LMFDB - Embedded newform 1500.2.m.d.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1201.1
Character	$\chi$	$=$	1500.1201
Dual form			1500.2.m.d.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} -4.62675 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} -4.62675 q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.00366 + 2.90883i) q^{11} +(-3.04414 + 2.21170i) q^{13} +(0.831378 - 2.55872i) q^{17} +(1.81426 - 5.58371i) q^{19} +(1.42974 + 4.40030i) q^{21} +(5.40285 + 3.92540i) q^{23} +(0.809017 + 0.587785i) q^{27} +(0.370972 + 1.14173i) q^{29} +(1.02048 - 3.14072i) q^{31} +(1.52926 - 4.70659i) q^{33} +(1.51873 - 1.10342i) q^{37} +(3.04414 + 2.21170i) q^{39} +(2.45366 - 1.78269i) q^{41} +10.6626 q^{43} +(-0.0801015 - 0.246527i) q^{47} +14.4068 q^{49} -2.69040 q^{51} +(-3.02731 - 9.31711i) q^{53} -5.87106 q^{57} +(7.78643 - 5.65717i) q^{59} +(-5.07552 - 3.68758i) q^{61} +(3.74312 - 2.71953i) q^{63} +(-0.791247 + 2.43521i) q^{67} +(2.06370 - 6.35143i) q^{69} +(2.68143 + 8.25259i) q^{71} +(3.94381 + 2.86534i) q^{73} +(-18.5239 - 13.4584i) q^{77} +(3.85443 + 11.8627i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.74724 - 8.45513i) q^{83} +(0.971218 - 0.705631i) q^{87} +(-11.7934 - 8.56841i) q^{89} +(14.0845 - 10.2330i) q^{91} -3.30235 q^{93} +(1.23202 + 3.79176i) q^{97} -4.94880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.62675			−1.74875			−0.874373	−	0.485254i	$-0.838727\pi$
$7$	−4.62675			−1.74875			−0.874373	+	0.485254i	$0.838727\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	4.00366	+	2.90883i	1.20715	+	0.877045i	0.994969	−	0.100185i	$-0.0319435\pi$
$11$	4.00366	+	2.90883i	1.20715	+	0.877045i	0.212180	+	0.977231i	$0.431944\pi$
$12$		0			0
$13$	−3.04414	+	2.21170i	−0.844294	+	0.613415i	−0.923567	−	0.383438i	$-0.874740\pi$
$13$	−3.04414	+	2.21170i	−0.844294	+	0.613415i	0.0792730	+	0.996853i	$0.474740\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.831378	−	2.55872i	0.201639	−	0.620580i	−0.798196	−	0.602398i	$-0.794212\pi$
$17$	0.831378	−	2.55872i	0.201639	−	0.620580i	0.999835	−	0.0181824i	$-0.00578795\pi$
$18$		0			0
$19$	1.81426	−	5.58371i	0.416219	−	1.28099i	−0.494937	−	0.868929i	$-0.664809\pi$
$19$	1.81426	−	5.58371i	0.416219	−	1.28099i	0.911156	−	0.412062i	$-0.135191\pi$
$20$		0			0
$21$	1.42974	+	4.40030i	0.311996	+	0.960224i
$22$		0			0
$23$	5.40285	+	3.92540i	1.12657	+	0.818502i	0.985192	−	0.171453i	$-0.0548463\pi$
$23$	5.40285	+	3.92540i	1.12657	+	0.818502i	0.141379	+	0.989955i	$0.454846\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	0.370972	+	1.14173i	0.0688878	+	0.212015i	0.979574	−	0.201084i	$-0.0644464\pi$
$29$	0.370972	+	1.14173i	0.0688878	+	0.212015i	−0.910686	+	0.413099i	$0.864446\pi$
$30$		0			0
$31$	1.02048	−	3.14072i	0.183284	−	0.564090i	−0.816631	−	0.577161i	$-0.804161\pi$
$31$	1.02048	−	3.14072i	0.183284	−	0.564090i	0.999915	+	0.0130708i	$0.00416068\pi$
$32$		0			0
$33$	1.52926	−	4.70659i	0.266210	−	0.819311i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.51873	−	1.10342i	0.249677	−	0.181401i	−0.455907	−	0.890028i	$-0.650685\pi$
$37$	1.51873	−	1.10342i	0.249677	−	0.181401i	0.705584	+	0.708627i	$0.250685\pi$
$38$		0			0
$39$	3.04414	+	2.21170i	0.487453	+	0.354156i
$40$		0			0
$41$	2.45366	−	1.78269i	0.383198	−	0.278410i	−0.379464	−	0.925206i	$-0.623892\pi$
$41$	2.45366	−	1.78269i	0.383198	−	0.278410i	0.762663	+	0.646797i	$0.223892\pi$
$42$		0			0
$43$	10.6626			1.62603			0.813014	−	0.582244i	$-0.197825\pi$
$43$	10.6626			1.62603			0.813014	+	0.582244i	$0.197825\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0801015	−	0.246527i	−0.0116840	−	0.0359597i	0.945045	−	0.326942i	$-0.106018\pi$
$47$	−0.0801015	−	0.246527i	−0.0116840	−	0.0359597i	−0.956729	+	0.290982i	$0.906018\pi$
$48$		0			0
$49$	14.4068			2.05811
$50$		0			0
$51$	−2.69040			−0.376731
$52$		0			0
$53$	−3.02731	−	9.31711i	−0.415833	−	1.27980i	−0.911504	−	0.411292i	$-0.865078\pi$
$53$	−3.02731	−	9.31711i	−0.415833	−	1.27980i	0.495670	−	0.868511i	$-0.334922\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.87106			−0.777641
$58$		0			0
$59$	7.78643	−	5.65717i	1.01371	−	0.736501i	0.0487233	−	0.998812i	$-0.484485\pi$
$59$	7.78643	−	5.65717i	1.01371	−	0.736501i	0.964983	+	0.262311i	$0.0844847\pi$
$60$		0			0
$61$	−5.07552	−	3.68758i	−0.649854	−	0.472147i	0.213367	−	0.976972i	$-0.431557\pi$
$61$	−5.07552	−	3.68758i	−0.649854	−	0.472147i	−0.863222	+	0.504825i	$0.831557\pi$
$62$		0			0
$63$	3.74312	−	2.71953i	0.471589	−	0.342629i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.791247	+	2.43521i	−0.0966662	+	0.297508i	−0.987684	−	0.156460i	$-0.949992\pi$
$67$	−0.791247	+	2.43521i	−0.0966662	+	0.297508i	0.891018	+	0.453968i	$0.149992\pi$
$68$		0			0
$69$	2.06370	−	6.35143i	0.248441	−	0.764622i
$70$		0			0
$71$	2.68143	+	8.25259i	0.318227	+	0.979403i	0.974406	+	0.224797i	$0.0721718\pi$
$71$	2.68143	+	8.25259i	0.318227	+	0.979403i	−0.656178	+	0.754606i	$0.727828\pi$
$72$		0			0
$73$	3.94381	+	2.86534i	0.461588	+	0.335363i	0.794154	−	0.607717i	$-0.207914\pi$
$73$	3.94381	+	2.86534i	0.461588	+	0.335363i	−0.332566	+	0.943080i	$0.607914\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−18.5239	−	13.4584i	−2.11100	−	1.53373i
$78$		0			0
$79$	3.85443	+	11.8627i	0.433657	+	1.33466i	0.894457	+	0.447155i	$0.147563\pi$
$79$	3.85443	+	11.8627i	0.433657	+	1.33466i	−0.460800	+	0.887504i	$0.652437\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	2.74724	−	8.45513i	0.301549	−	0.928071i	−0.679394	−	0.733774i	$-0.737757\pi$
$83$	2.74724	−	8.45513i	0.301549	−	0.928071i	0.980943	−	0.194298i	$-0.0622428\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.971218	−	0.705631i	0.104125	−	0.0756516i
$88$		0			0
$89$	−11.7934	−	8.56841i	−1.25010	−	0.908249i	−0.251870	−	0.967761i	$-0.581046\pi$
$89$	−11.7934	−	8.56841i	−1.25010	−	0.908249i	−0.998228	+	0.0595118i	$0.981046\pi$
$90$		0			0
$91$	14.0845	−	10.2330i	1.47646	−	1.07271i
$92$		0			0
$93$	−3.30235			−0.342437
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.23202	+	3.79176i	0.125092	+	0.384995i	0.993918	−	0.110123i	$-0.0351246\pi$
