LMFDB - Embedded newform 144.3.j.a.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	144.53
Dual form			144.3.j.a.125.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.252839 - 1.98395i) q^{2} +(-3.87214 + 1.00324i) q^{4} +(-1.66372 + 1.66372i) q^{5} +13.3224i q^{7} +(2.96942 + 7.42850i) q^{8} +O(q^{10})$	\(q+(-0.252839 - 1.98395i) q^{2} +(-3.87214 + 1.00324i) q^{4} +(-1.66372 + 1.66372i) q^{5} +13.3224i q^{7} +(2.96942 + 7.42850i) q^{8} +(3.72140 + 2.88010i) q^{10} +(7.81788 - 7.81788i) q^{11} +(-10.4955 + 10.4955i) q^{13} +(26.4310 - 3.36843i) q^{14} +(13.9870 - 7.76940i) q^{16} +10.0304i q^{17} +(5.07048 - 5.07048i) q^{19} +(4.77306 - 8.11130i) q^{20} +(-17.4870 - 13.5336i) q^{22} -29.7810 q^{23} +19.4640i q^{25} +(23.4763 + 18.1689i) q^{26} +(-13.3656 - 51.5863i) q^{28} +(18.6855 + 18.6855i) q^{29} +27.1537 q^{31} +(-18.9506 - 25.7852i) q^{32} +(19.8998 - 2.53607i) q^{34} +(-22.1648 - 22.1648i) q^{35} +(13.3368 + 13.3368i) q^{37} +(-11.3416 - 8.77758i) q^{38} +(-17.2993 - 7.41868i) q^{40} -34.9561 q^{41} +(7.29114 + 7.29114i) q^{43} +(-22.4287 + 38.1152i) q^{44} +(7.52980 + 59.0841i) q^{46} -51.5850i q^{47} -128.487 q^{49} +(38.6158 - 4.92127i) q^{50} +(30.1106 - 51.1697i) q^{52} +(-68.4354 + 68.4354i) q^{53} +26.0136i q^{55} +(-98.9655 + 39.5598i) q^{56} +(32.3468 - 41.7957i) q^{58} +(31.5812 - 31.5812i) q^{59} +(72.6595 - 72.6595i) q^{61} +(-6.86552 - 53.8717i) q^{62} +(-46.3651 + 44.1166i) q^{64} -34.9233i q^{65} +(60.3054 - 60.3054i) q^{67} +(-10.0629 - 38.8390i) q^{68} +(-38.3698 + 49.5781i) q^{70} -3.09226 q^{71} +2.05367i q^{73} +(23.0875 - 29.8316i) q^{74} +(-14.5467 + 24.7206i) q^{76} +(104.153 + 104.153i) q^{77} +53.3986 q^{79} +(-10.3444 + 36.1966i) q^{80} +(8.83826 + 69.3512i) q^{82} +(21.7960 + 21.7960i) q^{83} +(-16.6877 - 16.6877i) q^{85} +(12.6218 - 16.3088i) q^{86} +(81.2896 + 34.8606i) q^{88} +137.585 q^{89} +(-139.826 - 139.826i) q^{91} +(115.316 - 29.8776i) q^{92} +(-102.342 + 13.0427i) q^{94} +16.8718i q^{95} -17.1890 q^{97} +(32.4864 + 254.911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.252839	−	1.98395i	−0.126420	−	0.991977i
$2$	−0.252839	−	1.98395i	−0.126420	−	0.991977i
$3$		0			0
$3$		0			0
$4$	−3.87214	+	1.00324i	−0.968036	+	0.250811i
$5$	−1.66372	+	1.66372i	−0.332745	+	0.332745i	−0.853628	−	0.520883i	$-0.825603\pi$
$5$	−1.66372	+	1.66372i	−0.332745	+	0.332745i	0.520883	+	0.853628i	$0.325603\pi$
$6$		0			0
$7$			13.3224i			1.90320i	0.307337	+	0.951601i	$0.400562\pi$
$7$			13.3224i			1.90320i	−0.307337	+	0.951601i	$0.599438\pi$
$8$	2.96942	+	7.42850i	0.371177	+	0.928562i
$9$		0			0
$10$	3.72140	+	2.88010i	0.372140	+	0.288010i
$11$	7.81788	−	7.81788i	0.710716	−	0.710716i	−0.255969	−	0.966685i	$-0.582394\pi$
$11$	7.81788	−	7.81788i	0.710716	−	0.710716i	0.966685	+	0.255969i	$0.0823944\pi$
$12$		0			0
$13$	−10.4955	+	10.4955i	−0.807347	+	0.807347i	−0.984232	−	0.176884i	$-0.943398\pi$
$13$	−10.4955	+	10.4955i	−0.807347	+	0.807347i	0.176884	+	0.984232i	$0.443398\pi$
$14$	26.4310	−	3.36843i	1.88793	−	0.240602i
$15$		0			0
$16$	13.9870	−	7.76940i	0.874188	−	0.485587i
$17$			10.0304i			0.590021i	0.955494	+	0.295011i	$0.0953232\pi$
$17$			10.0304i			0.590021i	−0.955494	+	0.295011i	$0.904677\pi$
$18$		0			0
$19$	5.07048	−	5.07048i	0.266867	−	0.266867i	−0.560969	−	0.827837i	$-0.689571\pi$
$19$	5.07048	−	5.07048i	0.266867	−	0.266867i	0.827837	+	0.560969i	$0.189571\pi$
$20$	4.77306	−	8.11130i	0.238653	−	0.405565i
$21$		0			0
$22$	−17.4870	−	13.5336i	−0.794863	−	0.615166i
$23$	−29.7810			−1.29483			−0.647413	−	0.762140i	$-0.724149\pi$
$23$	−29.7810			−1.29483			−0.647413	+	0.762140i	$0.724149\pi$
$24$		0			0
$25$			19.4640i			0.778562i
$26$	23.4763	+	18.1689i	0.902934	+	0.698805i
$27$		0			0
$28$	−13.3656	−	51.5863i	−0.477343	−	1.84237i
$29$	18.6855	+	18.6855i	0.644329	+	0.644329i	0.951617	−	0.307288i	$-0.0994213\pi$
$29$	18.6855	+	18.6855i	0.644329	+	0.644329i	−0.307288	+	0.951617i	$0.599421\pi$
$30$		0			0
$31$	27.1537			0.875926			0.437963	−	0.898993i	$-0.355700\pi$
$31$	27.1537			0.875926			0.437963	+	0.898993i	$0.355700\pi$
$32$	−18.9506	−	25.7852i	−0.592206	−	0.805787i
$33$		0			0
$34$	19.8998	−	2.53607i	0.585288	−	0.0745903i
$35$	−22.1648	−	22.1648i	−0.633280	−	0.633280i
$36$		0			0
$37$	13.3368	+	13.3368i	0.360453	+	0.360453i	0.863980	−	0.503526i	$-0.167964\pi$
$37$	13.3368	+	13.3368i	0.360453	+	0.360453i	−0.503526	+	0.863980i	$0.667964\pi$
$38$	−11.3416	−	8.77758i	−0.298464	−	0.230989i
$39$		0			0
$40$	−17.2993	−	7.41868i	−0.432481	−	0.185467i
$41$	−34.9561			−0.852587			−0.426293	−	0.904585i	$-0.640181\pi$
$41$	−34.9561			−0.852587			−0.426293	+	0.904585i	$0.640181\pi$
$42$		0			0
$43$	7.29114	+	7.29114i	0.169561	+	0.169561i	0.786787	−	0.617225i	$-0.211743\pi$
$43$	7.29114	+	7.29114i	0.169561	+	0.169561i	−0.617225	+	0.786787i	$0.711743\pi$
$44$	−22.4287	+	38.1152i	−0.509744	+	0.866254i
$45$		0			0
$46$	7.52980	+	59.0841i	0.163691	+	1.28444i
$47$		−	51.5850i		−	1.09755i	−0.835969	−	0.548777i	$-0.815094\pi$
$47$		−	51.5850i		−	1.09755i	0.835969	−	0.548777i	$-0.184906\pi$
$48$		0			0
$49$	−128.487			−2.62217
$50$	38.6158	−	4.92127i	0.772315	−	0.0984255i
$51$		0			0
$52$	30.1106	−	51.1697i	0.579050	−	0.984032i
$53$	−68.4354	+	68.4354i	−1.29123	+	1.29123i	−0.357209	+	0.934024i	$0.616272\pi$
$53$	−68.4354	+	68.4354i	−1.29123	+	1.29123i	−0.934024	+	0.357209i	$0.883728\pi$
$54$		0			0
$55$			26.0136i			0.472974i
$56$	−98.9655	+	39.5598i	−1.76724	+	0.706425i
$57$		0			0
$58$	32.3468	−	41.7957i	0.557704	−	0.720616i
$59$	31.5812	−	31.5812i	0.535275	−	0.535275i	−0.386862	−	0.922138i	$-0.626441\pi$
$59$	31.5812	−	31.5812i	0.535275	−	0.535275i	0.922138	+	0.386862i	$0.126441\pi$
$60$		0			0
$61$	72.6595	−	72.6595i	1.19114	−	1.19114i	0.214392	−	0.976748i	$-0.431223\pi$
$61$	72.6595	−	72.6595i	1.19114	−	1.19114i	0.976748	−	0.214392i	$-0.0687771\pi$
$62$	−6.86552	−	53.8717i	−0.110734	−	0.868899i
$63$		0			0
$64$	−46.3651	+	44.1166i	−0.724455	+	0.689322i
$65$		−	34.9233i		−	0.537281i
$66$		0			0
$67$	60.3054	−	60.3054i	0.900080	−	0.900080i	−0.0953625	−	0.995443i	$-0.530401\pi$
$67$	60.3054	−	60.3054i	0.900080	−	0.900080i	0.995443	+	0.0953625i	$0.0304010\pi$
$68$	−10.0629	−	38.8390i	−0.147984	−	0.571162i
$69$		0			0
$70$	−38.3698	+	49.5781i	−0.548140	+	0.708258i
$71$	−3.09226			−0.0435530			−0.0217765	−	0.999763i	$-0.506932\pi$
$71$	−3.09226			−0.0435530			−0.0217765	+	0.999763i	$0.506932\pi$
$72$		0			0
$73$			2.05367i			0.0281324i	0.999901	+	0.0140662i	$0.00447757\pi$
$73$			2.05367i			0.0281324i	−0.999901	+	0.0140662i	$0.995522\pi$
$74$	23.0875	−	29.8316i	0.311993	−	0.403130i
$75$		0			0
$76$	−14.5467	+	24.7206i	−0.191404	+	0.325270i
$77$	104.153	+	104.153i	1.35264	+	1.35264i
$78$		0			0
$79$	53.3986			0.675932			0.337966	−	0.941158i	$-0.390261\pi$
$79$	53.3986			0.675932			0.337966	+	0.941158i	$0.390261\pi$
$80$	−10.3444	+	36.1966i	−0.129305	+	0.452458i
$81$		0			0
$82$	8.83826	+	69.3512i	0.107784	+	0.845747i
$83$	21.7960	+	21.7960i	0.262602	+	0.262602i	0.826110	−	0.563508i	$-0.190549\pi$
$83$	21.7960	+	21.7960i	0.262602	+	0.262602i	−0.563508	+	0.826110i	$0.690549\pi$
