LMFDB - Embedded newform 1500.2.o.c.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, 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 $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.c.949.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{3} +4.62675i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{3} +4.62675i q^{7} +(0.809017 - 0.587785i) q^{9} +(4.00366 + 2.90883i) q^{11} +(-2.21170 - 3.04414i) q^{13} +(-2.55872 - 0.831378i) q^{17} +(-1.81426 + 5.58371i) q^{19} +(1.42974 + 4.40030i) q^{21} +(-3.92540 + 5.40285i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-0.370972 - 1.14173i) q^{29} +(1.02048 - 3.14072i) q^{31} +(4.70659 + 1.52926i) q^{33} +(-1.10342 - 1.51873i) q^{37} +(-3.04414 - 2.21170i) q^{39} +(2.45366 - 1.78269i) q^{41} +10.6626i q^{43} +(-0.246527 + 0.0801015i) q^{47} -14.4068 q^{49} -2.69040 q^{51} +(9.31711 - 3.02731i) q^{53} +5.87106i q^{57} +(-7.78643 + 5.65717i) q^{59} +(-5.07552 - 3.68758i) q^{61} +(2.71953 + 3.74312i) q^{63} +(2.43521 + 0.791247i) q^{67} +(-2.06370 + 6.35143i) q^{69} +(2.68143 + 8.25259i) q^{71} +(-2.86534 + 3.94381i) q^{73} +(-13.4584 + 18.5239i) q^{77} +(-3.85443 - 11.8627i) q^{79} +(0.309017 - 0.951057i) q^{81} +(8.45513 + 2.74724i) q^{83} +(-0.705631 - 0.971218i) q^{87} +(11.7934 + 8.56841i) q^{89} +(14.0845 - 10.2330i) q^{91} -3.30235i q^{93} +(3.79176 - 1.23202i) q^{97} +4.94880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

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
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.62675i			1.74875i	0.485254	+	0.874373i	$0.338727\pi$
$7$			4.62675i			1.74875i	−0.485254	+	0.874373i	$0.661273\pi$
$8$		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
$13$	−2.21170	−	3.04414i	−0.613415	−	0.844294i	0.383438	−	0.923567i	$-0.374740\pi$
$13$	−2.21170	−	3.04414i	−0.613415	−	0.844294i	−0.996853	+	0.0792730i	$0.974740\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.55872	−	0.831378i	−0.620580	−	0.201639i	−0.0181824	−	0.999835i	$-0.505788\pi$
$17$	−2.55872	−	0.831378i	−0.620580	−	0.201639i	−0.602398	+	0.798196i	$0.705788\pi$
$18$		0			0
$19$	−1.81426	+	5.58371i	−0.416219	+	1.28099i	0.494937	+	0.868929i	$0.335191\pi$
$19$	−1.81426	+	5.58371i	−0.416219	+	1.28099i	−0.911156	+	0.412062i	$0.864809\pi$
$20$		0			0
$21$	1.42974	+	4.40030i	0.311996	+	0.960224i
$22$		0			0
$23$	−3.92540	+	5.40285i	−0.818502	+	1.12657i	0.171453	+	0.985192i	$0.445154\pi$
$23$	−3.92540	+	5.40285i	−0.818502	+	1.12657i	−0.989955	+	0.141379i	$0.954846\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$		0			0
$29$	−0.370972	−	1.14173i	−0.0688878	−	0.212015i	0.910686	−	0.413099i	$-0.135554\pi$
$29$	−0.370972	−	1.14173i	−0.0688878	−	0.212015i	−0.979574	+	0.201084i	$0.935554\pi$
$30$		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
$33$	4.70659	+	1.52926i	0.819311	+	0.266210i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.10342	−	1.51873i	−0.181401	−	0.249677i	0.708627	−	0.705584i	$-0.249315\pi$
$37$	−1.10342	−	1.51873i	−0.181401	−	0.249677i	−0.890028	+	0.455907i	$0.849315\pi$
$38$		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
$43$			10.6626i			1.62603i	0.582244	+	0.813014i	$0.302175\pi$
$43$			10.6626i			1.62603i	−0.582244	+	0.813014i	$0.697825\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.246527	+	0.0801015i	−0.0359597	+	0.0116840i	−0.326942	−	0.945045i	$-0.606018\pi$
$47$	−0.246527	+	0.0801015i	−0.0359597	+	0.0116840i	0.290982	+	0.956729i	$0.406018\pi$
$48$		0			0
$49$	−14.4068			−2.05811
$50$		0			0
$51$	−2.69040			−0.376731
$52$		0			0
$53$	9.31711	−	3.02731i	1.27980	−	0.415833i	0.411292	−	0.911504i	$-0.365078\pi$
$53$	9.31711	−	3.02731i	1.27980	−	0.415833i	0.868511	+	0.495670i	$0.165078\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			5.87106i			0.777641i
$58$		0			0
$59$	−7.78643	+	5.65717i	−1.01371	+	0.736501i	−0.964983	−	0.262311i	$-0.915515\pi$
$59$	−7.78643	+	5.65717i	−1.01371	+	0.736501i	−0.0487233	+	0.998812i	$0.515515\pi$
$60$		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
$63$	2.71953	+	3.74312i	0.342629	+	0.471589i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.43521	+	0.791247i	0.297508	+	0.0966662i	0.453968	−	0.891018i	$-0.350008\pi$
$67$	2.43521	+	0.791247i	0.297508	+	0.0966662i	−0.156460	+	0.987684i	$0.550008\pi$
$68$		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
$73$	−2.86534	+	3.94381i	−0.335363	+	0.461588i	−0.943080	−	0.332566i	$-0.892086\pi$
$73$	−2.86534	+	3.94381i	−0.335363	+	0.461588i	0.607717	+	0.794154i	$0.292086\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−13.4584	+	18.5239i	−1.53373	+	2.11100i
$78$		0			0
$79$	−3.85443	−	11.8627i	−0.433657	−	1.33466i	−0.894457	−	0.447155i	$-0.852437\pi$
$79$	−3.85443	−	11.8627i	−0.433657	−	1.33466i	0.460800	−	0.887504i	$-0.347563\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	8.45513	+	2.74724i	0.928071	+	0.301549i	0.733774	−	0.679394i	$-0.237757\pi$
$83$	8.45513	+	2.74724i	0.928071	+	0.301549i	0.194298	+	0.980943i	$0.437757\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.705631	−	0.971218i	−0.0756516	−	0.104125i