$97$	1.23202	+	3.79176i	0.125092	+	0.384995i	−0.868825	+	0.495119i	$0.835125\pi$
$98$		0			0
$99$	−4.94880			−0.497373
$100$		0			0
$101$	9.36896			0.932246			0.466123	−	0.884720i	$-0.345650\pi$
$101$	9.36896			0.932246			0.466123	+	0.884720i	$0.345650\pi$
$102$		0			0
$103$	−3.22123	−	9.91391i	−0.317397	−	0.976847i	−0.974757	−	0.223270i	$-0.928327\pi$
$103$	−3.22123	−	9.91391i	−0.317397	−	0.976847i	0.657360	−	0.753577i	$-0.271673\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.220683			0.0213342			0.0106671	−	0.999943i	$-0.496604\pi$
$107$	0.220683			0.0213342			0.0106671	+	0.999943i	$0.496604\pi$
$108$		0			0
$109$	−5.40941	+	3.93017i	−0.518127	+	0.376442i	−0.815898	−	0.578196i	$-0.803757\pi$
$109$	−5.40941	+	3.93017i	−0.518127	+	0.376442i	0.297771	+	0.954637i	$0.403757\pi$
$110$		0			0
$111$	−1.51873	−	1.10342i	−0.144151	−	0.104732i
$112$		0			0
$113$	7.77355	−	5.64782i	0.731274	−	0.531302i	−0.158692	−	0.987328i	$-0.550728\pi$
$113$	7.77355	−	5.64782i	0.731274	−	0.531302i	0.889966	+	0.456026i	$0.150728\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.16276	−	3.57861i	0.107497	−	0.330842i
$118$		0			0
$119$	−3.84658	+	11.8385i	−0.352615	+	1.08524i
$120$		0			0
$121$	4.16882	+	12.8303i	0.378984	+	1.16639i
$122$		0			0
$123$	−2.45366	−	1.78269i	−0.221239	−	0.160740i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	12.9380	+	9.40003i	1.14806	+	0.834118i	0.988222	−	0.153025i	$-0.0489015\pi$
$127$	12.9380	+	9.40003i	1.14806	+	0.834118i	0.159842	+	0.987143i	$0.448902\pi$
$128$		0			0
$129$	−3.29492	−	10.1407i	−0.290101	−	0.892840i
$130$		0			0
$131$	−3.80795	+	11.7197i	−0.332702	+	1.02395i	0.635140	+	0.772397i	$0.280942\pi$
$131$	−3.80795	+	11.7197i	−0.332702	+	1.02395i	−0.967843	+	0.251556i	$0.919058\pi$
$132$		0			0
$133$	−8.39411	+	25.8344i	−0.727862	+	2.24013i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.60698	+	3.34717i	−0.393601	+	0.285968i	−0.766930	−	0.641731i	$-0.778216\pi$
$137$	−4.60698	+	3.34717i	−0.393601	+	0.285968i	0.373329	+	0.927699i	$0.378216\pi$
$138$		0			0
$139$	14.5598	+	10.5783i	1.23495	+	0.897242i	0.997251	−	0.0740969i	$-0.0236074\pi$
$139$	14.5598	+	10.5783i	1.23495	+	0.897242i	0.237697	+	0.971339i	$0.423607\pi$
$140$		0			0
$141$	−0.209709	+	0.152362i	−0.0176606	+	0.0128312i
$142$		0			0
$143$	−18.6212			−1.55718
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.45195	−	13.7017i	−0.367190	−	1.13010i
$148$		0			0
$149$	−1.09001			−0.0892972			−0.0446486	−	0.999003i	$-0.514217\pi$
$149$	−1.09001			−0.0892972			−0.0446486	+	0.999003i	$0.514217\pi$
$150$		0			0
$151$	11.3789			0.926004			0.463002	−	0.886357i	$-0.346772\pi$
$151$	11.3789			0.926004			0.463002	+	0.886357i	$0.346772\pi$
$152$		0			0
$153$	0.831378	+	2.55872i	0.0672129	+	0.206860i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.98415			0.317970			0.158985	−	0.987281i	$-0.449178\pi$
$157$	3.98415			0.317970			0.158985	+	0.987281i	$0.449178\pi$
$158$		0			0
$159$	−7.92560	+	5.75829i	−0.628541	+	0.456662i
$160$		0			0
$161$	−24.9976	−	18.1618i	−1.97009	−	1.43135i
$162$		0			0
$163$	17.6620	−	12.8322i	1.38339	−	1.00509i	0.386837	−	0.922148i	$-0.373568\pi$
$163$	17.6620	−	12.8322i	1.38339	−	1.00509i	0.996554	−	0.0829441i	$-0.0264323\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.78015	−	14.7118i	0.369899	−	1.13843i	−0.576957	−	0.816775i	$-0.695760\pi$
$167$	4.78015	−	14.7118i	0.369899	−	1.13843i	0.946856	−	0.321658i	$-0.104240\pi$
$168$		0			0
$169$	0.357976	−	1.10174i	0.0275366	−	0.0847490i
$170$		0			0
$171$	1.81426	+	5.58371i	0.138740	+	0.426997i
$172$		0			0
$173$	13.8911	+	10.0925i	1.05612	+	0.767317i	0.973367	−	0.229253i	$-0.0736282\pi$
$173$	13.8911	+	10.0925i	1.05612	+	0.767317i	0.0827547	+	0.996570i	$0.473628\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.78643	−	5.65717i	−0.585264	−	0.425219i
$178$		0			0
$179$	−4.46392	−	13.7385i	−0.333649	−	1.02687i	−0.967384	−	0.253316i	$-0.918479\pi$
$179$	−4.46392	−	13.7385i	−0.333649	−	1.02687i	0.633734	−	0.773551i	$-0.281521\pi$
$180$		0			0
$181$	3.83071	−	11.7897i	0.284734	−	0.876322i	−0.701744	−	0.712429i	$-0.747595\pi$
$181$	3.83071	−	11.7897i	0.284734	−	0.876322i	0.986478	−	0.163893i	$-0.0524051\pi$
$182$		0			0
$183$	−1.93868	+	5.96664i	−0.143311	+	0.441066i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	10.7714	−	7.82590i	0.787685	−	0.572287i
$188$		0			0
$189$	−3.74312	−	2.71953i	−0.272272	−	0.197817i
$190$		0			0
$191$	1.33930	−	0.973056i	0.0969081	−	0.0704078i	−0.538276	−	0.842769i	$-0.680924\pi$
$191$	1.33930	−	0.973056i	0.0969081	−	0.0704078i	0.635184	+	0.772361i	$0.280924\pi$
$192$		0			0
$193$	−16.3253			−1.17512			−0.587560	−	0.809181i	$-0.699911\pi$
$193$	−16.3253			−1.17512			−0.587560	+	0.809181i	$0.699911\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.21264	+	12.9652i	0.300138	+	0.923730i	0.981447	+	0.191734i	$0.0614111\pi$
$197$	4.21264	+	12.9652i	0.300138	+	0.923730i	−0.681309	+	0.731996i	$0.738589\pi$
$198$		0			0
$199$	−6.07817			−0.430870			−0.215435	−	0.976518i	$-0.569117\pi$
$199$	−6.07817			−0.430870			−0.215435	+	0.976518i	$0.569117\pi$
$200$		0			0
$201$	2.56053			0.180606
$202$		0			0
$203$	−1.71639	−	5.28252i	−0.120467	−	0.370760i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.67829			−0.464173
$208$		0			0
$209$	23.5057	−	17.0779i	1.62593	−	1.18130i
$210$		0			0
$211$	−13.8200	−	10.0408i	−0.951409	−	0.691239i	−0.000268984	−	1.00000i	$-0.500086\pi$
$211$	−13.8200	−	10.0408i	−0.951409	−	0.691239i	−0.951140	+	0.308761i	$0.900086\pi$
$212$		0			0
$213$	7.02007	−	5.10038i	0.481008	−	0.349472i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.72151	+	14.5313i	−0.320517	+	0.986450i
$218$		0			0
$219$	1.50640	−	4.63622i	0.101793	−	0.313287i
$220$		0			0
$221$	3.12828	+	9.62787i	0.210431	+	0.647640i
$222$		0			0
$223$	0.634100	+	0.460700i	0.0424624	+	0.0308508i	0.608814	−	0.793313i	$-0.291646\pi$
$223$	0.634100	+	0.460700i	0.0424624	+	0.0308508i	−0.566352	+	0.824164i	$0.691646\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	19.3755	+	14.0771i	1.28600	+	0.934331i	0.999716	−	0.0238153i	$-0.00758137\pi$
