LMFDB - Embedded newform 315.2.p.e.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(118,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, 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("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (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:	$2.51528766367$
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			307.4
Root			$1.36166 + 0.381939i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.e.118.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +O(q^{10})$	\(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +(-1.63006 + 0.510348i) q^{10} +3.85136 q^{11} +(-3.66816 - 3.66816i) q^{13} +(-1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(-2.80654 - 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +3.96267i q^{26} +(0.869810 - 3.64535i) q^{28} -2.77107i q^{29} -2.39674i q^{31} +(4.14420 + 4.14420i) q^{32} +1.60970 q^{34} +(3.88408 - 4.46250i) q^{35} +(6.18757 + 6.18757i) q^{37} +(-0.0376844 - 0.0376844i) q^{38} +(1.74360 + 5.56908i) q^{40} -8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(-5.49042 + 5.49042i) q^{47} +(6.24586 + 3.16057i) q^{49} +(-0.678376 + 3.75866i) q^{50} +(-5.19592 + 5.19592i) q^{52} +(-6.13823 + 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(-5.88231 + 3.61595i) q^{56} +(-1.49678 + 1.49678i) q^{58} +6.97440 q^{59} +14.3107i q^{61} +(-1.29458 + 1.29458i) q^{62} -2.79807i q^{64} +(-11.0699 + 3.46582i) q^{65} +(0.416491 + 0.416491i) q^{67} +(2.11067 + 2.11067i) q^{68} +(-4.50835 + 0.312431i) q^{70} +8.12783 q^{71} +(9.55210 + 9.55210i) q^{73} -6.68434i q^{74} -0.0988248i q^{76} +(9.91150 + 2.36497i) q^{77} -9.86329i q^{79} +(-0.870061 + 1.66319i) q^{80} +(-4.68886 + 4.68886i) q^{82} +(-1.63570 - 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +2.99355 q^{86} +(-7.10728 + 7.10728i) q^{88} +5.05313 q^{89} +(-7.18757 - 11.6925i) q^{91} +(-0.756656 - 0.756656i) q^{92} +5.93123 q^{94} +(0.0723134 - 0.138232i) q^{95} +(6.85851 - 6.85851i) q^{97} +(-1.66650 - 5.08082i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.540143	−	0.540143i	−0.381939	−	0.381939i	0.489861	−	0.871800i	$-0.337047\pi$
$2$	−0.540143	−	0.540143i	−0.381939	−	0.381939i	−0.871800	+	0.489861i	$0.837047\pi$
$3$		0			0
$3$		0			0
$4$		−	1.41649i		−	0.708245i
$5$	1.03649	−	1.98133i	0.463534	−	0.886079i
$5$	1.03649	−	1.98133i	0.463534	−	0.886079i
$6$		0			0
$7$	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
$9$		0			0
$10$	−1.63006	+	0.510348i	−0.515470	+	0.161386i
$11$	3.85136			1.16123			0.580615	−	0.814179i	$-0.302812\pi$
$11$	3.85136			1.16123			0.580615	+	0.814179i	$0.302812\pi$
$12$		0			0
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.999847	−	0.0175187i	$-0.994423\pi$
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.0175187	−	0.999847i	$-0.505577\pi$
$14$	−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	−0.864326	−	0.502931i	$-0.832255\pi$
$17$	−1.49007	+	1.49007i	−0.361395	+	0.361395i	0.502931	+	0.864326i	$0.332255\pi$
$18$		0			0
$19$	0.0697674			0.0160057			0.00800286	−	0.999968i	$-0.497453\pi$
$19$	0.0697674			0.0160057			0.00800286	+	0.999968i	$0.497453\pi$
$20$	−2.80654	−	1.46818i	−0.627561	−	0.328296i
$21$		0			0
$22$	−2.08029	−	2.08029i	−0.443519	−	0.443519i
$23$	0.534176	−	0.534176i	0.111383	−	0.111383i	−0.649218	−	0.760602i	$-0.724904\pi$
$23$	0.534176	−	0.534176i	0.111383	−	0.111383i	0.760602	+	0.649218i	$0.224904\pi$
$24$		0			0
$25$	−2.85136	−	4.10728i	−0.570272	−	0.821456i
$26$			3.96267i			0.777143i
$27$		0			0
$28$	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	$-0.930949\pi$
$31$		−	2.39674i		−	0.430467i	0.976563	−	0.215233i	$-0.0690512\pi$
$32$	4.14420	+	4.14420i	0.732598	+	0.732598i
$33$		0			0
$34$	1.60970			0.276062
$35$	3.88408	−	4.46250i	0.656529	−	0.754301i
$36$		0			0
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.999849	+	0.0173805i	$0.00553267\pi$
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.0173805	+	0.999849i	$0.494467\pi$
$38$	−0.0376844	−	0.0376844i	−0.00611321	−	0.00611321i
$39$		0			0
$40$	1.74360	+	5.56908i	0.275687	+	0.880549i
$41$		−	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			0
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	−0.886093	−	0.463508i	$-0.846591\pi$
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	0.463508	+	0.886093i	$0.346591\pi$
$44$		−	5.45542i		−	0.822435i
$45$		0			0
$46$	−0.577063			−0.0850834
$47$	−5.49042	+	5.49042i	−0.800860	+	0.800860i	−0.983230	−	0.182370i	$-0.941623\pi$
$47$	−5.49042	+	5.49042i	−0.800860	+	0.800860i	0.182370	+	0.983230i	$0.441623\pi$
$48$		0			0
$49$	6.24586	+	3.16057i	0.892266	+	0.451510i
$50$	−0.678376	+	3.75866i	−0.0959368	+	0.531555i
$51$		0			0
$52$	−5.19592	+	5.19592i	−0.720544	+	0.720544i
$53$	−6.13823	+	6.13823i	−0.843151	+	0.843151i	−0.989267	−	0.146116i	$-0.953323\pi$
$53$	−6.13823	+	6.13823i	−0.843151	+	0.843151i	0.146116	+	0.989267i	$0.453323\pi$
$54$		0			0
$55$	3.99191	−	7.63083i	0.538269	−	1.02894i
$56$	−5.88231	+	3.61595i	−0.786057	+	0.483202i
$57$		0			0
$58$	−1.49678	+	1.49678i	−0.196536	+	0.196536i
$59$	6.97440			0.907990			0.453995	−	0.891004i	$-0.349998\pi$
$59$	6.97440			0.907990			0.453995	+	0.891004i	$0.349998\pi$
$60$		0			0
$61$			14.3107i			1.83230i	0.400835	+	0.916150i	$0.368720\pi$
$61$			14.3107i			1.83230i	−0.400835	+	0.916150i	$0.631280\pi$
$62$	−1.29458	+	1.29458i	−0.164412	+	0.164412i
$63$		0			0
$64$		−	2.79807i		−	0.349758i
$65$	−11.0699	+	3.46582i	−1.37305	+	0.429883i
$66$		0			0
$67$	0.416491	+	0.416491i	0.0508824	+	0.0508824i	0.732090	−	0.681208i	$-0.238545\pi$
$67$	0.416491	+	0.416491i	0.0508824	+	0.0508824i	−0.681208	+	0.732090i	$0.738545\pi$
$68$	2.11067	+	2.11067i	0.255957	+	0.255957i
$69$		0			0
$70$	−4.50835	+	0.312431i	−0.538851	+	0.0373426i
$71$	8.12783			0.964595			0.482298	−	0.876007i	$-0.339802\pi$
$71$	8.12783			0.964595			0.482298	+	0.876007i	$0.339802\pi$
$72$		0			0
$73$	9.55210	+	9.55210i	1.11799	+	1.11799i	0.992036	+	0.125953i	$0.0401987\pi$
$73$	9.55210	+	9.55210i	1.11799	+	1.11799i	0.125953	+	0.992036i	$0.459801\pi$
