LMFDB - Embedded newform 525.2.m.b.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.3
Root			$-1.36166 - 0.381939i$ of defining polynomial
Character	$\chi$	$=$	525.118
Dual form			525.2.m.b.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540143 + 0.540143i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.41649i q^{4} -0.763878i q^{6} +(-2.57351 + 0.614060i) q^{7} +(-1.84539 - 1.84539i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.540143 + 0.540143i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.41649i q^{4} -0.763878i q^{6} +(-2.57351 + 0.614060i) q^{7} +(-1.84539 - 1.84539i) q^{8} -1.00000i q^{9} -3.85136 q^{11} +(-1.00161 - 1.00161i) q^{12} +(3.66816 - 3.66816i) q^{13} +(1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(-1.49007 - 1.49007i) q^{17} +(0.540143 + 0.540143i) q^{18} +0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(2.08029 - 2.08029i) q^{22} +(0.534176 + 0.534176i) q^{23} +2.60978 q^{24} +3.96267i q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.869810 - 3.64535i) q^{28} -2.77107i q^{29} +2.39674i q^{31} +(4.14420 - 4.14420i) q^{32} +(2.72332 - 2.72332i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(-6.18757 + 6.18757i) q^{37} +(-0.0376844 + 0.0376844i) q^{38} +5.18757i q^{39} -8.68077i q^{41} +(0.469067 + 1.96584i) q^{42} +(2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(-5.49042 - 5.49042i) q^{47} +(0.593565 - 0.593565i) q^{48} +(6.24586 - 3.16057i) q^{49} +2.10728 q^{51} +(5.19592 + 5.19592i) q^{52} +(-6.13823 - 6.13823i) q^{53} -0.763878 q^{54} +(5.88231 + 3.61595i) q^{56} +(-0.0493330 + 0.0493330i) q^{57} +(1.49678 + 1.49678i) q^{58} -6.97440 q^{59} -14.3107i q^{61} +(-1.29458 - 1.29458i) q^{62} +(0.614060 + 2.57351i) q^{63} +2.79807i q^{64} +2.94197i q^{66} +(-0.416491 + 0.416491i) q^{67} +(2.11067 - 2.11067i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(-1.84539 + 1.84539i) q^{72} +(-9.55210 + 9.55210i) q^{73} -6.68434i q^{74} +0.0988248i q^{76} +(9.91150 - 2.36497i) q^{77} +(-2.80203 - 2.80203i) q^{78} +9.86329i q^{79} -1.00000 q^{81} +(4.68886 + 4.68886i) q^{82} +(-1.63570 + 1.63570i) q^{83} +(3.19270 + 1.96260i) q^{84} -2.99355 q^{86} +(1.95945 + 1.95945i) q^{87} +(7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-7.18757 + 11.6925i) q^{91} +(-0.756656 + 0.756656i) q^{92} +(-1.69475 - 1.69475i) q^{93} +5.93123 q^{94} +5.86078i q^{96} +(-6.85851 - 6.85851i) q^{97} +(-1.66650 + 5.08082i) q^{98} +3.85136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) $ 16 * q + 8 * q^7 - 24 * q^8	$ 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.540143	+	0.540143i	−0.381939	+	0.381939i	−0.871800	−	0.489861i	$-0.837047\pi$
$2$	−0.540143	+	0.540143i	−0.381939	+	0.381939i	0.489861	+	0.871800i	$0.337047\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$			1.41649i			0.708245i
$5$		0			0
$5$		0			0
$6$		−	0.763878i		−	0.311852i
$7$	−2.57351	+	0.614060i	−0.972694	+	0.232093i
$7$	−2.57351	+	0.614060i	−0.972694	+	0.232093i
$8$	−1.84539	−	1.84539i	−0.652445	−	0.652445i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.85136			−1.16123			−0.580615	−	0.814179i	$-0.697188\pi$
$11$	−3.85136			−1.16123			−0.580615	+	0.814179i	$0.697188\pi$
$12$	−1.00161	−	1.00161i	−0.289140	−	0.289140i
$13$	3.66816	−	3.66816i	1.01737	−	1.01737i	0.0175187	−	0.999847i	$-0.494423\pi$
$13$	3.66816	−	3.66816i	1.01737	−	1.01737i	0.999847	−	0.0175187i	$-0.00557667\pi$
$14$	1.05838	−	1.72174i	0.282864	−	0.460155i
$15$		0			0
$16$	−0.839427			−0.209857
$17$	−1.49007	−	1.49007i	−0.361395	−	0.361395i	0.502931	−	0.864326i	$-0.332255\pi$
$17$	−1.49007	−	1.49007i	−0.361395	−	0.361395i	−0.864326	+	0.502931i	$0.832255\pi$
$18$	0.540143	+	0.540143i	0.127313	+	0.127313i
$19$	0.0697674			0.0160057			0.00800286	−	0.999968i	$-0.497453\pi$
$19$	0.0697674			0.0160057			0.00800286	+	0.999968i	$0.497453\pi$
$20$		0			0
$21$	1.38554	−	2.25395i	0.302349	−	0.491852i
$22$	2.08029	−	2.08029i	0.443519	−	0.443519i
$23$	0.534176	+	0.534176i	0.111383	+	0.111383i	0.760602	−	0.649218i	$-0.224904\pi$
$23$	0.534176	+	0.534176i	0.111383	+	0.111383i	−0.649218	+	0.760602i	$0.724904\pi$
$24$	2.60978			0.532719
$25$		0			0
$26$			3.96267i			0.777143i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.869810	−	3.64535i	−0.164379	−	0.688906i
$29$		−	2.77107i		−	0.514576i	−0.966335	−	0.257288i	$-0.917171\pi$
$29$		−	2.77107i		−	0.514576i	0.966335	−	0.257288i	$-0.0828288\pi$
$30$		0			0
$31$			2.39674i			0.430467i	0.976563	+	0.215233i	$0.0690512\pi$
$31$			2.39674i			0.430467i	−0.976563	+	0.215233i	$0.930949\pi$
$32$	4.14420	−	4.14420i	0.732598	−	0.732598i
$33$	2.72332	−	2.72332i	0.474070	−	0.474070i
$34$	1.60970			0.276062
$35$		0			0
$36$	1.41649			0.236082
$37$	−6.18757	+	6.18757i	−1.01723	+	1.01723i	−0.0173805	+	0.999849i	$0.505533\pi$
$37$	−6.18757	+	6.18757i	−1.01723	+	1.01723i	−0.999849	+	0.0173805i	$0.994467\pi$
$38$	−0.0376844	+	0.0376844i	−0.00611321	+	0.00611321i
$39$			5.18757i			0.830675i
$40$		0			0
$41$		−	8.68077i		−	1.35571i	−0.735196	−	0.677854i	$-0.762910\pi$
$41$		−	8.68077i		−	1.35571i	0.735196	−	0.677854i	$-0.237090\pi$
$42$	0.469067	+	1.96584i	0.0723786	+	0.303336i
$43$	2.77107	+	2.77107i	0.422585	+	0.422585i	0.886093	−	0.463508i	$-0.153409\pi$
$43$	2.77107	+	2.77107i	0.422585	+	0.422585i	−0.463508	+	0.886093i	$0.653409\pi$
$44$		−	5.45542i		−	0.822435i
$45$		0			0
$46$	−0.577063			−0.0850834
$47$	−5.49042	−	5.49042i	−0.800860	−	0.800860i	0.182370	−	0.983230i	$-0.441623\pi$
$47$	−5.49042	−	5.49042i	−0.800860	−	0.800860i	−0.983230	+	0.182370i	$0.941623\pi$
$48$	0.593565	−	0.593565i	0.0856737	−	0.0856737i
$49$	6.24586	−	3.16057i	0.892266	−	0.451510i
$50$		0			0
$51$	2.10728			0.295078
$52$	5.19592	+	5.19592i	0.720544	+	0.720544i
$53$	−6.13823	−	6.13823i	−0.843151	−	0.843151i	0.146116	−	0.989267i	$-0.453323\pi$
$53$	−6.13823	−	6.13823i	−0.843151	−	0.843151i	−0.989267	+	0.146116i	$0.953323\pi$
$54$	−0.763878			−0.103951
$55$		0			0
$56$	5.88231	+	3.61595i	0.786057	+	0.483202i
$57$	−0.0493330	+	0.0493330i	−0.00653431	+	0.00653431i
$58$	1.49678	+	1.49678i	0.196536	+	0.196536i
$59$	−6.97440			−0.907990			−0.453995	−	0.891004i	$-0.650002\pi$
$59$	−6.97440			−0.907990			−0.453995	+	0.891004i	$0.650002\pi$
$60$		0			0
$61$		−	14.3107i		−	1.83230i	−0.400835	−	0.916150i	$-0.631280\pi$
$61$		−	14.3107i		−	1.83230i	0.400835	−	0.916150i	$-0.368720\pi$
$62$	−1.29458	−	1.29458i	−0.164412	−	0.164412i
$63$	0.614060	+	2.57351i	0.0773643	+	0.324231i
$64$			2.79807i			0.349758i
$65$		0			0
$66$			2.94197i			0.362131i
$67$	−0.416491	+	0.416491i	−0.0508824	+	0.0508824i	−0.732090	−	0.681208i	$-0.761455\pi$
$67$	−0.416491	+	0.416491i	−0.0508824	+	0.0508824i	0.681208	+	0.732090i	$0.261455\pi$
$68$	2.11067	−	2.11067i	0.255957	−	0.255957i
$69$	−0.755439			−0.0909442
$70$		0			0
$71$	−8.12783			−0.964595			−0.482298	−	0.876007i	$-0.660198\pi$
$71$	−8.12783			−0.964595			−0.482298	+	0.876007i	$0.660198\pi$
$72$	−1.84539	+	1.84539i	−0.217482	+	0.217482i
$73$	−9.55210	+	9.55210i	−1.11799	+	1.11799i	−0.125953	+	0.992036i	$0.540199\pi$
$73$	−9.55210	+	9.55210i	−1.11799	+	1.11799i	−0.992036	+	0.125953i	$0.959801\pi$
$74$		−	6.68434i		−	0.777039i
$75$		0			0
$76$			0.0988248i			0.0113360i
$77$	9.91150	−	2.36497i	1.12952	−	0.269513i
$78$	−2.80203	−	2.80203i	−0.317267	−	0.317267i
$79$			9.86329i			1.10971i	0.831948	+	0.554854i	$0.187226\pi$