$88$		0			0
$89$	11.7934	+	8.56841i	1.25010	+	0.908249i	0.998228	−	0.0595118i	$-0.0189544\pi$
$89$	11.7934	+	8.56841i	1.25010	+	0.908249i	0.251870	+	0.967761i	$0.418954\pi$
$90$		0			0
$91$	14.0845	−	10.2330i	1.47646	−	1.07271i
$92$		0			0
$93$		−	3.30235i		−	0.342437i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.79176	−	1.23202i	0.384995	−	0.125092i	−0.110123	−	0.993918i	$-0.535125\pi$
$97$	3.79176	−	1.23202i	0.384995	−	0.125092i	0.495119	+	0.868825i	$0.335125\pi$
$98$		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
$103$	9.91391	−	3.22123i	0.976847	−	0.317397i	0.223270	−	0.974757i	$-0.428327\pi$
$103$	9.91391	−	3.22123i	0.976847	−	0.317397i	0.753577	+	0.657360i	$0.228327\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	0.220683i		−	0.0213342i	−0.999943	−	0.0106671i	$-0.996604\pi$
$107$		−	0.220683i		−	0.0213342i	0.999943	−	0.0106671i	$-0.00339551\pi$
$108$		0			0
$109$	5.40941	−	3.93017i	0.518127	−	0.376442i	−0.297771	−	0.954637i	$-0.596243\pi$
$109$	5.40941	−	3.93017i	0.518127	−	0.376442i	0.815898	+	0.578196i	$0.196243\pi$
$110$		0			0
$111$	−1.51873	−	1.10342i	−0.144151	−	0.104732i
$112$		0			0
$113$	5.64782	+	7.77355i	0.531302	+	0.731274i	0.987328	−	0.158692i	$-0.0507277\pi$
$113$	5.64782	+	7.77355i	0.531302	+	0.731274i	−0.456026	+	0.889966i	$0.650728\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.57861	−	1.16276i	−0.330842	−	0.107497i
$118$		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
$123$	1.78269	−	2.45366i	0.160740	−	0.221239i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.40003	−	12.9380i	0.834118	−	1.14806i	−0.153025	−	0.988222i	$-0.548902\pi$
$127$	9.40003	−	12.9380i	0.834118	−	1.14806i	0.987143	−	0.159842i	$-0.0510985\pi$
$128$		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
$133$	−25.8344	−	8.39411i	−2.24013	−	0.727862i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.34717	+	4.60698i	0.285968	+	0.393601i	0.927699	−	0.373329i	$-0.121784\pi$
$137$	3.34717	+	4.60698i	0.285968	+	0.393601i	−0.641731	+	0.766930i	$0.721784\pi$
$138$		0			0
$139$	−14.5598	−	10.5783i	−1.23495	−	0.897242i	−0.237697	−	0.971339i	$-0.576393\pi$
$139$	−14.5598	−	10.5783i	−1.23495	−	0.897242i	−0.997251	+	0.0740969i	$0.976393\pi$
$140$		0			0
$141$	−0.209709	+	0.152362i	−0.0176606	+	0.0128312i
$142$		0			0
$143$		−	18.6212i		−	1.55718i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−13.7017	+	4.45195i	−1.13010	+	0.367190i
$148$		0			0
$149$	1.09001			0.0892972			0.0446486	−	0.999003i	$-0.485783\pi$
$149$	1.09001			0.0892972			0.0446486	+	0.999003i	$0.485783\pi$
$150$		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
$153$	−2.55872	+	0.831378i	−0.206860	+	0.0672129i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	3.98415i		−	0.317970i	−0.987281	−	0.158985i	$-0.949178\pi$
$157$		−	3.98415i		−	0.317970i	0.987281	−	0.158985i	$-0.0508221\pi$
$158$		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
$163$	12.8322	+	17.6620i	1.00509	+	1.38339i	0.922148	+	0.386837i	$0.126432\pi$
$163$	12.8322	+	17.6620i	1.00509	+	1.38339i	0.0829441	+	0.996554i	$0.473568\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.7118	−	4.78015i	−1.13843	−	0.369899i	−0.321658	−	0.946856i	$-0.604240\pi$
$167$	−14.7118	−	4.78015i	−1.13843	−	0.369899i	−0.816775	+	0.576957i	$0.804240\pi$
$168$		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
$173$	−10.0925	+	13.8911i	−0.767317	+	1.05612i	0.229253	+	0.973367i	$0.426372\pi$
$173$	−10.0925	+	13.8911i	−0.767317	+	1.05612i	−0.996570	+	0.0827547i	$0.973628\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.65717	+	7.78643i	−0.425219	+	0.585264i
$178$		0			0
$179$	4.46392	+	13.7385i	0.333649	+	1.02687i	0.967384	+	0.253316i	$0.0815213\pi$
$179$	4.46392	+	13.7385i	0.333649	+	1.02687i	−0.633734	+	0.773551i	$0.718479\pi$
$180$		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
$183$	−5.96664	−	1.93868i	−0.441066	−	0.143311i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.82590	−	10.7714i	−0.572287	−	0.787685i
$188$		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
$193$		−	16.3253i		−	1.17512i	−0.809181	−	0.587560i	$-0.800089\pi$
$193$		−	16.3253i		−	1.17512i	0.809181	−	0.587560i	$-0.199911\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.9652	−	4.21264i	0.923730	−	0.300138i	0.191734	−	0.981447i	$-0.438589\pi$
$197$	12.9652	−	4.21264i	0.923730	−	0.300138i	0.731996	+	0.681309i	$0.238589\pi$
$198$		0			0
$199$	6.07817			0.430870			0.215435	−	0.976518i	$-0.430883\pi$
$199$	6.07817			0.430870			0.215435	+	0.976518i	$0.430883\pi$
$200$		0			0
$201$	2.56053			0.180606
$202$		0			0
$203$	5.28252	−	1.71639i	0.370760	−	0.120467i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.67829i			0.464173i
$208$		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
$213$	5.10038	+	7.02007i	0.349472	+	0.481008i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	14.5313	+	4.72151i	0.986450	+	0.320517i
$218$		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
