433559\pi$
$617$	−293540.	−	293540.i	−0.771075	−	0.771075i	−0.978294	+	0.207219i	$0.933559\pi$
$618$		0			0
$619$	−344693.	−	344693.i	−0.899604	−	0.899604i	0.0957965	−	0.995401i	$-0.469460\pi$
$619$	−344693.	−	344693.i	−0.899604	−	0.899604i	−0.995401	+	0.0957965i	$0.969460\pi$
$620$		0			0
$621$	78546.8	+	78546.8i	0.203678	+	0.203678i
$622$		0			0
$623$	−2923.94	+	2923.94i	−0.00753342	+	0.00753342i
$624$		0			0
$625$	31751.7			0.0812843
$626$		0			0
$627$	119933.	+	119933.i	0.305072	+	0.305072i
$628$		0			0
$629$	−307231.			−0.776540
$630$		0			0
$631$		−	4114.51i		−	0.0103338i	−0.999987	−	0.00516690i	$-0.998355\pi$
$631$		−	4114.51i		−	0.0103338i	0.999987	−	0.00516690i	$-0.00164468\pi$
$632$		0			0
$633$	−631730.			−1.57661
$634$		0			0
$635$	436332.	+	436332.i	1.08211	+	1.08211i
$636$		0			0
$637$		−	304226.i		−	0.749751i
$638$		0			0
$639$	654684.			1.60336
$640$		0			0
$641$	172115.	−	172115.i	0.418893	−	0.418893i	−0.465929	−	0.884822i	$-0.654280\pi$
$641$	172115.	−	172115.i	0.418893	−	0.418893i	0.884822	+	0.465929i	$0.154280\pi$
$642$		0			0
$643$			691844.i			1.67335i	0.547701	+	0.836674i	$0.315503\pi$
$643$			691844.i			1.67335i	−0.547701	+	0.836674i	$0.684497\pi$
$644$		0			0
$645$	−1.74588e6			−4.19657
$646$		0			0
$647$			330415.i			0.789317i	0.918828	+	0.394658i	$0.129137\pi$
$647$			330415.i			0.789317i	−0.918828	+	0.394658i	$0.870863\pi$
$648$		0			0
$649$	5589.95	−	5589.95i	0.0132715	−	0.0132715i
$650$		0			0
$651$		−	20750.5i		−	0.0489629i
$652$		0			0
$653$	−262278.	−	262278.i	−0.615086	−	0.615086i	0.329181	−	0.944267i	$-0.393228\pi$
$653$	−262278.	−	262278.i	−0.615086	−	0.615086i	−0.944267	+	0.329181i	$0.893228\pi$
$654$		0			0
$655$	−165399.	+	165399.i	−0.385523	+	0.385523i
$656$		0			0
$657$	−236142.	+	236142.i	−0.547070	+	0.547070i
$658$		0			0
$659$	−76977.1	+	76977.1i	−0.177252	+	0.177252i	−0.790157	−	0.612905i	$-0.790001\pi$
$659$	−76977.1	+	76977.1i	−0.177252	+	0.177252i	0.612905	+	0.790157i	$0.290001\pi$
$660$		0			0
$661$	−630040.			−1.44200			−0.721000	−	0.692936i	$-0.756317\pi$
$661$	−630040.			−1.44200			−0.721000	+	0.692936i	$0.756317\pi$
$662$		0			0
$663$	918786.			2.09020
$664$		0			0
$665$	14328.3	+	14328.3i	0.0324005	+	0.0324005i
$666$		0			0
$667$	−265928.	−	315818.i	−0.597740	−	0.709880i
$668$		0			0
$669$	353384.	−	353384.i	0.789577	−	0.789577i
$670$		0			0
$671$			843846.i			1.87421i
$672$		0			0
$673$		−	651683.i		−	1.43882i	−0.694586	−	0.719410i	$-0.744412\pi$
$673$		−	651683.i		−	1.43882i	0.694586	−	0.719410i	$-0.255588\pi$
$674$		0			0
$675$	−165379.	−	165379.i	−0.362973	−	0.362973i
$676$		0			0
$677$	628871.	+	628871.i	1.37210	+	1.37210i	0.857332	+	0.514764i	$0.172120\pi$