$84$		0			0
$85$	−16.6877	−	16.6877i	−0.196326	−	0.196326i
$86$	12.6218	−	16.3088i	0.146765	−	0.189637i
$87$		0			0
$88$	81.2896	+	34.8606i	0.923746	+	0.396143i
$89$	137.585			1.54590			0.772948	−	0.634470i	$-0.218782\pi$
$89$	137.585			1.54590			0.772948	+	0.634470i	$0.218782\pi$
$90$		0			0
$91$	−139.826	−	139.826i	−1.53654	−	1.53654i
$92$	115.316	−	29.8776i	1.25344	−	0.324756i
$93$		0			0
$94$	−102.342	+	13.0427i	−1.08875	+	0.138752i
$95$			16.8718i			0.177597i
$96$		0			0
$97$	−17.1890			−0.177206			−0.0886030	−	0.996067i	$-0.528240\pi$
$97$	−17.1890			−0.177206			−0.0886030	+	0.996067i	$0.528240\pi$
$98$	32.4864	+	254.911i	0.331494	+	2.60114i
$99$		0			0
$100$	−19.5272	−	75.3676i	−0.195272	−	0.753676i
$101$	89.4355	−	89.4355i	0.885500	−	0.885500i	−0.108587	−	0.994087i	$-0.534632\pi$
$101$	89.4355	−	89.4355i	0.885500	−	0.885500i	0.994087	+	0.108587i	$0.0346325\pi$
$102$		0			0
$103$			124.313i			1.20693i	0.797391	+	0.603463i	$0.206213\pi$
$103$			124.313i			1.20693i	−0.797391	+	0.603463i	$0.793787\pi$
$104$	−109.131	−	46.8003i	−1.04934	−	0.450003i
$105$		0			0
$106$	153.076	+	118.469i	1.44411	+	1.11764i
$107$	117.662	−	117.662i	1.09964	−	1.09964i	0.105191	−	0.994452i	$-0.466455\pi$
$107$	117.662	−	117.662i	1.09964	−	1.09964i	0.994452	−	0.105191i	$-0.0335454\pi$
$108$		0			0
$109$	1.84962	−	1.84962i	0.0169690	−	0.0169690i	−0.698571	−	0.715540i	$-0.746181\pi$
$109$	1.84962	−	1.84962i	0.0169690	−	0.0169690i	0.715540	+	0.698571i	$0.246181\pi$
$110$	51.6097	−	6.57725i	0.469179	−	0.0597932i
$111$		0			0
$112$	103.507	+	186.341i	0.924171	+	1.66376i
$113$			28.3900i			0.251239i	0.992079	+	0.125619i	$0.0400918\pi$
$113$			28.3900i			0.251239i	−0.992079	+	0.125619i	$0.959908\pi$
$114$		0			0
$115$	49.5473	−	49.5473i	0.430846	−	0.430846i
$116$	−91.0993	−	53.6070i	−0.785339	−	0.462129i
$117$		0			0
$118$	−70.6407	−	54.6708i	−0.598650	−	0.463312i
$119$	−133.629			−1.12293
$120$		0			0
$121$		−	1.23847i		−	0.0102353i
$122$	−162.524	−	125.782i	−1.33217	−	1.03100i
$123$		0			0
$124$	−105.143	+	27.2418i	−0.847928	+	0.219692i
$125$	−73.9759	−	73.9759i	−0.591807	−	0.591807i
$126$		0			0
$127$	31.7899			0.250314			0.125157	−	0.992137i	$-0.460056\pi$
$127$	31.7899			0.250314			0.125157	+	0.992137i	$0.460056\pi$
$128$	99.2482	+	80.8319i	0.775377	+	0.631499i
$129$		0			0
$130$	−69.2861	+	8.82997i	−0.532970	+	0.0679228i
$131$	160.832	+	160.832i	1.22772	+	1.22772i	0.964823	+	0.262902i	$0.0846796\pi$
$131$	160.832	+	160.832i	1.22772	+	1.22772i	0.262902	+	0.964823i	$0.415320\pi$
$132$		0			0
$133$	67.5510	+	67.5510i	0.507902	+	0.507902i
$134$	−134.891	−	104.396i	−1.00665	−	0.779071i
$135$		0			0
$136$	−74.5105	+	29.7843i	−0.547871	+	0.219002i
$137$	−224.414			−1.63805			−0.819027	−	0.573754i	$-0.805486\pi$
$137$	−224.414			−1.63805			−0.819027	+	0.573754i	$0.805486\pi$
$138$		0			0
$139$	−55.3627	−	55.3627i	−0.398292	−	0.398292i	0.479338	−	0.877630i	$-0.340877\pi$
$139$	−55.3627	−	55.3627i	−0.398292	−	0.398292i	−0.877630	+	0.479338i	$0.840877\pi$
$140$	108.062	+	63.5887i	0.771871	+	0.454205i
$141$		0			0
$142$	0.781845	+	6.13490i	0.00550595	+	0.0432035i
$143$			164.105i			1.14759i
$144$		0			0
$145$	−62.1752			−0.428794
$146$	4.07438	−	0.519248i	0.0279067	−	0.00355649i
$147$		0			0
$148$	−65.0219	−	38.2619i	−0.439337	−	0.258526i
$149$	−99.5497	+	99.5497i	−0.668119	+	0.668119i	−0.957280	−	0.289162i	$-0.906623\pi$
$149$	−99.5497	+	99.5497i	−0.668119	+	0.668119i	0.289162	+	0.957280i	$0.406623\pi$
$150$		0			0
$151$			130.380i			0.863442i	0.902007	+	0.431721i	$0.142094\pi$
$151$			130.380i			0.863442i	−0.902007	+	0.431721i	$0.857906\pi$
$152$	52.7224	+	22.6097i	0.346858	+	0.148748i
$153$		0			0
$154$	180.301	−	232.969i	1.17078	−	1.51278i
$155$	−45.1763	+	45.1763i	−0.291460	+	0.291460i
$156$		0			0
$157$	145.961	−	145.961i	0.929686	−	0.929686i	−0.0679992	−	0.997685i	$-0.521662\pi$
$157$	145.961	−	145.961i	0.929686	−	0.929686i	0.997685	+	0.0679992i	$0.0216615\pi$
$158$	−13.5013	−	105.940i	−0.0854510	−	0.670509i
$159$		0			0
$160$	74.4279	+	11.3708i	0.465175	+	0.0710678i
$161$		−	396.755i		−	2.46431i
$162$		0			0
$163$	−41.4323	+	41.4323i	−0.254186	+	0.254186i	−0.822684	−	0.568498i	$-0.807525\pi$
$163$	−41.4323	+	41.4323i	−0.254186	+	0.254186i	0.568498	+	0.822684i	$0.307525\pi$
$164$	135.355	−	35.0694i	0.825335	−	0.213838i
$165$		0			0
$166$	37.7313	−	48.7530i	0.227297	−	0.293693i
$167$	−13.8976			−0.0832192			−0.0416096	−	0.999134i	$-0.513249\pi$
$167$	−13.8976			−0.0832192			−0.0416096	+	0.999134i	$0.513249\pi$
$168$		0			0
$169$		−	51.3116i		−	0.303619i
$170$	−28.8884	+	37.3270i	−0.169932	+	0.219571i
$171$		0			0
$172$	−35.5471	−	20.9176i	−0.206669	−	0.121614i
$173$	43.8507	+	43.8507i	0.253473	+	0.253473i	0.822393	−	0.568920i	$-0.192639\pi$
$173$	43.8507	+	43.8507i	0.253473	+	0.253473i	−0.568920	+	0.822393i	$0.692639\pi$
$174$		0			0
$175$	−259.308			−1.48176
$176$	48.6085	−	170.089i	0.276185	−	0.966415i
$177$		0			0
$178$	−34.7868	−	272.962i	−0.195431	−	1.53349i
$179$	−154.797	−	154.797i	−0.864788	−	0.864788i	0.127102	−	0.991890i	$-0.459432\pi$
$179$	−154.797	−	154.797i	−0.864788	−	0.864788i	−0.991890	+	0.127102i	$0.959432\pi$
$180$		0			0
$181$	105.914	+	105.914i	0.585160	+	0.585160i	0.936317	−	0.351157i	$-0.114212\pi$
$181$	105.914	+	105.914i	0.585160	+	0.585160i	−0.351157	+	0.936317i	$0.614212\pi$
$182$	−242.054	+	312.761i	−1.32997	+	1.71847i
$183$		0			0
$184$	−88.4322	−	221.228i	−0.480610	−	1.20233i
$185$	−44.3774			−0.239878
$186$		0			0
$187$	78.4162	+	78.4162i	0.419338	+	0.419338i
$188$	51.7523	+	199.745i	0.275278	+	1.06247i
$189$		0			0
$190$	33.4728	−	4.26584i	0.176173	−	0.0224518i
$191$			69.4546i			0.363637i	0.983332	+	0.181818i	$0.0581983\pi$
$191$			69.4546i			0.363637i	−0.983332	+	0.181818i	$0.941802\pi$
$192$		0			0
$193$	35.5238			0.184061			0.0920306	−	0.995756i	$-0.470664\pi$
$193$	35.5238			0.184061			0.0920306	+	0.995756i	$0.470664\pi$
$194$	4.34605	+	34.1022i	0.0224023	+	0.175784i
$195$		0			0
$196$	497.519	−	128.903i	2.53836	−	0.657669i
$197$	7.74617	−	7.74617i	0.0393206	−	0.0393206i	−0.687173	−	0.726494i	$-0.741149\pi$
$197$	7.74617	−	7.74617i	0.0393206	−	0.0393206i	0.726494	+	0.687173i	$0.241149\pi$
$198$		0			0
$199$		−	158.474i		−	0.796352i	−0.917309	−	0.398176i	$-0.869643\pi$
$199$		−	158.474i		−	0.796352i	0.917309	−	0.398176i	$-0.130357\pi$
$200$	−144.589	+	57.7969i	−0.722943	+	0.288984i
$201$		0			0
$202$	−200.049	−	154.823i	−0.990341	−	0.766451i
$203$	−248.936	+	248.936i	−1.22629	+	1.22629i
$204$		0			0
$205$	58.1572	−	58.1572i	0.283694	−	0.283694i
$206$	246.632	−	31.4313i	1.19724	−	0.152579i
$207$		0			0
$208$	−65.2570	+	228.345i	−0.313736	+	1.09781i
$209$		−	79.2808i		−	0.379334i
$210$		0			0
$211$	−168.889	+	168.889i	−0.800422	+	0.800422i	−0.983161	−	0.182739i	$-0.941504\pi$
$211$	−168.889	+	168.889i	−0.800422	+	0.800422i	0.182739	+	0.983161i	$0.441504\pi$
$212$	196.334	−	333.649i	0.926106	−	1.57382i
$213$		0			0
$214$	−263.185	−	203.686i	−1.22984	−	0.951804i
$215$	−24.2609			−0.112841
$216$		0			0
$217$			361.753i			1.66706i