$74$		−	6.68434i		−	0.777039i
$75$		0			0
$76$		−	0.0988248i		−	0.0113360i
$77$	9.91150	+	2.36497i	1.12952	+	0.269513i
$78$		0			0
$79$		−	9.86329i		−	1.10971i	−0.831948	−	0.554854i	$-0.812774\pi$
$79$		−	9.86329i		−	1.10971i	0.831948	−	0.554854i	$-0.187226\pi$
$80$	−0.870061	+	1.66319i	−0.0972758	+	0.185950i
$81$		0			0
$82$	−4.68886	+	4.68886i	−0.517798	+	0.517798i
$83$	−1.63570	−	1.63570i	−0.179541	−	0.179541i	0.611615	−	0.791156i	$-0.290520\pi$
$83$	−1.63570	−	1.63570i	−0.179541	−	0.179541i	−0.791156	+	0.611615i	$0.790520\pi$
$84$		0			0
$85$	1.40788	+	4.49678i	0.152706	+	0.487744i
$86$	2.99355			0.322803
$87$		0			0
$88$	−7.10728	+	7.10728i	−0.757638	+	0.757638i
$89$	5.05313			0.535631			0.267815	−	0.963470i	$-0.413698\pi$
$89$	5.05313			0.535631			0.267815	+	0.963470i	$0.413698\pi$
$90$		0			0
$91$	−7.18757	−	11.6925i	−0.753462	−	1.22571i
$92$	−0.756656	−	0.756656i	−0.0788868	−	0.0788868i
$93$		0			0
$94$	5.93123			0.611759
$95$	0.0723134	−	0.138232i	0.00741920	−	0.0141823i
$96$		0			0
$97$	6.85851	−	6.85851i	0.696376	−	0.696376i	−0.267251	−	0.963627i	$-0.586115\pi$
$97$	6.85851	−	6.85851i	0.696376	−	0.696376i	0.963627	+	0.267251i	$0.0861152\pi$
$98$	−1.66650	−	5.08082i	−0.168342	−	0.513240i
$99$		0			0
$100$	−5.81792	+	4.03893i	−0.581792	+	0.403893i
$101$			19.1953i			1.91000i	0.296605	+	0.955000i	$0.404145\pi$
$101$			19.1953i			1.91000i	−0.296605	+	0.955000i	$0.595855\pi$
$102$		0			0
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	0.812857	−	0.582463i	$-0.197911\pi$
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	−0.582463	+	0.812857i	$0.697911\pi$
$104$	13.5384			1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	6.39747	+	6.39747i	0.618467	+	0.618467i	0.945138	−	0.326671i	$-0.105927\pi$
$107$	6.39747	+	6.39747i	0.618467	+	0.618467i	−0.326671	+	0.945138i	$0.605927\pi$
$108$		0			0
$109$		−	2.16057i		−	0.206945i	−0.994632	−	0.103473i	$-0.967005\pi$
$109$		−	2.16057i		−	0.206945i	0.994632	−	0.103473i	$-0.0329954\pi$
$110$	−6.27794	+	1.96554i	−0.598578	+	0.187407i
$111$		0			0
$112$	−2.16027	−	0.515459i	−0.204126	−	0.0487063i
$113$	4.13823	−	4.13823i	0.389292	−	0.389292i	−0.485143	−	0.874435i	$-0.661232\pi$
$113$	4.13823	−	4.13823i	0.389292	−	0.389292i	0.874435	+	0.485143i	$0.161232\pi$
$114$		0			0
$115$	−0.504711	−	1.61205i	−0.0470645	−	0.150325i
$116$	−3.92520			−0.364446
$117$		0			0
$118$	−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
$123$		0			0
$124$	−3.39496			−0.304876
$125$	−11.0933	+	1.39233i	−0.992215	+	0.124533i
$126$		0			0
$127$	−4.83298	−	4.83298i	−0.428858	−	0.428858i	0.459381	−	0.888239i	$-0.348071\pi$
$127$	−4.83298	−	4.83298i	−0.428858	−	0.428858i	−0.888239	+	0.459381i	$0.848071\pi$
$128$	6.77704	−	6.77704i	0.599011	−	0.599011i
$129$		0			0
$130$	7.85136	+	4.10728i	0.688610	+	0.360232i
$131$		−	0.647499i		−	0.0565722i	−0.999600	−	0.0282861i	$-0.990995\pi$
$131$		−	0.647499i		−	0.0565722i	0.999600	−	0.0282861i	$-0.00900495\pi$
$132$		0			0
$133$	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	0.118372	−	0.992969i	$-0.462232\pi$
$137$	−10.2369	−	10.2369i	−0.874597	−	0.874597i	−0.992969	+	0.118372i	$0.962232\pi$
$138$		0			0
$139$	−22.1663			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$139$	−22.1663			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$140$	−6.32109	−	5.50176i	−0.534230	−	0.464984i
$141$		0			0
$142$	−4.39019	−	4.39019i	−0.368417	−	0.368417i
$143$	−14.1274	−	14.1274i	−1.18139	−	1.18139i
$144$		0			0
$145$	−5.49042	−	2.87220i	−0.455955	−	0.238523i
$146$		−	10.3190i		−	0.854007i
$147$		0			0
$148$	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
$153$		0			0
$154$	−4.07621	−	6.63105i	−0.328470	−	0.534345i
$155$	−4.74873	−	2.48420i	−0.381428	−	0.199536i
$156$		0			0
$157$	−1.04994	+	1.04994i	−0.0837946	+	0.0837946i	−0.747762	−	0.663967i	$-0.768871\pi$
$157$	−1.04994	+	1.04994i	−0.0837946	+	0.0837946i	0.663967	+	0.747762i	$0.268871\pi$
$158$	−5.32759	+	5.32759i	−0.423840	+	0.423840i
$159$		0			0
$160$	12.5065	−	3.91560i	0.988724	−	0.309555i
$161$	1.70272	−	1.04669i	0.134193	−	0.0824907i
$162$		0			0
$163$	5.50539	−	5.50539i	0.431215	−	0.431215i	−0.457826	−	0.889042i	$-0.651372\pi$
$163$	5.50539	−	5.50539i	0.431215	−	0.431215i	0.889042	+	0.457826i	$0.151372\pi$
$164$	−12.2962			−0.960174
$165$		0			0
$166$			1.76702i			0.137147i
$167$	−1.88968	+	1.88968i	−0.146228	+	0.146228i	−0.776431	−	0.630203i	$-0.782972\pi$
$167$	−1.88968	+	1.88968i	−0.146228	+	0.146228i	0.630203	+	0.776431i	$0.282972\pi$
$168$		0			0
$169$			13.9108i			1.07006i
$170$	1.66845	−	3.18936i	0.127964	−	0.244613i
$171$		0			0
$172$	3.92520	+	3.92520i	0.299294	+	0.299294i
$173$	4.90751	+	4.90751i	0.373111	+	0.373111i	0.868609	−	0.495498i	$-0.165014\pi$
$173$	4.90751	+	4.90751i	0.373111	+	0.373111i	−0.495498	+	0.868609i	$0.665014\pi$
$174$		0			0
$175$	−4.81588	−	12.3210i	−0.364046	−	0.931381i
$176$	−3.23294			−0.243692
$177$		0			0
$178$	−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	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	−2.43331	+	10.1979i	−0.180369	+	0.755922i
$183$		0			0
$184$			1.97153i			0.145343i
$185$	18.6730	−	5.84625i	1.37287	−	0.429825i
$186$		0			0
$187$	−5.73880	+	5.73880i	−0.419663	+	0.419663i
$188$	7.77713	+	7.77713i	0.567206	+	0.567206i
$189$		0			0
$190$	−0.113725	+	0.0356057i	−0.00825047	+	0.00258311i
$191$	5.39351			0.390261			0.195130	−	0.980777i	$-0.437487\pi$
$191$	5.39351			0.390261			0.195130	+	0.980777i	$0.437487\pi$
$192$		0			0
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	−0.858596	−	0.512653i	$-0.828663\pi$
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	0.512653	+	0.858596i	$0.328663\pi$
$194$	−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	0.0927124	−	0.995693i	$-0.470446\pi$
$197$	−12.6739	−	12.6739i	−0.902981	−	0.902981i	−0.995693	+	0.0927124i	$0.970446\pi$
$198$		0			0
$199$	−2.67111			−0.189350			−0.0946750	−	0.995508i	$-0.530181\pi$
$199$	−2.67111			−0.189350			−0.0946750	+	0.995508i	$0.530181\pi$
$200$	12.8414	+	2.31766i	0.908026	+	0.163884i
$201$		0			0