$79$			9.86329i			1.10971i	−0.831948	+	0.554854i	$0.812774\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	4.68886	+	4.68886i	0.517798	+	0.517798i
$83$	−1.63570	+	1.63570i	−0.179541	+	0.179541i	−0.791156	−	0.611615i	$-0.790520\pi$
$83$	−1.63570	+	1.63570i	−0.179541	+	0.179541i	0.611615	+	0.791156i	$0.290520\pi$
$84$	3.19270	+	1.96260i	0.348352	+	0.214137i
$85$		0			0
$86$	−2.99355			−0.322803
$87$	1.95945	+	1.95945i	0.210075	+	0.210075i
$88$	7.10728	+	7.10728i	0.757638	+	0.757638i
$89$	−5.05313			−0.535631			−0.267815	−	0.963470i	$-0.586302\pi$
$89$	−5.05313			−0.535631			−0.267815	+	0.963470i	$0.586302\pi$
$90$		0			0
$91$	−7.18757	+	11.6925i	−0.753462	+	1.22571i
$92$	−0.756656	+	0.756656i	−0.0788868	+	0.0788868i
$93$	−1.69475	−	1.69475i	−0.175737	−	0.175737i
$94$	5.93123			0.611759
$95$		0			0
$96$			5.86078i			0.598164i
$97$	−6.85851	−	6.85851i	−0.696376	−	0.696376i	0.267251	−	0.963627i	$-0.413885\pi$
$97$	−6.85851	−	6.85851i	−0.696376	−	0.696376i	−0.963627	+	0.267251i	$0.913885\pi$
$98$	−1.66650	+	5.08082i	−0.168342	+	0.513240i
$99$			3.85136i			0.387076i
$100$		0			0
$101$			19.1953i			1.91000i	0.296605	+	0.955000i	$0.404145\pi$
$101$			19.1953i			1.91000i	−0.296605	+	0.955000i	$0.595855\pi$
$102$	−1.13823	+	1.13823i	−0.112702	+	0.112702i
$103$	−2.33825	+	2.33825i	−0.230394	+	0.230394i	−0.812857	−	0.582463i	$-0.802089\pi$
$103$	−2.33825	+	2.33825i	−0.230394	+	0.230394i	0.582463	+	0.812857i	$0.302089\pi$
$104$	−13.5384			−1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	6.39747	−	6.39747i	0.618467	−	0.618467i	−0.326671	−	0.945138i	$-0.605927\pi$
$107$	6.39747	−	6.39747i	0.618467	−	0.618467i	0.945138	+	0.326671i	$0.105927\pi$
$108$	−1.00161	+	1.00161i	−0.0963800	+	0.0963800i
$109$			2.16057i			0.206945i	0.994632	+	0.103473i	$0.0329954\pi$
$109$			2.16057i			0.206945i	−0.994632	+	0.103473i	$0.967005\pi$
$110$		0			0
$111$		−	8.75054i		−	0.830564i
$112$	2.16027	−	0.515459i	0.204126	−	0.0487063i
$113$	4.13823	+	4.13823i	0.389292	+	0.389292i	0.874435	−	0.485143i	$-0.161232\pi$
$113$	4.13823	+	4.13823i	0.389292	+	0.389292i	−0.485143	+	0.874435i	$0.661232\pi$
$114$		−	0.0532937i		−	0.00499142i
$115$		0			0
$116$	3.92520			0.364446
$117$	−3.66816	−	3.66816i	−0.339122	−	0.339122i
$118$	3.76718	−	3.76718i	0.346797	−	0.346797i
$119$	4.74970	+	2.91971i	0.435404	+	0.267650i
$120$		0			0
$121$	3.83298			0.348453
$122$	7.72984	+	7.72984i	0.699827	+	0.699827i
$123$	6.13823	+	6.13823i	0.553466	+	0.553466i
$124$	−3.39496			−0.304876
$125$		0			0
$126$	−1.72174	−	1.05838i	−0.153385	−	0.0942881i
$127$	4.83298	−	4.83298i	0.428858	−	0.428858i	−0.459381	−	0.888239i	$-0.651929\pi$
$127$	4.83298	−	4.83298i	0.428858	−	0.428858i	0.888239	+	0.459381i	$0.151929\pi$
$128$	6.77704	+	6.77704i	0.599011	+	0.599011i
$129$	−3.91889			−0.345039
$130$		0			0
$131$		−	0.647499i		−	0.0565722i	−0.999600	−	0.0282861i	$-0.990995\pi$
$131$		−	0.647499i		−	0.0565722i	0.999600	−	0.0282861i	$-0.00900495\pi$
$132$	3.85756	+	3.85756i	0.335758	+	0.335758i
$133$	−0.179547	+	0.0428413i	−0.0155687	+	0.00371481i
$134$		−	0.449929i		−	0.0388680i
$135$		0			0
$136$			5.49954i			0.471581i
$137$	−10.2369	+	10.2369i	−0.874597	+	0.874597i	−0.992969	−	0.118372i	$-0.962232\pi$
$137$	−10.2369	+	10.2369i	−0.874597	+	0.874597i	0.118372	+	0.992969i	$0.462232\pi$
$138$	0.408045	−	0.408045i	0.0347351	−	0.0347351i
$139$	−22.1663			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$139$	−22.1663			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$140$		0			0
$141$	7.76463			0.653900
$142$	4.39019	−	4.39019i	0.368417	−	0.368417i
$143$	−14.1274	+	14.1274i	−1.18139	+	1.18139i
$144$			0.839427i			0.0699523i
$145$		0			0
$146$		−	10.3190i		−	0.854007i
$147$	−2.18163	+	6.65135i	−0.179938	+	0.548594i
$148$	−8.76463	−	8.76463i	−0.720448	−	0.720448i
$149$			11.0475i			0.905050i	0.891752	+	0.452525i	$0.149477\pi$
$149$			11.0475i			0.905050i	−0.891752	+	0.452525i	$0.850523\pi$
$150$		0			0
$151$	18.3990			1.49729			0.748645	−	0.662972i	$-0.230705\pi$
$151$	18.3990			1.49729			0.748645	+	0.662972i	$0.230705\pi$
$152$	−0.128748	−	0.128748i	−0.0104429	−	0.0104429i
$153$	−1.49007	+	1.49007i	−0.120465	+	0.120465i
$154$	−4.07621	+	6.63105i	−0.328470	+	0.534345i
$155$		0			0
$156$	−7.34814			−0.588322
$157$	1.04994	+	1.04994i	0.0837946	+	0.0837946i	0.747762	−	0.663967i	$-0.231129\pi$
$157$	1.04994	+	1.04994i	0.0837946	+	0.0837946i	−0.663967	+	0.747762i	$0.731129\pi$
$158$	−5.32759	−	5.32759i	−0.423840	−	0.423840i
$159$	8.68077			0.688430
$160$		0			0
$161$	−1.70272	−	1.04669i	−0.134193	−	0.0824907i
$162$	0.540143	−	0.540143i	0.0424377	−	0.0424377i
$163$	−5.50539	−	5.50539i	−0.431215	−	0.431215i	0.457826	−	0.889042i	$-0.348628\pi$
$163$	−5.50539	−	5.50539i	−0.431215	−	0.431215i	−0.889042	+	0.457826i	$0.848628\pi$
$164$	12.2962			0.960174
$165$		0			0
$166$		−	1.76702i		−	0.137147i
$167$	−1.88968	−	1.88968i	−0.146228	−	0.146228i	0.630203	−	0.776431i	$-0.282972\pi$
$167$	−1.88968	−	1.88968i	−0.146228	−	0.146228i	−0.776431	+	0.630203i	$0.782972\pi$
$168$	−6.71629	+	1.60256i	−0.518173	+	0.123640i
$169$		−	13.9108i		−	1.07006i
$170$		0			0
$171$		−	0.0697674i		−	0.00533524i
$172$	−3.92520	+	3.92520i	−0.299294	+	0.299294i
$173$	4.90751	−	4.90751i	0.373111	−	0.373111i	−0.495498	−	0.868609i	$-0.665014\pi$
$173$	4.90751	−	4.90751i	0.373111	−	0.373111i	0.868609	+	0.495498i	$0.165014\pi$
$174$	−2.11676			−0.160471
$175$		0			0
$176$	3.23294			0.243692
$177$	4.93165	−	4.93165i	0.370685	−	0.370685i
$178$	2.72941	−	2.72941i	0.204578	−	0.204578i
$179$		−	18.5857i		−	1.38916i	−0.719416	−	0.694579i	$-0.755591\pi$
$179$		−	18.5857i		−	1.38916i	0.719416	−	0.694579i	$-0.244409\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	−2.43331	−	10.1979i	−0.180369	−	0.755922i
$183$	10.1192	+	10.1192i	0.748034	+	0.748034i
$184$		−	1.97153i		−	0.145343i
$185$		0			0
$186$	1.83081			0.134242
$187$	5.73880	+	5.73880i	0.419663	+	0.419663i
$188$	7.77713	−	7.77713i	0.567206	−	0.567206i
$189$	−2.25395	−	1.38554i	−0.163951	−	0.100783i
$190$		0			0
$191$	−5.39351			−0.390261			−0.195130	−	0.980777i	$-0.562513\pi$
$191$	−5.39351			−0.390261			−0.195130	+	0.980777i	$0.562513\pi$
$192$	−1.97853	−	1.97853i	−0.142788	−	0.142788i
$193$	4.80599	+	4.80599i	0.345943	+	0.345943i	0.858596	−	0.512653i	$-0.171337\pi$
$193$	4.80599	+	4.80599i	0.345943	+	0.345943i	−0.512653	+	0.858596i	$0.671337\pi$
$194$	7.40916			0.531946
$195$		0			0
$196$	4.47692	+	8.84720i	0.319780	+	0.631943i
$197$	−12.6739	+	12.6739i	−0.902981	+	0.902981i	−0.995693	−	0.0927124i	$-0.970446\pi$
$197$	−12.6739	+	12.6739i	−0.902981	+	0.902981i	0.0927124	+	0.995693i	$0.470446\pi$
$198$	−2.08029	−	2.08029i	−0.147840	−	0.147840i
$199$	−2.67111			−0.189350			−0.0946750	−	0.995508i	$-0.530181\pi$
$199$	−2.67111			−0.189350			−0.0946750	+	0.995508i	$0.530181\pi$
$200$		0			0
$201$		−	0.589007i		−	0.0415453i
$202$	−10.3682	−	10.3682i	−0.729503	−	0.729503i
$203$	1.70161	+	7.13138i	0.119429	+	0.500524i
$204$			2.98494i			0.208988i
$205$		0			0
$206$		−	2.52597i		−	0.175993i
$207$	0.534176	−	0.534176i	0.0371278	−	0.0371278i
$208$	−3.07916	+	3.07916i	−0.213501	+	0.213501i
$209$	−0.268699			−0.0185863
$210$		0			0
$211$	−12.0239			−0.827757			−0.413879	−	0.910332i	$-0.635826\pi$
$211$	−12.0239			−0.827757			−0.413879	+	0.910332i	$0.635826\pi$
$212$	8.69475	−	8.69475i	0.597158	−	0.597158i
$213$	5.74724	−	5.74724i	0.393794	−	0.393794i
$214$			6.91110i			0.472433i
$215$		0			0
$216$		−	2.60978i		−	0.177573i
$217$	−1.47174	−	6.16802i	−0.0999082	−	0.418712i