$218$	−4.13723	−	3.20191i	−0.0189781	−	0.0146877i
$219$		0			0
$220$	−26.0979	−	100.728i	−0.118627	−	0.457856i
$221$	−105.274	−	105.274i	−0.476352	−	0.476352i
$222$		0			0
$223$	83.6618			0.375165			0.187582	−	0.982249i	$-0.439935\pi$
$223$	83.6618			0.375165			0.187582	+	0.982249i	$0.439935\pi$
$224$	343.521	−	252.468i	1.53357	−	1.12709i
$225$		0			0
$226$	56.3244	−	7.17810i	0.249223	−	0.0317615i
$227$	72.4600	+	72.4600i	0.319207	+	0.319207i	0.848463	−	0.529255i	$-0.177529\pi$
$227$	72.4600	+	72.4600i	0.319207	+	0.319207i	−0.529255	+	0.848463i	$0.677529\pi$
$228$		0			0
$229$	119.027	+	119.027i	0.519767	+	0.519767i	0.917501	−	0.397734i	$-0.130203\pi$
$229$	119.027	+	119.027i	0.519767	+	0.519767i	−0.397734	+	0.917501i	$0.630203\pi$
$230$	−110.827	−	85.7721i	−0.481857	−	0.372922i
$231$		0			0
$232$	−83.3204	+	194.291i	−0.359139	+	0.837460i
$233$	105.840			0.454248			0.227124	−	0.973866i	$-0.427068\pi$
$233$	105.840			0.454248			0.227124	+	0.973866i	$0.427068\pi$
$234$		0			0
$235$	85.8232	+	85.8232i	0.365205	+	0.365205i
$236$	−90.6035	+	153.971i	−0.383913	+	0.652419i
$237$		0			0
$238$	33.7865	+	265.113i	0.141960	+	1.11392i
$239$			149.734i			0.626502i	0.949670	+	0.313251i	$0.101418\pi$
$239$			149.734i			0.626502i	−0.949670	+	0.313251i	$0.898582\pi$
$240$		0			0
$241$	158.414			0.657321			0.328661	−	0.944448i	$-0.393403\pi$
$241$	158.414			0.657321			0.328661	+	0.944448i	$0.393403\pi$
$242$	−2.45706	+	0.313133i	−0.0101531	+	0.00129394i
$243$		0			0
$244$	−208.453	+	354.243i	−0.854316	+	1.45182i
$245$	213.766	−	213.766i	0.872515	−	0.872515i
$246$		0			0
$247$			106.435i			0.430909i
$248$	80.6307	+	201.711i	0.325124	+	0.813352i
$249$		0			0
$250$	−128.061	+	165.469i	−0.512243	+	0.661875i
$251$	8.32722	−	8.32722i	0.0331762	−	0.0331762i	−0.690324	−	0.723500i	$-0.742532\pi$
$251$	8.32722	−	8.32722i	0.0331762	−	0.0331762i	0.723500	+	0.690324i	$0.242532\pi$
$252$		0			0
$253$	−232.824	+	232.824i	−0.920254	+	0.920254i
$254$	−8.03774	−	63.0698i	−0.0316446	−	0.248306i
$255$		0			0
$256$	135.273	−	217.341i	0.528410	−	0.848990i
$257$			352.499i			1.37159i	0.727794	+	0.685796i	$0.240546\pi$
$257$			352.499i			1.37159i	−0.727794	+	0.685796i	$0.759454\pi$
$258$		0			0
$259$	−177.678	+	177.678i	−0.686015	+	0.686015i
$260$	35.0365	+	135.228i	0.134756	+	0.520107i
$261$		0			0
$262$	278.418	−	359.748i	1.06267	−	1.37308i
$263$	301.404			1.14602			0.573011	−	0.819548i	$-0.305775\pi$
$263$	301.404			1.14602			0.573011	+	0.819548i	$0.305775\pi$
$264$		0			0
$265$		−	227.715i		−	0.859302i
$266$	116.939	−	151.098i	0.439619	−	0.568036i
$267$		0			0
$268$	−173.010	+	294.012i	−0.645560	+	1.09706i
$269$	−216.782	−	216.782i	−0.805879	−	0.805879i	0.178128	−	0.984007i	$-0.442996\pi$
$269$	−216.782	−	216.782i	−0.805879	−	0.805879i	−0.984007	+	0.178128i	$0.942996\pi$
$270$		0			0
$271$	−92.3711			−0.340853			−0.170426	−	0.985370i	$-0.554514\pi$
$271$	−92.3711			−0.340853			−0.170426	+	0.985370i	$0.554514\pi$
$272$	77.9299	+	140.295i	0.286507	+	0.515790i
$273$		0			0
$274$	56.7405	+	445.226i	0.207082	+	1.62491i
$275$	152.168	+	152.168i	0.553337	+	0.553337i
$276$		0			0
$277$	−300.909	−	300.909i	−1.08631	−	1.08631i	−0.995905	−	0.0904098i	$-0.971182\pi$
$277$	−300.909	−	300.909i	−1.08631	−	1.08631i	−0.0904098	−	0.995905i	$-0.528818\pi$
$278$	−95.8391	+	123.835i	−0.344745	+	0.445449i
$279$		0			0
$280$	98.8346	−	230.468i	0.352981	−	0.823099i
$281$	−85.6163			−0.304684			−0.152342	−	0.988328i	$-0.548682\pi$
$281$	−85.6163			−0.304684			−0.152342	+	0.988328i	$0.548682\pi$
$282$		0			0
$283$	−99.4025	−	99.4025i	−0.351246	−	0.351246i	0.509327	−	0.860573i	$-0.329894\pi$
$283$	−99.4025	−	99.4025i	−0.351246	−	0.351246i	−0.860573	+	0.509327i	$0.829894\pi$
$284$	11.9737	−	3.10229i	0.0421608	−	0.0109235i
$285$		0			0
$286$	325.577	−	41.4922i	1.13838	−	0.145078i
$287$		−	465.699i		−	1.62264i
$288$		0			0
$289$	188.392			0.651875
$290$	15.7203	+	123.353i	0.0542080	+	0.425354i
$291$		0			0
$292$	−2.06033	−	7.95210i	−0.00705592	−	0.0272332i
$293$	−130.268	+	130.268i	−0.444602	+	0.444602i	−0.893555	−	0.448953i	$-0.851797\pi$
$293$	−130.268	+	130.268i	−0.444602	+	0.444602i	0.448953	+	0.893555i	$0.351797\pi$
$294$		0			0
$295$			105.085i			0.356220i
$296$	−59.4697	+	138.675i	−0.200911	+	0.468495i
$297$		0			0
$298$	222.672	+	172.332i	0.747221	+	0.578295i
$299$	312.567	−	312.567i	1.04537	−	1.04537i
$300$		0			0
$301$	−97.1356	+	97.1356i	−0.322709	+	0.322709i
$302$	258.667	−	32.9651i	0.856515	−	0.109156i
$303$		0			0
$304$	31.5263	−	110.315i	0.103705	−	0.362880i
$305$			241.771i			0.792691i
$306$		0			0
$307$	425.171	−	425.171i	1.38492	−	1.38492i	0.549286	−	0.835635i	$-0.314900\pi$
$307$	425.171	−	425.171i	1.38492	−	1.38492i	0.835635	−	0.549286i	$-0.185100\pi$
$308$	−507.786	−	298.805i	−1.64866	−	0.970145i
$309$		0			0
$310$	101.050	+	78.2053i	0.325968	+	0.252275i
$311$	−28.3005			−0.0909985			−0.0454993	−	0.998964i	$-0.514488\pi$
$311$	−28.3005			−0.0909985			−0.0454993	+	0.998964i	$0.514488\pi$
$312$		0			0
$313$		−	501.098i		−	1.60095i	−0.599366	−	0.800475i	$-0.704580\pi$
$313$		−	501.098i		−	1.60095i	0.599366	−	0.800475i	$-0.295420\pi$
$314$	−326.484	−	252.675i	−1.03976	−	0.804697i
$315$		0			0
$316$	−206.767	+	53.5718i	−0.654326	+	0.169531i
$317$	72.5630	+	72.5630i	0.228905	+	0.228905i	0.812235	−	0.583330i	$-0.198251\pi$
$317$	72.5630	+	72.5630i	0.228905	+	0.228905i	−0.583330	+	0.812235i	$0.698251\pi$
$318$		0			0
$319$	292.163			0.915871
$320$	3.74093	−	150.537i	0.0116904	−	0.470427i
$321$		0			0
$322$	−787.143	+	100.315i	−2.44454	+	0.311538i
$323$	50.8588	+	50.8588i	0.157457	+	0.157457i
$324$		0			0
$325$	−204.285	−	204.285i	−0.628570	−	0.628570i
$326$	92.6754	+	71.7240i	0.284281	+	0.220012i
$327$		0			0
$328$	−103.799	−	259.671i	−0.316461	−	0.791680i
$329$	687.237			2.08887
$330$		0			0
$331$	128.092	+	128.092i	0.386985	+	0.386985i	0.873610	−	0.486626i	$-0.161773\pi$
$331$	128.092	+	128.092i	0.386985	+	0.386985i	−0.486626	+	0.873610i	$0.661773\pi$
$332$	−106.264	−	62.5305i	−0.320071	−	0.188345i
$333$		0			0
$334$	3.51386	+	27.5722i	0.0105205	+	0.0825515i
$335$			200.663i			0.598994i
$336$		0			0
$337$	429.921			1.27573			0.637865	−	0.770148i	$-0.279818\pi$
$337$	429.921			1.27573			0.637865	+	0.770148i	$0.279818\pi$
$338$	−101.800	+	12.9736i	−0.301183	+	0.0383834i
$339$		0			0
$340$	81.3592	+	47.8755i	0.239292	+	0.140810i
$341$	212.284	−	212.284i	0.622535	−	0.622535i
$342$		0			0
$343$		−	1058.95i		−	3.08733i
$344$	−32.5118	+	75.8126i	−0.0945110	+	0.220386i
$345$		0			0
$346$	75.9107	−	98.0850i	0.219395	−	0.283483i
$347$	−360.070	+	360.070i	−1.03766	+	1.03766i	−0.0384019	+	0.999262i	$0.512227\pi$
$347$	−360.070	+	360.070i	−1.03766	+	1.03766i	−0.999262	+	0.0384019i	$0.987773\pi$
$348$		0			0
$349$	−276.674	+	276.674i	−0.792763	+	0.792763i	−0.981942	−	0.189180i	$-0.939417\pi$
$349$	−276.674	+	276.674i	−0.792763	+	0.792763i	0.189180	+	0.981942i	$0.439417\pi$
$350$	65.5632	+	514.455i	0.187324	+	1.46987i
$351$		0			0
$352$	−349.739	−	53.4319i	−0.993576	−	0.151795i
$353$			453.982i			1.28607i	0.765837	+	0.643035i	$0.222325\pi$