$227$	19.3755	+	14.0771i	1.28600	+	0.934331i	0.286280	+	0.958146i	$0.407581\pi$
$228$		0			0
$229$	−1.71005	−	5.26299i	−0.113003	−	0.347788i	0.878522	−	0.477702i	$-0.158530\pi$
$229$	−1.71005	−	5.26299i	−0.113003	−	0.347788i	−0.991525	+	0.129914i	$0.958530\pi$
$230$		0			0
$231$	−7.07551	+	21.7762i	−0.465535	+	1.43277i
$232$		0			0
$233$	−0.280508	+	0.863314i	−0.0183767	+	0.0565576i	−0.959824	−	0.280602i	$-0.909466\pi$
$233$	−0.280508	+	0.863314i	−0.0183767	+	0.0565576i	0.941448	+	0.337159i	$0.109466\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	10.0910	−	7.33156i	0.655482	−	0.476236i
$238$		0			0
$239$	9.09227	+	6.60592i	0.588130	+	0.427302i	0.841646	−	0.540030i	$-0.181587\pi$
$239$	9.09227	+	6.60592i	0.588130	+	0.427302i	−0.253516	+	0.967331i	$0.581587\pi$
$240$		0			0
$241$	16.3840	−	11.9037i	1.05539	−	0.766783i	0.0821564	−	0.996619i	$-0.473819\pi$
$241$	16.3840	−	11.9037i	1.05539	−	0.766783i	0.973229	+	0.229837i	$0.0738193\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.82663	+	21.0102i	0.434368	+	1.33685i
$248$		0			0
$249$	−8.89025			−0.563397
$250$		0			0
$251$	−30.6919			−1.93725			−0.968627	−	0.248520i	$-0.920056\pi$
$251$	−30.6919			−1.93725			−0.968627	+	0.248520i	$0.920056\pi$
$252$		0			0
$253$	10.2129	+	31.4319i	0.642077	+	1.97611i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.77543			−0.297883			−0.148941	−	0.988846i	$-0.547587\pi$
$257$	−4.77543			−0.297883			−0.148941	+	0.988846i	$0.547587\pi$
$258$		0			0
$259$	−7.02676	+	5.10524i	−0.436622	+	0.317224i
$260$		0			0
$261$	−0.971218	−	0.705631i	−0.0601169	−	0.0436775i
$262$		0			0
$263$	0.978638	−	0.711022i	0.0603454	−	0.0438435i	−0.557204	−	0.830376i	$-0.688126\pi$
$263$	0.978638	−	0.711022i	0.0603454	−	0.0438435i	0.617549	+	0.786532i	$0.288126\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.50468	+	13.8640i	−0.275682	+	0.848461i
$268$		0			0
$269$	−7.88763	+	24.2756i	−0.480917	+	1.48011i	0.356891	+	0.934146i	$0.383837\pi$
$269$	−7.88763	+	24.2756i	−0.480917	+	1.48011i	−0.837808	+	0.545965i	$0.816163\pi$
$270$		0			0
$271$	−1.81499	−	5.58596i	−0.110253	−	0.339323i	0.880675	−	0.473722i	$-0.157090\pi$
$271$	−1.81499	−	5.58596i	−0.110253	−	0.339323i	−0.990927	+	0.134399i	$0.957090\pi$
$272$		0			0
$273$	−14.0845	−	10.2330i	−0.852432	−	0.619328i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.96855	−	2.88332i	−0.238447	−	0.173242i	0.462144	−	0.886805i	$-0.347080\pi$
$277$	−3.96855	−	2.88332i	−0.238447	−	0.173242i	−0.700591	+	0.713563i	$0.747080\pi$
$278$		0			0
$279$	1.02048	+	3.14072i	0.0610946	+	0.188030i
$280$		0			0
$281$	−0.400257	+	1.23186i	−0.0238773	+	0.0734868i	−0.962285	−	0.272043i	$-0.912301\pi$
$281$	−0.400257	+	1.23186i	−0.0238773	+	0.0734868i	0.938408	+	0.345530i	$0.112301\pi$
$282$		0			0
$283$	−9.34149	+	28.7501i	−0.555294	+	1.70902i	0.139873	+	0.990169i	$0.455331\pi$
$283$	−9.34149	+	28.7501i	−0.555294	+	1.70902i	−0.695166	+	0.718849i	$0.744669\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.3525	+	8.24807i	−0.670116	+	0.486868i
$288$		0			0
$289$	7.89744	+	5.73783i	0.464555	+	0.337519i
$290$		0			0
$291$	3.22546	−	2.34344i	0.189080	−	0.137375i
$292$		0			0
$293$	−8.06831			−0.471356			−0.235678	−	0.971831i	$-0.575731\pi$
$293$	−8.06831			−0.471356			−0.235678	+	0.971831i	$0.575731\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.52926	+	4.70659i	0.0887368	+	0.273104i
$298$		0			0
$299$	−25.1289			−1.45324
$300$		0			0
$301$	−49.3331			−2.84351
$302$		0			0
$303$	−2.89517	−	8.91041i	−0.166323	−	0.511890i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.7750			0.843255			0.421628	−	0.906769i	$-0.361459\pi$
$307$	14.7750			0.843255			0.421628	+	0.906769i	$0.361459\pi$
$308$		0			0
$309$	−8.43328	+	6.12713i	−0.479752	+	0.348560i
$310$		0			0
$311$	7.40552	+	5.38043i	0.419929	+	0.305096i	0.777609	−	0.628748i	$-0.216432\pi$
$311$	7.40552	+	5.38043i	0.419929	+	0.305096i	−0.357680	+	0.933844i	$0.616432\pi$
$312$		0			0
$313$	−10.7238	+	7.79128i	−0.606144	+	0.440389i	−0.848054	−	0.529909i	$-0.822226\pi$
$313$	−10.7238	+	7.79128i	−0.606144	+	0.440389i	0.241910	+	0.970299i	$0.422226\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.244293	−	0.751858i	0.0137209	−	0.0422286i	−0.943962	−	0.330055i	$-0.892933\pi$
$317$	0.244293	−	0.751858i	0.0137209	−	0.0422286i	0.957683	+	0.287827i	$0.0929327\pi$
$318$		0			0
$319$	−1.83587	+	5.65021i	−0.102789	+	0.316351i
$320$		0			0
$321$	−0.0681947	−	0.209882i	−0.00380626	−	0.0117145i
$322$		0			0
$323$	−12.7788	−	9.28434i	−0.711032	−	0.516595i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.40941	+	3.93017i	0.299141	+	0.217339i
$328$		0			0
$329$	0.370610	+	1.14062i	0.0204324	+	0.0628844i
$330$		0			0
$331$	−1.04253	+	3.20858i	−0.0573026	+	0.176359i	−0.975611	−	0.219506i	$-0.929555\pi$
$331$	−1.04253	+	3.20858i	−0.0573026	+	0.176359i	0.918308	+	0.395866i	$0.129555\pi$
$332$		0			0
$333$	−0.580102	+	1.78537i	−0.0317894	+	0.0978376i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−14.6157	+	10.6189i	−0.796166	+	0.578449i	−0.909787	−	0.415076i	$-0.863755\pi$
$337$	−14.6157	+	10.6189i	−0.796166	+	0.578449i	0.113621	+	0.993524i	$0.463755\pi$
$338$		0			0
$339$	−7.77355	−	5.64782i	−0.422201	−	0.306747i
$340$		0			0
$341$	13.2215	−	9.60597i	0.715983	−	0.520192i
$342$		0			0
$343$	−34.2694			−1.85037
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.943191	+	2.90284i	0.0506332	+	0.155833i	0.973176	−	0.230062i	$-0.0738928\pi$
$347$	0.943191	+	2.90284i	0.0506332	+	0.155833i	−0.922543	+	0.385895i	$0.873893\pi$
$348$		0			0
$349$	−0.628744			−0.0336559			−0.0168280	−	0.999858i	$-0.505357\pi$
$349$	−0.628744			−0.0336559			−0.0168280	+	0.999858i	$0.505357\pi$
$350$		0			0
$351$	−3.76277			−0.200842
$352$		0			0
$353$	−5.83721	−	17.9651i	−0.310683	−	0.956184i	−0.977495	−	0.210958i	$-0.932342\pi$
$353$	−5.83721	−	17.9651i	−0.310683	−	0.956184i	0.666812	−	0.745226i	$-0.267658\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	12.4478			0.658807