$218$	−1.16702	−	1.16702i	−0.0790405	−	0.0790405i
$219$		−	13.5087i		−	0.912834i
$220$		0			0
$221$	−10.9316			−0.735342
$222$	4.72654	+	4.72654i	0.317225	+	0.317225i
$223$	11.6925	−	11.6925i	0.782988	−	0.782988i	−0.197346	−	0.980334i	$-0.563232\pi$
$223$	11.6925	−	11.6925i	0.782988	−	0.782988i	0.980334	+	0.197346i	$0.0632321\pi$
$224$	−8.12033	+	13.2099i	−0.542563	+	0.882624i
$225$		0			0
$226$	−4.47048			−0.297372
$227$	−1.10518	−	1.10518i	−0.0733535	−	0.0733535i	0.669478	−	0.742832i	$-0.266518\pi$
$227$	−1.10518	−	1.10518i	−0.0733535	−	0.0733535i	−0.742832	+	0.669478i	$0.766518\pi$
$228$	−0.0698797	−	0.0698797i	−0.00462790	−	0.00462790i
$229$	7.83309			0.517625			0.258812	−	0.965928i	$-0.416669\pi$
$229$	7.83309			0.517625			0.258812	+	0.965928i	$0.416669\pi$
$230$		0			0
$231$	−5.33620	+	8.68077i	−0.351096	+	0.571153i
$232$	−5.11372	+	5.11372i	−0.335732	+	0.335732i
$233$	−1.00797	−	1.00797i	−0.0660345	−	0.0660345i	0.673318	−	0.739353i	$-0.264868\pi$
$233$	−1.00797	−	1.00797i	−0.0660345	−	0.0660345i	−0.739353	+	0.673318i	$0.764868\pi$
$234$	3.96267			0.259048
$235$		0			0
$236$		−	9.87918i		−	0.643080i
$237$	−6.97440	−	6.97440i	−0.453036	−	0.453036i
$238$	−4.14258	+	0.988454i	−0.268524	+	0.0640720i
$239$			20.2805i			1.31183i	0.754833	+	0.655917i	$0.227718\pi$
$239$			20.2805i			1.31183i	−0.754833	+	0.655917i	$0.772282\pi$
$240$		0			0
$241$		−	2.76994i		−	0.178427i	−0.996013	−	0.0892136i	$-0.971565\pi$
$241$		−	2.76994i		−	0.178427i	0.996013	−	0.0892136i	$-0.0284354\pi$
$242$	−2.07036	+	2.07036i	−0.133088	+	0.133088i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	20.2710			1.29772
$245$		0			0
$246$	−6.63105			−0.422780
$247$	0.255918	−	0.255918i	0.0162837	−	0.0162837i
$248$	4.42292	−	4.42292i	0.280856	−	0.280856i
$249$		−	2.31322i		−	0.146595i
$250$		0			0
$251$			6.09982i			0.385017i	0.981295	+	0.192509i	$0.0616623\pi$
$251$			6.09982i			0.385017i	−0.981295	+	0.192509i	$0.938338\pi$
$252$	−3.64535	+	0.869810i	−0.229635	+	0.0547929i
$253$	−2.05731	−	2.05731i	−0.129342	−	0.129342i
$254$			5.22100i			0.327595i
$255$		0			0
$256$	−12.9173			−0.807330
$257$	2.01843	+	2.01843i	0.125906	+	0.125906i	0.767252	−	0.641346i	$-0.221624\pi$
$257$	2.01843	+	2.01843i	0.125906	+	0.125906i	−0.641346	+	0.767252i	$0.721624\pi$
$258$	2.11676	−	2.11676i	0.131784	−	0.131784i
$259$	12.1242	−	19.7233i	0.753361	−	1.22554i
$260$		0			0
$261$	−2.77107			−0.171525
$262$	0.349742	+	0.349742i	0.0216071	+	0.0216071i
$263$	−16.7686	−	16.7686i	−1.03400	−	1.03400i	−0.999401	−	0.0345941i	$-0.988986\pi$
$263$	−16.7686	−	16.7686i	−1.03400	−	1.03400i	−0.0345941	−	0.999401i	$-0.511014\pi$
$264$	−10.0512			−0.618609
$265$		0			0
$266$	0.0738405	−	0.120121i	0.00452745	−	0.00736511i
$267$	3.57310	−	3.57310i	0.218670	−	0.218670i
$268$	−0.589955	−	0.589955i	−0.0360372	−	0.0360372i
$269$	24.7351			1.50813			0.754064	−	0.656801i	$-0.228091\pi$
$269$	24.7351			1.50813			0.754064	+	0.656801i	$0.228091\pi$
$270$		0			0
$271$		−	4.13470i		−	0.251165i	−0.992083	−	0.125583i	$-0.959920\pi$
$271$		−	4.13470i		−	0.251165i	0.992083	−	0.125583i	$-0.0400800\pi$
$272$	1.25081	+	1.25081i	0.0758413	+	0.0758413i
$273$	−3.18548	−	13.3502i	−0.192794	−	0.807993i
$274$		−	11.0588i		−	0.668085i
$275$		0			0
$276$		−	1.07007i		−	0.0644108i
$277$	12.1128	−	12.1128i	0.727786	−	0.727786i	−0.242393	−	0.970178i	$-0.577932\pi$
$277$	12.1128	−	12.1128i	0.727786	−	0.727786i	0.970178	+	0.242393i	$0.0779322\pi$
$278$	11.9730	−	11.9730i	0.718091	−	0.718091i
$279$	2.39674			0.143489
$280$		0			0
$281$	5.25279			0.313355			0.156678	−	0.987650i	$-0.449922\pi$
$281$	5.25279			0.313355			0.156678	+	0.987650i	$0.449922\pi$
$282$	−4.19401	+	4.19401i	−0.249750	+	0.249750i
$283$	1.66729	−	1.66729i	0.0991101	−	0.0991101i	−0.655813	−	0.754923i	$-0.727674\pi$
$283$	1.66729	−	1.66729i	0.0991101	−	0.0991101i	0.754923	+	0.655813i	$0.227674\pi$
$284$		−	11.5130i		−	0.683170i
$285$		0			0
$286$		−	15.2617i		−	0.902441i
$287$	5.33051	+	22.3400i	0.314650	+	1.31869i
$288$	−4.14420	−	4.14420i	−0.244199	−	0.244199i
$289$		−	12.5594i		−	0.738787i
$290$		0			0
$291$	9.69940			0.568589
$292$	−13.5305	−	13.5305i	−0.791810	−	0.791810i
$293$	15.2556	−	15.2556i	0.891240	−	0.891240i	−0.103400	−	0.994640i	$-0.532972\pi$
$293$	15.2556	−	15.2556i	0.891240	−	0.891240i	0.994640	+	0.103400i	$0.0329722\pi$
$294$	−2.41429	−	4.77107i	−0.140804	−	0.278255i
$295$		0			0
$296$	22.8370			1.32737
$297$	−2.72332	−	2.72332i	−0.158023	−	0.158023i
$298$	−5.96725	−	5.96725i	−0.345674	−	0.345674i
$299$	3.91889			0.226635
$300$		0			0
$301$	−8.83298	−	5.42977i	−0.509125	−	0.312967i
$302$	−9.93809	+	9.93809i	−0.571873	+	0.571873i
$303$	−13.5731	−	13.5731i	−0.779754	−	0.779754i
$304$	−0.0585646			−0.00335891
$305$		0			0
$306$		−	1.60970i		−	0.0920206i
$307$	14.6198	+	14.6198i	0.834394	+	0.834394i	0.988114	−	0.153721i	$-0.0491256\pi$
$307$	14.6198	+	14.6198i	0.834394	+	0.834394i	−0.153721	+	0.988114i	$0.549126\pi$
$308$	3.34995	+	14.0395i	0.190881	+	0.799977i
$309$		−	3.30678i		−	0.188116i
$310$		0			0
$311$		−	2.86218i		−	0.162299i	−0.996702	−	0.0811497i	$-0.974141\pi$
$311$		−	2.86218i		−	0.162299i	0.996702	−	0.0811497i	$-0.0258592\pi$
$312$	9.57310	−	9.57310i	0.541970	−	0.541970i
$313$	9.41824	−	9.41824i	0.532350	−	0.532350i	−0.388921	−	0.921271i	$-0.627152\pi$
$313$	9.41824	−	9.41824i	0.532350	−	0.532350i	0.921271	+	0.388921i	$0.127152\pi$
$314$	−1.13424			−0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	−7.38310	+	7.38310i	−0.414676	+	0.414676i	−0.883364	−	0.468688i	$-0.844727\pi$
$317$	−7.38310	+	7.38310i	−0.414676	+	0.414676i	0.468688	+	0.883364i	$0.344727\pi$
$318$	−4.68886	+	4.68886i	−0.262938	+	0.262938i
$319$			10.6724i			0.597540i
$320$		0			0
$321$			9.04739i			0.504976i
$322$	1.48508	−	0.354351i	0.0827600	−	0.0197472i
$323$	−0.103958	−	0.103958i	−0.00578440	−	0.00578440i
$324$		−	1.41649i		−	0.0786939i
$325$		0			0
$326$	5.94740			0.329396
$327$	−1.52776	−	1.52776i	−0.0844851	−	0.0844851i
$328$	−16.0194	+	16.0194i	−0.884526	+	0.884526i
$329$	17.5011	+	10.7582i	0.964866	+	0.593118i
$330$		0			0
$331$	23.6200			1.29827			0.649136	−	0.760672i	$-0.275130\pi$
$331$	23.6200			1.29827			0.649136	+	0.760672i	$0.275130\pi$
$332$	−2.31695	−	2.31695i	−0.127159	−	0.127159i
$333$	6.18757	+	6.18757i	0.339076	+	0.339076i
$334$	2.04139			0.111700
$335$		0			0
$336$	−1.16306	+	1.89203i	−0.0634500	+	0.103219i
$337$	4.93809	−	4.93809i	0.268995	−	0.268995i	−0.559700	−	0.828695i	$-0.689084\pi$
$337$	4.93809	−	4.93809i	0.268995	−	0.268995i	0.828695	+	0.559700i	$0.189084\pi$
$338$	7.51384	+	7.51384i	0.408699	+	0.408699i
$339$	−5.85234			−0.317856
$340$		0			0
$341$		−	9.23070i		−	0.499870i
$342$	0.0376844	+	0.0376844i	0.00203774	+	0.00203774i
$343$	−14.1330	+	11.9691i	−0.763109	+	0.646270i
$344$		−	10.2274i		−	0.551427i
$345$		0			0
$346$			5.30151i			0.285011i
$347$	−5.83694	+	5.83694i	−0.313343	+	0.313343i	−0.846203	−	0.532860i	$-0.821117\pi$
$347$	−5.83694	+	5.83694i	−0.313343	+	0.313343i	0.532860	+	0.846203i	$0.321117\pi$
$348$	−2.77554	+	2.77554i	−0.148784	+	0.148784i
$349$	−16.9121			−0.905282			−0.452641	−	0.891693i	$-0.649518\pi$
$349$	−16.9121			−0.905282			−0.452641	+	0.891693i	$0.649518\pi$
$350$		0			0
$351$	5.18757			0.276892
$352$	−15.9608	+	15.9608i	−0.850714	+	0.850714i
$353$	11.1265	−	11.1265i	0.592202	−	0.592202i	−0.346024	−	0.938226i	$-0.612468\pi$
$353$	11.1265	−	11.1265i	0.592202	−	0.592202i	0.938226	+	0.346024i	$0.112468\pi$