$353$			453.982i			1.28607i	−0.765837	+	0.643035i	$0.777675\pi$
$354$		0			0
$355$	5.14467	−	5.14467i	0.0144920	−	0.0144920i
$356$	−532.748	+	138.031i	−1.49648	+	0.387727i
$357$		0			0
$358$	−267.971	+	346.249i	−0.748523	+	0.967176i
$359$	247.893			0.690510			0.345255	−	0.938509i	$-0.387792\pi$
$359$	247.893			0.690510			0.345255	+	0.938509i	$0.387792\pi$
$360$		0			0
$361$			309.580i			0.857564i
$362$	183.349	−	236.907i	0.506489	−	0.654440i
$363$		0			0
$364$	681.703	+	401.146i	1.87281	+	1.10205i
$365$	−3.41674	−	3.41674i	−0.00936092	−	0.00936092i
$366$		0			0
$367$	−195.121			−0.531665			−0.265832	−	0.964019i	$-0.585647\pi$
$367$	−195.121			−0.531665			−0.265832	+	0.964019i	$0.585647\pi$
$368$	−416.547	+	231.380i	−1.13192	+	0.628751i
$369$		0			0
$370$	11.2203	+	88.0427i	0.0303253	+	0.237953i
$371$	−911.724	−	911.724i	−2.45748	−	2.45748i
$372$		0			0
$373$	−146.937	−	146.937i	−0.393932	−	0.393932i	0.482154	−	0.876086i	$-0.339855\pi$
$373$	−146.937	−	146.937i	−0.393932	−	0.393932i	−0.876086	+	0.482154i	$0.839855\pi$
$374$	135.747	−	175.401i	0.362961	−	0.468986i
$375$		0			0
$376$	383.199	−	153.177i	1.01915	−	0.407387i
$377$	−392.229			−1.04039
$378$		0			0
$379$	80.0235	+	80.0235i	0.211144	+	0.211144i	0.804753	−	0.593609i	$-0.202298\pi$
$379$	80.0235	+	80.0235i	0.211144	+	0.211144i	−0.593609	+	0.804753i	$0.702298\pi$
$380$	−16.9265	−	65.3299i	−0.0445433	−	0.171921i
$381$		0			0
$382$	137.795	−	17.5608i	0.360719	−	0.0459708i
$383$		−	412.277i		−	1.07644i	−0.842804	−	0.538221i	$-0.819097\pi$
$383$		−	412.277i		−	1.07644i	0.842804	−	0.538221i	$-0.180903\pi$
$384$		0			0
$385$	−346.563			−0.900165
$386$	−8.98181	−	70.4776i	−0.0232689	−	0.182584i
$387$		0			0
$388$	66.5582	−	17.2447i	0.171542	−	0.0444452i
$389$	−177.471	+	177.471i	−0.456223	+	0.456223i	−0.897414	−	0.441190i	$-0.854556\pi$
$389$	−177.471	+	177.471i	−0.456223	+	0.456223i	0.441190	+	0.897414i	$0.354556\pi$
$390$		0			0
$391$		−	298.714i		−	0.763975i
$392$	−381.530	−	954.462i	−0.973291	−	2.43485i
$393$		0			0
$394$	−17.3266	−	13.4095i	−0.0439761	−	0.0340343i
$395$	−88.8405	+	88.8405i	−0.224913	+	0.224913i
$396$		0			0
$397$	51.6079	−	51.6079i	0.129995	−	0.129995i	−0.639116	−	0.769110i	$-0.720700\pi$
$397$	51.6079	−	51.6079i	0.129995	−	0.129995i	0.769110	+	0.639116i	$0.220700\pi$
$398$	−314.405	+	40.0685i	−0.789963	+	0.100675i
$399$		0			0
$400$	151.224	+	272.244i	0.378060	+	0.680610i
$401$		−	87.1607i		−	0.217358i	−0.994077	−	0.108679i	$-0.965338\pi$
$401$		−	87.1607i		−	0.217358i	0.994077	−	0.108679i	$-0.0346621\pi$
$402$		0			0
$403$	−284.992	+	284.992i	−0.707177	+	0.707177i
$404$	−256.582	+	436.033i	−0.635104	+	1.07929i
$405$		0			0
$406$	556.819	+	430.938i	1.37148	+	1.06142i
$407$	208.531			0.512360
$408$		0			0
$409$		−	367.848i		−	0.899383i	−0.893184	−	0.449691i	$-0.851534\pi$
$409$		−	367.848i		−	0.899383i	0.893184	−	0.449691i	$-0.148466\pi$
$410$	−130.086	−	100.677i	−0.317282	−	0.245553i
$411$		0			0
$412$	−124.717	−	481.360i	−0.302710	−	1.16835i
$413$	420.738	+	420.738i	1.01874	+	1.01874i
$414$		0			0
$415$	−72.5249			−0.174759
$416$	469.525	+	71.7324i	1.12867	+	0.172434i
$417$		0			0
$418$	−157.289	+	20.0453i	−0.376291	+	0.0479552i
$419$	−20.1974	−	20.1974i	−0.0482037	−	0.0482037i	0.682594	−	0.730798i	$-0.260852\pi$
$419$	−20.1974	−	20.1974i	−0.0482037	−	0.0482037i	−0.730798	+	0.682594i	$0.760852\pi$
$420$		0			0
$421$	−353.549	−	353.549i	−0.839784	−	0.839784i	0.149046	−	0.988830i	$-0.452380\pi$
$421$	−353.549	−	353.549i	−0.839784	−	0.839784i	−0.988830	+	0.149046i	$0.952380\pi$
$422$	377.770	+	292.366i	0.895189	+	0.692811i
$423$		0			0
$424$	−711.585	−	305.159i	−1.67827	−	0.719714i
$425$	−195.231			−0.459368
$426$		0			0
$427$	968.000	+	968.000i	2.26698	+	2.26698i
$428$	−337.560	+	573.647i	−0.788692	+	1.34030i
$429$		0			0
$430$	6.13410	+	48.1325i	0.0142654	+	0.111936i
$431$		−	534.507i		−	1.24015i	−0.784541	−	0.620077i	$-0.787101\pi$
$431$		−	534.507i		−	1.24015i	0.784541	−	0.620077i	$-0.212899\pi$
$432$		0			0
$433$	102.953			0.237768			0.118884	−	0.992908i	$-0.462068\pi$
$433$	102.953			0.237768			0.118884	+	0.992908i	$0.462068\pi$
$434$	717.701	−	91.4653i	1.65369	−	0.210750i
$435$		0			0
$436$	−5.30639	+	9.01763i	−0.0121706	+	0.0206826i
$437$	−151.004	+	151.004i	−0.345547	+	0.345547i
$438$		0			0
$439$		−	323.949i		−	0.737925i	−0.929444	−	0.368963i	$-0.879713\pi$
$439$		−	323.949i		−	0.737925i	0.929444	−	0.368963i	$-0.120287\pi$
$440$	−193.242	+	77.2451i	−0.439186	+	0.175557i
$441$		0			0
$442$	−182.241	+	235.476i	−0.412310	+	0.532750i
$443$	36.0517	−	36.0517i	0.0813809	−	0.0813809i	−0.665245	−	0.746625i	$-0.731673\pi$
$443$	36.0517	−	36.0517i	0.0813809	−	0.0813809i	0.746625	+	0.665245i	$0.231673\pi$
$444$		0			0
$445$	−228.903	+	228.903i	−0.514388	+	0.514388i
$446$	−21.1530	−	165.981i	−0.0474282	−	0.372155i
$447$		0			0
$448$	−587.739	−	617.695i	−1.31192	−	1.37878i
$449$			556.262i			1.23889i	0.785040	+	0.619445i	$0.212642\pi$
$449$			556.262i			1.23889i	−0.785040	+	0.619445i	$0.787358\pi$
$450$		0			0
$451$	−273.282	+	273.282i	−0.605947	+	0.605947i
$452$	−28.4820	−	109.930i	−0.0630133	−	0.243208i
$453$		0			0
$454$	125.437	−	162.078i	0.276292	−	0.357000i
$455$	465.262			1.02255
$456$		0			0
$457$			118.453i			0.259196i	0.991567	+	0.129598i	$0.0413687\pi$
$457$			118.453i			0.259196i	−0.991567	+	0.129598i	$0.958631\pi$
$458$	206.049	−	266.238i	0.449888	−	0.581305i
$459$		0			0
$460$	−142.146	+	241.562i	−0.309014	+	0.525136i
$461$	−231.411	−	231.411i	−0.501977	−	0.501977i	0.410075	−	0.912052i	$-0.365503\pi$
$461$	−231.411	−	231.411i	−0.501977	−	0.501977i	−0.912052	+	0.410075i	$0.865503\pi$
$462$		0			0
$463$	256.298			0.553559			0.276780	−	0.960933i	$-0.410733\pi$
$463$	256.298			0.553559			0.276780	+	0.960933i	$0.410733\pi$
$464$	406.530	+	116.179i	0.876143	+	0.250387i
$465$		0			0
$466$	−26.7604	−	209.981i	−0.0574258	−	0.450603i
$467$	529.492	+	529.492i	1.13382	+	1.13382i	0.989537	+	0.144278i	$0.0460859\pi$
$467$	529.492	+	529.492i	1.13382	+	1.13382i	0.144278	+	0.989537i	$0.453914\pi$
$468$		0			0
$469$	803.413	+	803.413i	1.71303	+	1.71303i
$470$	148.570	−	191.969i	0.316106	−	0.408444i
$471$		0			0
$472$	328.379	+	140.823i	0.695718	+	0.298355i
$473$	114.003			0.241020
$474$		0			0
$475$	98.6921	+	98.6921i	0.207773	+	0.207773i
$476$	517.429	−	134.062i	1.08704	−	0.281643i
$477$		0			0
$478$	297.065	−	37.8586i	0.621475	−	0.0792021i
$479$			315.124i			0.657879i	0.944351	+	0.328939i	$0.106691\pi$
$479$			315.124i			0.657879i	−0.944351	+	0.328939i	$0.893309\pi$
$480$		0			0
$481$	−279.953			−0.582022
$482$	−40.0534	−	314.287i	−0.0830983	−	0.652048i
$483$		0			0
$484$	1.24248	+	4.79552i	0.00256711	+	0.00990811i
$485$	28.5977	−	28.5977i	0.0589644	−	0.0589644i
$486$		0			0
$487$			490.083i			1.00633i	0.864190	+	0.503165i	$0.167831\pi$
$487$			490.083i			1.00633i	−0.864190	+	0.503165i	$0.832169\pi$
$488$	755.508	+	323.995i	1.54817	+	0.663924i
$489$		0			0
$490$	−478.151	−	370.054i	−0.975817	−	0.755211i
$491$	583.373	−	583.373i	1.18813	−	1.18813i	0.210550	−	0.977583i	$-0.432475\pi$