$358$		0			0
$359$	−23.4087	+	17.0074i	−1.23546	+	0.897617i	−0.997287	−	0.0736053i	$-0.976550\pi$
$359$	−23.4087	+	17.0074i	−1.23546	+	0.897617i	−0.238176	+	0.971222i	$0.576550\pi$
$360$		0			0
$361$	−12.5149	−	9.09264i	−0.658681	−	0.478560i
$362$		0			0
$363$	10.9141	−	7.92957i	0.572843	−	0.416195i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.66342	−	5.11949i	0.0868299	−	0.267235i	−0.898209	−	0.439570i	$-0.855131\pi$
$367$	1.66342	−	5.11949i	0.0868299	−	0.267235i	0.985038	+	0.172334i	$0.0551310\pi$
$368$		0			0
$369$	−0.937217	+	2.88446i	−0.0487895	+	0.150159i
$370$		0			0
$371$	14.0066	+	43.1079i	0.727187	+	2.23805i
$372$		0			0
$373$	8.89714	+	6.46415i	0.460677	+	0.334701i	0.793797	−	0.608183i	$-0.208101\pi$
$373$	8.89714	+	6.46415i	0.460677	+	0.334701i	−0.333120	+	0.942884i	$0.608101\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.65447	−	2.65513i	−0.188215	−	0.136746i
$378$		0			0
$379$	2.18405	+	6.72183i	0.112187	+	0.345277i	0.991350	−	0.131245i	$-0.0418974\pi$
$379$	2.18405	+	6.72183i	0.112187	+	0.345277i	−0.879163	+	0.476522i	$0.841897\pi$
$380$		0			0
$381$	4.94189	−	15.2096i	0.253181	−	0.779210i
$382$		0			0
$383$	2.50346	−	7.70484i	0.127921	−	0.393699i	−0.866501	−	0.499175i	$-0.833637\pi$
$383$	2.50346	−	7.70484i	0.127921	−	0.393699i	0.994422	+	0.105476i	$0.0336365\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.62621	+	6.26731i	−0.438495	+	0.318585i
$388$		0			0
$389$	−26.7325	−	19.4223i	−1.35539	−	0.984750i	−0.998723	−	0.0505192i	$-0.983912\pi$
$389$	−26.7325	−	19.4223i	−1.35539	−	0.984750i	−0.356669	−	0.934231i	$-0.616088\pi$
$390$		0			0
$391$	14.5358	−	10.5609i	0.735107	−	0.534086i
$392$		0			0
$393$	12.3228			0.621603
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.82155	−	11.7615i	−0.191798	−	0.590294i	−0.999999	−	0.00138688i	$-0.999559\pi$
$397$	−3.82155	−	11.7615i	−0.191798	−	0.590294i	0.808201	−	0.588907i	$-0.200441\pi$
$398$		0			0
$399$	27.1639			1.35990
$400$		0			0
$401$	−14.7983			−0.738993			−0.369496	−	0.929232i	$-0.620470\pi$
$401$	−14.7983			−0.738993			−0.369496	+	0.929232i	$0.620470\pi$
$402$		0			0
$403$	3.83984	+	11.8178i	0.191276	+	0.588687i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.29012			0.460494
$408$		0			0
$409$	19.1618	−	13.9219i	0.947491	−	0.688392i	−0.00272132	−	0.999996i	$-0.500866\pi$
$409$	19.1618	−	13.9219i	0.947491	−	0.688392i	0.950212	+	0.311604i	$0.100866\pi$
$410$		0			0
$411$	4.60698	+	3.34717i	0.227246	+	0.165104i
$412$		0			0
$413$	−36.0258	+	26.1743i	−1.77272	+	1.28795i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.56136	−	17.1161i	0.272341	−	0.838179i
$418$		0			0
$419$	0.477059	−	1.46824i	0.0233058	−	0.0717280i	−0.938727	−	0.344661i	$-0.887994\pi$
$419$	0.477059	−	1.46824i	0.0233058	−	0.0717280i	0.962033	+	0.272933i	$0.0879938\pi$
$420$		0			0
$421$	−5.43760	−	16.7352i	−0.265013	−	0.815625i	−0.991691	−	0.128647i	$-0.958937\pi$
$421$	−5.43760	−	16.7352i	−0.265013	−	0.815625i	0.726678	−	0.686978i	$-0.241063\pi$
$422$		0			0
$423$	0.209709	+	0.152362i	0.0101964	+	0.00740810i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	23.4832	+	17.0615i	1.13643	+	0.825665i
$428$		0			0
$429$	5.75426	+	17.7098i	0.277818	+	0.855037i
$430$		0			0
$431$	4.83527	−	14.8814i	0.232907	−	0.716814i	−0.764485	−	0.644641i	$-0.777007\pi$
$431$	4.83527	−	14.8814i	0.232907	−	0.716814i	0.997392	−	0.0721724i	$-0.0229932\pi$
$432$		0			0
$433$	−0.0707586	+	0.217772i	−0.00340044	+	0.0104655i	−0.952742	−	0.303780i	$-0.901751\pi$
$433$	−0.0707586	+	0.217772i	−0.00340044	+	0.0104655i	0.949342	+	0.314245i	$0.101751\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	31.7204	−	23.0462i	1.51739	−	1.10245i
$438$		0			0
$439$	−15.7111	−	11.4147i	−0.749848	−	0.544796i	0.145932	−	0.989295i	$-0.453382\pi$
$439$	−15.7111	−	11.4147i	−0.749848	−	0.544796i	−0.895780	+	0.444498i	$0.853382\pi$
$440$		0			0
$441$	−11.6553	+	8.46810i	−0.555016	+	0.403243i
$442$		0			0
$443$	12.7980			0.608051			0.304026	−	0.952664i	$-0.401669\pi$
$443$	12.7980			0.608051			0.304026	+	0.952664i	$0.401669\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.336832	+	1.03666i	0.0159316	+	0.0490325i
$448$		0			0
$449$	−21.1499			−0.998124			−0.499062	−	0.866566i	$-0.666322\pi$
$449$	−21.1499			−0.998124			−0.499062	+	0.866566i	$0.666322\pi$
$450$		0			0
$451$	15.0092			0.706755
$452$		0			0
$453$	−3.51628	−	10.8220i	−0.165209	−	0.508462i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.97118			0.419654			0.209827	−	0.977739i	$-0.432710\pi$
$457$	8.97118			0.419654			0.209827	+	0.977739i	$0.432710\pi$
$458$		0			0
$459$	2.17658	−	1.58137i	0.101594	−	0.0738123i
$460$		0			0
$461$	−22.2764	−	16.1847i	−1.03751	−	0.753797i	−0.0677146	−	0.997705i	$-0.521571\pi$
$461$	−22.2764	−	16.1847i	−1.03751	−	0.753797i	−0.969799	+	0.243907i	$0.921571\pi$
$462$		0			0
$463$	23.7859	−	17.2815i	1.10543	−	0.803140i	0.123489	−	0.992346i	$-0.460591\pi$
$463$	23.7859	−	17.2815i	1.10543	−	0.803140i	0.981937	+	0.189206i	$0.0605915\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.09785	+	12.6119i	−0.189626	+	0.583609i	−0.999997	−	0.00230768i	$-0.999265\pi$
$467$	−4.09785	+	12.6119i	−0.189626	+	0.583609i	0.810371	+	0.585917i	$0.199265\pi$
$468$		0			0
$469$	3.66090	−	11.2671i	0.169045	−	0.520266i
$470$		0			0
$471$	−1.23117	−	3.78915i	−0.0567293	−	0.174595i
$472$		0			0
$473$	42.6893	+	31.0156i	1.96286	+	1.42610i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.92560	+	5.75829i	0.362888	+	0.263654i
$478$		0			0
$479$	−5.58057	−	17.1752i	−0.254983	−	0.784757i	−0.993833	−	0.110887i	$-0.964631\pi$
$479$	−5.58057	−	17.1752i	−0.254983	−	0.784757i	0.738850	−	0.673870i	$-0.235369\pi$
$480$		0			0
$481$	−2.18279	+	6.71793i	−0.0995266	+	0.306311i
$482$		0			0
$483$	−9.54824	+	29.3865i	−0.434460	+	1.33713i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	11.3725	−	8.26258i	0.515336	−	0.374413i	−0.299508	−	0.954094i	$-0.596823\pi$
$487$	11.3725	−	8.26258i	0.515336	−	0.374413i	0.814844	+	0.579681i	$0.196823\pi$
$488$		0			0
$489$	−17.6620	−	12.8322i	−0.798701	−	0.580290i