$354$			5.32759i			0.283158i
$355$		0			0
$356$		−	7.15771i		−	0.379358i
$357$	−5.42309	+	1.29400i	−0.287021	+	0.0684855i
$358$	10.0389	+	10.0389i	0.530574	+	0.530574i
$359$			8.14864i			0.430069i	0.976606	+	0.215034i	$0.0689864\pi$
$359$			8.14864i			0.430069i	−0.976606	+	0.215034i	$0.931014\pi$
$360$		0			0
$361$	−18.9951			−0.999744
$362$	4.58327	+	4.58327i	0.240891	+	0.240891i
$363$	−2.71033	+	2.71033i	−0.142255	+	0.142255i
$364$	−16.5623	−	10.1811i	−0.868102	−	0.533636i
$365$		0			0
$366$	−10.9316			−0.571406
$367$	−14.7480	−	14.7480i	−0.769840	−	0.769840i	0.208238	−	0.978078i	$-0.433227\pi$
$367$	−14.7480	−	14.7480i	−0.769840	−	0.769840i	−0.978078	+	0.208238i	$0.933227\pi$
$368$	−0.448402	−	0.448402i	−0.0233746	−	0.0233746i
$369$	−8.68077			−0.451903
$370$		0			0
$371$	19.5660	+	12.0275i	1.01582	+	0.624438i
$372$	2.40060	−	2.40060i	0.124465	−	0.124465i
$373$	−1.49461	−	1.49461i	−0.0773880	−	0.0773880i	0.667353	−	0.744741i	$-0.267427\pi$
$373$	−1.49461	−	1.49461i	−0.0773880	−	0.0773880i	−0.744741	+	0.667353i	$0.767427\pi$
$374$	−6.19955			−0.320571
$375$		0			0
$376$			20.2640i			1.04504i
$377$	−10.1648	−	10.1648i	−0.523511	−	0.523511i
$378$	1.96584	−	0.469067i	0.101112	−	0.0241262i
$379$			18.7135i			0.961248i	0.876927	+	0.480624i	$0.159590\pi$
$379$			18.7135i			0.961248i	−0.876927	+	0.480624i	$0.840410\pi$
$380$		0			0
$381$			6.83487i			0.350161i
$382$	2.91327	−	2.91327i	0.149056	−	0.149056i
$383$	−20.9354	+	20.9354i	−1.06975	+	1.06975i	−0.0723706	+	0.997378i	$0.523056\pi$
$383$	−20.9354	+	20.9354i	−1.06975	+	1.06975i	−0.997378	+	0.0723706i	$0.976944\pi$
$384$	−9.58418			−0.489091
$385$		0			0
$386$	−5.19184			−0.264258
$387$	2.77107	−	2.77107i	0.140862	−	0.140862i
$388$	9.71502	−	9.71502i	0.493205	−	0.493205i
$389$			25.6611i			1.30107i	0.759477	+	0.650535i	$0.225455\pi$
$389$			25.6611i			1.30107i	−0.759477	+	0.650535i	$0.774545\pi$
$390$		0			0
$391$		−	1.59192i		−	0.0805069i
$392$	−17.3586	−	5.69357i	−0.876741	−	0.287569i
$393$	0.457851	+	0.457851i	0.0230955	+	0.0230955i
$394$		−	13.6915i		−	0.689767i
$395$		0			0
$396$	−5.45542			−0.274145
$397$	−6.73585	−	6.73585i	−0.338063	−	0.338063i	0.517575	−	0.855638i	$-0.326835\pi$
$397$	−6.73585	−	6.73585i	−0.338063	−	0.338063i	−0.855638	+	0.517575i	$0.826835\pi$
$398$	1.44278	−	1.44278i	0.0723201	−	0.0723201i
$399$	0.0966653	−	0.157252i	0.00483932	−	0.00787245i
$400$		0			0
$401$	14.7503			0.736593			0.368296	−	0.929708i	$-0.379941\pi$
$401$	14.7503			0.736593			0.368296	+	0.929708i	$0.379941\pi$
$402$	0.318148	+	0.318148i	0.0158678	+	0.0158678i
$403$	8.79162	+	8.79162i	0.437942	+	0.437942i
$404$	−27.1899			−1.35275
$405$		0			0
$406$	−4.77107	−	2.93285i	−0.236784	−	0.145555i
$407$	23.8305	−	23.8305i	1.18124	−	1.18124i
$408$	−3.88876	−	3.88876i	−0.192522	−	0.192522i
$409$	10.5604			0.522180			0.261090	−	0.965315i	$-0.415918\pi$
$409$	10.5604			0.522180			0.261090	+	0.965315i	$0.415918\pi$
$410$		0			0
$411$		−	14.4772i		−	0.714106i
$412$	−3.31210	−	3.31210i	−0.163176	−	0.163176i
$413$	17.9487	−	4.28270i	0.883196	−	0.210738i
$414$			0.577063i			0.0283611i
$415$		0			0
$416$		−	30.4032i		−	1.49064i
$417$	15.6739	−	15.6739i	0.767556	−	0.767556i
$418$	0.145136	−	0.145136i	0.00709884	−	0.00709884i
$419$	15.5472			0.759532			0.379766	−	0.925083i	$-0.376004\pi$
$419$	15.5472			0.759532			0.379766	+	0.925083i	$0.376004\pi$
$420$		0			0
$421$	3.29886			0.160776			0.0803882	−	0.996764i	$-0.474384\pi$
$421$	3.29886			0.160776			0.0803882	+	0.996764i	$0.474384\pi$
$422$	6.49461	−	6.49461i	0.316153	−	0.316153i
$423$	−5.49042	+	5.49042i	−0.266953	+	0.266953i
$424$			22.6549i			1.10022i
$425$		0			0
$426$			6.20867i			0.300811i
$427$	8.78764	+	36.8287i	0.425264	+	1.78227i
$428$	9.06196	+	9.06196i	0.438026	+	0.438026i
$429$		−	19.9792i		−	0.964604i
$430$		0			0
$431$	−14.0911			−0.678743			−0.339371	−	0.940652i	$-0.610214\pi$
$431$	−14.0911			−0.678743			−0.339371	+	0.940652i	$0.610214\pi$
$432$	−0.593565	−	0.593565i	−0.0285579	−	0.0285579i
$433$	1.72650	−	1.72650i	0.0829702	−	0.0829702i	−0.664404	−	0.747374i	$-0.731314\pi$
$433$	1.72650	−	1.72650i	0.0829702	−	0.0829702i	0.747374	+	0.664404i	$0.231314\pi$
$434$	4.12656	+	2.53666i	0.198081	+	0.121764i
$435$		0			0
$436$	−3.06043			−0.146568
$437$	0.0372681	+	0.0372681i	0.00178277	+	0.00178277i
$438$	7.29664	+	7.29664i	0.348647	+	0.348647i
$439$	−27.1172			−1.29423			−0.647116	−	0.762392i	$-0.724025\pi$
$439$	−27.1172			−1.29423			−0.647116	+	0.762392i	$0.724025\pi$
$440$		0			0
$441$	−3.16057	−	6.24586i	−0.150503	−	0.297422i
$442$	5.90465	−	5.90465i	0.280856	−	0.280856i
$443$	24.1502	+	24.1502i	1.14741	+	1.14741i	0.987060	+	0.160349i	$0.0512618\pi$
$443$	24.1502	+	24.1502i	1.14741	+	1.14741i	0.160349	+	0.987060i	$0.448738\pi$
$444$	12.3951			0.588243
$445$		0			0
$446$			12.6313i			0.598107i
$447$	−7.81179	−	7.81179i	−0.369485	−	0.369485i
$448$	−1.71818	−	7.20084i	−0.0811764	−	0.340208i
$449$		−	9.80267i		−	0.462617i	−0.972881	−	0.231308i	$-0.925699\pi$
$449$		−	9.80267i		−	0.462617i	0.972881	−	0.231308i	$-0.0743006\pi$
$450$		0			0
$451$			33.4328i			1.57429i
$452$	−5.86177	+	5.86177i	−0.275714	+	0.275714i
$453$	−13.0101	+	13.0101i	−0.611266	+	0.611266i
$454$	1.19391			0.0560331
$455$		0			0
$456$	0.182078			0.00852656
$457$	−0.550071	+	0.550071i	−0.0257312	+	0.0257312i	−0.719855	−	0.694124i	$-0.755792\pi$
$457$	−0.550071	+	0.550071i	−0.0257312	+	0.0257312i	0.694124	+	0.719855i	$0.255792\pi$
$458$	−4.23099	+	4.23099i	−0.197701	+	0.197701i
$459$		−	2.10728i		−	0.0983594i
$460$		0			0
$461$		−	0.831786i		−	0.0387401i	−0.999812	−	0.0193701i	$-0.993834\pi$
$461$		−	0.831786i		−	0.0387401i	0.999812	−	0.0193701i	$-0.00616607\pi$
$462$	−1.80655	−	7.57117i	−0.0840481	−	0.352243i
$463$	−5.45140	−	5.45140i	−0.253348	−	0.253348i	0.568994	−	0.822342i	$-0.307333\pi$
$463$	−5.45140	−	5.45140i	−0.253348	−	0.253348i	−0.822342	+	0.568994i	$0.807333\pi$
$464$			2.32612i			0.107987i
$465$		0			0
$466$	1.08890			0.0504423
$467$	23.2827	+	23.2827i	1.07740	+	1.07740i	0.996742	+	0.0806551i	$0.0257012\pi$
$467$	23.2827	+	23.2827i	1.07740	+	1.07740i	0.0806551	+	0.996742i	$0.474299\pi$
$468$	5.19592	−	5.19592i	0.240181	−	0.240181i
$469$	0.816091	−	1.32759i	0.0376836	−	0.0613025i
$470$		0			0
$471$	−1.48484			−0.0684180
$472$	12.8705	+	12.8705i	0.592414	+	0.592414i
$473$	−10.6724	−	10.6724i	−0.490718	−	0.490718i
$474$	7.53435			0.346064
$475$		0			0
$476$	−4.13575	+	6.72791i	−0.189562	+	0.308373i
$477$	−6.13823	+	6.13823i	−0.281050	+	0.281050i
$478$	−10.9544	−	10.9544i	−0.501041	−	0.501041i
$479$	−40.4319			−1.84738			−0.923691	−	0.383138i	$-0.874843\pi$
$479$	−40.4319			−1.84738			−0.923691	+	0.383138i	$0.874843\pi$
$480$		0			0
$481$			45.3940i			2.06979i
$482$	1.49616	+	1.49616i	0.0681483	+	0.0681483i
$483$	1.94413	−	0.463885i	0.0884609	−	0.0211075i
$484$			5.42938i			0.246790i
$485$		0			0
$486$			0.763878i			0.0346502i
$487$	7.22893	−	7.22893i	0.327574	−	0.327574i	−0.524089	−	0.851663i	$-0.675594\pi$
$487$	7.22893	−	7.22893i	0.327574	−	0.327574i	0.851663	+	0.524089i	$0.175594\pi$
$488$	−26.4089	+	26.4089i	−1.19548	+	1.19548i
$489$	7.78580			0.352086
$490$		0			0
$491$	20.1040			0.907279			0.453639	−	0.891185i	$-0.350125\pi$
$491$	20.1040			0.907279			0.453639	+	0.891185i	$0.350125\pi$
$492$	−8.69475	+	8.69475i	−0.391990	+	0.391990i
$493$	−4.12910	+	4.12910i	−0.185965	+	0.185965i
$494$			0.276465i			0.0124387i
$495$		0			0