$223$	−0.460700	+	0.634100i	−0.0308508	+	0.0424624i	−0.824164	−	0.566352i	$-0.808354\pi$
$223$	−0.460700	+	0.634100i	−0.0308508	+	0.0424624i	0.793313	+	0.608814i	$0.208354\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.0771	−	19.3755i	0.934331	−	1.28600i	−0.0238153	−	0.999716i	$-0.507581\pi$
$227$	14.0771	−	19.3755i	0.934331	−	1.28600i	0.958146	−	0.286280i	$-0.0924186\pi$
$228$		0			0
$229$	1.71005	+	5.26299i	0.113003	+	0.347788i	0.991525	−	0.129914i	$-0.0414700\pi$
$229$	1.71005	+	5.26299i	0.113003	+	0.347788i	−0.878522	+	0.477702i	$0.841470\pi$
$230$		0			0
$231$	−7.07551	+	21.7762i	−0.465535	+	1.43277i
$232$		0			0
$233$	−0.863314	−	0.280508i	−0.0565576	−	0.0183767i	0.280602	−	0.959824i	$-0.409466\pi$
$233$	−0.863314	−	0.280508i	−0.0565576	−	0.0183767i	−0.337159	+	0.941448i	$0.609466\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.33156	−	10.0910i	−0.476236	−	0.655482i
$238$		0			0
$239$	−9.09227	−	6.60592i	−0.588130	−	0.427302i	0.253516	−	0.967331i	$-0.418413\pi$
$239$	−9.09227	−	6.60592i	−0.588130	−	0.427302i	−0.841646	+	0.540030i	$0.818413\pi$
$240$		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
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	21.0102	−	6.82663i	1.33685	−	0.434368i
$248$		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
$253$	−31.4319	+	10.2129i	−1.97611	+	0.642077i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			4.77543i			0.297883i	0.988846	+	0.148941i	$0.0475866\pi$
$257$			4.77543i			0.297883i	−0.988846	+	0.148941i	$0.952413\pi$
$258$		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
$263$	0.711022	+	0.978638i	0.0438435	+	0.0603454i	0.830376	−	0.557204i	$-0.188126\pi$
$263$	0.711022	+	0.978638i	0.0438435	+	0.0603454i	−0.786532	+	0.617549i	$0.788126\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	13.8640	+	4.50468i	0.848461	+	0.275682i
$268$		0			0
$269$	7.88763	−	24.2756i	0.480917	−	1.48011i	−0.356891	−	0.934146i	$-0.616163\pi$
$269$	7.88763	−	24.2756i	0.480917	−	1.48011i	0.837808	−	0.545965i	$-0.183837\pi$
$270$		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
$273$	10.2330	−	14.0845i	0.619328	−	0.852432i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.88332	+	3.96855i	−0.173242	+	0.238447i	−0.886805	−	0.462144i	$-0.847080\pi$
$277$	−2.88332	+	3.96855i	−0.173242	+	0.238447i	0.713563	+	0.700591i	$0.247080\pi$
$278$		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
$283$	−28.7501	−	9.34149i	−1.70902	−	0.555294i	−0.718849	−	0.695166i	$-0.755331\pi$
$283$	−28.7501	−	9.34149i	−1.70902	−	0.555294i	−0.990169	+	0.139873i	$0.955331\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.24807	+	11.3525i	0.486868	+	0.670116i
$288$		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
$293$		−	8.06831i		−	0.471356i	−0.971831	−	0.235678i	$-0.924269\pi$
$293$		−	8.06831i		−	0.471356i	0.971831	−	0.235678i	$-0.0757310\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.70659	−	1.52926i	0.273104	−	0.0887368i
$298$		0			0
$299$	25.1289			1.45324
$300$		0			0
$301$	−49.3331			−2.84351
$302$		0			0
$303$	8.91041	−	2.89517i	0.511890	−	0.166323i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	14.7750i		−	0.843255i	−0.906769	−	0.421628i	$-0.861459\pi$
$307$		−	14.7750i		−	0.843255i	0.906769	−	0.421628i	$-0.138541\pi$
$308$		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
$313$	−7.79128	−	10.7238i	−0.440389	−	0.606144i	0.529909	−	0.848054i	$-0.322226\pi$
$313$	−7.79128	−	10.7238i	−0.440389	−	0.606144i	−0.970299	+	0.241910i	$0.922226\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.751858	−	0.244293i	−0.0422286	−	0.0137209i	0.287827	−	0.957683i	$-0.407067\pi$
$317$	−0.751858	−	0.244293i	−0.0422286	−	0.0137209i	−0.330055	+	0.943962i	$0.607067\pi$
$318$		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
$323$	9.28434	−	12.7788i	0.516595	−	0.711032i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.93017	−	5.40941i	0.217339	−	0.299141i
$328$		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
$333$	−1.78537	−	0.580102i	−0.0978376	−	0.0317894i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.6189	+	14.6157i	0.578449	+	0.796166i	0.993524	−	0.113621i	$-0.0362449\pi$
$337$	10.6189	+	14.6157i	0.578449	+	0.796166i	−0.415076	+	0.909787i	$0.636245\pi$
$338$		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
$343$		−	34.2694i		−	1.85037i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.90284	−	0.943191i	0.155833	−	0.0506332i	−0.230062	−	0.973176i	$-0.573893\pi$
$347$	2.90284	−	0.943191i	0.155833	−	0.0506332i	0.385895	+	0.922543i	$0.373893\pi$
$348$		0			0
$349$	0.628744			0.0336559			0.0168280	−	0.999858i	$-0.494643\pi$
$349$	0.628744			0.0336559			0.0168280	+	0.999858i	$0.494643\pi$
$350$		0			0
$351$	−3.76277			−0.200842
$352$		0			0
$353$	17.9651	−	5.83721i	0.956184	−	0.310683i	0.210958	−	0.977495i	$-0.432342\pi$
$353$	17.9651	−	5.83721i	0.956184	−	0.310683i	0.745226	+	0.666812i	$0.232342\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	12.4478i		−	0.658807i
$358$		0			0