$202$	10.3682	−	10.3682i	0.729503	−	0.729503i
$203$	1.70161	−	7.13138i	0.119429	−	0.500524i
$204$		0			0
$205$	−17.1995	−	8.99757i	−1.20127	−	0.628417i
$206$		−	2.52597i		−	0.175993i
$207$		0			0
$208$	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
$213$		0			0
$214$		−	6.91110i		−	0.472433i
$215$	2.61822	+	8.36262i	0.178561	+	0.570326i
$216$		0			0
$217$	1.47174	−	6.16802i	0.0999082	−	0.418712i
$218$	−1.16702	+	1.16702i	−0.0790405	+	0.0790405i
$219$		0			0
$220$	−10.8090	−	5.65451i	−0.728742	−	0.381227i
$221$	10.9316			0.735342
$222$		0			0
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	0.197346	−	0.980334i	$-0.436768\pi$
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	−0.980334	+	0.197346i	$0.936768\pi$
$224$	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	−0.742832	−	0.669478i	$-0.766518\pi$
$227$	−1.10518	+	1.10518i	−0.0733535	+	0.0733535i	0.669478	+	0.742832i	$0.266518\pi$
$228$		0			0
$229$	7.83309			0.517625			0.258812	−	0.965928i	$-0.416669\pi$
$229$	7.83309			0.517625			0.258812	+	0.965928i	$0.416669\pi$
$230$	−0.598123	+	1.14335i	−0.0394390	+	0.0753906i
$231$		0			0
$232$	5.11372	+	5.11372i	0.335732	+	0.335732i
$233$	−1.00797	+	1.00797i	−0.0660345	+	0.0660345i	−0.739353	−	0.673318i	$-0.764868\pi$
$233$	−1.00797	+	1.00797i	−0.0660345	+	0.0660345i	0.673318	+	0.739353i	$0.264868\pi$
$234$		0			0
$235$	5.18757	+	16.5691i	0.338399	+	1.08085i
$236$		−	9.87918i		−	0.643080i
$237$		0			0
$238$	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	$0.0284354\pi$
$241$			2.76994i			0.178427i	−0.996013	+	0.0892136i	$0.971565\pi$
$242$	−2.07036	−	2.07036i	−0.133088	−	0.133088i
$243$		0			0
$244$	20.2710			1.29772
$245$	12.7359	−	9.09922i	0.813670	−	0.581328i
$246$		0			0
$247$	−0.255918	−	0.255918i	−0.0162837	−	0.0162837i
$248$	4.42292	+	4.42292i	0.280856	+	0.280856i
$249$		0			0
$250$	6.74403	+	5.23992i	0.426530	+	0.331401i
$251$			6.09982i			0.385017i	0.981295	+	0.192509i	$0.0616623\pi$
$251$			6.09982i			0.385017i	−0.981295	+	0.192509i	$0.938338\pi$
$252$		0			0
$253$	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	−0.641346	−	0.767252i	$-0.721624\pi$
$257$	2.01843	−	2.01843i	0.125906	−	0.125906i	0.767252	+	0.641346i	$0.221624\pi$
$258$		0			0
$259$	12.1242	+	19.7233i	0.753361	+	1.22554i
$260$	4.90931	+	15.6804i	0.304462	+	0.972456i
$261$		0			0
$262$	−0.349742	+	0.349742i	−0.0216071	+	0.0216071i
$263$	−16.7686	+	16.7686i	−1.03400	+	1.03400i	−0.0345941	+	0.999401i	$0.511014\pi$
$263$	−16.7686	+	16.7686i	−1.03400	+	1.03400i	−0.999401	+	0.0345941i	$0.988986\pi$
$264$		0			0
$265$	5.79964	+	18.5241i	0.356269	+	1.13793i
$266$	−0.0738405	−	0.120121i	−0.00452745	−	0.00736511i
$267$		0			0
$268$	0.589955	−	0.589955i	0.0360372	−	0.0360372i
$269$	−24.7351			−1.50813			−0.754064	−	0.656801i	$-0.771909\pi$
$269$	−24.7351			−1.50813			−0.754064	+	0.656801i	$0.771909\pi$
$270$		0			0
$271$			4.13470i			0.251165i	0.992083	+	0.125583i	$0.0400800\pi$
$271$			4.13470i			0.251165i	−0.992083	+	0.125583i	$0.959920\pi$
$272$	1.25081	−	1.25081i	0.0758413	−	0.0758413i
$273$		0			0
$274$			11.0588i			0.668085i
$275$	−10.9816	−	15.8186i	−0.662217	−	0.953898i
$276$		0			0
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	0.242393	−	0.970178i	$-0.422068\pi$
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	−0.970178	+	0.242393i	$0.922068\pi$
$278$	11.9730	+	11.9730i	0.718091	+	0.718091i
$279$		0			0
$280$	1.06742	+	15.4027i	0.0637904	+	0.920489i
$281$	−5.25279			−0.313355			−0.156678	−	0.987650i	$-0.550078\pi$
$281$	−5.25279			−0.313355			−0.156678	+	0.987650i	$0.550078\pi$
$282$		0			0
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	0.655813	−	0.754923i	$-0.272326\pi$
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	−0.754923	+	0.655813i	$0.772326\pi$
$284$		−	11.5130i		−	0.683170i
$285$		0			0
$286$			15.2617i			0.902441i
$287$	5.33051	−	22.3400i	0.314650	−	1.31869i
$288$		0			0
$289$			12.5594i			0.738787i
$290$	1.41421	+	4.51701i	0.0830455	+	0.265248i
$291$		0			0
$292$	13.5305	−	13.5305i	0.791810	−	0.791810i
$293$	15.2556	+	15.2556i	0.891240	+	0.891240i	0.994640	−	0.103400i	$-0.0329722\pi$
$293$	15.2556	+	15.2556i	0.891240	+	0.891240i	−0.103400	+	0.994640i	$0.532972\pi$
$294$		0			0
$295$	7.22893	−	13.8186i	0.420884	−	0.804551i
$296$	−22.8370			−1.32737
$297$		0			0
$298$	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
$303$		0			0
$304$	−0.0585646			−0.00335891
$305$	28.3543	+	14.8330i	1.62356	+	0.849334i
$306$		0			0
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	−0.988114	−	0.153721i	$-0.950874\pi$
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	0.153721	+	0.988114i	$0.450874\pi$
$308$	3.34995	−	14.0395i	0.190881	−	0.799977i
$309$		0			0
$310$	1.22317	+	3.90682i	0.0694714	+	0.221893i
$311$		−	2.86218i		−	0.162299i	−0.996702	−	0.0811497i	$-0.974141\pi$
$311$		−	2.86218i		−	0.162299i	0.996702	−	0.0811497i	$-0.0258592\pi$
$312$		0			0
$313$	−9.41824	−	9.41824i	−0.532350	−	0.532350i	0.388921	−	0.921271i	$-0.372848\pi$
$313$	−9.41824	−	9.41824i	−0.532350	−	0.532350i	−0.921271	+	0.388921i	$0.872848\pi$
$314$	1.13424			0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	−7.38310	−	7.38310i	−0.414676	−	0.414676i	0.468688	−	0.883364i	$-0.344727\pi$
$317$	−7.38310	−	7.38310i	−0.414676	−	0.414676i	−0.883364	+	0.468688i	$0.844727\pi$
$318$		0			0
$319$		−	10.6724i		−	0.597540i
$320$	−5.54390	−	2.90018i	−0.309914	−	0.162125i
$321$		0			0
$322$	−1.48508	−	0.354351i	−0.0827600	−	0.0197472i
$323$	−0.103958	+	0.103958i	−0.00578440	+	0.00578440i
$324$		0			0
$325$	−4.60691	+	25.5254i	−0.255545	+	1.41590i
$326$	−5.94740			−0.329396
$327$		0			0
$328$	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
$333$		0			0
$334$	2.04139			0.111700
$335$	1.25690	−	0.393517i	0.0686716	−	0.0215001i
$336$		0			0
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	0.559700	−	0.828695i	$-0.310916\pi$
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	−0.828695	+	0.559700i	$0.810916\pi$
$338$	7.51384	−	7.51384i	0.408699	−	0.408699i
$339$		0			0
$340$	6.36964	−	1.99425i	0.345442	−	0.108153i