$490$		0			0
$491$	22.0310	−	16.0065i	0.994247	−	0.722363i	0.0334000	−	0.999442i	$-0.489366\pi$
$491$	22.0310	−	16.0065i	0.994247	−	0.722363i	0.960847	+	0.277079i	$0.0893665\pi$
$492$		0			0
$493$	3.22980			0.145463
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.4063	−	38.1827i	−0.556499	−	1.71273i
$498$		0			0
$499$	−8.17654			−0.366032			−0.183016	−	0.983110i	$-0.558586\pi$
$499$	−8.17654			−0.366032			−0.183016	+	0.983110i	$0.558586\pi$
$500$		0			0
$501$	−15.4689			−0.691099
$502$		0			0
$503$	−3.07311	−	9.45805i	−0.137023	−	0.421714i	0.858876	−	0.512183i	$-0.171163\pi$
$503$	−3.07311	−	9.45805i	−0.137023	−	0.421714i	−0.995899	+	0.0904697i	$0.971163\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.15844			−0.0514479
$508$		0			0
$509$	−13.9758	+	10.1540i	−0.619464	+	0.450067i	−0.852734	−	0.522345i	$-0.825057\pi$
$509$	−13.9758	+	10.1540i	−0.619464	+	0.450067i	0.233270	+	0.972412i	$0.425057\pi$
$510$		0			0
$511$	−18.2470	−	13.2572i	−0.807200	−	0.586465i
$512$		0			0
$513$	4.74979	−	3.45092i	0.209708	−	0.152362i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.396406	−	1.22001i	0.0174339	−	0.0536561i
$518$		0			0
$519$	5.30593	−	16.3300i	0.232905	−	0.716807i
$520$		0			0
$521$	−3.43786	−	10.5807i	−0.150615	−	0.463547i	0.847075	−	0.531474i	$-0.178362\pi$
$521$	−3.43786	−	10.5807i	−0.150615	−	0.463547i	−0.997690	+	0.0679269i	$0.978362\pi$
$522$		0			0
$523$	−3.03609	−	2.20585i	−0.132759	−	0.0964551i	0.519424	−	0.854517i	$-0.326147\pi$
$523$	−3.03609	−	2.20585i	−0.132759	−	0.0964551i	−0.652183	+	0.758062i	$0.726147\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.18781	−	5.22225i	−0.313106	−	0.227485i
$528$		0			0
$529$	6.67462	+	20.5424i	0.290201	+	0.893146i
$530$		0			0
$531$	−2.97415	+	9.15350i	−0.129067	+	0.397228i
$532$		0			0
$533$	−3.52653	+	10.8535i	−0.152751	+	0.470119i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.6867	+	8.49089i	−0.504318	+	0.366409i
$538$		0			0
$539$	57.6799	+	41.9069i	2.48445	+	1.80506i
$540$		0			0
$541$	−15.2752	+	11.0981i	−0.656731	+	0.477143i	−0.865557	−	0.500810i	$-0.833036\pi$
$541$	−15.2752	+	11.0981i	−0.656731	+	0.477143i	0.208826	+	0.977953i	$0.433036\pi$
$542$		0			0
$543$	−12.3964			−0.531982
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.0479926	−	0.147706i	−0.00205201	−	0.00631545i	0.950025	−	0.312173i	$-0.101057\pi$
$547$	−0.0479926	−	0.147706i	−0.00205201	−	0.00631545i	−0.952077	+	0.305858i	$0.901057\pi$
$548$		0			0
$549$	6.27369			0.267755
$550$		0			0
$551$	7.04815			0.300261
$552$		0			0
$553$	−17.8335	−	54.8858i	−0.758356	−	2.33398i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.0371			0.806626			0.403313	−	0.915062i	$-0.367859\pi$
$557$	19.0371			0.806626			0.403313	+	0.915062i	$0.367859\pi$
$558$		0			0
$559$	−32.4584	+	23.5824i	−1.37285	+	0.997430i
$560$		0			0
$561$	−10.7714	−	7.82590i	−0.454770	−	0.330410i
$562$		0			0
$563$	−25.1369	+	18.2630i	−1.05939	+	0.769694i	−0.973976	−	0.226652i	$-0.927222\pi$
$563$	−25.1369	+	18.2630i	−1.05939	+	0.769694i	−0.0854166	+	0.996345i	$0.527222\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.42974	+	4.40030i	−0.0600436	+	0.184795i
$568$		0			0
$569$	12.1573	−	37.4162i	0.509659	−	1.56857i	−0.283135	−	0.959080i	$-0.591374\pi$
$569$	12.1573	−	37.4162i	0.509659	−	1.56857i	0.792794	−	0.609490i	$-0.208626\pi$
$570$		0			0
$571$	8.78632	+	27.0415i	0.367696	+	1.13165i	0.948276	+	0.317448i	$0.102826\pi$
$571$	8.78632	+	27.0415i	0.367696	+	1.13165i	−0.580580	+	0.814203i	$0.697174\pi$
$572$		0			0
$573$	−1.33930	−	0.973056i	−0.0559499	−	0.0406500i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−18.1701	−	13.2014i	−0.756433	−	0.549581i	0.141381	−	0.989955i	$-0.454846\pi$
$577$	−18.1701	−	13.2014i	−0.756433	−	0.549581i	−0.897814	+	0.440375i	$0.854846\pi$
$578$		0			0
$579$	5.04479	+	15.5263i	0.209654	+	0.645250i
$580$		0			0
$581$	−12.7108	+	39.1198i	−0.527332	+	1.62296i
$582$		0			0
$583$	14.9815	−	46.1085i	0.620472	−	1.90962i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.0114	+	9.45335i	−0.537039	+	0.390182i	−0.822984	−	0.568064i	$-0.807692\pi$
$587$	−13.0114	+	9.45335i	−0.537039	+	0.390182i	0.285945	+	0.958246i	$0.407692\pi$
$588$		0			0
$589$	−15.6854	−	11.3961i	−0.646307	−	0.469570i
$590$		0			0
$591$	11.0288	−	8.01291i	0.453665	−	0.329607i
$592$		0			0
$593$	−20.4648			−0.840389			−0.420194	−	0.907434i	$-0.638038\pi$
$593$	−20.4648			−0.840389			−0.420194	+	0.907434i	$0.638038\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.87826	+	5.78068i	0.0768720	+	0.236588i
$598$		0			0
$599$	18.5688			0.758699			0.379349	−	0.925253i	$-0.376148\pi$
$599$	18.5688			0.758699			0.379349	+	0.925253i	$0.376148\pi$
$600$		0			0
$601$	47.2047			1.92552			0.962761	−	0.270355i	$-0.0871409\pi$
$601$	47.2047			1.92552			0.962761	+	0.270355i	$0.0871409\pi$
$602$		0			0
$603$	−0.791247	−	2.43521i	−0.0322221	−	0.0991693i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.0786576			−0.00319261			−0.00159631	−	0.999999i	$-0.500508\pi$
$607$	−0.0786576			−0.00319261			−0.00159631	+	0.999999i	$0.500508\pi$
$608$		0			0
$609$	−4.49358	+	3.26478i	−0.182089	+	0.132295i
$610$		0			0
$611$	0.789085	+	0.573304i	0.0319230	+	0.0231934i
$612$		0			0
$613$	4.29654	−	3.12162i	0.173536	−	0.126081i	−0.497627	−	0.867391i	$-0.665795\pi$
$613$	4.29654	−	3.12162i	0.173536	−	0.126081i	0.671163	+	0.741310i	$0.265795\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.40411	+	28.9429i	−0.378595	+	1.16520i	0.562426	+	0.826848i	$0.309868\pi$
$617$	−9.40411	+	28.9429i	−0.378595	+	1.16520i	−0.941021	+	0.338349i	$0.890132\pi$
$618$		0			0
$619$	−9.77918	+	30.0972i	−0.393058	+	1.20971i	0.537405	+	0.843324i	$0.319405\pi$
$619$	−9.77918	+	30.0972i	−0.393058	+	1.20971i	−0.930463	+	0.366385i	$0.880595\pi$
$620$		0			0
$621$	2.06370	+	6.35143i	0.0828136	+	0.254874i
$622$		0			0
$623$	54.5651	+	39.6439i	2.18610	+	1.58830i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−23.5057	−	17.0779i	−0.938728	−	0.682026i
$628$		0			0
$629$	−1.56070	−	4.80335i	−0.0622293	−	0.191522i