$359$	23.4087	−	17.0074i	1.23546	−	0.897617i	0.238176	−	0.971222i	$-0.423450\pi$
$359$	23.4087	−	17.0074i	1.23546	−	0.897617i	0.997287	+	0.0736053i	$0.0234505\pi$
$360$		0			0
$361$	−12.5149	−	9.09264i	−0.658681	−	0.478560i
$362$		0			0
$363$	7.92957	+	10.9141i	0.416195	+	0.572843i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.11949	−	1.66342i	−0.267235	−	0.0868299i	0.172334	−	0.985038i	$-0.444869\pi$
$367$	−5.11949	−	1.66342i	−0.267235	−	0.0868299i	−0.439570	+	0.898209i	$0.644869\pi$
$368$		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
$373$	−6.46415	+	8.89714i	−0.334701	+	0.460677i	−0.942884	−	0.333120i	$-0.891899\pi$
$373$	−6.46415	+	8.89714i	−0.334701	+	0.460677i	0.608183	+	0.793797i	$0.291899\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.65513	+	3.65447i	−0.136746	+	0.188215i
$378$		0			0
$379$	−2.18405	−	6.72183i	−0.112187	−	0.345277i	0.879163	−	0.476522i	$-0.158103\pi$
$379$	−2.18405	−	6.72183i	−0.112187	−	0.345277i	−0.991350	+	0.131245i	$0.958103\pi$
$380$		0			0
$381$	4.94189	−	15.2096i	0.253181	−	0.779210i
$382$		0			0
$383$	7.70484	+	2.50346i	0.393699	+	0.127921i	0.499175	−	0.866501i	$-0.333637\pi$
$383$	7.70484	+	2.50346i	0.393699	+	0.127921i	−0.105476	+	0.994422i	$0.533637\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.26731	+	8.62621i	0.318585	+	0.438495i
$388$		0			0
$389$	26.7325	+	19.4223i	1.35539	+	0.984750i	0.998723	+	0.0505192i	$0.0160876\pi$
$389$	26.7325	+	19.4223i	1.35539	+	0.984750i	0.356669	+	0.934231i	$0.383912\pi$
$390$		0			0
$391$	14.5358	−	10.5609i	0.735107	−	0.534086i
$392$		0			0
$393$			12.3228i			0.621603i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.7615	+	3.82155i	−0.590294	+	0.191798i	−0.588907	−	0.808201i	$-0.700441\pi$
$397$	−11.7615	+	3.82155i	−0.590294	+	0.191798i	−0.00138688	+	0.999999i	$0.500441\pi$
$398$		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
$403$	−11.8178	+	3.83984i	−0.588687	+	0.191276i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	9.29012i		−	0.460494i
$408$		0			0
$409$	−19.1618	+	13.9219i	−0.947491	+	0.688392i	−0.950212	−	0.311604i	$-0.899134\pi$
$409$	−19.1618	+	13.9219i	−0.947491	+	0.688392i	0.00272132	+	0.999996i	$0.499134\pi$
$410$		0			0
$411$	4.60698	+	3.34717i	0.227246	+	0.165104i
$412$		0			0
$413$	−26.1743	−	36.0258i	−1.28795	−	1.77272i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−17.1161	−	5.56136i	−0.838179	−	0.272341i
$418$		0			0
$419$	−0.477059	+	1.46824i	−0.0233058	+	0.0717280i	−0.962033	−	0.272933i	$-0.912006\pi$
$419$	−0.477059	+	1.46824i	−0.0233058	+	0.0717280i	0.938727	+	0.344661i	$0.112006\pi$
$420$		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
$423$	−0.152362	+	0.209709i	−0.00740810	+	0.0101964i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	17.0615	−	23.4832i	0.825665	−	1.13643i
$428$		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
$433$	−0.217772	−	0.0707586i	−0.0104655	−	0.00340044i	0.303780	−	0.952742i	$-0.401751\pi$
$433$	−0.217772	−	0.0707586i	−0.0104655	−	0.00340044i	−0.314245	+	0.949342i	$0.601751\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.0462	−	31.7204i	−1.10245	−	1.51739i
$438$		0			0
$439$	15.7111	+	11.4147i	0.749848	+	0.544796i	0.895780	−	0.444498i	$-0.146618\pi$
$439$	15.7111	+	11.4147i	0.749848	+	0.544796i	−0.145932	+	0.989295i	$0.546618\pi$
$440$		0			0
$441$	−11.6553	+	8.46810i	−0.555016	+	0.403243i
$442$		0			0
$443$			12.7980i			0.608051i	0.952664	+	0.304026i	$0.0983309\pi$
$443$			12.7980i			0.608051i	−0.952664	+	0.304026i	$0.901669\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.03666	−	0.336832i	0.0490325	−	0.0159316i
$448$		0			0
$449$	21.1499			0.998124			0.499062	−	0.866566i	$-0.333678\pi$
$449$	21.1499			0.998124			0.499062	+	0.866566i	$0.333678\pi$
$450$		0			0
$451$	15.0092			0.706755
$452$		0			0
$453$	10.8220	−	3.51628i	0.508462	−	0.165209i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	8.97118i		−	0.419654i	−0.977739	−	0.209827i	$-0.932710\pi$
$457$		−	8.97118i		−	0.419654i	0.977739	−	0.209827i	$-0.0672901\pi$
$458$		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
$463$	17.2815	+	23.7859i	0.803140	+	1.10543i	0.992346	+	0.123489i	$0.0394085\pi$
$463$	17.2815	+	23.7859i	0.803140	+	1.10543i	−0.189206	+	0.981937i	$0.560591\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.6119	+	4.09785i	0.583609	+	0.189626i	0.585917	−	0.810371i	$-0.300735\pi$
$467$	12.6119	+	4.09785i	0.583609	+	0.189626i	−0.00230768	+	0.999997i	$0.500735\pi$
$468$		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
$473$	−31.0156	+	42.6893i	−1.42610	+	1.96286i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.75829	−	7.92560i	0.263654	−	0.362888i
$478$		0			0
$479$	5.58057	+	17.1752i	0.254983	+	0.784757i	0.993833	+	0.110887i	$0.0353692\pi$
$479$	5.58057	+	17.1752i	0.254983	+	0.784757i	−0.738850	+	0.673870i	$0.764631\pi$
$480$		0			0
$481$	−2.18279	+	6.71793i	−0.0995266	+	0.306311i
$482$		0			0
$483$	−29.3865	−	9.54824i	−1.33713	−	0.434460i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.26258	−	11.3725i	−0.374413	−	0.515336i	0.579681	−	0.814844i	$-0.303177\pi$