$677$	628871.	+	628871.i	1.37210	+	1.37210i	0.514764	+	0.857332i	$0.327880\pi$
$678$		0			0
$679$	31661.4	+	31661.4i	0.0686736	+	0.0686736i
$680$		0			0
$681$	478068.	−	478068.i	1.03085	−	1.03085i
$682$		0			0
$683$	817192.			1.75179			0.875897	−	0.482498i	$-0.160271\pi$
$683$	817192.			1.75179			0.875897	+	0.482498i	$0.160271\pi$
$684$		0			0
$685$	1.01444e6	+	1.01444e6i	2.16194	+	2.16194i
$686$		0			0
$687$	−767747.			−1.62669
$688$		0			0
$689$			112847.i			0.237713i
$690$		0			0
$691$	85525.8			0.179119			0.0895594	−	0.995981i	$-0.471454\pi$
$691$	85525.8			0.179119			0.0895594	+	0.995981i	$0.471454\pi$
$692$		0			0
$693$	88803.7	+	88803.7i	0.184912	+	0.184912i
$694$		0			0
$695$		−	39841.5i		−	0.0824833i
$696$		0			0
$697$	1.13292e6			2.33203
$698$		0			0
$699$	−568005.	+	568005.i	−1.16251	+	1.16251i
$700$		0			0
$701$		−	37523.5i		−	0.0763602i	−0.999271	−	0.0381801i	$-0.987844\pi$
$701$		−	37523.5i		−	0.0763602i	0.999271	−	0.0381801i	$-0.0121561\pi$
$702$		0			0
$703$	40599.0			0.0821494
$704$		0			0
$705$			92878.1i			0.186868i
$706$		0			0
$707$	15363.8	−	15363.8i	0.0307370	−	0.0307370i
$708$		0			0
$709$			451762.i			0.898705i	0.893354	+	0.449353i	$0.148345\pi$
$709$			451762.i			0.898705i	−0.893354	+	0.449353i	$0.851655\pi$
$710$		0			0
$711$	733862.	+	733862.i	1.45169	+	1.45169i
$712$		0			0
$713$	75910.7	−	75910.7i	0.149322	−	0.149322i
$714$		0			0
$715$	673838.	−	673838.i	1.31809	−	1.31809i
$716$		0			0
$717$	451653.	−	451653.i	0.878550	−	0.878550i
$718$		0			0
$719$	57862.6			0.111928			0.0559642	−	0.998433i	$-0.482177\pi$
$719$	57862.6			0.111928			0.0559642	+	0.998433i	$0.482177\pi$
$720$		0			0
$721$	−728.707			−0.00140179
$722$		0			0
$723$	200005.	+	200005.i	0.382616	+	0.382616i
$724$		0			0
$725$	559909.	+	664951.i	1.06522	+	1.26507i
$726$		0			0
$727$	−39425.0	+	39425.0i	−0.0745938	+	0.0745938i	−0.743419	−	0.668826i	$-0.766797\pi$
$727$	−39425.0	+	39425.0i	−0.0745938	+	0.0745938i	0.668826	+	0.743419i	$0.266797\pi$
$728$		0			0
$729$		−	725397.i		−	1.36496i
$730$		0			0
$731$		−	1.70098e6i		−	3.18320i
$732$		0			0
$733$	−126137.	−	126137.i	−0.234766	−	0.234766i	0.579912	−	0.814679i	$-0.303087\pi$
$733$	−126137.	−	126137.i	−0.234766	−	0.234766i	−0.814679	+	0.579912i	$0.803087\pi$
$734$		0			0
$735$	−905477.	−	905477.i	−1.67611	−	1.67611i
$736$		0			0
$737$	935962.	+	935962.i	1.72315	+	1.72315i
$738$		0			0
$739$	−580797.	+	580797.i	−1.06350	+	1.06350i	−0.0656532	+	0.997843i	$0.520913\pi$
$739$	−580797.	+	580797.i	−1.06350	+	1.06350i	−0.997843	+	0.0656532i	$0.979087\pi$
$740$		0			0
$741$	−121413.			−0.221120
$742$		0			0
$743$	551049.	+	551049.i	0.998188	+	0.998188i	0.999998	−	0.00181018i	$-0.000576200\pi$