$630$		0			0
$631$	−10.4722	+	32.2301i	−0.416891	+	1.28306i	0.493657	+	0.869657i	$0.335660\pi$
$631$	−10.4722	+	32.2301i	−0.416891	+	1.28306i	−0.910548	+	0.413403i	$0.864340\pi$
$632$		0			0
$633$	−5.27877	+	16.2464i	−0.209812	+	0.645736i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−43.8564	+	31.8635i	−1.73765	+	1.26248i
$638$		0			0
$639$	−7.02007	−	5.10038i	−0.277710	−	0.201768i
$640$		0			0
$641$	39.6699	−	28.8219i	1.56687	−	1.13840i	0.636788	−	0.771039i	$-0.280263\pi$
$641$	39.6699	−	28.8219i	1.56687	−	1.13840i	0.930080	−	0.367358i	$-0.119737\pi$
$642$		0			0
$643$	14.2509			0.562000			0.281000	−	0.959708i	$-0.409334\pi$
$643$	14.2509			0.562000			0.281000	+	0.959708i	$0.409334\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0820	−	40.2623i	−0.514307	−	1.58287i	−0.784539	−	0.620079i	$-0.787101\pi$
$647$	−13.0820	−	40.2623i	−0.514307	−	1.58287i	0.270233	−	0.962795i	$-0.412899\pi$
$648$		0			0
$649$	47.6300			1.86964
$650$		0			0
$651$	15.2791			0.598836
$652$		0			0
$653$	−14.5328	−	44.7274i	−0.568713	−	1.75032i	−0.656654	−	0.754192i	$-0.728029\pi$
$653$	−14.5328	−	44.7274i	−0.568713	−	1.75032i	0.0879407	−	0.996126i	$-0.471971\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4.87481			−0.190185
$658$		0			0
$659$	9.05013	−	6.57531i	0.352543	−	0.256138i	−0.397392	−	0.917649i	$-0.630085\pi$
$659$	9.05013	−	6.57531i	0.352543	−	0.256138i	0.749935	+	0.661511i	$0.230085\pi$
$660$		0			0
$661$	37.7102	+	27.3981i	1.46676	+	1.06566i	0.981538	+	0.191268i	$0.0612599\pi$
$661$	37.7102	+	27.3981i	1.46676	+	1.06566i	0.485218	+	0.874393i	$0.338740\pi$
$662$		0			0
$663$	8.18995	−	5.95035i	0.318071	−	0.231092i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.47746	+	7.62483i	−0.0959276	+	0.295235i
$668$		0			0
$669$	0.242204	−	0.745429i	0.00936417	−	0.0288199i
$670$		0			0
$671$	−9.59412	−	29.5277i	−0.370377	−	1.13990i
$672$		0			0
$673$	−11.1110	−	8.07264i	−0.428299	−	0.311178i	0.352669	−	0.935748i	$-0.385274\pi$
$673$	−11.1110	−	8.07264i	−0.428299	−	0.311178i	−0.780968	+	0.624570i	$0.785274\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.7888	+	21.6428i	1.14488	+	0.831801i	0.987791	−	0.155784i	$-0.0497905\pi$
$677$	29.7888	+	21.6428i	1.14488	+	0.831801i	0.157085	+	0.987585i	$0.449790\pi$
$678$		0			0
$679$	−5.70024	−	17.5435i	−0.218755	−	0.673259i
$680$		0			0
$681$	7.40078	−	22.7772i	0.283598	−	0.872826i
$682$		0			0
$683$	9.29850	−	28.6179i	0.355797	−	1.09503i	−0.599748	−	0.800189i	$-0.704733\pi$
$683$	9.29850	−	28.6179i	0.355797	−	1.09503i	0.955546	−	0.294843i	$-0.0952674\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.47697	+	3.25271i	−0.170807	+	0.124098i
$688$		0			0
$689$	29.8222	+	21.6671i	1.13614	+	0.825451i
$690$		0			0
$691$	6.76839	−	4.91752i	0.257482	−	0.187071i	−0.451554	−	0.892244i	$-0.649130\pi$
$691$	6.76839	−	4.91752i	0.257482	−	0.187071i	0.709036	+	0.705172i	$0.249130\pi$
$692$		0			0
$693$	22.8968			0.869779
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.52148	−	7.76033i	−0.0955080	−	0.293943i
$698$		0			0
$699$	0.907742			0.0343340
$700$		0			0
$701$	−3.42495			−0.129359			−0.0646794	−	0.997906i	$-0.520602\pi$
$701$	−3.42495			−0.129359			−0.0646794	+	0.997906i	$0.520602\pi$
$702$		0			0
$703$	−3.40581	−	10.4820i	−0.128453	−	0.395336i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−43.3478			−1.63026
$708$		0			0
$709$	40.0330	−	29.0857i	1.50347	−	1.09234i	0.534499	−	0.845169i	$-0.320500\pi$
$709$	40.0330	−	29.0857i	1.50347	−	1.09234i	0.968973	−	0.247168i	$-0.0794998\pi$
$710$		0			0
$711$	−10.0910	−	7.33156i	−0.378443	−	0.274955i
$712$		0			0
$713$	17.8421	−	12.9630i	0.668191	−	0.485469i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.47294	−	10.6886i	0.129699	−	0.399173i
$718$		0			0
$719$	8.08148	−	24.8722i	0.301388	−	0.927578i	−0.679612	−	0.733572i	$-0.737852\pi$
$719$	8.08148	−	24.8722i	0.301388	−	0.927578i	0.981000	−	0.194006i	$-0.0621481\pi$
$720$		0			0
$721$	14.9038	+	45.8692i	0.555046	+	1.70826i
$722$		0			0
$723$	−16.3840	−	11.9037i	−0.609327	−	0.442702i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−28.0059	−	20.3475i	−1.03868	−	0.754647i	−0.0686545	−	0.997640i	$-0.521871\pi$
$727$	−28.0059	−	20.3475i	−1.03868	−	0.754647i	−0.970028	+	0.242994i	$0.921871\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	8.86463	−	27.2825i	0.327870	−	1.00908i
$732$		0			0
$733$	−5.39704	+	16.6104i	−0.199344	+	0.613518i	0.800554	+	0.599260i	$0.204539\pi$
$733$	−5.39704	+	16.6104i	−0.199344	+	0.613518i	−0.999898	+	0.0142577i	$0.995461\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.2515	+	7.44814i	−0.377618	+	0.274356i
$738$		0			0
$739$	−16.2358	−	11.7960i	−0.597243	−	0.433922i	0.247656	−	0.968848i	$-0.420340\pi$
$739$	−16.2358	−	11.7960i	−0.597243	−	0.433922i	−0.844899	+	0.534926i	$0.820340\pi$
$740$		0			0
$741$	17.8724	−	12.9850i	0.656557	−	0.477017i
$742$		0			0
$743$	−5.84644			−0.214485			−0.107243	−	0.994233i	$-0.534202\pi$
$743$	−5.84644			−0.214485			−0.107243	+	0.994233i	$0.534202\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.74724	+	8.45513i	0.100516	+	0.309357i
$748$		0			0
$749$	−1.02104			−0.0373081
$750$		0			0
$751$	−32.7925			−1.19662			−0.598308	−	0.801266i	$-0.704160\pi$
$751$	−32.7925			−1.19662			−0.598308	+	0.801266i	$0.704160\pi$
$752$		0			0
$753$	9.48431	+	29.1897i	0.345627	+	1.06373i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−22.6371			−0.822759			−0.411379	−	0.911464i	$-0.634953\pi$
$757$	−22.6371			−0.822759			−0.411379	+	0.911464i	$0.634953\pi$
$758$		0			0
$759$	26.7376	−	19.4260i	0.970513	−	0.705119i
$760$		0			0
$761$	29.3923	+	21.3547i	1.06547	+	0.774109i	0.975092	−	0.221799i	$-0.0711929\pi$
$761$	29.3923	+	21.3547i	1.06547	+	0.774109i	0.0903767	+	0.995908i	$0.471193\pi$
$762$		0			0
$763$	25.0280	−	18.1839i	0.906073	−	0.658301i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.1910	+	34.4425i	−0.404085	+	1.24365i
$768$		0			0
$769$	4.51902	−	13.9081i	0.162960	−	0.501539i	−0.835920	−	0.548851i	$-0.815065\pi$
$769$	4.51902	−	13.9081i	0.162960	−	0.501539i	0.998880	+	0.0473119i	$0.0150655\pi$