$491$	583.373	−	583.373i	1.18813	−	1.18813i	0.977583	−	0.210550i	$-0.0675254\pi$
$492$		0			0
$493$	−187.423	+	187.423i	−0.380168	+	0.380168i
$494$	211.161	−	26.9108i	0.427452	−	0.0544754i
$495$		0			0
$496$	379.799	−	210.968i	0.765724	−	0.425339i
$497$		−	41.1964i		−	0.0828901i
$498$		0			0
$499$	310.729	−	310.729i	0.622703	−	0.622703i	−0.323519	−	0.946222i	$-0.604866\pi$
$499$	310.729	−	310.729i	0.622703	−	0.622703i	0.946222	+	0.323519i	$0.104866\pi$
$500$	360.661	+	212.230i	0.721322	+	0.424459i
$501$		0			0
$502$	−18.6263	−	14.4154i	−0.0371041	−	0.0287159i
$503$	−722.400			−1.43618			−0.718091	−	0.695949i	$-0.754984\pi$
$503$	−722.400			−1.43618			−0.718091	+	0.695949i	$0.754984\pi$
$504$		0			0
$505$			297.592i			0.589291i
$506$	520.779	+	403.045i	1.02921	+	0.796532i
$507$		0			0
$508$	−123.095	+	31.8930i	−0.242313	+	0.0627815i
$509$	−162.106	−	162.106i	−0.318479	−	0.318479i	0.529704	−	0.848183i	$-0.322303\pi$
$509$	−162.106	−	162.106i	−0.318479	−	0.318479i	−0.848183	+	0.529704i	$0.822303\pi$
$510$		0			0
$511$	−27.3598			−0.0535417
$512$	−465.397	−	213.423i	−0.908979	−	0.416841i
$513$		0			0
$514$	699.342	−	89.1256i	1.36059	−	0.173396i
$515$	−206.823	−	206.823i	−0.401598	−	0.401598i
$516$		0			0
$517$	−403.285	−	403.285i	−0.780049	−	0.780049i
$518$	397.429	+	307.581i	0.767237	+	0.593786i
$519$		0			0
$520$	259.427	−	103.702i	0.498899	−	0.199426i
$521$	184.583			0.354285			0.177143	−	0.984185i	$-0.443315\pi$
$521$	184.583			0.354285			0.177143	+	0.984185i	$0.443315\pi$
$522$		0			0
$523$	−593.324	−	593.324i	−1.13446	−	1.13446i	−0.989426	−	0.145035i	$-0.953670\pi$
$523$	−593.324	−	593.324i	−1.13446	−	1.13446i	−0.145035	−	0.989426i	$-0.546330\pi$
$524$	−784.118	−	461.411i	−1.49641	−	0.880555i
$525$		0			0
$526$	−76.2067	−	597.971i	−0.144880	−	1.13683i
$527$			272.362i			0.516815i
$528$		0			0
$529$	357.907			0.676573
$530$	−451.776	+	57.5753i	−0.852408	+	0.108633i
$531$		0			0
$532$	−329.337	−	193.797i	−0.619055	−	0.364281i
$533$	366.882	−	366.882i	0.688334	−	0.688334i
$534$		0			0
$535$			391.513i			0.731801i
$536$	627.050	+	268.906i	1.16987	+	0.501691i
$537$		0			0
$538$	−375.274	+	484.895i	−0.697535	+	0.901293i
$539$	−1004.49	+	1004.49i	−1.86362	+	1.86362i
$540$		0			0
$541$	−550.411	+	550.411i	−1.01739	+	1.01739i	−0.0175489	+	0.999846i	$0.505586\pi$
$541$	−550.411	+	550.411i	−1.01739	+	1.01739i	−0.999846	+	0.0175489i	$0.994414\pi$
$542$	23.3550	+	183.260i	0.0430905	+	0.338118i
$543$		0			0
$544$	258.635	−	190.081i	0.475431	−	0.349414i
$545$			6.15452i			0.0112927i
$546$		0			0
$547$	−177.395	+	177.395i	−0.324305	+	0.324305i	−0.850416	−	0.526111i	$-0.823650\pi$
$547$	−177.395	+	177.395i	−0.324305	+	0.324305i	0.526111	+	0.850416i	$0.323650\pi$
$548$	868.962	−	225.141i	1.58570	−	0.410842i
$549$		0			0
$550$	263.420	−	340.367i	0.478945	−	0.618850i
$551$	189.489			0.343901
$552$		0			0
$553$			711.398i			1.28643i
$554$	−520.908	+	673.071i	−0.940267	+	1.21493i
$555$		0			0
$556$	269.914	+	158.830i	0.485457	+	0.285666i
$557$	−374.619	−	374.619i	−0.672566	−	0.672566i	0.285741	−	0.958307i	$-0.407760\pi$
$557$	−374.619	−	374.619i	−0.672566	−	0.672566i	−0.958307	+	0.285741i	$0.907760\pi$
$558$		0			0
$559$	−153.049			−0.273790
$560$	−482.226	−	137.812i	−0.861119	−	0.246093i
$561$		0			0
$562$	21.6472	+	169.859i	0.0385181	+	0.302240i
$563$	−370.252	−	370.252i	−0.657640	−	0.657640i	0.297181	−	0.954821i	$-0.403954\pi$
$563$	−370.252	−	370.252i	−0.657640	−	0.657640i	−0.954821	+	0.297181i	$0.903954\pi$
$564$		0			0
$565$	−47.2331	−	47.2331i	−0.0835984	−	0.0835984i
$566$	−172.077	+	222.343i	−0.304023	+	0.392832i
$567$		0			0
$568$	−9.18221	−	22.9708i	−0.0161659	−	0.0404416i
$569$	30.3419			0.0533249			0.0266625	−	0.999644i	$-0.491512\pi$
$569$	30.3419			0.0533249			0.0266625	+	0.999644i	$0.491512\pi$
$570$		0			0
$571$	−336.964	−	336.964i	−0.590130	−	0.590130i	0.347537	−	0.937666i	$-0.387018\pi$
$571$	−336.964	−	336.964i	−0.590130	−	0.590130i	−0.937666	+	0.347537i	$0.887018\pi$
$572$	−164.637	−	635.439i	−0.287828	−	1.11091i
$573$		0			0
$574$	−923.925	+	117.747i	−1.60963	+	0.205134i
$575$		−	579.659i		−	1.00810i
$576$		0			0
$577$	959.056			1.66214			0.831071	−	0.556166i	$-0.187728\pi$
$577$	959.056			1.66214			0.831071	+	0.556166i	$0.187728\pi$
$578$	−47.6328	−	373.761i	−0.0824097	−	0.646645i
$579$		0			0
$580$	240.751	−	62.3768i	0.415088	−	0.107546i
$581$	−290.375	+	290.375i	−0.499784	+	0.499784i
$582$		0			0
$583$			1070.04i			1.83540i
$584$	−15.2557	+	6.09820i	−0.0261227	+	0.0104421i
$585$		0			0
$586$	291.383	+	225.510i	0.497241	+	0.384829i
$587$	242.869	−	242.869i	0.413747	−	0.413747i	−0.469295	−	0.883042i	$-0.655492\pi$
$587$	242.869	−	242.869i	0.413747	−	0.413747i	0.883042	+	0.469295i	$0.155492\pi$
$588$		0			0
$589$	137.682	−	137.682i	0.233756	−	0.233756i
$590$	208.484	−	26.5696i	0.353362	−	0.0450332i
$591$		0			0
$592$	290.160	+	82.9229i	0.490136	+	0.140072i
$593$		−	280.646i		−	0.473265i	−0.971599	−	0.236633i	$-0.923956\pi$
$593$		−	280.646i		−	0.473265i	0.971599	−	0.236633i	$-0.0760438\pi$
$594$		0			0
$595$	222.321	−	222.321i	0.373649	−	0.373649i
$596$	285.598	−	485.343i	0.479192	−	0.814334i
$597$		0			0
$598$	−699.147	−	541.089i	−1.16914	−	0.904831i
$599$	−945.632			−1.57868			−0.789342	−	0.613953i	$-0.789578\pi$
$599$	−945.632			−1.57868			−0.789342	+	0.613953i	$0.789578\pi$
$600$		0			0
$601$		−	414.239i		−	0.689250i	−0.938740	−	0.344625i	$-0.888006\pi$
$601$		−	414.239i		−	0.689250i	0.938740	−	0.344625i	$-0.111994\pi$
$602$	217.272	+	168.153i	0.360917	+	0.279324i
$603$		0			0
$604$	−130.803	−	504.849i	−0.216560	−	0.835843i
$605$	2.06047	+	2.06047i	0.00340573	+	0.00340573i
$606$		0			0
$607$	214.881			0.354005			0.177003	−	0.984210i	$-0.443360\pi$
$607$	214.881			0.354005			0.177003	+	0.984210i	$0.443360\pi$
$608$	−226.832	−	34.6546i	−0.373079	−	0.0569977i
$609$		0			0
$610$	479.662	−	61.1291i	0.786331	−	0.100212i
$611$	541.411	+	541.411i	0.886107	+	0.886107i
$612$		0			0
$613$	238.136	+	238.136i	0.388476	+	0.388476i	0.874143	−	0.485668i	$-0.161424\pi$
$613$	238.136	+	238.136i	0.388476	+	0.388476i	−0.485668	+	0.874143i	$0.661424\pi$
$614$	−951.018	−	736.019i	−1.54889	−	1.19873i
$615$		0			0
$616$	−464.427	+	1082.97i	−0.753939	+	1.75807i
$617$	−223.561			−0.362335			−0.181167	−	0.983452i	$-0.557988\pi$
$617$	−223.561			−0.362335			−0.181167	+	0.983452i	$0.557988\pi$
$618$		0			0
$619$	35.0122	+	35.0122i	0.0565626	+	0.0565626i	0.734822	−	0.678260i	$-0.237266\pi$
$619$	35.0122	+	35.0122i	0.0565626	+	0.0565626i	−0.678260	+	0.734822i	$0.737266\pi$
$620$	129.606	−	220.252i	0.209042	−	0.355245i
$621$		0			0
$622$	7.15548	+	56.1470i	0.0115040	+	0.0902684i
$623$			1832.96i			2.94215i
$624$		0			0
$625$	−240.450			−0.384721
$626$	−994.154	+	126.697i	−1.58811	+	0.202392i
$627$		0			0
$628$	−418.747	+	711.615i	−0.666795	+	1.13315i
$629$	−133.773	+	133.773i	−0.212675	+	0.212675i
$630$		0			0
$631$		−	613.896i		−	0.972894i	−0.873710	−	0.486447i	$-0.838293\pi$
$631$		−	613.896i		−	0.972894i	0.873710	−	0.486447i	$-0.161707\pi$
$632$	158.563	+	396.671i	0.250890	+	0.627645i