$487$	−8.26258	−	11.3725i	−0.374413	−	0.515336i	−0.954094	+	0.299508i	$0.903177\pi$
$488$		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
$493$			3.22980i			0.145463i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−38.1827	+	12.4063i	−1.71273	+	0.556499i
$498$		0			0
$499$	8.17654			0.366032			0.183016	−	0.983110i	$-0.441414\pi$
$499$	8.17654			0.366032			0.183016	+	0.983110i	$0.441414\pi$
$500$		0			0
$501$	−15.4689			−0.691099
$502$		0			0
$503$	9.45805	−	3.07311i	0.421714	−	0.137023i	−0.0904697	−	0.995899i	$-0.528837\pi$
$503$	9.45805	−	3.07311i	0.421714	−	0.137023i	0.512183	+	0.858876i	$0.328837\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			1.15844i			0.0514479i
$508$		0			0
$509$	13.9758	−	10.1540i	0.619464	−	0.450067i	−0.233270	−	0.972412i	$-0.574943\pi$
$509$	13.9758	−	10.1540i	0.619464	−	0.450067i	0.852734	+	0.522345i	$0.174943\pi$
$510$		0			0
$511$	−18.2470	−	13.2572i	−0.807200	−	0.586465i
$512$		0			0
$513$	3.45092	+	4.74979i	0.152362	+	0.209708i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.22001	−	0.396406i	−0.0536561	−	0.0174339i
$518$		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
$523$	2.20585	−	3.03609i	0.0964551	−	0.132759i	−0.758062	−	0.652183i	$-0.773853\pi$
$523$	2.20585	−	3.03609i	0.0964551	−	0.132759i	0.854517	+	0.519424i	$0.173853\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.22225	+	7.18781i	−0.227485	+	0.313106i
$528$		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
$533$	−10.8535	−	3.52653i	−0.470119	−	0.152751i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	8.49089	+	11.6867i	0.366409	+	0.504318i
$538$		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
$543$		−	12.3964i		−	0.531982i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.147706	+	0.0479926i	−0.00631545	+	0.00205201i	−0.312173	−	0.950025i	$-0.601057\pi$
$547$	−0.147706	+	0.0479926i	−0.00631545	+	0.00205201i	0.305858	+	0.952077i	$0.401057\pi$
$548$		0			0
$549$	−6.27369			−0.267755
$550$		0			0
$551$	7.04815			0.300261
$552$		0			0
$553$	54.8858	−	17.8335i	2.33398	−	0.758356i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	19.0371i		−	0.806626i	−0.915062	−	0.403313i	$-0.867859\pi$
$557$		−	19.0371i		−	0.806626i	0.915062	−	0.403313i	$-0.132141\pi$
$558$		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
$563$	−18.2630	−	25.1369i	−0.769694	−	1.05939i	−0.996345	−	0.0854166i	$-0.972778\pi$
$563$	−18.2630	−	25.1369i	−0.769694	−	1.05939i	0.226652	−	0.973976i	$-0.427222\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.40030	+	1.42974i	0.184795	+	0.0600436i
$568$		0			0
$569$	−12.1573	+	37.4162i	−0.509659	+	1.56857i	0.283135	+	0.959080i	$0.408626\pi$
$569$	−12.1573	+	37.4162i	−0.509659	+	1.56857i	−0.792794	+	0.609490i	$0.791374\pi$
$570$		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
$573$	0.973056	−	1.33930i	0.0406500	−	0.0559499i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.2014	+	18.1701i	−0.549581	+	0.756433i	−0.989955	−	0.141381i	$-0.954846\pi$
$577$	−13.2014	+	18.1701i	−0.549581	+	0.756433i	0.440375	+	0.897814i	$0.354846\pi$
$578$		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
$583$	46.1085	+	14.9815i	1.90962	+	0.620472i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.45335	+	13.0114i	0.390182	+	0.537039i	0.958246	−	0.285945i	$-0.0923076\pi$
$587$	9.45335	+	13.0114i	0.390182	+	0.537039i	−0.568064	+	0.822984i	$0.692308\pi$
$588$		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
$593$		−	20.4648i		−	0.840389i	−0.907434	−	0.420194i	$-0.861962\pi$
$593$		−	20.4648i		−	0.840389i	0.907434	−	0.420194i	$-0.138038\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.78068	−	1.87826i	0.236588	−	0.0768720i
$598$		0			0
$599$	−18.5688			−0.758699			−0.379349	−	0.925253i	$-0.623852\pi$
$599$	−18.5688			−0.758699			−0.379349	+	0.925253i	$0.623852\pi$
$600$		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
$603$	2.43521	−	0.791247i	0.0991693	−	0.0322221i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			0.0786576i			0.00319261i	0.999999	+	0.00159631i	$0.000508121\pi$
$607$			0.0786576i			0.00319261i	−0.999999	+	0.00159631i	$0.999492\pi$
$608$		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
$613$	3.12162	+	4.29654i	0.126081	+	0.173536i	0.867391	−	0.497627i	$-0.165795\pi$
$613$	3.12162	+	4.29654i	0.126081	+	0.173536i	−0.741310	+	0.671163i	$0.765795\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.9429	+	9.40411i	1.16520	+	0.378595i	0.826848	−	0.562426i	$-0.190132\pi$
$617$	28.9429	+	9.40411i	1.16520	+	0.378595i	0.338349	+	0.941021i	$0.390132\pi$
$618$		0			0
$619$	9.77918	−	30.0972i	0.393058	−	1.20971i	−0.537405	−	0.843324i	$-0.680595\pi$
$619$	9.77918	−	30.0972i	0.393058	−	1.20971i	0.930463	−	0.366385i	$-0.119405\pi$
$620$		0			0
$621$	2.06370	+	6.35143i	0.0828136	+	0.254874i
$622$		0			0
$623$	−39.6439	+	54.5651i	−1.58830	+	2.18610i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−17.0779	+	23.5057i	−0.682026	+	0.938728i
$628$		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