$743$	551049.	+	551049.i	0.998188	+	0.998188i	−0.00181018	+	0.999998i	$0.500576\pi$
$744$		0			0
$745$	1.45156e6			2.61531
$746$		0			0
$747$			29053.5i			0.0520664i
$748$		0			0
$749$	−121114.			−0.215890
$750$		0			0
$751$	82212.0	+	82212.0i	0.145766	+	0.145766i	0.776223	−	0.630458i	$-0.217133\pi$
$751$	82212.0	+	82212.0i	0.145766	+	0.145766i	−0.630458	+	0.776223i	$0.717133\pi$
$752$		0			0
$753$		−	62935.7i		−	0.110996i
$754$		0			0
$755$	−1.28290e6			−2.25061
$756$		0			0
$757$	334338.	−	334338.i	0.583438	−	0.583438i	−0.352409	−	0.935846i	$-0.614637\pi$
$757$	334338.	−	334338.i	0.583438	−	0.583438i	0.935846	+	0.352409i	$0.114637\pi$
$758$		0			0
$759$			1.18722e6i			2.06085i
$760$		0			0
$761$	−341996.			−0.590543			−0.295272	−	0.955413i	$-0.595410\pi$
$761$	−341996.			−0.590543			−0.295272	+	0.955413i	$0.595410\pi$
$762$		0			0
$763$			8655.55i			0.0148678i
$764$		0			0
$765$	1.49658e6	−	1.49658e6i	2.55728	−	2.55728i
$766$		0			0
$767$			5658.94i			0.00961932i
$768$		0			0
$769$	−535764.	−	535764.i	−0.905984	−	0.905984i	0.0899608	−	0.995945i	$-0.471326\pi$
$769$	−535764.	−	535764.i	−0.905984	−	0.905984i	−0.995945	+	0.0899608i	$0.971326\pi$
$770$		0			0
$771$	1.14104e6	−	1.14104e6i	1.91951	−	1.91951i
$772$		0			0
$773$	−319054.	+	319054.i	−0.533955	+	0.533955i	−0.921747	−	0.387792i	$-0.873238\pi$
$773$	−319054.	+	319054.i	−0.533955	+	0.533955i	0.387792	+	0.921747i	$0.373238\pi$
$774$		0			0
$775$	−159829.	+	159829.i	−0.266105	+	0.266105i
$776$		0			0
$777$	54929.3			0.0909834
$778$		0			0
$779$	−149710.			−0.246703
$780$		0			0
$781$	854778.	+	854778.i	1.40137	+	1.40137i
$782$		0			0
$783$	16259.7	−	189598.i	0.0265209	−	0.309251i
$784$		0			0
$785$	−1.34172e6	+	1.34172e6i	−2.17733	+	2.17733i
$786$		0			0
$787$			570876.i			0.921706i	0.887476	+	0.460853i	$0.152457\pi$
$787$			570876.i			0.921706i	−0.887476	+	0.460853i	$0.847543\pi$
$788$		0			0
$789$		−	1.01976e6i		−	1.63811i
$790$		0			0
$791$	45926.7	+	45926.7i	0.0734027	+	0.0734027i
$792$		0			0
$793$	−427130.	−	427130.i	−0.679226	−	0.679226i
$794$		0			0
$795$	335871.	+	335871.i	0.531420	+	0.531420i
$796$		0			0
$797$	473963.	−	473963.i	0.746152	−	0.746152i	−0.227602	−	0.973754i	$-0.573088\pi$
$797$	473963.	−	473963.i	0.746152	−	0.746152i	0.973754	+	0.227602i	$0.0730885\pi$
$798$		0			0
$799$	−90489.6			−0.141744
$800$		0			0
$801$	−40357.4	−	40357.4i	−0.0629011	−	0.0629011i
$802$		0			0
$803$	−616631.			−0.956301
$804$		0			0
$805$			141837.i			0.218875i
$806$		0			0
$807$	50219.3			0.0771123
$808$		0			0
$809$	−594352.	−	594352.i	−0.908127	−	0.908127i	0.0879938	−	0.996121i	$-0.471954\pi$
$809$	−594352.	−	594352.i	−0.908127	−	0.908127i	−0.996121	+	0.0879938i	$0.971954\pi$
$810$		0			0
$811$			213751.i			0.324987i	0.986710	+	0.162494i	$0.0519537\pi$