$341$		−	9.23070i		−	0.499870i
$342$		0			0
$343$	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	0.532860	−	0.846203i	$-0.321117\pi$
$347$	−5.83694	−	5.83694i	−0.313343	−	0.313343i	−0.846203	+	0.532860i	$0.821117\pi$
$348$		0			0
$349$	−16.9121			−0.905282			−0.452641	−	0.891693i	$-0.649518\pi$
$349$	−16.9121			−0.905282			−0.452641	+	0.891693i	$0.649518\pi$
$350$	−4.05385	+	9.25637i	−0.216687	+	0.494774i
$351$		0			0
$352$	15.9608	+	15.9608i	0.850714	+	0.850714i
$353$	11.1265	+	11.1265i	0.592202	+	0.592202i	0.938226	−	0.346024i	$-0.112468\pi$
$353$	11.1265	+	11.1265i	0.592202	+	0.592202i	−0.346024	+	0.938226i	$0.612468\pi$
$354$		0			0
$355$	8.42444	−	16.1039i	0.447123	−	0.854708i
$356$		−	7.15771i		−	0.379358i
$357$		0			0
$358$	−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
$363$		0			0
$364$	−16.5623	+	10.1811i	−0.868102	+	0.533636i
$365$	28.8266	−	9.02520i	1.50885	−	0.472401i
$366$		0			0
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	−0.208238	−	0.978078i	$-0.566773\pi$
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	0.978078	+	0.208238i	$0.0667728\pi$
$368$	−0.448402	+	0.448402i	−0.0233746	+	0.0233746i
$369$		0			0
$370$	−13.2439	−	6.92828i	−0.688518	−	0.360184i
$371$	−19.5660	+	12.0275i	−1.01582	+	0.624438i
$372$		0			0
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	−0.667353	−	0.744741i	$-0.732573\pi$
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	0.744741	+	0.667353i	$0.232573\pi$
$374$	6.19955			0.320571
$375$		0			0
$376$		−	20.2640i		−	1.04504i
$377$	−10.1648	+	10.1648i	−0.523511	+	0.523511i
$378$		0			0
$379$		−	18.7135i		−	0.961248i	−0.876927	−	0.480624i	$-0.840410\pi$
$379$		−	18.7135i		−	0.961248i	0.876927	−	0.480624i	$-0.159590\pi$
$380$	−0.195805	−	0.102431i	−0.0100446	−	0.00525461i
$381$		0			0
$382$	−2.91327	−	2.91327i	−0.149056	−	0.149056i
$383$	−20.9354	−	20.9354i	−1.06975	−	1.06975i	−0.997378	−	0.0723706i	$-0.976944\pi$
$383$	−20.9354	−	20.9354i	−1.06975	−	1.06975i	−0.0723706	−	0.997378i	$-0.523056\pi$
$384$		0			0
$385$	14.9590	−	17.1867i	0.762381	−	0.875916i
$386$	5.19184			0.264258
$387$		0			0
$388$	−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			0
$394$			13.6915i			0.689767i
$395$	−19.5425	−	10.2232i	−0.983288	−	0.514387i
$396$		0			0
$397$	6.73585	−	6.73585i	0.338063	−	0.338063i	−0.517575	−	0.855638i	$-0.673165\pi$
$397$	6.73585	−	6.73585i	0.338063	−	0.338063i	0.855638	+	0.517575i	$0.173165\pi$
$398$	1.44278	+	1.44278i	0.0723201	+	0.0723201i
$399$		0			0
$400$	2.39351	+	3.44776i	0.119676	+	0.172388i
$401$	−14.7503			−0.736593			−0.368296	−	0.929708i	$-0.620059\pi$
$401$	−14.7503			−0.736593			−0.368296	+	0.929708i	$0.620059\pi$
$402$		0			0
$403$	−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
$408$		0			0
$409$	10.5604			0.522180			0.261090	−	0.965315i	$-0.415918\pi$
$409$	10.5604			0.522180			0.261090	+	0.965315i	$0.415918\pi$
$410$	4.43022	+	14.1502i	0.218793	+	0.698827i
$411$		0			0
$412$	3.31210	−	3.31210i	0.163176	−	0.163176i
$413$	17.9487	+	4.28270i	0.883196	+	0.210738i
$414$		0			0
$415$	−4.93625	+	1.54547i	−0.242311	+	0.0758641i
$416$		−	30.4032i		−	1.49064i
$417$		0			0
$418$	−0.145136	−	0.145136i	−0.00709884	−	0.00709884i
$419$	−15.5472			−0.759532			−0.379766	−	0.925083i	$-0.623996\pi$
$419$	−15.5472			−0.759532			−0.379766	+	0.925083i	$0.623996\pi$
$420$		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
$423$		0			0
$424$		−	22.6549i		−	1.10022i
$425$	10.3689	+	1.87141i	0.502964	+	0.0907766i
$426$		0			0
$427$	−8.78764	+	36.8287i	−0.425264	+	1.78227i
$428$	9.06196	−	9.06196i	0.438026	−	0.438026i
$429$		0			0
$430$	3.10280	−	5.93123i	0.149630	−	0.286029i
$431$	14.0911			0.678743			0.339371	−	0.940652i	$-0.389786\pi$
$431$	14.0911			0.678743			0.339371	+	0.940652i	$0.389786\pi$
$432$		0			0
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	0.664404	−	0.747374i	$-0.268686\pi$
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	−0.747374	+	0.664404i	$0.768686\pi$
$434$	−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
$438$		0			0
$439$	−27.1172			−1.29423			−0.647116	−	0.762392i	$-0.724025\pi$
$439$	−27.1172			−1.29423			−0.647116	+	0.762392i	$0.724025\pi$
$440$	6.71524	+	21.4485i	0.320136	+	1.02252i
$441$		0			0
$442$	−5.90465	−	5.90465i	−0.280856	−	0.280856i
$443$	24.1502	−	24.1502i	1.14741	−	1.14741i	0.160349	−	0.987060i	$-0.448738\pi$
$443$	24.1502	−	24.1502i	1.14741	−	1.14741i	0.987060	−	0.160349i	$-0.0512618\pi$
$444$		0			0
$445$	5.23754	−	10.0119i	0.248283	−	0.474611i
$446$			12.6313i			0.598107i
$447$		0			0
$448$	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
$453$		0			0
$454$	1.19391			0.0560331
$455$	−30.6166	+	2.12175i	−1.43533	+	0.0994691i
$456$		0			0
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	0.719855	−	0.694124i	$-0.244208\pi$
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	−0.694124	+	0.719855i	$0.744208\pi$
$458$	−4.23099	−	4.23099i	−0.197701	−	0.197701i
$459$		0			0
$460$	−2.28346	+	0.714918i	−0.106467	+	0.0333332i
$461$		−	0.831786i		−	0.0387401i	−0.999812	−	0.0193701i	$-0.993834\pi$
$461$		−	0.831786i		−	0.0387401i	0.999812	−	0.0193701i	$-0.00616607\pi$
$462$		0			0
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	−0.568994	−	0.822342i	$-0.692667\pi$
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	0.822342	+	0.568994i	$0.192667\pi$
$464$			2.32612i			0.107987i
$465$		0			0
$466$	1.08890			0.0504423
$467$	23.2827	−	23.2827i	1.07740	−	1.07740i	0.0806551	−	0.996742i	$-0.474299\pi$
$467$	23.2827	−	23.2827i	1.07740	−	1.07740i	0.996742	−	0.0806551i	$-0.0257012\pi$
$468$		0			0
$469$	0.816091	+	1.32759i	0.0376836	+	0.0613025i
$470$	6.14768	−	11.7517i	0.283571	−	0.542067i
$471$		0			0
$472$	−12.8705	+	12.8705i	−0.592414	+	0.592414i
$473$	−10.6724	+	10.6724i	−0.490718	+	0.490718i
$474$		0			0
$475$	−0.198932	−	0.286554i	−0.00912762	−	0.0131480i
$476$	4.13575	+	6.72791i	0.189562	+	0.308373i
$477$		0			0
$478$	10.9544	−	10.9544i	0.501041	−	0.501041i
$479$	40.4319			1.84738			0.923691	−	0.383138i	$-0.125157\pi$
$479$	40.4319			1.84738			0.923691	+	0.383138i	$0.125157\pi$