$633$		0			0
$634$	125.615	−	162.308i	0.198131	−	0.256007i
$635$	−52.8896	+	52.8896i	−0.0832908	+	0.0832908i
$636$		0			0
$637$	1348.53	−	1348.53i	2.11701	−	2.11701i
$638$	−73.8702	−	579.637i	−0.115784	−	0.908522i
$639$		0			0
$640$	−299.603	+	30.6397i	−0.468130	+	0.0478745i
$641$		−	340.013i		−	0.530442i	−0.964188	−	0.265221i	$-0.914555\pi$
$641$		−	340.013i		−	0.530442i	0.964188	−	0.265221i	$-0.0854449\pi$
$642$		0			0
$643$	−516.730	+	516.730i	−0.803624	+	0.803624i	−0.983660	−	0.180036i	$-0.942379\pi$
$643$	−516.730	+	516.730i	−0.803624	+	0.803624i	0.180036	+	0.983660i	$0.442379\pi$
$644$	398.041	+	1536.29i	0.618076	+	2.38554i
$645$		0			0
$646$	88.0423	−	113.761i	0.136288	−	0.176100i
$647$	541.491			0.836926			0.418463	−	0.908234i	$-0.362569\pi$
$647$	541.491			0.836926			0.418463	+	0.908234i	$0.362569\pi$
$648$		0			0
$649$		−	493.797i		−	0.760858i
$650$	−353.641	+	456.944i	−0.544063	+	0.702990i
$651$		0			0
$652$	118.865	−	201.998i	0.182309	−	0.309814i
$653$	−329.446	−	329.446i	−0.504512	−	0.504512i	0.408325	−	0.912837i	$-0.366113\pi$
$653$	−329.446	−	329.446i	−0.504512	−	0.504512i	−0.912837	+	0.408325i	$0.866113\pi$
$654$		0			0
$655$	−535.160			−0.817038
$656$	−488.931	+	271.588i	−0.745321	+	0.414006i
$657$		0			0
$658$	−173.760	−	1363.45i	−0.264073	−	2.07211i
$659$	70.8742	+	70.8742i	0.107548	+	0.107548i	0.758833	−	0.651285i	$-0.225770\pi$
$659$	70.8742	+	70.8742i	0.107548	+	0.107548i	−0.651285	+	0.758833i	$0.725770\pi$
$660$		0			0
$661$	−192.446	−	192.446i	−0.291143	−	0.291143i	0.546388	−	0.837532i	$-0.316002\pi$
$661$	−192.446	−	192.446i	−0.291143	−	0.291143i	−0.837532	+	0.546388i	$0.816002\pi$
$662$	221.742	−	286.515i	0.334957	−	0.432802i
$663$		0			0
$664$	−97.1899	+	226.632i	−0.146370	+	0.341314i
$665$	−224.772			−0.338004
$666$		0			0
$667$	−556.474	−	556.474i	−0.834294	−	0.834294i
$668$	53.8136	−	13.9427i	0.0805592	−	0.0208723i
$669$		0			0
$670$	398.106	−	50.7354i	0.594188	−	0.0757245i
$671$		−	1136.09i		−	1.69313i
$672$		0			0
$673$	−672.958			−0.999937			−0.499968	−	0.866044i	$-0.666655\pi$
$673$	−672.958			−0.999937			−0.499968	+	0.866044i	$0.666655\pi$
$674$	−108.701	−	852.943i	−0.161277	−	1.26549i
$675$		0			0
$676$	51.4779	+	198.686i	0.0761508	+	0.293914i
$677$	569.590	−	569.590i	0.841344	−	0.841344i	−0.147690	−	0.989034i	$-0.547184\pi$
$677$	569.590	−	569.590i	0.841344	−	0.841344i	0.989034	+	0.147690i	$0.0471837\pi$
$678$		0			0
$679$		−	228.999i		−	0.337259i
$680$	74.4120	−	173.518i	0.109429	−	0.255173i
$681$		0			0
$682$	−474.836	−	367.489i	−0.696241	−	0.538840i
$683$	474.354	−	474.354i	0.694515	−	0.694515i	−0.268707	−	0.963222i	$-0.586596\pi$
$683$	474.354	−	474.354i	0.694515	−	0.694515i	0.963222	+	0.268707i	$0.0865963\pi$
$684$		0			0
$685$	373.362	−	373.362i	0.545054	−	0.545054i
$686$	−2100.91	+	267.745i	−3.06256	+	0.390298i
$687$		0			0
$688$	158.629	+	45.3335i	0.230565	+	0.0658917i
$689$		−	1436.53i		−	2.08495i
$690$		0			0
$691$	399.972	−	399.972i	0.578831	−	0.578831i	−0.355750	−	0.934581i	$-0.615775\pi$
$691$	399.972	−	399.972i	0.578831	−	0.578831i	0.934581	+	0.355750i	$0.115775\pi$
$692$	−213.789	−	125.803i	−0.308944	−	0.181797i
$693$		0			0
$694$	805.401	+	623.322i	1.16052	+	0.898158i
$695$	184.216			0.265059
$696$		0			0
$697$		−	350.622i		−	0.503045i
$698$	618.863	+	478.955i	0.886623	+	0.686181i
$699$		0			0
$700$	1004.08	−	260.149i	1.43440	−	0.371641i
$701$	218.780	+	218.780i	0.312098	+	0.312098i	0.845722	−	0.533624i	$-0.179170\pi$
$701$	218.780	+	218.780i	0.312098	+	0.312098i	−0.533624	+	0.845722i	$0.679170\pi$
$702$		0			0
$703$	135.248			0.192386
$704$	−17.5787	+	707.375i	−0.0249698	+	1.00479i
$705$		0			0
$706$	900.680	−	114.785i	1.27575	−	0.162584i
$707$	1191.50	+	1191.50i	1.68529	+	1.68529i
$708$		0			0
$709$	733.592	+	733.592i	1.03469	+	1.03469i	0.999376	+	0.0353089i	$0.0112415\pi$
$709$	733.592	+	733.592i	1.03469	+	1.03469i	0.0353089	+	0.999376i	$0.488759\pi$
$710$	−11.5076	−	8.90601i	−0.0162078	−	0.0125437i
$711$		0			0
$712$	408.546	+	1022.05i	0.573801	+	1.43546i
$713$	−808.664			−1.13417
$714$		0			0
$715$	−273.026	−	273.026i	−0.381854	−	0.381854i
$716$	754.695	+	444.097i	1.05404	+	0.620248i
$717$		0			0
$718$	−62.6771	−	491.808i	−0.0872939	−	0.684970i
$719$			773.403i			1.07567i	0.843052	+	0.537833i	$0.180757\pi$
$719$			773.403i			1.07567i	−0.843052	+	0.537833i	$0.819243\pi$
$720$		0			0
$721$	−1656.15			−2.29702
$722$	614.193	−	78.2741i	0.850683	−	0.108413i
$723$		0			0
$724$	−516.371	−	303.857i	−0.713220	−	0.419691i
$725$	−363.696	+	363.696i	−0.501650	+	0.501650i
$726$		0			0
$727$		−	158.236i		−	0.217656i	−0.994061	−	0.108828i	$-0.965290\pi$
$727$		−	158.236i		−	0.217656i	0.994061	−	0.108828i	$-0.0347098\pi$
$728$	623.493	−	1453.89i	0.856447	−	1.99711i
$729$		0			0
$730$	−5.91476	+	7.64253i	−0.00810241	+	0.0104692i
$731$	−73.1328	+	73.1328i	−0.100045	+	0.100045i
$732$		0			0
$733$	925.166	−	925.166i	1.26216	−	1.26216i	0.312122	−	0.950042i	$-0.398960\pi$
$733$	925.166	−	925.166i	1.26216	−	1.26216i	0.950042	−	0.312122i	$-0.101040\pi$
$734$	49.3342	+	387.111i	0.0672128	+	0.527399i
$735$		0			0
$736$	564.367	+	767.908i	0.766804	+	1.04335i
$737$		−	942.920i		−	1.27940i
$738$		0			0
$739$	313.893	−	313.893i	0.424754	−	0.424754i	−0.462083	−	0.886837i	$-0.652898\pi$
$739$	313.893	−	313.893i	0.424754	−	0.424754i	0.886837	+	0.462083i	$0.152898\pi$
$740$	171.836	−	44.5213i	0.232210	−	0.0601639i
$741$		0			0
$742$	−1578.30	+	2039.34i	−2.12709	+	2.74843i
$743$	116.397			0.156658			0.0783291	−	0.996928i	$-0.475042\pi$
$743$	116.397			0.156658			0.0783291	+	0.996928i	$0.475042\pi$
$744$		0			0
$745$		−	331.246i		−	0.444626i
$746$	−254.364	+	328.667i	−0.340971	+	0.440572i
$747$		0			0
$748$	−382.309	−	224.968i	−0.511109	−	0.300760i
$749$	1567.54	+	1567.54i	2.09284	+	2.09284i
$750$		0			0
$751$	−700.738			−0.933074			−0.466537	−	0.884502i	$-0.654499\pi$
$751$	−700.738			−0.933074			−0.466537	+	0.884502i	$0.654499\pi$
$752$	−400.785	−	721.520i	−0.532958	−	0.959468i
$753$		0			0
$754$	99.1708	+	778.164i	0.131526	+	1.03205i
$755$	−216.916	−	216.916i	−0.287306	−	0.287306i
$756$		0			0
$757$	248.839	+	248.839i	0.328717	+	0.328717i	0.852099	−	0.523381i	$-0.175330\pi$
$757$	248.839	+	248.839i	0.328717	+	0.328717i	−0.523381	+	0.852099i	$0.675330\pi$
$758$	138.530	−	178.996i	0.182757	−	0.236142i
$759$		0			0
$760$	−125.332	+	50.0993i	−0.164910	+	0.0659201i
$761$	1269.42			1.66809			0.834046	−	0.551695i	$-0.186019\pi$
$761$	1269.42			1.66809			0.834046	+	0.551695i	$0.186019\pi$
$762$		0			0
$763$	24.6414	+	24.6414i	0.0322955	+	0.0322955i
$764$	−69.6798	−	268.938i	−0.0912039	−	0.352013i
$765$		0			0
$766$	−817.938	+	104.240i	−1.06780	+	0.136083i
$767$			662.923i			0.864306i
$768$		0			0
$769$	261.949			0.340636			0.170318	−	0.985389i	$-0.445520\pi$
$769$	261.949			0.340636			0.170318	+	0.985389i	$0.445520\pi$
$770$	87.6248	+	687.566i	0.113798	+	0.892943i
$771$		0			0
$772$	−137.553	+	35.6390i	−0.178178	+	0.0461645i
$773$	−0.513628	+	0.513628i	−0.000664461	+	0.000664461i	−0.707439	−	0.706774i	$-0.750150\pi$