$496$		−	2.01189i		−	0.0903364i
$497$	20.9170	−	4.99097i	0.938256	−	0.223876i
$498$	1.24947	+	1.24947i	0.0559902	+	0.0559902i
$499$			15.4227i			0.690414i	0.938527	+	0.345207i	$0.112191\pi$
$499$			15.4227i			0.690414i	−0.938527	+	0.345207i	$0.887809\pi$
$500$		0			0
$501$	2.67241			0.119394
$502$	−3.29478	−	3.29478i	−0.147053	−	0.147053i
$503$	−25.9985	+	25.9985i	−1.15922	+	1.15922i	−0.174573	+	0.984644i	$0.555855\pi$
$503$	−25.9985	+	25.9985i	−1.15922	+	1.15922i	−0.984644	+	0.174573i	$0.944145\pi$
$504$	3.61595	−	5.88231i	0.161067	−	0.262019i
$505$		0			0
$506$	2.22248			0.0988013
$507$	9.83645	+	9.83645i	0.436852	+	0.436852i
$508$	6.84587	+	6.84587i	0.303737	+	0.303737i
$509$	37.1271			1.64563			0.822816	−	0.568309i	$-0.192402\pi$
$509$	37.1271			1.64563			0.822816	+	0.568309i	$0.192402\pi$
$510$		0			0
$511$	18.7168	−	30.4479i	0.827983	−	1.34694i
$512$	−6.57690	+	6.57690i	−0.290661	+	0.290661i
$513$	0.0493330	+	0.0493330i	0.00217810	+	0.00217810i
$514$	−2.18048			−0.0961768
$515$		0			0
$516$		−	5.55107i		−	0.244372i
$517$	21.1456	+	21.1456i	0.929982	+	0.929982i
$518$	4.10459	+	17.2022i	0.180345	+	0.755821i
$519$			6.94026i			0.304644i
$520$		0			0
$521$			2.59132i			0.113528i	0.998388	+	0.0567639i	$0.0180782\pi$
$521$			2.59132i			0.113528i	−0.998388	+	0.0567639i	$0.981922\pi$
$522$	1.49678	−	1.49678i	0.0655122	−	0.0655122i
$523$	6.08854	−	6.08854i	0.266233	−	0.266233i	−0.561347	−	0.827581i	$-0.689717\pi$
$523$	6.08854	−	6.08854i	0.266233	−	0.266233i	0.827581	+	0.561347i	$0.189717\pi$
$524$	0.917176			0.0400670
$525$		0			0
$526$	18.1149			0.789846
$527$	3.57131	−	3.57131i	0.155569	−	0.155569i
$528$	−2.28603	+	2.28603i	−0.0994868	+	0.0994868i
$529$		−	22.4293i		−	0.975187i
$530$		0			0
$531$			6.97440i			0.302663i
$532$	−0.0606843	−	0.254326i	−0.00263100	−	0.0110264i
$533$	−31.8425	−	31.8425i	−1.37925	−	1.37925i
$534$			3.85997i			0.167037i
$535$		0			0
$536$	1.53718			0.0663960
$537$	13.1421	+	13.1421i	0.567122	+	0.567122i
$538$	−13.3605	+	13.3605i	−0.576013	+	0.576013i
$539$	−24.0551	+	12.1725i	−1.03613	+	0.524307i
$540$		0			0
$541$	−33.4638			−1.43872			−0.719360	−	0.694638i	$-0.755565\pi$
$541$	−33.4638			−1.43872			−0.719360	+	0.694638i	$0.755565\pi$
$542$	2.23333	+	2.23333i	0.0959297	+	0.0959297i
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$	−12.3503			−0.529515
$545$		0			0
$546$	8.93165	+	5.49042i	0.382239	+	0.234968i
$547$	0.828381	−	0.828381i	0.0354190	−	0.0354190i	−0.689175	−	0.724594i	$-0.742027\pi$
$547$	0.828381	−	0.828381i	0.0354190	−	0.0354190i	0.724594	+	0.689175i	$0.242027\pi$
$548$	−14.5005	−	14.5005i	−0.619429	−	0.619429i
$549$	−14.3107			−0.610767
$550$		0			0
$551$		−	0.193331i		−	0.00823616i
$552$	1.39408	+	1.39408i	0.0593361	+	0.0593361i
$553$	−6.05665	−	25.3832i	−0.257555	−	1.07941i
$554$			13.0853i			0.555939i
$555$		0			0
$556$		−	31.3983i		−	1.33159i
$557$	−14.7120	+	14.7120i	−0.623366	+	0.623366i	−0.946391	−	0.323024i	$-0.895300\pi$
$557$	−14.7120	+	14.7120i	−0.623366	+	0.623366i	0.323024	+	0.946391i	$0.395300\pi$
$558$	−1.29458	+	1.29458i	−0.0548040	+	0.0548040i
$559$	20.3295			0.859846
$560$		0			0
$561$	−8.11589			−0.342653
$562$	−2.83726	+	2.83726i	−0.119683	+	0.119683i
$563$	23.9693	−	23.9693i	1.01019	−	1.01019i	0.0102391	−	0.999948i	$-0.496741\pi$
$563$	23.9693	−	23.9693i	1.01019	−	1.01019i	0.999948	−	0.0102391i	$-0.00325926\pi$
$564$			10.9985i			0.463121i
$565$		0			0
$566$			1.80115i			0.0757080i
$567$	2.57351	−	0.614060i	0.108077	−	0.0257881i
$568$	14.9990	+	14.9990i	0.629346	+	0.629346i
$569$			15.6660i			0.656751i	0.944547	+	0.328376i	$0.106501\pi$
$569$			15.6660i			0.656751i	−0.944547	+	0.328376i	$0.893499\pi$
$570$		0			0
$571$	36.9887			1.54793			0.773964	−	0.633229i	$-0.218271\pi$
$571$	36.9887			1.54793			0.773964	+	0.633229i	$0.218271\pi$
$572$	−20.0114	−	20.0114i	−0.836717	−	0.836717i
$573$	3.81379	−	3.81379i	0.159323	−	0.159323i
$574$	−14.9460	−	9.18757i	−0.623836	−	0.383482i
$575$		0			0
$576$	2.79807			0.116586
$577$	−15.5587	−	15.5587i	−0.647717	−	0.647717i	0.304724	−	0.952441i	$-0.401436\pi$
$577$	−15.5587	−	15.5587i	−0.647717	−	0.647717i	−0.952441	+	0.304724i	$0.901436\pi$
$578$	6.78386	+	6.78386i	0.282171	+	0.282171i
$579$	−6.79669			−0.282461
$580$		0			0
$581$	3.20506	−	5.21389i	0.132968	−	0.216309i
$582$	−5.23907	+	5.23907i	−0.217166	+	0.217166i
$583$	23.6405	+	23.6405i	0.979091	+	0.979091i
$584$	35.2548			1.45885
$585$		0			0
$586$			16.4804i			0.680798i
$587$	15.7111	+	15.7111i	0.648468	+	0.648468i	0.952623	−	0.304155i	$-0.0983740\pi$
$587$	15.7111	+	15.7111i	0.648468	+	0.648468i	−0.304155	+	0.952623i	$0.598374\pi$
$588$	−9.42158	−	3.09026i	−0.388539	−	0.127440i
$589$			0.167214i			0.00688993i
$590$		0			0
$591$		−	17.9237i		−	0.737281i
$592$	5.19401	−	5.19401i	0.213473	−	0.213473i
$593$	1.85199	−	1.85199i	0.0760523	−	0.0760523i	−0.668057	−	0.744110i	$-0.732874\pi$
$593$	1.85199	−	1.85199i	0.0760523	−	0.0760523i	0.744110	+	0.668057i	$0.232874\pi$
$594$	2.94197			0.120710
$595$		0			0
$596$	−15.6487			−0.640997
$597$	1.88876	−	1.88876i	0.0773018	−	0.0773018i
$598$	−2.11676	+	2.11676i	−0.0865609	+	0.0865609i
$599$		−	47.3151i		−	1.93324i	−0.256208	−	0.966622i	$-0.582473\pi$
$599$		−	47.3151i		−	1.93324i	0.256208	−	0.966622i	$-0.417527\pi$
$600$		0			0
$601$			11.0819i			0.452041i	0.974123	+	0.226021i	$0.0725717\pi$
$601$			11.0819i			0.452041i	−0.974123	+	0.226021i	$0.927428\pi$
$602$	7.70393	−	1.83822i	0.313989	−	0.0749203i
$603$	0.416491	+	0.416491i	0.0169608	+	0.0169608i
$604$			26.0620i			1.06045i
$605$		0			0
$606$	14.6628			0.595637
$607$	−7.54653	−	7.54653i	−0.306304	−	0.306304i	0.537170	−	0.843474i	$-0.319493\pi$
$607$	−7.54653	−	7.54653i	−0.306304	−	0.306304i	−0.843474	+	0.537170i	$0.819493\pi$
$608$	0.289130	−	0.289130i	0.0117258	−	0.0117258i
$609$	−6.24586	−	3.83943i	−0.253095	−	0.155581i
$610$		0			0
$611$	−40.2795			−1.62953
$612$	−2.11067	−	2.11067i	−0.0853189	−	0.0853189i
$613$	2.62487	+	2.62487i	0.106017	+	0.106017i	0.758126	−	0.652108i	$-0.226115\pi$
$613$	2.62487	+	2.62487i	0.106017	+	0.106017i	−0.652108	+	0.758126i	$0.726115\pi$
$614$	−15.7935			−0.637375
$615$		0			0
$616$	−22.6549	−	13.9263i	−0.912793	−	0.561108i
$617$	−11.3212	+	11.3212i	−0.455774	+	0.455774i	−0.897266	−	0.441491i	$-0.854450\pi$
$617$	−11.3212	+	11.3212i	−0.455774	+	0.455774i	0.441491	+	0.897266i	$0.354450\pi$
$618$	1.78613	+	1.78613i	0.0718488	+	0.0718488i
$619$	−9.06771			−0.364462			−0.182231	−	0.983256i	$-0.558332\pi$
$619$	−9.06771			−0.364462			−0.182231	+	0.983256i	$0.558332\pi$
$620$		0			0
$621$			0.755439i			0.0303147i
$622$	1.54599	+	1.54599i	0.0619884	+	0.0619884i
$623$	13.0043	−	3.10292i	0.521005	−	0.124316i
$624$		−	4.35458i		−	0.174323i
$625$		0			0
$626$			10.1744i			0.406651i
$627$	0.189999	−	0.189999i	0.00758783	−	0.00758783i
$628$	−1.48723	+	1.48723i	−0.0593471	+	0.0593471i
$629$	18.4398			0.735244
$630$		0			0
$631$	−9.67260			−0.385060			−0.192530	−	0.981291i	$-0.561669\pi$
$631$	−9.67260			−0.385060			−0.192530	+	0.981291i	$0.561669\pi$
$632$	18.2017	−	18.2017i	0.724023	−	0.724023i
$633$	8.50216	−	8.50216i	0.337930	−	0.337930i
$634$		−	7.97587i		−	0.316762i
$635$		0			0
$636$			12.2962i			0.487577i
$637$	11.3173	−	34.5043i	0.448409	−	1.36711i
$638$	−5.76463	−	5.76463i	−0.228224	−	0.228224i
$639$			8.12783i			0.321532i
$640$		0			0
$641$	−40.5847			−1.60300			−0.801500	−	0.597995i	$-0.795964\pi$
$641$	−40.5847			−1.60300			−0.801500	+	0.597995i	$0.795964\pi$