$480$		0			0
$481$		−	45.3940i		−	2.06979i
$482$	1.49616	−	1.49616i	0.0681483	−	0.0681483i
$483$		0			0
$484$		−	5.42938i		−	0.246790i
$485$	−6.48019	−	20.6978i	−0.294250	−	0.939839i
$486$		0			0
$487$	−7.22893	−	7.22893i	−0.327574	−	0.327574i	0.524089	−	0.851663i	$-0.324406\pi$
$487$	−7.22893	−	7.22893i	−0.327574	−	0.327574i	−0.851663	+	0.524089i	$0.824406\pi$
$488$	−26.4089	−	26.4089i	−1.19548	−	1.19548i
$489$		0			0
$490$	−11.7941	−	1.96435i	−0.532804	−	0.0887404i
$491$	−20.1040			−0.907279			−0.453639	−	0.891185i	$-0.649875\pi$
$491$	−20.1040			−0.907279			−0.453639	+	0.891185i	$0.649875\pi$
$492$		0			0
$493$	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
$498$		0			0
$499$		−	15.4227i		−	0.690414i	−0.938527	−	0.345207i	$-0.887809\pi$
$499$		−	15.4227i		−	0.690414i	0.938527	−	0.345207i	$-0.112191\pi$
$500$	1.97222	+	15.7136i	0.0882002	+	0.702732i
$501$		0			0
$502$	3.29478	−	3.29478i	0.147053	−	0.147053i
$503$	−25.9985	−	25.9985i	−1.15922	−	1.15922i	−0.984644	−	0.174573i	$-0.944145\pi$
$503$	−25.9985	−	25.9985i	−1.15922	−	1.15922i	−0.174573	−	0.984644i	$-0.555855\pi$
$504$		0			0
$505$	38.0322	+	19.8958i	1.69241	+	0.885350i
$506$	−2.22248			−0.0988013
$507$		0			0
$508$	−6.84587	+	6.84587i	−0.303737	+	0.303737i
$509$	−37.1271			−1.64563			−0.822816	−	0.568309i	$-0.807598\pi$
$509$	−37.1271			−1.64563			−0.822816	+	0.568309i	$0.807598\pi$
$510$		0			0
$511$	18.7168	+	30.4479i	0.827983	+	1.34694i
$512$	−6.57690	−	6.57690i	−0.290661	−	0.290661i
$513$		0			0
$514$	−2.18048			−0.0961768
$515$	7.05642	−	2.20927i	0.310943	−	0.0973519i
$516$		0			0
$517$	−21.1456	+	21.1456i	−0.929982	+	0.929982i
$518$	4.10459	−	17.2022i	0.180345	−	0.755821i
$519$		0			0
$520$	14.0325	−	26.8241i	0.615365	−	1.17631i
$521$			2.59132i			0.113528i	0.998388	+	0.0567639i	$0.0180782\pi$
$521$			2.59132i			0.113528i	−0.998388	+	0.0567639i	$0.981922\pi$
$522$		0			0
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	0.561347	−	0.827581i	$-0.310283\pi$
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	−0.827581	+	0.561347i	$0.810283\pi$
$524$	−0.917176			−0.0400670
$525$		0			0
$526$	18.1149			0.789846
$527$	3.57131	+	3.57131i	0.155569	+	0.155569i
$528$		0			0
$529$			22.4293i			0.975187i
$530$	6.87304	−	13.1383i	0.298546	−	0.570692i
$531$		0			0
$532$	0.0606843	−	0.254326i	0.00263100	−	0.0110264i
$533$	−31.8425	+	31.8425i	−1.37925	+	1.37925i
$534$		0			0
$535$	19.3065	−	6.04458i	0.834691	−	0.261330i
$536$	−1.53718			−0.0663960
$537$		0			0
$538$	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
$543$		0			0
$544$	−12.3503			−0.529515
$545$	−4.28081	−	2.23942i	−0.183370	−	0.0959262i
$546$		0			0
$547$	−0.828381	−	0.828381i	−0.0354190	−	0.0354190i	0.689175	−	0.724594i	$-0.257973\pi$
$547$	−0.828381	−	0.828381i	−0.0354190	−	0.0354190i	−0.724594	+	0.689175i	$0.757973\pi$
$548$	−14.5005	+	14.5005i	−0.619429	+	0.619429i
$549$		0			0
$550$	−2.61267	+	14.4760i	−0.111405	+	0.617257i
$551$		−	0.193331i		−	0.00823616i
$552$		0			0
$553$	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	0.323024	−	0.946391i	$-0.395300\pi$
$557$	−14.7120	−	14.7120i	−0.623366	−	0.623366i	−0.946391	+	0.323024i	$0.895300\pi$
$558$		0			0
$559$	20.3295			0.859846
$560$	−3.26040	+	3.74595i	−0.137777	+	0.158295i
$561$		0			0
$562$	2.83726	+	2.83726i	0.119683	+	0.119683i
$563$	23.9693	+	23.9693i	1.01019	+	1.01019i	0.999948	+	0.0102391i	$0.00325926\pi$
$563$	23.9693	+	23.9693i	1.01019	+	1.01019i	0.0102391	+	0.999948i	$0.496741\pi$
$564$		0			0
$565$	−3.90996	−	12.4885i	−0.164493	−	0.525394i
$566$			1.80115i			0.0757080i
$567$		0			0
$568$	−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
$573$		0			0
$574$	−14.9460	+	9.18757i	−0.623836	+	0.383482i
$575$	−3.71714	−	0.670882i	−0.155015	−	0.0279777i
$576$		0			0
$577$	15.5587	−	15.5587i	0.647717	−	0.647717i	−0.304724	−	0.952441i	$-0.598564\pi$
$577$	15.5587	−	15.5587i	0.647717	−	0.647717i	0.952441	+	0.304724i	$0.0985641\pi$
$578$	6.78386	−	6.78386i	0.282171	−	0.282171i
$579$		0			0
$580$	−4.06845	+	7.77713i	−0.168933	+	0.322928i
$581$	−3.20506	−	5.21389i	−0.132968	−	0.216309i
$582$		0			0
$583$	−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	−0.304155	−	0.952623i	$-0.598374\pi$
$587$	15.7111	−	15.7111i	0.648468	−	0.648468i	0.952623	+	0.304155i	$0.0983740\pi$
$588$		0			0
$589$		−	0.167214i		−	0.00688993i
$590$	−11.3687	+	3.55938i	−0.468041	+	0.146537i
$591$		0			0
$592$	−5.19401	−	5.19401i	−0.213473	−	0.213473i
$593$	1.85199	+	1.85199i	0.0760523	+	0.0760523i	0.744110	−	0.668057i	$-0.232874\pi$
$593$	1.85199	+	1.85199i	0.0760523	+	0.0760523i	−0.668057	+	0.744110i	$0.732874\pi$
$594$		0			0
$595$	0.861891	+	12.4370i	0.0353341	+	0.509867i
$596$	15.6487			0.640997
$597$		0			0
$598$	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	$-0.927428\pi$
$601$		−	11.0819i		−	0.452041i	0.974123	−	0.226021i	$-0.0725717\pi$
$602$	7.70393	+	1.83822i	0.313989	+	0.0749203i
$603$		0			0
$604$		−	26.0620i		−	1.06045i
$605$	3.97286	−	7.59441i	0.161520	−	0.308757i
$606$		0			0
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	−0.537170	−	0.843474i	$-0.680507\pi$
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$608$	0.289130	+	0.289130i	0.0117258	+	0.0117258i
$609$		0			0
$610$	−7.30346	−	23.3273i	−0.295708	−	0.944496i
$611$	40.2795			1.62953
$612$		0			0
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	−0.758126	−	0.652108i	$-0.773885\pi$
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	0.652108	+	0.758126i	$0.273885\pi$
$614$	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	0.441491	−	0.897266i	$-0.354450\pi$
$617$	−11.3212	−	11.3212i	−0.455774	−	0.455774i	−0.897266	+	0.441491i	$0.854450\pi$
$618$		0			0
$619$	−9.06771			−0.364462			−0.182231	−	0.983256i	$-0.558332\pi$
$619$	−9.06771			−0.364462			−0.182231	+	0.983256i	$0.558332\pi$
$620$	−3.51885	+	6.72654i	−0.141320	+	0.270144i
$621$		0			0
$622$	−1.54599	+	1.54599i	−0.0619884	+	0.0619884i
$623$	13.0043	+	3.10292i	0.521005	+	0.124316i
$624$		0			0
$625$	−8.73948	+	23.4227i	−0.349579	+	0.936907i