$770$		0			0
$771$	1.47569	+	4.54170i	0.0531456	+	0.163565i
$772$		0			0
$773$	24.6953	+	17.9422i	0.888229	+	0.645336i	0.935416	−	0.353550i	$-0.115025\pi$
$773$	24.6953	+	17.9422i	0.888229	+	0.645336i	−0.0471864	+	0.998886i	$0.515025\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.02676	+	5.10524i	0.252084	+	0.183150i
$778$		0			0
$779$	−5.50245	−	16.9348i	−0.197146	−	0.606752i
$780$		0			0
$781$	−13.2699	+	40.8404i	−0.474833	+	1.46138i
$782$		0			0
$783$	−0.370972	+	1.14173i	−0.0132575	+	0.0408023i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	39.7644	−	28.8905i	1.41745	−	1.02984i	0.425262	−	0.905070i	$-0.360182\pi$
$787$	39.7644	−	28.8905i	1.41745	−	1.02984i	0.992186	−	0.124766i	$-0.0398182\pi$
$788$		0			0
$789$	−0.978638	−	0.711022i	−0.0348404	−	0.0253130i
$790$		0			0
$791$	−35.9663	+	26.1310i	−1.27881	+	0.929112i
$792$		0			0
$793$	23.6065			0.838290
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.7613	+	42.3529i	0.487450	+	1.50022i	0.828401	+	0.560136i	$0.189251\pi$
$797$	13.7613	+	42.3529i	0.487450	+	1.50022i	−0.340951	+	0.940081i	$0.610749\pi$
$798$		0			0
$799$	−0.697388			−0.0246718
$800$		0			0
$801$	14.5774			0.515069
$802$		0			0
$803$	7.45487	+	22.9437i	0.263077	+	0.809667i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	25.5249			0.898519
$808$		0			0
$809$	24.5060	−	17.8046i	0.861584	−	0.625978i	−0.0667312	−	0.997771i	$-0.521257\pi$
$809$	24.5060	−	17.8046i	0.861584	−	0.625978i	0.928316	+	0.371793i	$0.121257\pi$
$810$		0			0
$811$	−5.05382	−	3.67182i	−0.177464	−	0.128935i	0.495507	−	0.868604i	$-0.334982\pi$
$811$	−5.05382	−	3.67182i	−0.177464	−	0.128935i	−0.672971	+	0.739669i	$0.734982\pi$
$812$		0			0
$813$	−4.75170	+	3.45231i	−0.166649	+	0.121078i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	19.3447	−	59.5367i	0.676784	−	2.08293i
$818$		0			0
$819$	−5.37980	+	16.5573i	−0.187985	+	0.578559i
$820$		0			0
$821$	−5.95524	−	18.3284i	−0.207839	−	0.639664i	−0.999585	−	0.0288127i	$-0.990827\pi$
$821$	−5.95524	−	18.3284i	−0.207839	−	0.639664i	0.791745	−	0.610851i	$-0.209173\pi$
$822$		0			0
$823$	−6.11414	−	4.44218i	−0.213126	−	0.154845i	0.476101	−	0.879391i	$-0.342050\pi$
$823$	−6.11414	−	4.44218i	−0.213126	−	0.154845i	−0.689227	+	0.724546i	$0.742050\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.3821	−	18.4412i	−0.882621	−	0.641262i	0.0513225	−	0.998682i	$-0.483656\pi$
$827$	−25.3821	−	18.4412i	−0.882621	−	0.641262i	−0.933944	+	0.357420i	$0.883656\pi$
$828$		0			0
$829$	8.55625	+	26.3334i	0.297171	+	0.914597i	0.982484	+	0.186349i	$0.0596654\pi$
$829$	8.55625	+	26.3334i	0.297171	+	0.914597i	−0.685313	+	0.728249i	$0.740335\pi$
$830$		0			0
$831$	−1.51585	+	4.66531i	−0.0525843	+	0.161838i
$832$		0			0
$833$	11.9775	−	36.8629i	0.414996	−	1.27723i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.67165	−	1.94107i	0.0923459	−	0.0670932i
$838$		0			0
$839$	30.5642	+	22.2062i	1.05519	+	0.766643i	0.973193	−	0.229990i	$-0.0738693\pi$
$839$	30.5642	+	22.2062i	1.05519	+	0.766643i	0.0819999	+	0.996632i	$0.473869\pi$
$840$		0			0
$841$	22.2956	−	16.1987i	0.768812	−	0.558575i
$842$		0			0
$843$	1.29526			0.0446110
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−19.2881	−	59.3626i	−0.662747	−	2.03972i
$848$		0			0
$849$	30.2297			1.03748
$850$		0			0
$851$	12.5368			0.429756
$852$		0			0
$853$	15.2552	+	46.9508i	0.522329	+	1.60756i	0.769537	+	0.638602i	$0.220487\pi$
$853$	15.2552	+	46.9508i	0.522329	+	1.60756i	−0.247208	+	0.968962i	$0.579513\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.7692			0.538667			0.269333	−	0.963047i	$-0.413197\pi$
$857$	15.7692			0.538667			0.269333	+	0.963047i	$0.413197\pi$
$858$		0			0
$859$	−7.60223	+	5.52335i	−0.259385	+	0.188454i	−0.709876	−	0.704327i	$-0.751249\pi$
$859$	−7.60223	+	5.52335i	−0.259385	+	0.188454i	0.450491	+	0.892781i	$0.351249\pi$
$860$		0			0
$861$	11.3525	+	8.24807i	0.386892	+	0.281093i
$862$		0			0
$863$	−14.4575	+	10.5040i	−0.492140	+	0.357560i	−0.806007	−	0.591907i	$-0.798375\pi$
$863$	−14.4575	+	10.5040i	−0.492140	+	0.357560i	0.313867	+	0.949467i	$0.398375\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.01655	−	9.28400i	0.102448	−	0.315301i
$868$		0			0
$869$	−19.0748	+	58.7061i	−0.647068	+	1.99147i
$870$		0			0
$871$	−2.97728	−	9.16312i	−0.100881	−	0.310481i
$872$		0			0
$873$	−3.22546	−	2.34344i	−0.109165	−	0.0793133i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.3238	−	10.4069i	−0.483681	−	0.351415i	0.319068	−	0.947732i	$-0.396630\pi$
$877$	−14.3238	−	10.4069i	−0.483681	−	0.351415i	−0.802749	+	0.596317i	$0.796630\pi$
$878$		0			0
$879$	2.49325	+	7.67342i	0.0840951	+	0.258818i
$880$		0			0
$881$	−9.82007	+	30.2231i	−0.330847	+	1.01824i	0.637885	+	0.770131i	$0.279809\pi$
$881$	−9.82007	+	30.2231i	−0.330847	+	1.01824i	−0.968732	+	0.248110i	$0.920191\pi$
$882$		0			0
$883$	−10.6950	+	32.9158i	−0.359916	+	1.10771i	0.593188	+	0.805064i	$0.297869\pi$
$883$	−10.6950	+	32.9158i	−0.359916	+	1.10771i	−0.953104	+	0.302643i	$0.902131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.0735	−	16.7639i	0.774732	−	0.562876i	−0.128661	−	0.991689i	$-0.541068\pi$
$887$	23.0735	−	16.7639i	0.774732	−	0.562876i	0.903393	+	0.428813i	$0.141068\pi$
$888$		0			0
$889$	−59.8610	−	43.4916i	−2.00767	−	1.45866i
$890$		0			0
$891$	4.00366	−	2.90883i	0.134128	−	0.0974495i
$892$		0			0
$893$	−1.52186			−0.0509271
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.76524	+	23.8990i	0.259274	+	0.797963i
$898$		0			0
$899$	3.96444			0.132221
$900$		0			0
$901$	−26.3567			−0.878069
$902$		0			0
$903$	15.2448	+	46.9185i	0.507314	+	1.56135i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.01754			−0.233013			−0.116507	−	0.993190i	$-0.537170\pi$
$907$	−7.01754			−0.233013			−0.116507	+	0.993190i	$0.537170\pi$
$908$		0			0
$909$	−7.57965	+	5.50693i	−0.251401	+	0.182653i
$910$		0			0
$911$	16.9145	+	12.2891i	0.560403	+	0.407157i	0.831606	−	0.555365i	$-0.187422\pi$
$911$	16.9145	+	12.2891i	0.560403	+	0.407157i	−0.271203	+	0.962522i	$0.587422\pi$
$912$		0			0