$811$			213751.i			0.324987i	−0.986710	+	0.162494i	$0.948046\pi$
$812$		0			0
$813$	382738.			0.579056
$814$		0			0
$815$	950615.	−	950615.i	1.43116	−	1.43116i
$816$		0			0
$817$			224776.i			0.336748i
$818$		0			0
$819$	−89899.8			−0.134027
$820$		0			0
$821$		−	1.00384e6i		−	1.48929i	−0.667463	−	0.744643i	$-0.732620\pi$
$821$		−	1.00384e6i		−	1.48929i	0.667463	−	0.744643i	$-0.267380\pi$
$822$		0			0
$823$	456517.	−	456517.i	0.673996	−	0.673996i	−0.284639	−	0.958635i	$-0.591874\pi$
$823$	456517.	−	456517.i	0.673996	−	0.673996i	0.958635	+	0.284639i	$0.0918738\pi$
$824$		0			0
$825$		−	2.49967e6i		−	3.67261i
$826$		0			0
$827$	31375.3	+	31375.3i	0.0458751	+	0.0458751i	0.729672	−	0.683797i	$-0.239673\pi$
$827$	31375.3	+	31375.3i	0.0458751	+	0.0458751i	−0.683797	+	0.729672i	$0.739673\pi$
$828$		0			0
$829$	−172264.	+	172264.i	−0.250660	+	0.250660i	−0.821241	−	0.570581i	$-0.806718\pi$
$829$	−172264.	+	172264.i	−0.250660	+	0.250660i	0.570581	+	0.821241i	$0.306718\pi$
$830$		0			0
$831$	−1.21944e6	+	1.21944e6i	−1.76587	+	1.76587i
$832$		0			0
$833$	882191.	−	882191.i	1.27137	−	1.27137i
$834$		0			0
$835$	−1.43026e6			−2.05137
$836$		0			0
$837$	49480.5			0.0706291
$838$		0			0
$839$	−362834.	−	362834.i	−0.515447	−	0.515447i	0.400743	−	0.916190i	$-0.368752\pi$
$839$	−362834.	−	362834.i	−0.515447	−	0.515447i	−0.916190	+	0.400743i	$0.868752\pi$
$840$		0			0
$841$	−120425.	+	696954.i	−0.170265	+	0.985398i
$842$		0			0
$843$	−97601.3	+	97601.3i	−0.137341	+	0.137341i
$844$		0			0
$845$		−	481029.i		−	0.673687i
$846$		0			0
$847$			128025.i			0.178455i
$848$		0			0
$849$	719807.	+	719807.i	0.998621	+	0.998621i
$850$		0			0
$851$	200945.	+	200945.i	0.277472	+	0.277472i
$852$		0			0
$853$	−169818.	−	169818.i	−0.233392	−	0.233392i	0.580715	−	0.814107i	$-0.302773\pi$
$853$	−169818.	−	169818.i	−0.233392	−	0.233392i	−0.814107	+	0.580715i	$0.802773\pi$
$854$		0			0
$855$	−197765.	+	197765.i	−0.270532	+	0.270532i
$856$		0			0
$857$	−759638.			−1.03430			−0.517148	−	0.855896i	$-0.673006\pi$
$857$	−759638.			−1.03430			−0.517148	+	0.855896i	$0.673006\pi$
$858$		0			0
$859$	553536.	+	553536.i	0.750170	+	0.750170i	0.974511	−	0.224341i	$-0.0720228\pi$
$859$	553536.	+	553536.i	0.750170	+	0.750170i	−0.224341	+	0.974511i	$0.572023\pi$
$860$		0			0
$861$	−202553.			−0.273233
$862$		0			0
$863$		−	154706.i		−	0.207723i	−0.994592	−	0.103862i	$-0.966880\pi$
$863$		−	154706.i		−	0.207723i	0.994592	−	0.103862i	$-0.0331199\pi$
$864$		0			0
$865$	1.82931e6			2.44486
$866$		0			0
$867$	1.87432e6	+	1.87432e6i	2.49348	+	2.49348i
$868$		0			0
$869$			1.91631e6i			2.53762i
$870$		0			0
$871$	−947514.			−1.24896
$872$		0			0
$873$	−437003.	+	437003.i	−0.573398	+	0.573398i