$626$			10.1744i			0.406651i
$627$		0			0
$628$	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
$633$		0			0
$634$			7.97587i			0.316762i
$635$	−14.5851	+	4.56639i	−0.578792	+	0.181212i
$636$		0			0
$637$	−11.3173	−	34.5043i	−0.448409	−	1.36711i
$638$	−5.76463	+	5.76463i	−0.228224	+	0.228224i
$639$		0			0
$640$	−6.40321	−	20.4519i	−0.253109	−	0.808434i
$641$	40.5847			1.60300			0.801500	−	0.597995i	$-0.204036\pi$
$641$	40.5847			1.60300			0.801500	+	0.597995i	$0.204036\pi$
$642$		0			0
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	0.779733	−	0.626112i	$-0.215355\pi$
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	−0.626112	+	0.779733i	$0.715355\pi$
$644$	−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	−0.955876	−	0.293772i	$-0.905089\pi$
$647$	−16.8414	+	16.8414i	−0.662104	+	0.662104i	0.293772	+	0.955876i	$0.405089\pi$
$648$		0			0
$649$	26.8609			1.05438
$650$	16.2758	−	11.2990i	0.638388	−	0.443183i
$651$		0			0
$652$	−7.79833	−	7.79833i	−0.305406	−	0.305406i
$653$	22.9951	−	22.9951i	0.899867	−	0.899867i	−0.0955569	−	0.995424i	$-0.530463\pi$
$653$	22.9951	−	22.9951i	0.899867	−	0.899867i	0.995424	+	0.0955569i	$0.0304632\pi$
$654$		0			0
$655$	−1.28291	−	0.671128i	−0.0501275	−	0.0262232i
$656$			7.28688i			0.284505i
$657$		0			0
$658$	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	$0.217926\pi$
$661$			32.5174i			1.26478i	−0.774650	+	0.632391i	$0.782074\pi$
$662$	−12.7582	−	12.7582i	−0.495861	−	0.495861i
$663$		0			0
$664$	6.03701			0.234281
$665$	0.270982	−	0.311337i	0.0105082	−	0.0120731i
$666$		0			0
$667$	−1.48024	−	1.48024i	−0.0573152	−	0.0573152i
$668$	2.67671	+	2.67671i	0.103565	+	0.103565i
$669$		0			0
$670$	−0.891460	−	0.466349i	−0.0344401	−	0.0180166i
$671$			55.1158i			2.12772i
$672$		0			0
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	−0.951974	−	0.306179i	$-0.900950\pi$
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	0.306179	+	0.951974i	$0.400950\pi$
$674$			5.33455i			0.205479i
$675$		0			0
$676$	19.7046			0.757868
$677$	6.85568	−	6.85568i	0.263485	−	0.263485i	−0.562983	−	0.826468i	$-0.690346\pi$
$677$	6.85568	−	6.85568i	0.263485	−	0.263485i	0.826468	+	0.562983i	$0.190346\pi$
$678$		0			0
$679$	21.8620	−	13.4389i	0.838985	−	0.515737i
$680$	−10.8964	−	5.70024i	−0.417858	−	0.218594i
$681$		0			0
$682$	−4.98590	+	4.98590i	−0.190920	+	0.190920i
$683$	−23.2345	+	23.2345i	−0.889042	+	0.889042i	−0.994431	−	0.105389i	$-0.966391\pi$
$683$	−23.2345	+	23.2345i	−0.889042	+	0.889042i	0.105389	+	0.994431i	$0.466391\pi$
$684$		0			0
$685$	−30.8932	+	9.67222i	−1.18037	+	0.369557i
$686$	−1.16881	−	14.0988i	−0.0446255	−	0.538297i
$687$		0			0
$688$	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	$0.299366\pi$
$691$			42.4714i			1.61569i	−0.589395	+	0.807845i	$0.700634\pi$
$692$	6.95144	−	6.95144i	0.264254	−	0.264254i
$693$		0			0
$694$			6.30557i			0.239356i
$695$	−22.9752	+	43.9188i	−0.871500	+	1.66594i
$696$		0			0
$697$	12.9350	+	12.9350i	0.489947	+	0.489947i
$698$	9.13494	+	9.13494i	0.345763	+	0.345763i
$699$		0			0
$700$	−17.4526	+	6.82165i	−0.659646	+	0.257834i
$701$	−17.0793			−0.645077			−0.322539	−	0.946556i	$-0.604536\pi$
$701$	−17.0793			−0.645077			−0.322539	+	0.946556i	$0.604536\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$			32.6742i			1.22710i	0.789654	+	0.613552i	$0.210260\pi$
$709$			32.6742i			1.22710i	−0.789654	+	0.613552i	$0.789740\pi$
$710$	−13.2488	+	4.14802i	−0.497220	+	0.155673i
$711$		0			0
$712$	−9.32502	+	9.32502i	−0.349470	+	0.349470i
$713$	−1.28028	−	1.28028i	−0.0479469	−	0.0479469i
$714$		0			0
$715$	−42.6341	+	13.3481i	−1.59443	+	0.499192i
$716$	−26.3264			−0.983865
$717$		0			0
$718$	4.40143	−	4.40143i	0.164260	−	0.164260i
$719$	19.3248			0.720693			0.360346	−	0.932819i	$-0.382659\pi$
$719$	19.3248			0.720693			0.360346	+	0.932819i	$0.382659\pi$
$720$		0			0
$721$	4.58166	+	7.45331i	0.170630	+	0.277576i
$722$	10.2601	+	10.2601i	0.381841	+	0.381841i
$723$		0			0
$724$	12.0193			0.446695
$725$	−11.3816	+	7.90133i	−0.422701	+	0.293448i
$726$		0			0
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	−0.654907	−	0.755710i	$-0.727292\pi$
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	0.755710	+	0.654907i	$0.227292\pi$
$728$	34.8412	+	8.31339i	1.29130	+	0.308115i
$729$		0			0
$730$	−20.4454	−	10.6956i	−0.756718	−	0.395861i
$731$		−	8.25820i		−	0.305440i
$732$		0			0
$733$	−2.38437	−	2.38437i	−0.0880686	−	0.0880686i	0.661700	−	0.749769i	$-0.269835\pi$
$733$	−2.38437	−	2.38437i	−0.0880686	−	0.0880686i	−0.749769	+	0.661700i	$0.769835\pi$
$734$	−15.9321			−0.588064
$735$		0			0
$736$	4.42747			0.163199
$737$	1.60406	+	1.60406i	0.0590862	+	0.0590862i
$738$		0			0
$739$			4.95679i			0.182339i	0.995835	+	0.0911693i	$0.0290605\pi$
$739$			4.95679i			0.182339i	−0.995835	+	0.0911693i	$0.970940\pi$
$740$	−8.28116	−	26.4501i	−0.304422	−	0.972326i
$741$		0			0
$742$	17.0650	+	4.07186i	0.626477	+	0.149483i
$743$	−15.6556	+	15.6556i	−0.574347	+	0.574347i	−0.933340	−	0.358993i	$-0.883120\pi$
$743$	−15.6556	+	15.6556i	−0.574347	+	0.574347i	0.358993	+	0.933340i	$0.383120\pi$
$744$		0			0
$745$	21.8889	+	11.4507i	0.801946	+	0.419521i
$746$	−1.61461			−0.0591150
$747$		0			0
$748$	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
$753$		0			0
$754$	10.9808			0.399899
$755$	19.0704	−	36.4545i	0.694045	−	1.32672i
$756$		0			0
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.997189	+	0.0749214i	$0.0238706\pi$
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.0749214	+	0.997189i	$0.476129\pi$
$758$	−10.1080	+	10.1080i	−0.367138	+	0.367138i
$759$		0			0
$760$	0.121646	+	0.388540i	0.00441258	+	0.0140938i
$761$		−	28.1175i		−	1.01926i	−0.860395	−	0.509629i	$-0.829783\pi$
$761$		−	28.1175i		−	1.01926i	0.860395	−	0.509629i	$-0.170217\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$	6.61248			0.238452			0.119226	−	0.992867i	$-0.461959\pi$
$769$	6.61248			0.238452			0.119226	+	0.992867i	$0.461959\pi$
$770$	−17.3633	+	1.20328i	−0.625729	+	0.0433634i
$771$		0			0
$772$	6.80764	+	6.80764i	0.245012	+	0.245012i