$773$	−0.513628	+	0.513628i	−0.000664461	+	0.000664461i	0.706774	+	0.707439i	$0.250150\pi$
$774$		0			0
$775$			528.521i			0.681963i
$776$	−51.0413	−	127.688i	−0.0657748	−	0.164547i
$777$		0			0
$778$	396.966	+	307.222i	0.510239	+	0.394887i
$779$	−177.244	+	177.244i	−0.227528	+	0.227528i
$780$		0			0
$781$	−24.1749	+	24.1749i	−0.0309538	+	0.0309538i
$782$	−592.635	+	75.5266i	−0.757845	+	0.0965814i
$783$		0			0
$784$	−1797.14	+	998.264i	−2.29227	+	1.27330i
$785$			485.677i			0.618696i
$786$		0			0
$787$	−40.5482	+	40.5482i	−0.0515226	+	0.0515226i	−0.732399	−	0.680876i	$-0.761599\pi$
$787$	−40.5482	+	40.5482i	−0.0515226	+	0.0515226i	0.680876	+	0.732399i	$0.261599\pi$
$788$	−22.2230	+	37.7656i	−0.0282018	+	0.0479258i
$789$		0			0
$790$	198.718	+	153.793i	0.251542	+	0.194675i
$791$	−378.223			−0.478158
$792$		0			0
$793$			1525.20i			1.92333i
$794$	−115.436	−	89.3391i	−0.145385	−	0.112518i
$795$		0			0
$796$	158.988	+	613.635i	0.199734	+	0.770898i
$797$	−316.113	−	316.113i	−0.396629	−	0.396629i	0.480413	−	0.877042i	$-0.340487\pi$
$797$	−316.113	−	316.113i	−0.396629	−	0.396629i	−0.877042	+	0.480413i	$0.840487\pi$
$798$		0			0
$799$	517.416			0.647580
$800$	501.884	−	368.855i	0.627355	−	0.461069i
$801$		0			0
$802$	−172.923	+	22.0376i	−0.215614	+	0.0274783i
$803$	16.0553	+	16.0553i	0.0199942	+	0.0199942i
$804$		0			0
$805$	660.090	+	660.090i	0.819987	+	0.819987i
$806$	637.468	+	493.354i	0.790904	+	0.612102i
$807$		0			0
$808$	929.943	+	398.800i	1.15092	+	0.493565i
$809$	701.360			0.866947			0.433473	−	0.901166i	$-0.357288\pi$
$809$	701.360			0.866947			0.433473	+	0.901166i	$0.357288\pi$
$810$		0			0
$811$	−266.653	−	266.653i	−0.328795	−	0.328795i	0.523333	−	0.852128i	$-0.324688\pi$
$811$	−266.653	−	266.653i	−0.328795	−	0.328795i	−0.852128	+	0.523333i	$0.824688\pi$
$812$	714.174	−	1213.66i	0.879525	−	1.49466i
$813$		0			0
$814$	−52.7247	−	413.715i	−0.0647724	−	0.508249i
$815$		−	137.864i		−	0.169158i
$816$		0			0
$817$	73.9392			0.0905008
$818$	−729.793	+	93.0063i	−0.892167	+	0.113700i
$819$		0			0
$820$	−166.847	+	283.539i	−0.203472	+	0.345779i
$821$	468.141	−	468.141i	0.570209	−	0.570209i	−0.361978	−	0.932187i	$-0.617898\pi$
$821$	468.141	−	468.141i	0.570209	−	0.570209i	0.932187	+	0.361978i	$0.117898\pi$
$822$		0			0
$823$			285.382i			0.346758i	0.984855	+	0.173379i	$0.0554685\pi$
$823$			285.382i			0.346758i	−0.984855	+	0.173379i	$0.944531\pi$
$824$	−923.462	+	369.138i	−1.12071	+	0.447983i
$825$		0			0
$826$	728.346	−	941.104i	0.881775	−	1.13935i
$827$	560.223	−	560.223i	0.677416	−	0.677416i	−0.281999	−	0.959415i	$-0.590997\pi$
$827$	560.223	−	560.223i	0.677416	−	0.677416i	0.959415	+	0.281999i	$0.0909974\pi$
$828$		0			0
$829$	−350.009	+	350.009i	−0.422206	+	0.422206i	−0.885963	−	0.463757i	$-0.846501\pi$
$829$	−350.009	+	350.009i	−0.422206	+	0.422206i	0.463757	+	0.885963i	$0.346501\pi$
$830$	18.3371	+	143.886i	0.0220929	+	0.173357i
$831$		0			0
$832$	23.5995	−	949.652i	0.0283648	−	1.14141i
$833$		−	1288.77i		−	1.54714i
$834$		0			0
$835$	23.1218	−	23.1218i	0.0276908	−	0.0276908i
$836$	79.5379	+	306.987i	0.0951410	+	0.367209i
$837$		0			0
$838$	−34.9640	+	45.1773i	−0.0417231	+	0.0539109i
$839$	−635.294			−0.757204			−0.378602	−	0.925560i	$-0.623595\pi$
$839$	−635.294			−0.757204			−0.378602	+	0.925560i	$0.623595\pi$
$840$		0			0
$841$		−	142.701i		−	0.169680i
$842$	−612.034	+	790.816i	−0.726881	+	0.939211i
$843$		0			0
$844$	484.526	−	823.400i	0.574083	−	0.975592i
$845$	85.3683	+	85.3683i	0.101028	+	0.101028i
$846$		0			0
$847$	16.4994			0.0194798
$848$	−425.504	+	1488.91i	−0.501774	+	1.75579i
$849$		0			0
$850$	49.3622	+	387.330i	0.0580731	+	0.455683i
$851$	−397.182	−	397.182i	−0.466724	−	0.466724i
$852$		0			0
$853$	−729.331	−	729.331i	−0.855018	−	0.855018i	0.135728	−	0.990746i	$-0.456663\pi$
$853$	−729.331	−	729.331i	−0.855018	−	0.855018i	−0.990746	+	0.135728i	$0.956663\pi$
$854$	1675.72	−	2165.22i	1.96220	−	2.53538i
$855$		0			0
$856$	1223.44	+	524.663i	1.42925	+	0.612925i
$857$	−1560.63			−1.82104			−0.910522	−	0.413461i	$-0.864320\pi$
$857$	−1560.63			−1.82104			−0.910522	+	0.413461i	$0.864320\pi$
$858$		0			0
$859$	−880.955	−	880.955i	−1.02556	−	1.02556i	−0.999665	−	0.0258940i	$-0.991757\pi$
$859$	−880.955	−	880.955i	−1.02556	−	1.02556i	−0.0258940	−	0.999665i	$-0.508243\pi$
$860$	93.9416	−	24.3395i	0.109234	−	0.0283018i
$861$		0			0
$862$	−1060.44	+	135.144i	−1.23021	+	0.156780i
$863$			314.655i			0.364606i	0.983242	+	0.182303i	$0.0583551\pi$
$863$			314.655i			0.364606i	−0.983242	+	0.182303i	$0.941645\pi$
$864$		0			0
$865$	−145.911			−0.168683
$866$	−26.0307	−	204.255i	−0.0300585	−	0.235860i
$867$		0			0
$868$	−362.926	−	1400.76i	−0.418117	−	1.61378i
$869$	417.464	−	417.464i	0.480396	−	0.480396i
$870$		0			0
$871$			1265.87i			1.45335i
$872$	19.2322	+	8.24762i	0.0220553	+	0.00945828i
$873$		0			0
$874$	337.765	+	261.405i	0.386458	+	0.299090i
$875$	985.537	−	985.537i	1.12633	−	1.12633i
$876$		0			0
$877$	−377.957	+	377.957i	−0.430966	+	0.430966i	−0.888957	−	0.457991i	$-0.848569\pi$
$877$	−377.957	+	377.957i	−0.430966	+	0.430966i	0.457991	+	0.888957i	$0.348569\pi$
$878$	−642.700	+	81.9070i	−0.732005	+	0.0932882i
$879$		0			0
$880$	202.110	+	363.852i	0.229670	+	0.413468i
$881$			1208.58i			1.37183i	0.727681	+	0.685916i	$0.240598\pi$
$881$			1208.58i			1.37183i	−0.727681	+	0.685916i	$0.759402\pi$
$882$		0			0
$883$	840.437	−	840.437i	0.951797	−	0.951797i	−0.0470934	−	0.998890i	$-0.514996\pi$
$883$	840.437	−	840.437i	0.951797	−	0.951797i	0.998890	+	0.0470934i	$0.0149958\pi$
$884$	513.251	+	302.020i	0.580600	+	0.341652i
$885$		0			0
$886$	−80.6403	−	62.4097i	−0.0910161	−	0.0704398i
$887$	−343.674			−0.387456			−0.193728	−	0.981055i	$-0.562058\pi$
$887$	−343.674			−0.387456			−0.193728	+	0.981055i	$0.562058\pi$
$888$		0			0
$889$			423.518i			0.476399i
$890$	512.008	+	396.257i	0.575290	+	0.445233i
$891$		0			0
$892$	−323.951	+	83.9331i	−0.363173	+	0.0940954i
$893$	−261.561	−	261.561i	−0.292901	−	0.292901i
$894$		0			0
$895$	515.079			0.575507
$896$	−1076.88	+	1322.23i	−1.20187	+	1.47570i
$897$		0			0
$898$	1103.60	−	140.645i	1.22895	−	0.156620i
$899$	507.382	+	507.382i	0.564385	+	0.564385i
$900$		0			0
$901$	−686.432	−	686.432i	−0.761855	−	0.761855i
$902$	611.276	+	473.083i	0.677689	+	0.524482i
$903$		0			0
$904$	−210.895	+	84.3017i	−0.233291	+	0.0932541i
$905$	−352.423			−0.389417
$906$		0			0
$907$	319.782	+	319.782i	0.352571	+	0.352571i	0.861065	−	0.508494i	$-0.169798\pi$
$907$	319.782	+	319.782i	0.352571	+	0.352571i	−0.508494	+	0.861065i	$0.669798\pi$
$908$	−353.271	−	207.881i	−0.389065	−	0.228943i
$909$		0			0
$910$	−117.636	−	923.058i	−0.129271	−	1.01435i
$911$			444.391i			0.487806i	0.969800	+	0.243903i	$0.0784279\pi$
$911$			444.391i			0.487806i	−0.969800	+	0.243903i	$0.921572\pi$
$912$		0			0
$913$	340.796			0.373271
$914$	235.004	−	29.9495i	0.257116	−	0.0327675i
$915$		0			0
$916$	−580.301	−	341.476i	−0.633516	−	0.372790i
$917$	−2142.67	+	2142.67i	−2.33661	+	2.33661i
$918$		0			0
$919$			1096.81i			1.19348i	0.802435	+	0.596739i	$0.203537\pi$