$642$	−4.88689	−	4.88689i	−0.192870	−	0.192870i
$643$	−3.89544	+	3.89544i	−0.153621	+	0.153621i	−0.779733	−	0.626112i	$-0.784645\pi$
$643$	−3.89544	+	3.89544i	−0.153621	+	0.153621i	0.626112	+	0.779733i	$0.284645\pi$
$644$	1.48263	−	2.41189i	0.0584236	−	0.0950418i
$645$		0			0
$646$	0.112305			0.00441857
$647$	−16.8414	−	16.8414i	−0.662104	−	0.662104i	0.293772	−	0.955876i	$-0.405089\pi$
$647$	−16.8414	−	16.8414i	−0.662104	−	0.662104i	−0.955876	+	0.293772i	$0.905089\pi$
$648$	1.84539	+	1.84539i	0.0724939	+	0.0724939i
$649$	26.8609			1.05438
$650$		0			0
$651$	5.40212	+	3.32077i	0.211726	+	0.130151i
$652$	7.79833	−	7.79833i	0.305406	−	0.305406i
$653$	22.9951	+	22.9951i	0.899867	+	0.899867i	0.995424	−	0.0955569i	$-0.0304632\pi$
$653$	22.9951	+	22.9951i	0.899867	+	0.899867i	−0.0955569	+	0.995424i	$0.530463\pi$
$654$	1.65041			0.0645363
$655$		0			0
$656$			7.28688i			0.284505i
$657$	9.55210	+	9.55210i	0.372663	+	0.372663i
$658$	−15.2640	+	3.64213i	−0.595054	+	0.141985i
$659$		−	32.7543i		−	1.27593i	−0.770067	−	0.637963i	$-0.779777\pi$
$659$		−	32.7543i		−	1.27593i	0.770067	−	0.637963i	$-0.220223\pi$
$660$		0			0
$661$		−	32.5174i		−	1.26478i	−0.774650	−	0.632391i	$-0.782074\pi$
$661$		−	32.5174i		−	1.26478i	0.774650	−	0.632391i	$-0.217926\pi$
$662$	−12.7582	+	12.7582i	−0.495861	+	0.495861i
$663$	7.72984	−	7.72984i	0.300202	−	0.300202i
$664$	6.03701			0.234281
$665$		0			0
$666$	−6.68434			−0.259013
$667$	1.48024	−	1.48024i	0.0573152	−	0.0573152i
$668$	2.67671	−	2.67671i	0.103565	−	0.103565i
$669$			16.5357i			0.639307i
$670$		0			0
$671$			55.1158i			2.12772i
$672$	−3.59887	−	15.0828i	−0.138829	−	0.581830i
$673$	16.7534	+	16.7534i	0.645796	+	0.645796i	0.951974	−	0.306179i	$-0.0990504\pi$
$673$	16.7534	+	16.7534i	0.645796	+	0.645796i	−0.306179	+	0.951974i	$0.599050\pi$
$674$			5.33455i			0.205479i
$675$		0			0
$676$	19.7046			0.757868
$677$	6.85568	+	6.85568i	0.263485	+	0.263485i	0.826468	−	0.562983i	$-0.190346\pi$
$677$	6.85568	+	6.85568i	0.263485	+	0.263485i	−0.562983	+	0.826468i	$0.690346\pi$
$678$	3.16110	−	3.16110i	0.121401	−	0.121401i
$679$	21.8620	+	13.4389i	0.838985	+	0.515737i
$680$		0			0
$681$	1.56296			0.0598929
$682$	4.98590	+	4.98590i	0.190920	+	0.190920i
$683$	−23.2345	−	23.2345i	−0.889042	−	0.889042i	0.105389	−	0.994431i	$-0.466391\pi$
$683$	−23.2345	−	23.2345i	−0.889042	−	0.889042i	−0.994431	+	0.105389i	$0.966391\pi$
$684$	0.0988248			0.00377866
$685$		0			0
$686$	1.16881	−	14.0988i	0.0446255	−	0.538297i
$687$	−5.53883	+	5.53883i	−0.211319	+	0.211319i
$688$	−2.32612	−	2.32612i	−0.0886823	−	0.0886823i
$689$	−45.0321			−1.71559
$690$		0			0
$691$		−	42.4714i		−	1.61569i	−0.589395	−	0.807845i	$-0.700634\pi$
$691$		−	42.4714i		−	1.61569i	0.589395	−	0.807845i	$-0.299366\pi$
$692$	6.95144	+	6.95144i	0.264254	+	0.264254i
$693$	−2.36497	−	9.91150i	−0.0898376	−	0.376507i
$694$		−	6.30557i		−	0.239356i
$695$		0			0
$696$		−	7.23190i		−	0.274124i
$697$	−12.9350	+	12.9350i	−0.489947	+	0.489947i
$698$	9.13494	−	9.13494i	0.345763	−	0.345763i
$699$	1.42549			0.0539169
$700$		0			0
$701$	17.0793			0.645077			0.322539	−	0.946556i	$-0.395464\pi$
$701$	17.0793			0.645077			0.322539	+	0.946556i	$0.395464\pi$
$702$	−2.80203	+	2.80203i	−0.105756	+	0.105756i
$703$	−0.431690	+	0.431690i	−0.0162815	+	0.0162815i
$704$		−	10.7764i		−	0.406150i
$705$		0			0
$706$			12.0198i			0.452370i
$707$	−11.7870	−	49.3991i	−0.443297	−	1.85785i
$708$	6.98563	+	6.98563i	0.262536	+	0.262536i
$709$		−	32.6742i		−	1.22710i	−0.789654	−	0.613552i	$-0.789740\pi$
$709$		−	32.6742i		−	1.22710i	0.789654	−	0.613552i	$-0.210260\pi$
$710$		0			0
$711$	9.86329			0.369902
$712$	9.32502	+	9.32502i	0.349470	+	0.349470i
$713$	−1.28028	+	1.28028i	−0.0479469	+	0.0479469i
$714$	2.23030	−	3.62819i	0.0834670	−	0.135782i
$715$		0			0
$716$	26.3264			0.983865
$717$	−14.3405	−	14.3405i	−0.535554	−	0.535554i
$718$	−4.40143	−	4.40143i	−0.164260	−	0.164260i
$719$	−19.3248			−0.720693			−0.360346	−	0.932819i	$-0.617341\pi$
$719$	−19.3248			−0.720693			−0.360346	+	0.932819i	$0.617341\pi$
$720$		0			0
$721$	4.58166	−	7.45331i	0.170630	−	0.277576i
$722$	10.2601	−	10.2601i	0.381841	−	0.381841i
$723$	1.95864	+	1.95864i	0.0728426	+	0.0728426i
$724$	12.0193			0.446695
$725$		0			0
$726$		−	2.92793i		−	0.108666i
$727$	−2.71795	−	2.71795i	−0.100803	−	0.100803i	0.654907	−	0.755710i	$-0.272708\pi$
$727$	−2.71795	−	2.71795i	−0.100803	−	0.100803i	−0.755710	+	0.654907i	$0.772708\pi$
$728$	34.8412	−	8.31339i	1.29130	−	0.308115i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	8.25820i		−	0.305440i
$732$	−14.3338	+	14.3338i	−0.529791	+	0.529791i
$733$	2.38437	−	2.38437i	0.0880686	−	0.0880686i	−0.661700	−	0.749769i	$-0.730165\pi$
$733$	2.38437	−	2.38437i	0.0880686	−	0.0880686i	0.749769	+	0.661700i	$0.230165\pi$
$734$	15.9321			0.588064
$735$		0			0
$736$	4.42747			0.163199
$737$	1.60406	−	1.60406i	0.0590862	−	0.0590862i
$738$	4.68886	−	4.68886i	0.172599	−	0.172599i
$739$		−	4.95679i		−	0.182339i	−0.995835	−	0.0911693i	$-0.970940\pi$
$739$		−	4.95679i		−	0.182339i	0.995835	−	0.0911693i	$-0.0290605\pi$
$740$		0			0
$741$			0.361923i			0.0132956i
$742$	−17.0650	+	4.07186i	−0.626477	+	0.149483i
$743$	−15.6556	−	15.6556i	−0.574347	−	0.574347i	0.358993	−	0.933340i	$-0.383120\pi$
$743$	−15.6556	−	15.6556i	−0.574347	−	0.574347i	−0.933340	+	0.358993i	$0.883120\pi$
$744$			6.25496i			0.229318i
$745$		0			0
$746$	1.61461			0.0591150
$747$	1.63570	+	1.63570i	0.0598470	+	0.0598470i
$748$	−8.12896	+	8.12896i	−0.297224	+	0.297224i
$749$	−12.5355	+	20.3924i	−0.458037	+	0.745120i
$750$		0			0
$751$	−11.1909			−0.408361			−0.204181	−	0.978933i	$-0.565453\pi$
$751$	−11.1909			−0.408361			−0.204181	+	0.978933i	$0.565453\pi$
$752$	4.60881	+	4.60881i	0.168066	+	0.168066i
$753$	−4.31322	−	4.31322i	−0.157183	−	0.157183i
$754$	10.9808			0.399899
$755$		0			0
$756$	1.96260	−	3.19270i	0.0713791	−	0.116117i
$757$	−29.4977	+	29.4977i	−1.07211	+	1.07211i	−0.0749214	+	0.997189i	$0.523871\pi$
$757$	−29.4977	+	29.4977i	−1.07211	+	1.07211i	−0.997189	+	0.0749214i	$0.976129\pi$
$758$	−10.1080	−	10.1080i	−0.367138	−	0.367138i
$759$	2.90947			0.105607
$760$		0			0
$761$		−	28.1175i		−	1.01926i	−0.860395	−	0.509629i	$-0.829783\pi$
$761$		−	28.1175i		−	1.01926i	0.860395	−	0.509629i	$-0.170217\pi$
$762$	−3.69181	−	3.69181i	−0.133740	−	0.133740i
$763$	−1.32672	−	5.56025i	−0.0480305	−	0.201294i
$764$		−	7.63986i		−	0.276400i
$765$		0			0
$766$		−	22.6162i		−	0.817157i
$767$	−25.5832	+	25.5832i	−0.923757	+	0.923757i
$768$	9.13390	−	9.13390i	0.329591	−	0.329591i
$769$	6.61248			0.238452			0.119226	−	0.992867i	$-0.461959\pi$
$769$	6.61248			0.238452			0.119226	+	0.992867i	$0.461959\pi$
$770$		0			0
$771$	−2.85449			−0.102802
$772$	−6.80764	+	6.80764i	−0.245012	+	0.245012i
$773$	−31.7247	+	31.7247i	−1.14106	+	1.14106i	−0.152800	+	0.988257i	$0.548829\pi$
$773$	−31.7247	+	31.7247i	−1.14106	+	1.14106i	−0.988257	+	0.152800i	$0.951171\pi$
$774$			2.99355i			0.107601i
$775$		0			0
$776$			25.3133i			0.908695i
$777$	5.37335	+	22.5196i	0.192768	+	0.807885i
$778$	−13.8607	−	13.8607i	−0.496929	−	0.496929i
$779$		−	0.605634i		−	0.0216991i
$780$		0			0
$781$	31.3032			1.12012
$782$	0.859866	+	0.859866i	0.0307487	+	0.0307487i
$783$	1.95945	−	1.95945i	0.0700249	−	0.0700249i
$784$	−5.24295	+	2.65307i	−0.187248	+	0.0947525i
$785$		0			0
$786$	−0.494610			−0.0176422
$787$	−22.4472	−	22.4472i	−0.800155	−	0.800155i	0.182964	−	0.983120i	$-0.441431\pi$