$874$		0			0
$875$		−	118062.i		−	0.154203i
$876$		0			0
$877$	−922498.			−1.19941			−0.599703	−	0.800222i	$-0.704715\pi$
$877$	−922498.			−1.19941			−0.599703	+	0.800222i	$0.704715\pi$
$878$		0			0
$879$			393896.i			0.509804i
$880$		0			0
$881$	−326153.	+	326153.i	−0.420213	+	0.420213i	−0.885277	−	0.465064i	$-0.846031\pi$
$881$	−326153.	+	326153.i	−0.420213	+	0.420213i	0.465064	+	0.885277i	$0.346031\pi$
$882$		0			0
$883$		−	598316.i		−	0.767378i	−0.923462	−	0.383689i	$-0.874653\pi$
$883$		−	598316.i		−	0.767378i	0.923462	−	0.383689i	$-0.125347\pi$
$884$		0			0
$885$	16842.9	+	16842.9i	0.0215045	+	0.0215045i
$886$		0			0
$887$	−813195.	+	813195.i	−1.03359	+	1.03359i	−0.0341727	+	0.999416i	$0.510880\pi$
$887$	−813195.	+	813195.i	−1.03359	+	1.03359i	−0.999416	+	0.0341727i	$0.989120\pi$
$888$		0			0
$889$	76004.9	−	76004.9i	0.0961697	−	0.0961697i
$890$		0			0
$891$	627021.	−	627021.i	0.789817	−	0.789817i
$892$		0			0
$893$	11957.7			0.0149950
$894$		0			0
$895$	3310.80			0.00413321
$896$		0			0
$897$	−600935.	−	600935.i	−0.746865	−	0.746865i
$898$		0			0
$899$	−183235.	−	15714.0i	−0.226720	−	0.0194432i
$900$		0			0
$901$	−327233.	+	327233.i	−0.403095	+	0.403095i
$902$		0			0
$903$			304115.i			0.372960i
$904$		0			0
$905$			54593.8i			0.0666570i
$906$		0			0
$907$	−474402.	−	474402.i	−0.576676	−	0.576676i	0.357310	−	0.933986i	$-0.383694\pi$
$907$	−474402.	−	474402.i	−0.576676	−	0.576676i	−0.933986	+	0.357310i	$0.883694\pi$
$908$		0			0
$909$	212058.	+	212058.i	0.256642	+	0.256642i
$910$		0			0
$911$	350774.	+	350774.i	0.422660	+	0.422660i	0.886119	−	0.463459i	$-0.153392\pi$
$911$	350774.	+	350774.i	0.422660	+	0.422660i	−0.463459	+	0.886119i	$0.653392\pi$
$912$		0			0
$913$	−37933.3	+	37933.3i	−0.0455071	+	0.0455071i
$914$		0			0
$915$	−2.54256e6			−3.03689
$916$		0			0
$917$	28810.9	+	28810.9i	0.0342625	+	0.0342625i
$918$		0			0
$919$	−972483.			−1.15147			−0.575733	−	0.817638i	$-0.695283\pi$
$919$	−972483.			−1.15147			−0.575733	+	0.817638i	$0.695283\pi$
$920$		0			0
$921$		−	321673.i		−	0.379224i
$922$		0			0
$923$	−865328.			−1.01573
$924$		0			0
$925$	−423088.	−	423088.i	−0.494479	−	0.494479i
$926$		0			0
$927$		−	10057.9i		−	0.0117044i
$928$		0			0
$929$	−359756.			−0.416847			−0.208424	−	0.978039i	$-0.566833\pi$
$929$	−359756.			−0.416847			−0.208424	+	0.978039i	$0.566833\pi$
$930$		0			0
$931$	−116577.	+	116577.i	−0.134497	+	0.134497i
$932$		0			0
$933$		−	69051.9i		−	0.0793254i
$934$		0			0
$935$	3.90798e6			4.47022
$936$		0			0
$937$			729562.i			0.830966i	0.909601	+	0.415483i	$0.136387\pi$
$937$			729562.i			0.830966i	−0.909601	+	0.415483i	$0.863613\pi$
$938$		0			0
$939$	−714428.	+	714428.i	−0.810266	+	0.810266i