$773$	−31.7247	−	31.7247i	−1.14106	−	1.14106i	−0.988257	−	0.152800i	$-0.951171\pi$
$773$	−31.7247	−	31.7247i	−1.14106	−	1.14106i	−0.152800	−	0.988257i	$-0.548829\pi$
$774$		0			0
$775$	−9.84407	+	6.83396i	−0.353609	+	0.245483i
$776$			25.3133i			0.908695i
$777$		0			0
$778$	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
$783$		0			0
$784$	−5.24295	−	2.65307i	−0.187248	−	0.0947525i
$785$	0.992027	+	3.16855i	0.0354070	+	0.113090i
$786$		0			0
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	−0.182964	−	0.983120i	$-0.558569\pi$
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	0.983120	+	0.182964i	$0.0585693\pi$
$788$	−17.9525	+	17.9525i	−0.639532	+	0.639532i
$789$		0			0
$790$	5.03372	+	16.0777i	0.179092	+	0.572021i
$791$	13.1909	−	8.10864i	0.469014	−	0.288310i
$792$		0			0
$793$	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	−0.792361	−	0.610053i	$-0.791148\pi$
$797$	−5.14677	+	5.14677i	−0.182308	+	0.182308i	0.610053	+	0.792361i	$0.291148\pi$
$798$		0			0
$799$		−	16.3622i		−	0.578854i
$800$	5.20477	−	28.8380i	0.184017	−	1.01958i
$801$		0			0
$802$	7.96725	+	7.96725i	0.281333	+	0.281333i
$803$	36.7886	+	36.7886i	1.29824	+	1.29824i
$804$		0			0
$805$	−0.308980	−	4.45855i	−0.0108901	−	0.157143i
$806$	9.49747			0.334534
$807$		0			0
$808$	−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	$-0.789960\pi$
$811$		−	34.9145i		−	1.22602i	0.790077	−	0.613008i	$-0.210040\pi$
$812$	−10.1015	−	2.41031i	−0.354494	−	0.0845852i
$813$		0			0
$814$		−	25.7438i		−	0.902320i
$815$	−5.20171	−	16.6143i	−0.182208	−	0.581974i
$816$		0			0
$817$	−0.193331	+	0.193331i	−0.00676378	+	0.00676378i
$818$	−5.70414	−	5.70414i	−0.199441	−	0.199441i
$819$		0			0
$820$	−12.7450	+	24.3629i	−0.445074	+	0.850790i
$821$	−8.52640			−0.297573			−0.148787	−	0.988869i	$-0.547537\pi$
$821$	−8.52640			−0.297573			−0.148787	+	0.988869i	$0.547537\pi$
$822$		0			0
$823$	−33.9044	+	33.9044i	−1.18183	+	1.18183i	−0.202564	+	0.979269i	$0.564927\pi$
$823$	−33.9044	+	33.9044i	−1.18183	+	1.18183i	−0.979269	+	0.202564i	$0.935073\pi$
$824$	−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	0.916940	+	0.399025i	$0.130651\pi$
$827$	37.8440	+	37.8440i	1.31597	+	1.31597i	0.399025	+	0.916940i	$0.369349\pi$
$828$		0			0
$829$	−33.7140			−1.17094			−0.585469	−	0.810695i	$-0.699089\pi$
$829$	−33.7140			−1.17094			−0.585469	+	0.810695i	$0.699089\pi$
$830$	3.50106	+	1.83151i	0.121523	+	0.0635725i
$831$		0			0
$832$	−10.2638	+	10.2638i	−0.355832	+	0.355832i
$833$	−14.0163	+	4.59730i	−0.485635	+	0.159287i
$834$		0			0
$835$	1.78544	+	5.70272i	0.0617878	+	0.197351i
$836$		−	0.380610i		−	0.0131637i
$837$		0			0
$838$	8.39773	+	8.39773i	0.290095	+	0.290095i
$839$	16.0665			0.554679			0.277339	−	0.960772i	$-0.410547\pi$
$839$	16.0665			0.554679			0.277339	+	0.960772i	$0.410547\pi$
$840$		0			0
$841$	21.3211			0.735212
$842$	−1.78185	−	1.78185i	−0.0614068	−	0.0614068i
$843$		0			0
$844$			17.0317i			0.586255i
$845$	27.5620	+	14.4185i	0.948161	+	0.496011i
$846$		0			0
$847$	9.86420	+	2.35368i	0.338938	+	0.0808734i
$848$	5.15260	−	5.15260i	0.176941	−	0.176941i
$849$		0			0
$850$	−4.58985	−	6.61150i	−0.157430	−	0.226773i
$851$	6.61050			0.226605
$852$		0			0
$853$	5.14393	+	5.14393i	0.176125	+	0.176125i	0.789664	−	0.613539i	$-0.210255\pi$
$853$	5.14393	+	5.14393i	0.176125	+	0.176125i	−0.613539	+	0.789664i	$0.710255\pi$
$854$	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	−0.603976	−	0.797002i	$-0.706418\pi$
$857$	5.65076	−	5.65076i	0.193026	−	0.193026i	0.797002	+	0.603976i	$0.206418\pi$
$858$		0			0
$859$	42.0801			1.43575			0.717877	−	0.696170i	$-0.245114\pi$
$859$	42.0801			1.43575			0.717877	+	0.696170i	$0.245114\pi$
$860$	11.8456	−	3.70868i	0.403931	−	0.126465i
$861$		0			0
$862$	−7.61119	−	7.61119i	−0.259238	−	0.259238i
$863$	11.9777	−	11.9777i	0.407724	−	0.407724i	−0.473220	−	0.880944i	$-0.656908\pi$
$863$	11.9777	−	11.9777i	0.407724	−	0.407724i	0.880944	+	0.473220i	$0.156908\pi$
$864$		0			0
$865$	14.8100	−	4.63680i	0.503555	−	0.157656i
$866$			1.86511i			0.0633791i
$867$		0			0
$868$	−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
$873$		0			0
$874$	−0.0402602			−0.00136182
$875$	−29.4037	−	3.22879i	−0.994025	−	0.109153i
$876$		0			0
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	0.483989	−	0.875074i	$-0.339187\pi$
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	−0.875074	+	0.483989i	$0.839187\pi$
$878$	14.6471	+	14.6471i	0.494317	+	0.494317i
$879$		0			0
$880$	−3.35092	+	6.40553i	−0.112959	+	0.215930i
$881$		−	8.72058i		−	0.293804i	−0.989151	−	0.146902i	$-0.953070\pi$
$881$		−	8.72058i		−	0.293804i	0.989151	−	0.146902i	$-0.0469301\pi$
$882$		0			0
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	−0.358490	−	0.933534i	$-0.616708\pi$
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	0.933534	+	0.358490i	$0.116708\pi$
$884$		−	15.4846i		−	0.520803i
$885$		0			0
$886$	−26.0891			−0.876480
$887$	−26.4024	+	26.4024i	−0.886507	+	0.886507i	−0.994186	−	0.107679i	$-0.965658\pi$
$887$	−26.4024	+	26.4024i	−0.886507	+	0.886507i	0.107679	+	0.994186i	$0.465658\pi$
$888$		0			0
$889$	−9.46996	−	15.4054i	−0.317612	−	0.516682i
$890$	−8.23690	+	2.57886i	−0.276101	+	0.0864435i
$891$		0			0
$892$	−16.5623	+	16.5623i	−0.554548	+	0.554548i
$893$	−0.383052	+	0.383052i	−0.0128184	+	0.0128184i
$894$		0			0
$895$	−36.8244	−	19.2639i	−1.23090	−	0.643922i
$896$	21.6023	−	13.2792i	0.721681	−	0.443628i
$897$		0			0
$898$	−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
$903$		0			0
$904$			15.2733i			0.507984i
$905$	16.8122	+	8.79494i	0.558855	+	0.292354i
$906$		0			0
$907$	−23.6454	−	23.6454i	−0.785133	−	0.785133i	0.195559	−	0.980692i	$-0.437348\pi$
$907$	−23.6454	−	23.6454i	−0.785133	−	0.785133i	−0.980692	+	0.195559i	$0.937348\pi$
$908$	1.56548	+	1.56548i	0.0519523	+	0.0519523i
$909$		0			0
$910$	17.6834	+	15.3913i	0.586199	+	0.510217i
$911$	17.8226			0.590490			0.295245	−	0.955422i	$-0.404599\pi$
$911$	17.8226			0.590490			0.295245	+	0.955422i	$0.404599\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$			21.5752i			0.711701i	0.934543	+	0.355850i	$0.115809\pi$