$633$	−16.2464	−	5.27877i	−0.645736	−	0.209812i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	31.8635	+	43.8564i	1.26248	+	1.73765i
$638$		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
$643$			14.2509i			0.562000i	0.959708	+	0.281000i	$0.0906660\pi$
$643$			14.2509i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−40.2623	+	13.0820i	−1.58287	+	0.514307i	−0.962795	−	0.270233i	$-0.912899\pi$
$647$	−40.2623	+	13.0820i	−1.58287	+	0.514307i	−0.620079	+	0.784539i	$0.712899\pi$
$648$		0			0
$649$	−47.6300			−1.86964
$650$		0			0
$651$	15.2791			0.598836
$652$		0			0
$653$	44.7274	−	14.5328i	1.75032	−	0.568713i	0.754192	−	0.656654i	$-0.228029\pi$
$653$	44.7274	−	14.5328i	1.75032	−	0.568713i	0.996126	+	0.0879407i	$0.0280286\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			4.87481i			0.190185i
$658$		0			0
$659$	−9.05013	+	6.57531i	−0.352543	+	0.256138i	−0.749935	−	0.661511i	$-0.769915\pi$
$659$	−9.05013	+	6.57531i	−0.352543	+	0.256138i	0.397392	+	0.917649i	$0.369915\pi$
$660$		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
$663$	5.95035	+	8.18995i	0.231092	+	0.318071i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.62483	+	2.47746i	0.295235	+	0.0959276i
$668$		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
$673$	8.07264	−	11.1110i	0.311178	−	0.428299i	−0.624570	−	0.780968i	$-0.714726\pi$
$673$	8.07264	−	11.1110i	0.311178	−	0.428299i	0.935748	+	0.352669i	$0.114726\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.6428	−	29.7888i	0.831801	−	1.14488i	−0.155784	−	0.987791i	$-0.549790\pi$
$677$	21.6428	−	29.7888i	0.831801	−	1.14488i	0.987585	−	0.157085i	$-0.0502095\pi$
$678$		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
$683$	28.6179	+	9.29850i	1.09503	+	0.355797i	0.800189	−	0.599748i	$-0.204733\pi$
$683$	28.6179	+	9.29850i	1.09503	+	0.355797i	0.294843	+	0.955546i	$0.404733\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.25271	+	4.47697i	0.124098	+	0.170807i
$688$		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
$693$			22.8968i			0.869779i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−7.76033	+	2.52148i	−0.293943	+	0.0955080i
$698$		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
$703$	10.4820	−	3.40581i	0.395336	−	0.128453i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			43.3478i			1.63026i
$708$		0			0
$709$	−40.0330	+	29.0857i	−1.50347	+	1.09234i	−0.534499	+	0.845169i	$0.679500\pi$
$709$	−40.0330	+	29.0857i	−1.50347	+	1.09234i	−0.968973	+	0.247168i	$0.920500\pi$
$710$		0			0
$711$	−10.0910	−	7.33156i	−0.378443	−	0.274955i
$712$		0			0
$713$	12.9630	+	17.8421i	0.485469	+	0.668191i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.6886	−	3.47294i	−0.399173	−	0.129699i
$718$		0			0
$719$	−8.08148	+	24.8722i	−0.301388	+	0.927578i	0.679612	+	0.733572i	$0.262148\pi$
$719$	−8.08148	+	24.8722i	−0.301388	+	0.927578i	−0.981000	+	0.194006i	$0.937852\pi$
$720$		0			0
$721$	14.9038	+	45.8692i	0.555046	+	1.70826i
$722$		0			0
$723$	11.9037	−	16.3840i	0.442702	−	0.609327i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−20.3475	+	28.0059i	−0.754647	+	1.03868i	0.242994	+	0.970028i	$0.421871\pi$
$727$	−20.3475	+	28.0059i	−0.754647	+	1.03868i	−0.997640	+	0.0686545i	$0.978129\pi$
$728$		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
$733$	−16.6104	−	5.39704i	−0.613518	−	0.199344i	−0.0142577	−	0.999898i	$-0.504539\pi$
$733$	−16.6104	−	5.39704i	−0.613518	−	0.199344i	−0.599260	+	0.800554i	$0.704539\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.44814	+	10.2515i	0.274356	+	0.377618i
$738$		0			0
$739$	16.2358	+	11.7960i	0.597243	+	0.433922i	0.844899	−	0.534926i	$-0.179660\pi$
$739$	16.2358	+	11.7960i	0.597243	+	0.433922i	−0.247656	+	0.968848i	$0.579660\pi$
$740$		0			0
$741$	17.8724	−	12.9850i	0.656557	−	0.477017i
$742$		0			0
$743$		−	5.84644i		−	0.214485i	−0.994233	−	0.107243i	$-0.965798\pi$
$743$		−	5.84644i		−	0.214485i	0.994233	−	0.107243i	$-0.0342022\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.45513	−	2.74724i	0.309357	−	0.100516i
$748$		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
$753$	−29.1897	+	9.48431i	−1.06373	+	0.345627i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			22.6371i			0.822759i	0.911464	+	0.411379i	$0.134953\pi$
$757$			22.6371i			0.822759i	−0.911464	+	0.411379i	$0.865047\pi$
$758$		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
$763$	18.1839	+	25.0280i	0.658301	+	0.906073i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	34.4425	+	11.1910i	1.24365	+	0.404085i
$768$		0			0
$769$	−4.51902	+	13.9081i	−0.162960	+	0.501539i	−0.998880	−	0.0473119i	$-0.984935\pi$
$769$	−4.51902	+	13.9081i	−0.162960	+	0.501539i	0.835920	+	0.548851i	$0.184935\pi$
$770$		0			0
$771$	1.47569	+	4.54170i	0.0531456	+	0.163565i
$772$		0			0
$773$	−17.9422	+	24.6953i	−0.645336	+	0.888229i	−0.998886	−	0.0471864i	$-0.984975\pi$
$773$	−17.9422	+	24.6953i	−0.645336	+	0.888229i	0.353550	+	0.935416i	$0.384975\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.10524	−	7.02676i	0.183150	−	0.252084i