$940$		0			0
$941$		−	644663.i		−	0.728037i	−0.931392	−	0.364018i	$-0.881405\pi$
$941$		−	644663.i		−	0.728037i	0.931392	−	0.364018i	$-0.118595\pi$
$942$		0			0
$943$	−740991.	−	740991.i	−0.833277	−	0.833277i
$944$		0			0
$945$	−46226.4	+	46226.4i	−0.0517638	+	0.0517638i
$946$		0			0
$947$	316196.	−	316196.i	0.352579	−	0.352579i	−0.508489	−	0.861068i	$-0.669796\pi$
$947$	316196.	−	316196.i	0.352579	−	0.352579i	0.861068	+	0.508489i	$0.169796\pi$
$948$		0			0
$949$	312121.	−	312121.i	0.346570	−	0.346570i
$950$		0			0
$951$	931357.			1.02981
$952$		0			0
$953$	−1.75063e6			−1.92757			−0.963784	−	0.266685i	$-0.914072\pi$
$953$	−1.75063e6			−1.92757			−0.963784	+	0.266685i	$0.914072\pi$
$954$		0			0
$955$	−1.26417e6	−	1.26417e6i	−1.38611	−	1.38611i
$956$		0			0
$957$	1.55575e6	−	1.30999e6i	1.69870	−	1.43035i
$958$		0			0
$959$	176705.	−	176705.i	0.192137	−	0.192137i
$960$		0			0
$961$			875701.i			0.948220i
$962$		0			0
$963$		−	1.67167e6i		−	1.80260i
$964$		0			0
$965$	−1.79280e6	−	1.79280e6i	−1.92521	−	1.92521i
$966$		0			0
$967$	614157.	+	614157.i	0.656790	+	0.656790i	0.954619	−	0.297829i	$-0.0962626\pi$
$967$	614157.	+	614157.i	0.656790	+	0.656790i	−0.297829	+	0.954619i	$0.596263\pi$
$968$		0			0
$969$	−352071.	−	352071.i	−0.374959	−	0.374959i
$970$		0			0
$971$	711809.	−	711809.i	0.754962	−	0.754962i	−0.220439	−	0.975401i	$-0.570749\pi$
$971$	711809.	−	711809.i	0.754962	−	0.754962i	0.975401	+	0.220439i	$0.0707489\pi$
$972$		0			0
$973$	−6940.02			−0.00733052
$974$		0			0
$975$	1.26526e6	+	1.26526e6i	1.33098	+	1.33098i
$976$		0			0
$977$	906813.			0.950011			0.475005	−	0.879983i	$-0.342446\pi$
$977$	906813.			0.950011			0.475005	+	0.879983i	$0.342446\pi$
$978$		0			0
$979$		−	105384.i		−	0.109954i
$980$		0			0
$981$	−119468.			−0.124140
$982$		0			0
$983$	−1.31463e6	−	1.31463e6i	−1.36049	−	1.36049i	−0.873293	−	0.487196i	$-0.838020\pi$
$983$	−1.31463e6	−	1.31463e6i	−1.36049	−	1.36049i	−0.487196	−	0.873293i	$-0.661980\pi$
$984$		0			0
$985$			822973.i			0.848229i
$986$		0			0
$987$	16178.5			0.0166075
$988$		0			0
$989$	−1.11253e6	+	1.11253e6i	−1.13742	+	1.13742i
$990$		0			0
$991$			1.36793e6i			1.39289i	0.717610	+	0.696445i	$0.245236\pi$
$991$			1.36793e6i			1.39289i	−0.717610	+	0.696445i	$0.754764\pi$
$992$		0			0
$993$	1.36347e6			1.38276
$994$		0			0
$995$			752406.i			0.759986i
$996$		0			0
$997$	−361820.	+	361820.i	−0.364000	+	0.364000i	−0.865283	−	0.501283i	$-0.832862\pi$
$997$	−361820.	+	361820.i	−0.364000	+	0.364000i	0.501283	+	0.865283i	$0.332862\pi$
$998$		0			0
$999$			130981.i			0.131244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.5.j.a.17.3	✓	30
29.12	odd	4	inner	232.5.j.a.41.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.5.j.a.17.3	✓	30	1.1	even	1	trivial