$919$			1096.81i			1.19348i	−0.802435	+	0.596739i	$0.796463\pi$
$920$	515.189	+	220.936i	0.559988	+	0.240147i
$921$		0			0
$922$	−400.600	+	517.620i	−0.434490	+	0.561409i
$923$	32.4549	−	32.4549i	0.0351624	−	0.0351624i
$924$		0			0
$925$	−259.588	+	259.588i	−0.280635	+	0.280635i
$926$	−64.8022	−	508.483i	−0.0699807	−	0.549118i
$927$		0			0
$928$	127.708	−	835.912i	0.137616	−	0.900767i
$929$			362.291i			0.389979i	0.980805	+	0.194990i	$0.0624673\pi$
$929$			362.291i			0.389979i	−0.980805	+	0.194990i	$0.937533\pi$
$930$		0			0
$931$	−651.489	+	651.489i	−0.699773	+	0.699773i
$932$	−409.827	+	106.183i	−0.439728	+	0.113930i
$933$		0			0
$934$	916.611	−	1184.36i	0.981382	−	1.26805i
$935$	−260.926			−0.279065
$936$		0			0
$937$		−	1339.48i		−	1.42954i	−0.699362	−	0.714768i	$-0.746532\pi$
$937$		−	1339.48i		−	1.42954i	0.699362	−	0.714768i	$-0.253468\pi$
$938$	1390.80	−	1797.07i	1.48273	−	1.91585i
$939$		0			0
$940$	−418.421	−	246.218i	−0.445129	−	0.261934i
$941$	28.2194	+	28.2194i	0.0299887	+	0.0299887i	0.721942	−	0.691953i	$-0.243250\pi$
$941$	28.2194	+	28.2194i	0.0299887	+	0.0299887i	−0.691953	+	0.721942i	$0.743250\pi$
$942$		0			0
$943$	1041.03			1.10395
$944$	196.360	−	687.095i	0.208008	−	0.727854i
$945$		0			0
$946$	−28.8243	−	226.176i	−0.0304697	−	0.239086i
$947$	−632.413	−	632.413i	−0.667807	−	0.667807i	0.289401	−	0.957208i	$-0.406544\pi$
$947$	−632.413	−	632.413i	−0.667807	−	0.667807i	−0.957208	+	0.289401i	$0.906544\pi$
$948$		0			0
$949$	−21.5543	−	21.5543i	−0.0227126	−	0.0227126i
$950$	170.847	−	220.754i	0.179839	−	0.232372i
$951$		0			0
$952$	−396.799	−	992.660i	−0.416806	−	1.04271i
$953$	1203.56			1.26291			0.631456	−	0.775411i	$-0.282457\pi$
$953$	1203.56			1.26291			0.631456	+	0.775411i	$0.282457\pi$
$954$		0			0
$955$	−115.553	−	115.553i	−0.120998	−	0.120998i
$956$	−150.219	−	579.792i	−0.157133	−	0.606477i
$957$		0			0
$958$	625.191	−	79.6757i	0.652601	−	0.0831688i
$959$		−	2989.73i		−	3.11755i
$960$		0			0
$961$	−223.676			−0.232753
$962$	70.7830	+	555.413i	0.0735790	+	0.577352i
$963$		0			0
$964$	−613.404	+	158.928i	−0.636311	+	0.164863i
$965$	−59.1018	+	59.1018i	−0.0612454	+	0.0612454i
$966$		0			0
$967$			1155.76i			1.19521i	0.801792	+	0.597603i	$0.203880\pi$
$967$			1155.76i			1.19521i	−0.801792	+	0.597603i	$0.796120\pi$
$968$	9.19995	−	3.67752i	0.00950408	−	0.00379910i
$969$		0			0
$970$	−63.9672	−	49.5059i	−0.0659455	−	0.0510370i
$971$	177.985	−	177.985i	0.183301	−	0.183301i	−0.609492	−	0.792793i	$-0.708626\pi$
$971$	177.985	−	177.985i	0.183301	−	0.183301i	0.792793	+	0.609492i	$0.208626\pi$
$972$		0			0
$973$	737.564	−	737.564i	0.758031	−	0.758031i
$974$	972.302	−	123.912i	0.998257	−	0.127220i
$975$		0			0
$976$	451.769	−	1580.81i	0.462878	−	1.61968i
$977$			1662.86i			1.70200i	0.525163	+	0.851002i	$0.324004\pi$
$977$			1662.86i			1.70200i	−0.525163	+	0.851002i	$0.675996\pi$
$978$		0			0
$979$	1075.62	−	1075.62i	1.09869	−	1.09869i
$980$	−613.274	+	1042.19i	−0.625790	+	1.06346i
$981$		0			0
$982$	−1304.89	−	1009.89i	−1.32880	−	1.02840i
$983$	−1467.82			−1.49320			−0.746600	−	0.665273i	$-0.768315\pi$
$983$	−1467.82			−1.49320			−0.746600	+	0.665273i	$0.768315\pi$
$984$		0			0
$985$			25.7750i			0.0261675i
$986$	419.226	+	324.450i	0.425179	+	0.329057i
$987$		0			0
$988$	−106.780	−	412.130i	−0.108077	−	0.417136i
$989$	−217.137	−	217.137i	−0.219552	−	0.219552i
$990$		0			0
$991$	685.863			0.692091			0.346046	−	0.938218i	$-0.387524\pi$
$991$	685.863			0.692091			0.346046	+	0.938218i	$0.387524\pi$
$992$	−514.579	−	700.163i	−0.518729	−	0.705810i
$993$		0			0
$994$	−81.7317	+	10.4161i	−0.0822250	+	0.0104789i
$995$	263.657	+	263.657i	0.264982	+	0.264982i
$996$		0			0
$997$	1209.62	+	1209.62i	1.21326	+	1.21326i	0.969947	+	0.243317i	$0.0782354\pi$
$997$	1209.62	+	1209.62i	1.21326	+	1.21326i	0.243317	+	0.969947i	$0.421765\pi$
$998$	−695.036	−	537.907i	−0.696428	−	0.538985i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.53.7	✓	32
3.2	odd	2	inner	144.3.j.a.53.10	yes	32
4.3	odd	2		576.3.j.a.305.7		32
8.3	odd	2		1152.3.j.b.737.10		32
8.5	even	2		1152.3.j.a.737.10		32
12.11	even	2		576.3.j.a.305.10		32
16.3	odd	4		576.3.j.a.17.10		32
16.5	even	4		1152.3.j.a.161.7		32
16.11	odd	4		1152.3.j.b.161.7		32
16.13	even	4	inner	144.3.j.a.125.10	yes	32
24.5	odd	2		1152.3.j.a.737.7		32
24.11	even	2		1152.3.j.b.737.7		32
48.5	odd	4		1152.3.j.a.161.10		32
48.11	even	4		1152.3.j.b.161.10		32
48.29	odd	4	inner	144.3.j.a.125.7	yes	32
48.35	even	4		576.3.j.a.17.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.7	✓	32	1.1	even	1	trivial
144.3.j.a.53.10	yes	32	3.2	odd	2	inner
144.3.j.a.125.7	yes	32	48.29	odd	4	inner
144.3.j.a.125.10	yes	32	16.13	even	4	inner
576.3.j.a.17.7		32	48.35	even	4
576.3.j.a.17.10		32	16.3	odd	4
576.3.j.a.305.7		32	4.3	odd	2
576.3.j.a.305.10		32	12.11	even	2
1152.3.j.a.161.7		32	16.5	even	4
1152.3.j.a.161.10		32	48.5	odd	4
1152.3.j.a.737.7		32	24.5	odd	2
1152.3.j.a.737.10		32	8.5	even	2
1152.3.j.b.161.7		32	16.11	odd	4
1152.3.j.b.161.10		32	48.11	even	4
1152.3.j.b.737.7		32	24.11	even	2
1152.3.j.b.737.10		32	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.252839 - 1.98395i) q^{2} +(-3.87214 + 1.00324i) q^{4} +(-1.66372 + 1.66372i) q^{5} +13.3224i q^{7} +(2.96942 + 7.42850i) q^{8} +O(q^{10})\)	\(q+(-0.252839 - 1.98395i) q^{2} +(-3.87214 + 1.00324i) q^{4} +(-1.66372 + 1.66372i) q^{5} +13.3224i q^{7} +(2.96942 + 7.42850i) q^{8} +(3.72140 + 2.88010i) q^{10} +(7.81788 - 7.81788i) q^{11} +(-10.4955 + 10.4955i) q^{13} +(26.4310 - 3.36843i) q^{14} +(13.9870 - 7.76940i) q^{16} +10.0304i q^{17} +(5.07048 - 5.07048i) q^{19} +(4.77306 - 8.11130i) q^{20} +(-17.4870 - 13.5336i) q^{22} -29.7810 q^{23} +19.4640i q^{25} +(23.4763 + 18.1689i) q^{26} +(-13.3656 - 51.5863i) q^{28} +(18.6855 + 18.6855i) q^{29} +27.1537 q^{31} +(-18.9506 - 25.7852i) q^{32} +(19.8998 - 2.53607i) q^{34} +(-22.1648 - 22.1648i) q^{35} +(13.3368 + 13.3368i) q^{37} +(-11.3416 - 8.77758i) q^{38} +(-17.2993 - 7.41868i) q^{40} -34.9561 q^{41} +(7.29114 + 7.29114i) q^{43} +(-22.4287 + 38.1152i) q^{44} +(7.52980 + 59.0841i) q^{46} -51.5850i q^{47} -128.487 q^{49} +(38.6158 - 4.92127i) q^{50} +(30.1106 - 51.1697i) q^{52} +(-68.4354 + 68.4354i) q^{53} +26.0136i q^{55} +(-98.9655 + 39.5598i) q^{56} +(32.3468 - 41.7957i) q^{58} +(31.5812 - 31.5812i) q^{59} +(72.6595 - 72.6595i) q^{61} +(-6.86552 - 53.8717i) q^{62} +(-46.3651 + 44.1166i) q^{64} -34.9233i q^{65} +(60.3054 - 60.3054i) q^{67} +(-10.0629 - 38.8390i) q^{68} +(-38.3698 + 49.5781i) q^{70} -3.09226 q^{71} +2.05367i q^{73} +(23.0875 - 29.8316i) q^{74} +(-14.5467 + 24.7206i) q^{76} +(104.153 + 104.153i) q^{77} +53.3986 q^{79} +(-10.3444 + 36.1966i) q^{80} +(8.83826 + 69.3512i) q^{82} +(21.7960 + 21.7960i) q^{83} +(-16.6877 - 16.6877i) q^{85} +(12.6218 - 16.3088i) q^{86} +(81.2896 + 34.8606i) q^{88} +137.585 q^{89} +(-139.826 - 139.826i) q^{91} +(115.316 - 29.8776i) q^{92} +(-102.342 + 13.0427i) q^{94} +16.8718i q^{95} -17.1890 q^{97} +(32.4864 + 254.911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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