$778$		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
$783$	−1.14173	−	0.370972i	−0.0408023	−	0.0132575i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−28.8905	−	39.7644i	−1.02984	−	1.41745i	−0.905070	−	0.425262i	$-0.860182\pi$
$787$	−28.8905	−	39.7644i	−1.02984	−	1.41745i	−0.124766	−	0.992186i	$-0.539818\pi$
$788$		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
$793$			23.6065i			0.838290i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	42.3529	−	13.7613i	1.50022	−	0.487450i	0.560136	−	0.828401i	$-0.310749\pi$
$797$	42.3529	−	13.7613i	1.50022	−	0.487450i	0.940081	+	0.340951i	$0.110749\pi$
$798$		0			0
$799$	0.697388			0.0246718
$800$		0			0
$801$	14.5774			0.515069
$802$		0			0
$803$	−22.9437	+	7.45487i	−0.809667	+	0.263077i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	25.5249i		−	0.898519i
$808$		0			0
$809$	−24.5060	+	17.8046i	−0.861584	+	0.625978i	−0.928316	−	0.371793i	$-0.878743\pi$
$809$	−24.5060	+	17.8046i	−0.861584	+	0.625978i	0.0667312	+	0.997771i	$0.478743\pi$
$810$		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
$813$	−3.45231	−	4.75170i	−0.121078	−	0.166649i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−59.5367	−	19.3447i	−2.08293	−	0.676784i
$818$		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
$823$	4.44218	−	6.11414i	0.154845	−	0.213126i	−0.724546	−	0.689227i	$-0.757950\pi$
$823$	4.44218	−	6.11414i	0.154845	−	0.213126i	0.879391	+	0.476101i	$0.157950\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.4412	+	25.3821i	−0.641262	+	0.882621i	−0.998682	−	0.0513225i	$-0.983656\pi$
$827$	−18.4412	+	25.3821i	−0.641262	+	0.882621i	0.357420	+	0.933944i	$0.383656\pi$
$828$		0			0
$829$	−8.55625	−	26.3334i	−0.297171	−	0.914597i	−0.982484	−	0.186349i	$-0.940335\pi$
$829$	−8.55625	−	26.3334i	−0.297171	−	0.914597i	0.685313	−	0.728249i	$-0.259665\pi$
$830$		0			0
$831$	−1.51585	+	4.66531i	−0.0525843	+	0.161838i
$832$		0			0
$833$	36.8629	+	11.9775i	1.27723	+	0.414996i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.94107	−	2.67165i	−0.0670932	−	0.0923459i
$838$		0			0
$839$	−30.5642	−	22.2062i	−1.05519	−	0.766643i	−0.0819999	−	0.996632i	$-0.526131\pi$
$839$	−30.5642	−	22.2062i	−1.05519	−	0.766643i	−0.973193	+	0.229990i	$0.926131\pi$
$840$		0			0
$841$	22.2956	−	16.1987i	0.768812	−	0.558575i
$842$		0			0
$843$			1.29526i			0.0446110i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−59.3626	+	19.2881i	−2.03972	+	0.662747i
$848$		0			0
$849$	−30.2297			−1.03748
$850$		0			0
$851$	12.5368			0.429756
$852$		0			0
$853$	−46.9508	+	15.2552i	−1.60756	+	0.522329i	−0.968962	−	0.247208i	$-0.920487\pi$
$853$	−46.9508	+	15.2552i	−1.60756	+	0.522329i	−0.638602	+	0.769537i	$0.720487\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	15.7692i		−	0.538667i	−0.963047	−	0.269333i	$-0.913197\pi$
$857$		−	15.7692i		−	0.538667i	0.963047	−	0.269333i	$-0.0868034\pi$
$858$		0			0
$859$	7.60223	−	5.52335i	0.259385	−	0.188454i	−0.450491	−	0.892781i	$-0.648751\pi$
$859$	7.60223	−	5.52335i	0.259385	−	0.188454i	0.709876	+	0.704327i	$0.248751\pi$
$860$		0			0
$861$	11.3525	+	8.24807i	0.386892	+	0.281093i
$862$		0			0
$863$	−10.5040	−	14.4575i	−0.357560	−	0.492140i	0.591907	−	0.806007i	$-0.298375\pi$
$863$	−10.5040	−	14.4575i	−0.357560	−	0.492140i	−0.949467	+	0.313867i	$0.898375\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−9.28400	−	3.01655i	−0.315301	−	0.102448i
$868$		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
$873$	2.34344	−	3.22546i	0.0793133	−	0.109165i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.4069	+	14.3238i	−0.351415	+	0.483681i	−0.947732	−	0.319068i	$-0.896630\pi$
$877$	−10.4069	+	14.3238i	−0.351415	+	0.483681i	0.596317	+	0.802749i	$0.296630\pi$
$878$		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
$883$	−32.9158	−	10.6950i	−1.10771	−	0.359916i	−0.302643	−	0.953104i	$-0.597869\pi$
$883$	−32.9158	−	10.6950i	−1.10771	−	0.359916i	−0.805064	+	0.593188i	$0.797869\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.7639	−	23.0735i	−0.562876	−	0.774732i	0.428813	−	0.903393i	$-0.358932\pi$
$887$	−16.7639	−	23.0735i	−0.562876	−	0.774732i	−0.991689	+	0.128661i	$0.958932\pi$
$888$		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
$893$		−	1.52186i		−	0.0509271i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	23.8990	−	7.76524i	0.797963	−	0.259274i
$898$		0			0
$899$	−3.96444			−0.132221
$900$		0			0
$901$	−26.3567			−0.878069
$902$		0			0
$903$	−46.9185	+	15.2448i	−1.56135	+	0.507314i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			7.01754i			0.233013i	0.993190	+	0.116507i	$0.0371697\pi$
$907$			7.01754i			0.233013i	−0.993190	+	0.116507i	$0.962830\pi$
$908$		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
$913$	25.8602	+	35.5936i	0.855849	+	1.17797i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−54.2240	−	17.6184i	−1.79063	−	0.581812i
$918$		0			0
$919$	−18.4658	+	56.8320i	−0.609132	+	1.87471i	−0.143726	+	0.989618i	$0.545908\pi$
$919$	−18.4658	+	56.8320i	−0.609132	+	1.87471i	−0.465406	+	0.885097i	$0.654092\pi$