$787$	−22.4472	−	22.4472i	−0.800155	−	0.800155i	−0.983120	+	0.182964i	$0.941431\pi$
$788$	−17.9525	−	17.9525i	−0.639532	−	0.639532i
$789$	23.7144			0.844254
$790$		0			0
$791$	−13.1909	−	8.10864i	−0.469014	−	0.288310i
$792$	7.10728	−	7.10728i	0.252546	−	0.252546i
$793$	−52.4941	−	52.4941i	−1.86412	−	1.86412i
$794$	7.27665			0.258239
$795$		0			0
$796$		−	3.78360i		−	0.134106i
$797$	−5.14677	−	5.14677i	−0.182308	−	0.182308i	0.610053	−	0.792361i	$-0.291148\pi$
$797$	−5.14677	−	5.14677i	−0.182308	−	0.182308i	−0.792361	+	0.610053i	$0.791148\pi$
$798$	0.0327255	+	0.137152i	0.00115847	+	0.00485512i
$799$			16.3622i			0.578854i
$800$		0			0
$801$			5.05313i			0.178544i
$802$	−7.96725	+	7.96725i	−0.281333	+	0.281333i
$803$	36.7886	−	36.7886i	1.29824	−	1.29824i
$804$	0.834323			0.0294243
$805$		0			0
$806$	−9.49747			−0.334534
$807$	−17.4904	+	17.4904i	−0.615691	+	0.615691i
$808$	35.4228	−	35.4228i	1.24617	−	1.24617i
$809$		−	22.5215i		−	0.791815i	−0.918290	−	0.395907i	$-0.870430\pi$
$809$		−	22.5215i		−	0.791815i	0.918290	−	0.395907i	$-0.129570\pi$
$810$		0			0
$811$			34.9145i			1.22602i	0.790077	+	0.613008i	$0.210040\pi$
$811$			34.9145i			1.22602i	−0.790077	+	0.613008i	$0.789960\pi$
$812$	−10.1015	+	2.41031i	−0.354494	+	0.0845852i
$813$	2.92367	+	2.92367i	0.102538	+	0.102538i
$814$			25.7438i			0.902320i
$815$		0			0
$816$	−1.76891			−0.0619241
$817$	0.193331	+	0.193331i	0.00676378	+	0.00676378i
$818$	−5.70414	+	5.70414i	−0.199441	+	0.199441i
$819$	11.6925	+	7.18757i	0.408569	+	0.251154i
$820$		0			0
$821$	8.52640			0.297573			0.148787	−	0.988869i	$-0.452463\pi$
$821$	8.52640			0.297573			0.148787	+	0.988869i	$0.452463\pi$
$822$	7.81974	+	7.81974i	0.272745	+	0.272745i
$823$	33.9044	+	33.9044i	1.18183	+	1.18183i	0.979269	+	0.202564i	$0.0649273\pi$
$823$	33.9044	+	33.9044i	1.18183	+	1.18183i	0.202564	+	0.979269i	$0.435073\pi$
$824$	8.62997			0.300639
$825$		0			0
$826$	−7.38158	+	12.0081i	−0.256838	+	0.417816i
$827$	37.8440	−	37.8440i	1.31597	−	1.31597i	0.399025	−	0.916940i	$-0.369349\pi$
$827$	37.8440	−	37.8440i	1.31597	−	1.31597i	0.916940	−	0.399025i	$-0.130651\pi$
$828$	0.756656	+	0.756656i	0.0262956	+	0.0262956i
$829$	−33.7140			−1.17094			−0.585469	−	0.810695i	$-0.699089\pi$
$829$	−33.7140			−1.17094			−0.585469	+	0.810695i	$0.699089\pi$
$830$		0			0
$831$			17.1300i			0.594234i
$832$	10.2638	+	10.2638i	0.355832	+	0.355832i
$833$	−14.0163	−	4.59730i	−0.485635	−	0.159287i
$834$			16.9323i			0.586319i
$835$		0			0
$836$		−	0.380610i		−	0.0131637i
$837$	−1.69475	+	1.69475i	−0.0585791	+	0.0585791i
$838$	−8.39773	+	8.39773i	−0.290095	+	0.290095i
$839$	−16.0665			−0.554679			−0.277339	−	0.960772i	$-0.589453\pi$
$839$	−16.0665			−0.554679			−0.277339	+	0.960772i	$0.589453\pi$
$840$		0			0
$841$	21.3211			0.735212
$842$	−1.78185	+	1.78185i	−0.0614068	+	0.0614068i
$843$	−3.71429	+	3.71429i	−0.127927	+	0.127927i
$844$		−	17.0317i		−	0.586255i
$845$		0			0
$846$		−	5.93123i		−	0.203920i
$847$	−9.86420	+	2.35368i	−0.338938	+	0.0808734i
$848$	5.15260	+	5.15260i	0.176941	+	0.176941i
$849$			2.35790i			0.0809231i
$850$		0			0
$851$	−6.61050			−0.226605
$852$	8.14091	+	8.14091i	0.278903	+	0.278903i
$853$	−5.14393	+	5.14393i	−0.176125	+	0.176125i	−0.789664	−	0.613539i	$-0.789745\pi$
$853$	−5.14393	+	5.14393i	−0.176125	+	0.176125i	0.613539	+	0.789664i	$0.289745\pi$
$854$	−24.6394	−	15.1462i	−0.843142	−	0.518292i
$855$		0			0
$856$	−23.6117			−0.807032
$857$	5.65076	+	5.65076i	0.193026	+	0.193026i	0.797002	−	0.603976i	$-0.206418\pi$
$857$	5.65076	+	5.65076i	0.193026	+	0.193026i	−0.603976	+	0.797002i	$0.706418\pi$
$858$	10.7916	+	10.7916i	0.368420	+	0.368420i
$859$	42.0801			1.43575			0.717877	−	0.696170i	$-0.245114\pi$
$859$	42.0801			1.43575			0.717877	+	0.696170i	$0.245114\pi$
$860$		0			0
$861$	−19.5660	−	12.0275i	−0.666808	−	0.409897i
$862$	7.61119	−	7.61119i	0.259238	−	0.259238i
$863$	11.9777	+	11.9777i	0.407724	+	0.407724i	0.880944	−	0.473220i	$-0.156908\pi$
$863$	11.9777	+	11.9777i	0.407724	+	0.407724i	−0.473220	+	0.880944i	$0.656908\pi$
$864$	5.86078			0.199388
$865$		0			0
$866$			1.86511i			0.0633791i
$867$	8.88082	+	8.88082i	0.301608	+	0.301608i
$868$	8.73694	−	2.08471i	0.296551	−	0.0707595i
$869$		−	37.9871i		−	1.28862i
$870$		0			0
$871$			3.05551i			0.103532i
$872$	3.98711	−	3.98711i	0.135021	−	0.135021i
$873$	−6.85851	+	6.85851i	−0.232125	+	0.232125i
$874$	−0.0402602			−0.00136182
$875$		0			0
$876$	19.1350			0.646510
$877$	11.5817	−	11.5817i	0.391085	−	0.391085i	−0.483989	−	0.875074i	$-0.660813\pi$
$877$	11.5817	−	11.5817i	0.391085	−	0.391085i	0.875074	+	0.483989i	$0.160813\pi$
$878$	14.6471	−	14.6471i	0.494317	−	0.494317i
$879$			21.5746i			0.727694i
$880$		0			0
$881$		−	8.72058i		−	0.293804i	−0.989151	−	0.146902i	$-0.953070\pi$
$881$		−	8.72058i		−	0.293804i	0.989151	−	0.146902i	$-0.0469301\pi$
$882$	5.08082	+	1.66650i	0.171080	+	0.0561139i
$883$	−17.0876	−	17.0876i	−0.575044	−	0.575044i	0.358490	−	0.933534i	$-0.383292\pi$
$883$	−17.0876	−	17.0876i	−0.575044	−	0.575044i	−0.933534	+	0.358490i	$0.883292\pi$
$884$		−	15.4846i		−	0.520803i
$885$		0			0
$886$	−26.0891			−0.876480
$887$	−26.4024	−	26.4024i	−0.886507	−	0.886507i	0.107679	−	0.994186i	$-0.465658\pi$
$887$	−26.4024	−	26.4024i	−0.886507	−	0.886507i	−0.994186	+	0.107679i	$0.965658\pi$
$888$	−16.1482	+	16.1482i	−0.541898	+	0.541898i
$889$	−9.46996	+	15.4054i	−0.317612	+	0.516682i
$890$		0			0
$891$	3.85136			0.129025
$892$	16.5623	+	16.5623i	0.554548	+	0.554548i
$893$	−0.383052	−	0.383052i	−0.0128184	−	0.0128184i
$894$	8.43897			0.282241
$895$		0			0
$896$	−21.6023	−	13.2792i	−0.721681	−	0.443628i
$897$	−2.77107	+	2.77107i	−0.0925235	+	0.0925235i
$898$	5.29484	+	5.29484i	0.176691	+	0.176691i
$899$	6.64154			0.221508
$900$		0			0
$901$			18.2928i			0.609422i
$902$	−18.0585	−	18.0585i	−0.601282	−	0.601282i
$903$	10.0853	−	2.40643i	0.335617	−	0.0800811i
$904$		−	15.2733i		−	0.507984i
$905$		0			0
$906$		−	14.0546i		−	0.466932i
$907$	23.6454	−	23.6454i	0.785133	−	0.785133i	−0.195559	−	0.980692i	$-0.562652\pi$
$907$	23.6454	−	23.6454i	0.785133	−	0.785133i	0.980692	+	0.195559i	$0.0626521\pi$
$908$	1.56548	−	1.56548i	0.0519523	−	0.0519523i
$909$	19.1953			0.636667
$910$		0			0
$911$	−17.8226			−0.590490			−0.295245	−	0.955422i	$-0.595401\pi$
$911$	−17.8226			−0.590490			−0.295245	+	0.955422i	$0.595401\pi$
$912$	0.0414114	−	0.0414114i	0.00137127	−	0.00137127i
$913$	6.29966	−	6.29966i	0.208488	−	0.208488i
$914$		−	0.594234i		−	0.0196555i
$915$		0			0
$916$			11.0955i			0.366605i
$917$	0.397603	+	1.66634i	0.0131300	+	0.0550274i
$918$	1.13823	+	1.13823i	0.0375673	+	0.0375673i
$919$		−	21.5752i		−	0.711701i	−0.934543	−	0.355850i	$-0.884191\pi$
$919$		−	21.5752i		−	0.711701i	0.934543	−	0.355850i	$-0.115809\pi$
$920$		0			0
$921$	−20.6755			−0.681280
$922$	0.449284	+	0.449284i	0.0147964	+	0.0147964i
$923$	−29.8142	+	29.8142i	−0.981346	+	0.981346i
$924$	−12.2962	−	7.55868i	−0.404516	−	0.248662i
$925$		0			0
$926$	5.88908			0.193527
$927$	2.33825	+	2.33825i	0.0767980	+	0.0767980i
$928$	−11.4839	−	11.4839i	−0.376977	−	0.376977i
$929$	38.3070			1.25681			0.628405	−	0.777886i	$-0.283708\pi$
$929$	38.3070			1.25681			0.628405	+	0.777886i	$0.283708\pi$
$930$		0			0
$931$	0.435757	−	0.220505i	0.0142814	−	0.00722675i
$932$	1.42778	−	1.42778i	0.0467686	−	0.0467686i
$933$	2.02387	+	2.02387i	0.0662584	+	0.0662584i
$934$	−25.1520			−0.823000
$935$		0			0
$936$			13.5384i			0.442517i