232.5.j.a.41.3	yes	30	29.12	odd	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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	232.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.45823 + 9.45823i) q^{3} -40.7263i q^{5} -7.09414 q^{7} -97.9163i q^{9} +O(q^{10})\)	\(q+(-9.45823 + 9.45823i) q^{3} -40.7263i q^{5} -7.09414 q^{7} -97.9163i q^{9} +(127.843 - 127.843i) q^{11} +129.421i q^{13} +(385.199 + 385.199i) q^{15} +(-375.293 + 375.293i) q^{17} +(49.5930 - 49.5930i) q^{19} +(67.0980 - 67.0980i) q^{21} +490.923 q^{23} -1033.63 q^{25} +(159.998 + 159.998i) q^{27} +(-541.690 - 643.314i) q^{29} +(154.628 - 154.628i) q^{31} +2418.34i q^{33} +288.918i q^{35} +(409.322 + 409.322i) q^{37} +(-1224.09 - 1224.09i) q^{39} +(-1509.38 - 1509.38i) q^{41} +(-2266.20 + 2266.20i) q^{43} -3987.77 q^{45} +(120.559 + 120.559i) q^{47} -2350.67 q^{49} -7099.22i q^{51} +871.941 q^{53} +(-5206.57 - 5206.57i) q^{55} +938.124i q^{57} +43.7251 q^{59} +(-3300.32 + 3300.32i) q^{61} +694.632i q^{63} +5270.83 q^{65} +7321.19i q^{67} +(-4643.26 + 4643.26i) q^{69} +6686.16i q^{71} +(-2411.68 - 2411.68i) q^{73} +(9776.34 - 9776.34i) q^{75} +(-906.935 + 906.935i) q^{77} +(-7494.79 + 7494.79i) q^{79} +4904.62 q^{81} -296.718 q^{83} +(15284.3 + 15284.3i) q^{85} +(11208.0 + 961.185i) q^{87} +(412.162 - 412.162i) q^{89} -918.129i q^{91} +2925.02i q^{93} +(-2019.74 - 2019.74i) q^{95} +(-4463.03 - 4463.03i) q^{97} +(-12517.9 - 12517.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 16 q^{3} + 96 q^{7}+O(q^{10}) \) 30 * q - 16 * q^3 + 96 * q^7	\( 30 q - 16 q^{3} + 96 q^{7} - 240 q^{15} - 338 q^{17} - 936 q^{19} + 1400 q^{21} - 352 q^{23} - 2154 q^{25} + 2648 q^{27} + 500 q^{29} - 1896 q^{31} - 1862 q^{37} + 1088 q^{39} + 2854 q^{41} - 800 q^{43} + 4552 q^{45} - 696 q^{47} + 9698 q^{49} + 4584 q^{53} - 8560 q^{55} + 7144 q^{59} - 1070 q^{61} + 8672 q^{65} - 19352 q^{69} - 7942 q^{73} + 11072 q^{75} - 3048 q^{77} + 3560 q^{79} - 10398 q^{81} - 9848 q^{83} + 11968 q^{85} - 13704 q^{87} - 9634 q^{89} - 33160 q^{95} - 27582 q^{97} + 16480 q^{99}+O(q^{100}) \) 30 * q - 16 * q^3 + 96 * q^7 - 240 * q^15 - 338 * q^17 - 936 * q^19 + 1400 * q^21 - 352 * q^23 - 2154 * q^25 + 2648 * q^27 + 500 * q^29 - 1896 * q^31 - 1862 * q^37 + 1088 * q^39 + 2854 * q^41 - 800 * q^43 + 4552 * q^45 - 696 * q^47 + 9698 * q^49 + 4584 * q^53 - 8560 * q^55 + 7144 * q^59 - 1070 * q^61 + 8672 * q^65 - 19352 * q^69 - 7942 * q^73 + 11072 * q^75 - 3048 * q^77 + 3560 * q^79 - 10398 * q^81 - 9848 * q^83 + 11968 * q^85 - 13704 * q^87 - 9634 * q^89 - 33160 * q^95 - 27582 * q^97 + 16480 * q^99

Introduction

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