$920$		0			0
$921$	−4.56573	−	14.0519i	−0.150446	−	0.463025i
$922$		0			0
$923$	19.1916	−	26.4149i	0.631698	−	0.869458i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.12713	−	8.43328i	0.201241	−	0.276985i
$928$		0			0
$929$	12.4320	+	38.2618i	0.407881	+	1.25533i	0.918466	+	0.395501i	$0.129429\pi$
$929$	12.4320	+	38.2618i	0.407881	+	1.25533i	−0.510585	+	0.859828i	$0.670571\pi$
$930$		0			0
$931$	26.1376	−	80.4434i	0.856626	−	2.63642i
$932$		0			0
$933$	8.70572	+	2.82866i	0.285012	+	0.0926061i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.0457	+	39.9780i	0.948881	+	1.30602i	0.952022	+	0.306028i	$0.0990001\pi$
$937$	29.0457	+	39.9780i	0.948881	+	1.30602i	−0.00314114	+	0.999995i	$0.501000\pi$
$938$		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
$943$			20.2546i			0.659579i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.9316	−	11.0251i	1.10263	−	0.358266i	0.299516	−	0.954091i	$-0.403175\pi$
$947$	33.9316	−	11.0251i	1.10263	−	0.358266i	0.803114	+	0.595825i	$0.203175\pi$
$948$		0			0
$949$	18.3428			0.595433
$950$		0			0
$951$	−0.790550			−0.0256354
$952$		0			0
$953$	2.66940	−	0.867341i	0.0864704	−	0.0280959i	−0.265462	−	0.964121i	$-0.585525\pi$
$953$	2.66940	−	0.867341i	0.0864704	−	0.0280959i	0.351933	+	0.936025i	$0.385525\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	5.94099i		−	0.192045i
$958$		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
$963$	−0.129714	−	0.178536i	−0.00417998	−	0.00575324i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.9640	−	3.56243i	−0.352580	−	0.114560i	0.127372	−	0.991855i	$-0.459346\pi$
$967$	−10.9640	−	3.56243i	−0.352580	−	0.114560i	−0.479952	+	0.877295i	$0.659346\pi$
$968$		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
$973$	48.9433	−	67.3646i	1.56905	−	2.15961i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.85551	−	6.68304i	0.155342	−	0.213809i	−0.724252	−	0.689536i	$-0.757815\pi$
$977$	4.85551	−	6.68304i	0.155342	−	0.213809i	0.879593	+	0.475726i	$0.157815\pi$
$978$		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
$983$	18.8202	+	6.11506i	0.600271	+	0.195040i	0.593361	−	0.804936i	$-0.297800\pi$
$983$	18.8202	+	6.11506i	0.600271	+	0.195040i	0.00690994	+	0.999976i	$0.497800\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.704941	−	0.970269i	−0.0224385	−	0.0308840i
$988$		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
$993$			3.37370i			0.107061i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	16.7226	−	5.43350i	0.529610	−	0.172081i	−0.0319923	−	0.999488i	$-0.510185\pi$
$997$	16.7226	−	5.43350i	0.529610	−	0.172081i	0.561602	+	0.827407i	$0.310185\pi$
$998$		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.o.c.49.6		24
5.2	odd	4		1500.2.m.d.1201.1		24
5.3	odd	4		1500.2.m.c.1201.6		24
5.4	even	2		300.2.o.a.109.2	✓	24
15.14	odd	2		900.2.w.c.109.3		24
25.2	odd	20		1500.2.m.d.301.1		24
25.6	even	5		7500.2.d.g.1249.12		24
25.8	odd	20		7500.2.a.n.1.12		12
25.11	even	5		300.2.o.a.289.2	yes	24
25.14	even	10	inner	1500.2.o.c.949.6		24
25.17	odd	20		7500.2.a.m.1.1		12
25.19	even	10		7500.2.d.g.1249.13		24
25.23	odd	20		1500.2.m.c.301.6		24
75.11	odd	10		900.2.w.c.289.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.2	✓	24	5.4	even	2
300.2.o.a.289.2	yes	24	25.11	even	5
900.2.w.c.109.3		24	15.14	odd	2
900.2.w.c.289.3		24	75.11	odd	10
1500.2.m.c.301.6		24	25.23	odd	20
1500.2.m.c.1201.6		24	5.3	odd	4
1500.2.m.d.301.1		24	25.2	odd	20
1500.2.m.d.1201.1		24	5.2	odd	4
1500.2.o.c.49.6		24	1.1	even	1	trivial
1500.2.o.c.949.6		24	25.14	even	10	inner
7500.2.a.m.1.1		12	25.17	odd	20
7500.2.a.n.1.12		12	25.8	odd	20
7500.2.d.g.1249.12		24	25.6	even	5
7500.2.d.g.1249.13		24	25.19	even	10

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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{3} +4.62675i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{3} +4.62675i q^{7} +(0.809017 - 0.587785i) q^{9} +(4.00366 + 2.90883i) q^{11} +(-2.21170 - 3.04414i) q^{13} +(-2.55872 - 0.831378i) q^{17} +(-1.81426 + 5.58371i) q^{19} +(1.42974 + 4.40030i) q^{21} +(-3.92540 + 5.40285i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-0.370972 - 1.14173i) q^{29} +(1.02048 - 3.14072i) q^{31} +(4.70659 + 1.52926i) q^{33} +(-1.10342 - 1.51873i) q^{37} +(-3.04414 - 2.21170i) q^{39} +(2.45366 - 1.78269i) q^{41} +10.6626i q^{43} +(-0.246527 + 0.0801015i) q^{47} -14.4068 q^{49} -2.69040 q^{51} +(9.31711 - 3.02731i) q^{53} +5.87106i q^{57} +(-7.78643 + 5.65717i) q^{59} +(-5.07552 - 3.68758i) q^{61} +(2.71953 + 3.74312i) q^{63} +(2.43521 + 0.791247i) q^{67} +(-2.06370 + 6.35143i) q^{69} +(2.68143 + 8.25259i) q^{71} +(-2.86534 + 3.94381i) q^{73} +(-13.4584 + 18.5239i) q^{77} +(-3.85443 - 11.8627i) q^{79} +(0.309017 - 0.951057i) q^{81} +(8.45513 + 2.74724i) q^{83} +(-0.705631 - 0.971218i) q^{87} +(11.7934 + 8.56841i) q^{89} +(14.0845 - 10.2330i) q^{91} -3.30235i q^{93} +(3.79176 - 1.23202i) q^{97} +4.94880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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