$937$	−13.2317	−	13.2317i	−0.432262	−	0.432262i	0.457135	−	0.889397i	$-0.348875\pi$
$937$	−13.2317	−	13.2317i	−0.432262	−	0.432262i	−0.889397	+	0.457135i	$0.848875\pi$
$938$	0.276283	+	1.15790i	0.00902097	+	0.0378066i
$939$			13.3194i			0.434662i
$940$		0			0
$941$			2.58095i			0.0841366i	0.999115	+	0.0420683i	$0.0133947\pi$
$941$			2.58095i			0.0841366i	−0.999115	+	0.0420683i	$0.986605\pi$
$942$	0.802028	−	0.802028i	0.0261315	−	0.0261315i
$943$	4.63706	−	4.63706i	0.151004	−	0.151004i
$944$	5.85450			0.190548
$945$		0			0
$946$	11.5293			0.374848
$947$	−4.94205	+	4.94205i	−0.160595	+	0.160595i	−0.782830	−	0.622235i	$-0.786225\pi$
$947$	−4.94205	+	4.94205i	−0.160595	+	0.160595i	0.622235	+	0.782830i	$0.286225\pi$
$948$	9.87918	−	9.87918i	0.320861	−	0.320861i
$949$			70.0773i			2.27481i
$950$		0			0
$951$		−	10.4413i		−	0.338582i
$952$	−3.37705	−	14.1531i	−0.109451	−	0.458704i
$953$	16.3558	+	16.3558i	0.529818	+	0.529818i	0.920518	−	0.390700i	$-0.127767\pi$
$953$	16.3558	+	16.3558i	0.529818	+	0.529818i	−0.390700	+	0.920518i	$0.627767\pi$
$954$		−	6.63105i		−	0.214688i
$955$		0			0
$956$	−28.7271			−0.929101
$957$	−7.54653	−	7.54653i	−0.243945	−	0.243945i
$958$	21.8390	−	21.8390i	0.705587	−	0.705587i
$959$	20.0586	−	32.6308i	0.647727	−	1.05370i
$960$		0			0
$961$	25.2557			0.814698
$962$	−24.5193	−	24.5193i	−0.790533	−	0.790533i
$963$	−6.39747	−	6.39747i	−0.206156	−	0.206156i
$964$	3.92359			0.126370
$965$		0			0
$966$	−0.799543	+	1.30067i	−0.0257249	+	0.0418484i
$967$	−8.66781	+	8.66781i	−0.278738	+	0.278738i	−0.832605	−	0.553867i	$-0.813152\pi$
$967$	−8.66781	+	8.66781i	−0.278738	+	0.278738i	0.553867	+	0.832605i	$0.313152\pi$
$968$	−7.07336	−	7.07336i	−0.227346	−	0.227346i
$969$	0.147019			0.00472294
$970$		0			0
$971$			13.1861i			0.423163i	0.977360	+	0.211582i	$0.0678614\pi$
$971$			13.1861i			0.423163i	−0.977360	+	0.211582i	$0.932139\pi$
$972$	1.00161	+	1.00161i	0.0321267	+	0.0321267i
$973$	57.0451	−	13.6114i	1.82878	−	0.436362i
$974$			7.80931i			0.250226i
$975$		0			0
$976$			12.0128i			0.384521i
$977$	24.4925	−	24.4925i	0.783586	−	0.783586i	−0.196848	−	0.980434i	$-0.563071\pi$
$977$	24.4925	−	24.4925i	0.783586	−	0.783586i	0.980434	+	0.196848i	$0.0630705\pi$
$978$	−4.20545	+	4.20545i	−0.134475	+	0.134475i
$979$	19.4614			0.621990
$980$		0			0
$981$	2.16057			0.0689818
$982$	−10.8590	+	10.8590i	−0.346525	+	0.346525i
$983$	−15.7362	+	15.7362i	−0.501907	+	0.501907i	−0.912030	−	0.410123i	$-0.865486\pi$
$983$	−15.7362	+	15.7362i	−0.501907	+	0.501907i	0.410123	+	0.912030i	$0.365486\pi$
$984$		−	22.6549i		−	0.722212i
$985$		0			0
$986$		−	4.46061i		−	0.142055i
$987$	−19.9823	+	4.76795i	−0.636044	+	0.151765i
$988$	0.362505	+	0.362505i	0.0115328	+	0.0115328i
$989$			2.96048i			0.0941379i
$990$		0			0
$991$	−30.1031			−0.956257			−0.478128	−	0.878290i	$-0.658685\pi$
$991$	−30.1031			−0.956257			−0.478128	+	0.878290i	$0.658685\pi$
$992$	9.93256	+	9.93256i	0.315359	+	0.315359i
$993$	−16.7019	+	16.7019i	−0.530018	+	0.530018i
$994$	−8.60234	+	13.9940i	−0.272850	+	0.443863i
$995$		0			0
$996$	3.27666			0.103825
$997$	22.8721	+	22.8721i	0.724367	+	0.724367i	0.969491	−	0.245125i	$-0.0788290\pi$
$997$	22.8721	+	22.8721i	0.724367	+	0.724367i	−0.245125	+	0.969491i	$0.578829\pi$
$998$	−8.33045	−	8.33045i	−0.263696	−	0.263696i
$999$	−8.75054			−0.276855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.b.118.3		16
5.2	odd	4	inner	525.2.m.b.307.4		16
5.3	odd	4		105.2.m.a.97.5	yes	16
5.4	even	2		105.2.m.a.13.6	yes	16
7.6	odd	2	inner	525.2.m.b.118.4		16
15.8	even	4		315.2.p.e.307.3		16
15.14	odd	2		315.2.p.e.118.4		16
20.3	even	4		1680.2.cz.d.97.7		16
20.19	odd	2		1680.2.cz.d.433.2		16
35.3	even	12		735.2.v.a.607.4		32
35.4	even	6		735.2.v.a.313.5		32
35.9	even	6		735.2.v.a.178.4		32
35.13	even	4		105.2.m.a.97.6	yes	16
35.18	odd	12		735.2.v.a.607.3		32
35.19	odd	6		735.2.v.a.178.3		32
35.23	odd	12		735.2.v.a.472.6		32
35.24	odd	6		735.2.v.a.313.6		32
35.27	even	4	inner	525.2.m.b.307.3		16
35.33	even	12		735.2.v.a.472.5		32
35.34	odd	2		105.2.m.a.13.5	✓	16
105.83	odd	4		315.2.p.e.307.4		16
105.104	even	2		315.2.p.e.118.3		16
140.83	odd	4		1680.2.cz.d.97.2		16
140.139	even	2		1680.2.cz.d.433.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	35.34	odd	2
105.2.m.a.13.6	yes	16	5.4	even	2
105.2.m.a.97.5	yes	16	5.3	odd	4
105.2.m.a.97.6	yes	16	35.13	even	4
315.2.p.e.118.3		16	105.104	even	2
315.2.p.e.118.4		16	15.14	odd	2
315.2.p.e.307.3		16	15.8	even	4
315.2.p.e.307.4		16	105.83	odd	4
525.2.m.b.118.3		16	1.1	even	1	trivial
525.2.m.b.118.4		16	7.6	odd	2	inner
525.2.m.b.307.3		16	35.27	even	4	inner
525.2.m.b.307.4		16	5.2	odd	4	inner
735.2.v.a.178.3		32	35.19	odd	6
735.2.v.a.178.4		32	35.9	even	6
735.2.v.a.313.5		32	35.4	even	6
735.2.v.a.313.6		32	35.24	odd	6
735.2.v.a.472.5		32	35.33	even	12
735.2.v.a.472.6		32	35.23	odd	12
735.2.v.a.607.3		32	35.18	odd	12
735.2.v.a.607.4		32	35.3	even	12
1680.2.cz.d.97.2		16	140.83	odd	4
1680.2.cz.d.97.7		16	20.3	even	4
1680.2.cz.d.433.2		16	20.19	odd	2
1680.2.cz.d.433.7		16	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540143 + 0.540143i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.41649i q^{4} -0.763878i q^{6} +(-2.57351 + 0.614060i) q^{7} +(-1.84539 - 1.84539i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.540143 + 0.540143i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.41649i q^{4} -0.763878i q^{6} +(-2.57351 + 0.614060i) q^{7} +(-1.84539 - 1.84539i) q^{8} -1.00000i q^{9} -3.85136 q^{11} +(-1.00161 - 1.00161i) q^{12} +(3.66816 - 3.66816i) q^{13} +(1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(-1.49007 - 1.49007i) q^{17} +(0.540143 + 0.540143i) q^{18} +0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(2.08029 - 2.08029i) q^{22} +(0.534176 + 0.534176i) q^{23} +2.60978 q^{24} +3.96267i q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.869810 - 3.64535i) q^{28} -2.77107i q^{29} +2.39674i q^{31} +(4.14420 - 4.14420i) q^{32} +(2.72332 - 2.72332i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(-6.18757 + 6.18757i) q^{37} +(-0.0376844 + 0.0376844i) q^{38} +5.18757i q^{39} -8.68077i q^{41} +(0.469067 + 1.96584i) q^{42} +(2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(-5.49042 - 5.49042i) q^{47} +(0.593565 - 0.593565i) q^{48} +(6.24586 - 3.16057i) q^{49} +2.10728 q^{51} +(5.19592 + 5.19592i) q^{52} +(-6.13823 - 6.13823i) q^{53} -0.763878 q^{54} +(5.88231 + 3.61595i) q^{56} +(-0.0493330 + 0.0493330i) q^{57} +(1.49678 + 1.49678i) q^{58} -6.97440 q^{59} -14.3107i q^{61} +(-1.29458 - 1.29458i) q^{62} +(0.614060 + 2.57351i) q^{63} +2.79807i q^{64} +2.94197i q^{66} +(-0.416491 + 0.416491i) q^{67} +(2.11067 - 2.11067i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(-1.84539 + 1.84539i) q^{72} +(-9.55210 + 9.55210i) q^{73} -6.68434i q^{74} +0.0988248i q^{76} +(9.91150 - 2.36497i) q^{77} +(-2.80203 - 2.80203i) q^{78} +9.86329i q^{79} -1.00000 q^{81} +(4.68886 + 4.68886i) q^{82} +(-1.63570 + 1.63570i) q^{83} +(3.19270 + 1.96260i) q^{84} -2.99355 q^{86} +(1.95945 + 1.95945i) q^{87} +(7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-7.18757 + 11.6925i) q^{91} +(-0.756656 + 0.756656i) q^{92} +(-1.69475 - 1.69475i) q^{93} +5.93123 q^{94} +5.86078i q^{96} +(-6.85851 - 6.85851i) q^{97} +(-1.66650 + 5.08082i) q^{98} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q + 8 * q^7 - 24 * q^8	\( 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more