$913$	35.5936	−	25.8602i	1.17797	−	0.855849i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.6184	−	54.2240i	0.581812	−	1.79063i
$918$		0			0
$919$	18.4658	−	56.8320i	0.609132	−	1.87471i	0.143726	−	0.989618i	$-0.454092\pi$
$919$	18.4658	−	56.8320i	0.609132	−	1.87471i	0.465406	−	0.885097i	$-0.345908\pi$
$920$		0			0
$921$	−4.56573	−	14.0519i	−0.150446	−	0.463025i
$922$		0			0
$923$	−26.4149	−	19.1916i	−0.869458	−	0.631698i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	8.43328	+	6.12713i	0.276985	+	0.201241i
$928$		0			0
$929$	−12.4320	−	38.2618i	−0.407881	−	1.25533i	−0.918466	−	0.395501i	$-0.870571\pi$
$929$	−12.4320	−	38.2618i	−0.407881	−	1.25533i	0.510585	−	0.859828i	$-0.329429\pi$
$930$		0			0
$931$	26.1376	−	80.4434i	0.856626	−	2.63642i
$932$		0			0
$933$	2.82866	−	8.70572i	0.0926061	−	0.285012i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−39.9780	+	29.0457i	−1.30602	+	0.948881i	−0.999995	−	0.00314114i	$-0.999000\pi$
$937$	−39.9780	+	29.0457i	−1.30602	+	0.948881i	−0.306028	+	0.952022i	$0.599000\pi$
$938$		0			0
$939$	10.7238	+	7.79128i	0.349957	+	0.254259i
$940$		0			0
$941$	−18.0130	+	13.0872i	−0.587207	+	0.426631i	−0.841315	−	0.540545i	$-0.818218\pi$
$941$	−18.0130	+	13.0872i	−0.587207	+	0.426631i	0.254108	+	0.967176i	$0.418218\pi$
$942$		0			0
$943$	20.2546			0.659579
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.0251	+	33.9316i	0.358266	+	1.10263i	0.954091	+	0.299516i	$0.0968251\pi$
$947$	11.0251	+	33.9316i	0.358266	+	1.10263i	−0.595825	+	0.803114i	$0.703175\pi$
$948$		0			0
$949$	−18.3428			−0.595433
$950$		0			0
$951$	−0.790550			−0.0256354
$952$		0			0
$953$	−0.867341	−	2.66940i	−0.0280959	−	0.0864704i	0.936025	−	0.351933i	$-0.114475\pi$
$953$	−0.867341	−	2.66940i	−0.0280959	−	0.0864704i	−0.964121	+	0.265462i	$0.914475\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	5.94099			0.192045
$958$		0			0
$959$	21.3153	−	15.4865i	0.688308	−	0.500085i
$960$		0			0
$961$	16.2568	+	11.8113i	0.524413	+	0.381008i
$962$		0			0
$963$	−0.178536	+	0.129714i	−0.00575324	+	0.00417998i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	3.56243	−	10.9640i	0.114560	−	0.352580i	−0.877295	−	0.479952i	$-0.840654\pi$
$967$	3.56243	−	10.9640i	0.114560	−	0.352580i	0.991855	+	0.127372i	$0.0406542\pi$
$968$		0			0
$969$	−4.88107	+	15.0224i	−0.156803	+	0.482589i
$970$		0			0
$971$	7.15578	+	22.0232i	0.229640	+	0.706759i	0.997787	+	0.0664858i	$0.0211787\pi$
$971$	7.15578	+	22.0232i	0.229640	+	0.706759i	−0.768148	+	0.640273i	$0.778821\pi$
$972$		0			0
$973$	−67.3646	−	48.9433i	−2.15961	−	1.56905i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.68304	+	4.85551i	0.213809	+	0.155342i	0.689536	−	0.724252i	$-0.257815\pi$
$977$	6.68304	+	4.85551i	0.213809	+	0.155342i	−0.475726	+	0.879593i	$0.657815\pi$
$978$		0			0
$979$	−22.2927	−	68.6100i	−0.712479	−	2.19278i
$980$		0			0
$981$	2.06621	−	6.35914i	0.0659690	−	0.203032i
$982$		0			0
$983$	6.11506	−	18.8202i	0.195040	−	0.600271i	−0.804936	−	0.593361i	$-0.797800\pi$
$983$	6.11506	−	18.8202i	0.195040	−	0.600271i	0.999976	−	0.00690994i	$-0.00219952\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.970269	−	0.704941i	0.0308840	−	0.0224385i
$988$		0			0
$989$	57.6083	+	41.8549i	1.83184	+	1.33091i
$990$		0			0
$991$	−17.3036	+	12.5718i	−0.549666	+	0.399355i	−0.827662	−	0.561227i	$-0.810330\pi$
$991$	−17.3036	+	12.5718i	−0.549666	+	0.399355i	0.277997	+	0.960582i	$0.410330\pi$
$992$		0			0
$993$	3.37370			0.107061
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.43350	+	16.7226i	0.172081	+	0.529610i	0.999488	−	0.0319923i	$-0.0101852\pi$
$997$	5.43350	+	16.7226i	0.172081	+	0.529610i	−0.827407	+	0.561602i	$0.810185\pi$
$998$		0			0
$999$	1.87725			0.0593935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.1201.1		24
5.2	odd	4		300.2.o.a.109.2	✓	24
5.3	odd	4		1500.2.o.c.49.6		24
5.4	even	2		1500.2.m.c.1201.6		24
15.2	even	4		900.2.w.c.109.3		24
25.2	odd	20		1500.2.o.c.949.6		24
25.6	even	5		7500.2.a.m.1.1		12
25.8	odd	20		7500.2.d.g.1249.12		24
25.11	even	5	inner	1500.2.m.d.301.1		24
25.14	even	10		1500.2.m.c.301.6		24
25.17	odd	20		7500.2.d.g.1249.13		24
25.19	even	10		7500.2.a.n.1.12		12
25.23	odd	20		300.2.o.a.289.2	yes	24
75.23	even	20		900.2.w.c.289.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.2	✓	24	5.2	odd	4
300.2.o.a.289.2	yes	24	25.23	odd	20
900.2.w.c.109.3		24	15.2	even	4
900.2.w.c.289.3		24	75.23	even	20
1500.2.m.c.301.6		24	25.14	even	10
1500.2.m.c.1201.6		24	5.4	even	2
1500.2.m.d.301.1		24	25.11	even	5	inner
1500.2.m.d.1201.1		24	1.1	even	1	trivial
1500.2.o.c.49.6		24	5.3	odd	4
1500.2.o.c.949.6		24	25.2	odd	20
7500.2.a.m.1.1		12	25.6	even	5
7500.2.a.n.1.12		12	25.19	even	10
7500.2.d.g.1249.12		24	25.8	odd	20
7500.2.d.g.1249.13		24	25.17	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} -4.62675 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} -4.62675 q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.00366 + 2.90883i) q^{11} +(-3.04414 + 2.21170i) q^{13} +(0.831378 - 2.55872i) q^{17} +(1.81426 - 5.58371i) q^{19} +(1.42974 + 4.40030i) q^{21} +(5.40285 + 3.92540i) q^{23} +(0.809017 + 0.587785i) q^{27} +(0.370972 + 1.14173i) q^{29} +(1.02048 - 3.14072i) q^{31} +(1.52926 - 4.70659i) q^{33} +(1.51873 - 1.10342i) q^{37} +(3.04414 + 2.21170i) q^{39} +(2.45366 - 1.78269i) q^{41} +10.6626 q^{43} +(-0.0801015 - 0.246527i) q^{47} +14.4068 q^{49} -2.69040 q^{51} +(-3.02731 - 9.31711i) q^{53} -5.87106 q^{57} +(7.78643 - 5.65717i) q^{59} +(-5.07552 - 3.68758i) q^{61} +(3.74312 - 2.71953i) q^{63} +(-0.791247 + 2.43521i) q^{67} +(2.06370 - 6.35143i) q^{69} +(2.68143 + 8.25259i) q^{71} +(3.94381 + 2.86534i) q^{73} +(-18.5239 - 13.4584i) q^{77} +(3.85443 + 11.8627i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.74724 - 8.45513i) q^{83} +(0.971218 - 0.705631i) q^{87} +(-11.7934 - 8.56841i) q^{89} +(14.0845 - 10.2330i) q^{91} -3.30235 q^{93} +(1.23202 + 3.79176i) q^{97} -4.94880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

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