$919$			21.5752i			0.711701i	−0.934543	+	0.355850i	$0.884191\pi$
$920$	3.90626	+	2.04348i	0.128786	+	0.0673716i
$921$		0			0
$922$	−0.449284	+	0.449284i	−0.0147964	+	0.0147964i
$923$	−29.8142	−	29.8142i	−0.981346	−	0.981346i
$924$		0			0
$925$	7.77107	−	43.0570i	0.255511	−	1.41571i
$926$	−5.88908			−0.193527
$927$		0			0
$928$	11.4839	−	11.4839i	0.376977	−	0.376977i
$929$	−38.3070			−1.25681			−0.628405	−	0.777886i	$-0.716292\pi$
$929$	−38.3070			−1.25681			−0.628405	+	0.777886i	$0.716292\pi$
$930$		0			0
$931$	0.435757	+	0.220505i	0.0142814	+	0.00722675i
$932$	1.42778	+	1.42778i	0.0467686	+	0.0467686i
$933$		0			0
$934$	−25.1520			−0.823000
$935$	5.42225	+	17.3187i	0.177326	+	0.566382i
$936$		0			0
$937$	13.2317	−	13.2317i	0.432262	−	0.432262i	−0.457135	−	0.889397i	$-0.651125\pi$
$937$	13.2317	−	13.2317i	0.432262	−	0.432262i	0.889397	+	0.457135i	$0.151125\pi$
$938$	0.276283	−	1.15790i	0.00902097	−	0.0378066i
$939$		0			0
$940$	23.4700	−	7.34814i	0.765508	−	0.239670i
$941$			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			0
$943$	−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	0.622235	−	0.782830i	$-0.286225\pi$
$947$	−4.94205	−	4.94205i	−0.160595	−	0.160595i	−0.782830	+	0.622235i	$0.786225\pi$
$948$		0			0
$949$		−	70.0773i		−	2.27481i
$950$	−0.0473285	+	0.262232i	−0.00153554	+	0.00850793i
$951$		0			0
$952$	3.37705	−	14.1531i	0.109451	−	0.458704i
$953$	16.3558	−	16.3558i	0.529818	−	0.529818i	−0.390700	−	0.920518i	$-0.627767\pi$
$953$	16.3558	−	16.3558i	0.529818	−	0.529818i	0.920518	+	0.390700i	$0.127767\pi$
$954$		0			0
$955$	5.59034	−	10.6863i	0.180899	−	0.345802i
$956$	28.7271			0.929101
$957$		0			0
$958$	−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
$963$		0			0
$964$	3.92359			0.126370
$965$	4.54089	+	14.5036i	0.146176	+	0.466889i
$966$		0			0
$967$	8.66781	+	8.66781i	0.278738	+	0.278738i	0.832605	−	0.553867i	$-0.186848\pi$
$967$	8.66781	+	8.66781i	0.278738	+	0.278738i	−0.553867	+	0.832605i	$0.686848\pi$
$968$	−7.07336	+	7.07336i	−0.227346	+	0.227346i
$969$		0			0
$970$	−7.67955	+	14.6800i	−0.246575	+	0.471347i
$971$			13.1861i			0.423163i	0.977360	+	0.211582i	$0.0678614\pi$
$971$			13.1861i			0.423163i	−0.977360	+	0.211582i	$0.932139\pi$
$972$		0			0
$973$	−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	0.980434	−	0.196848i	$-0.0630705\pi$
$977$	24.4925	+	24.4925i	0.783586	+	0.783586i	−0.196848	+	0.980434i	$0.563071\pi$
$978$		0			0
$979$	19.4614			0.621990
$980$	−12.8890	−	18.0403i	−0.411723	−	0.576278i
$981$		0			0
$982$	10.8590	+	10.8590i	0.346525	+	0.346525i
$983$	−15.7362	−	15.7362i	−0.501907	−	0.501907i	0.410123	−	0.912030i	$-0.365486\pi$
$983$	−15.7362	−	15.7362i	−0.501907	−	0.501907i	−0.912030	+	0.410123i	$0.865486\pi$
$984$		0			0
$985$	−38.2477	+	11.9748i	−1.21867	+	0.381550i
$986$		−	4.46061i		−	0.142055i
$987$		0			0
$988$	−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
$993$		0			0
$994$	−8.60234	−	13.9940i	−0.272850	−	0.443863i
$995$	−2.76859	+	5.29236i	−0.0877702	+	0.167779i
$996$		0			0
$997$	−22.8721	+	22.8721i	−0.724367	+	0.724367i	−0.969491	−	0.245125i	$-0.921171\pi$
$997$	−22.8721	+	22.8721i	−0.724367	+	0.724367i	0.245125	+	0.969491i	$0.421171\pi$
$998$	−8.33045	+	8.33045i	−0.263696	+	0.263696i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.e.307.4		16
3.2	odd	2		105.2.m.a.97.6	yes	16
5.3	odd	4	inner	315.2.p.e.118.3		16
7.6	odd	2	inner	315.2.p.e.307.3		16
12.11	even	2		1680.2.cz.d.97.2		16
15.2	even	4		525.2.m.b.118.4		16
15.8	even	4		105.2.m.a.13.5	✓	16
15.14	odd	2		525.2.m.b.307.3		16
21.2	odd	6		735.2.v.a.472.5		32
21.5	even	6		735.2.v.a.472.6		32
21.11	odd	6		735.2.v.a.607.4		32
21.17	even	6		735.2.v.a.607.3		32
21.20	even	2		105.2.m.a.97.5	yes	16
35.13	even	4	inner	315.2.p.e.118.4		16
60.23	odd	4		1680.2.cz.d.433.7		16
84.83	odd	2		1680.2.cz.d.97.7		16
105.23	even	12		735.2.v.a.178.3		32
105.38	odd	12		735.2.v.a.313.5		32
105.53	even	12		735.2.v.a.313.6		32
105.62	odd	4		525.2.m.b.118.3		16
105.68	odd	12		735.2.v.a.178.4		32
105.83	odd	4		105.2.m.a.13.6	yes	16
105.104	even	2		525.2.m.b.307.4		16
420.83	even	4		1680.2.cz.d.433.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	15.8	even	4
105.2.m.a.13.6	yes	16	105.83	odd	4
105.2.m.a.97.5	yes	16	21.20	even	2
105.2.m.a.97.6	yes	16	3.2	odd	2
315.2.p.e.118.3		16	5.3	odd	4	inner
315.2.p.e.118.4		16	35.13	even	4	inner
315.2.p.e.307.3		16	7.6	odd	2	inner
315.2.p.e.307.4		16	1.1	even	1	trivial
525.2.m.b.118.3		16	105.62	odd	4
525.2.m.b.118.4		16	15.2	even	4
525.2.m.b.307.3		16	15.14	odd	2
525.2.m.b.307.4		16	105.104	even	2
735.2.v.a.178.3		32	105.23	even	12
735.2.v.a.178.4		32	105.68	odd	12
735.2.v.a.313.5		32	105.38	odd	12
735.2.v.a.313.6		32	105.53	even	12
735.2.v.a.472.5		32	21.2	odd	6
735.2.v.a.472.6		32	21.5	even	6
735.2.v.a.607.3		32	21.17	even	6
735.2.v.a.607.4		32	21.11	odd	6
1680.2.cz.d.97.2		16	12.11	even	2
1680.2.cz.d.97.7		16	84.83	odd	2
1680.2.cz.d.433.2		16	420.83	even	4
1680.2.cz.d.433.7		16	60.23	odd	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +O(q^{10})\)	\(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +(-1.63006 + 0.510348i) q^{10} +3.85136 q^{11} +(-3.66816 - 3.66816i) q^{13} +(-1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(-2.80654 - 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +3.96267i q^{26} +(0.869810 - 3.64535i) q^{28} -2.77107i q^{29} -2.39674i q^{31} +(4.14420 + 4.14420i) q^{32} +1.60970 q^{34} +(3.88408 - 4.46250i) q^{35} +(6.18757 + 6.18757i) q^{37} +(-0.0376844 - 0.0376844i) q^{38} +(1.74360 + 5.56908i) q^{40} -8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(-5.49042 + 5.49042i) q^{47} +(6.24586 + 3.16057i) q^{49} +(-0.678376 + 3.75866i) q^{50} +(-5.19592 + 5.19592i) q^{52} +(-6.13823 + 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(-5.88231 + 3.61595i) q^{56} +(-1.49678 + 1.49678i) q^{58} +6.97440 q^{59} +14.3107i q^{61} +(-1.29458 + 1.29458i) q^{62} -2.79807i q^{64} +(-11.0699 + 3.46582i) q^{65} +(0.416491 + 0.416491i) q^{67} +(2.11067 + 2.11067i) q^{68} +(-4.50835 + 0.312431i) q^{70} +8.12783 q^{71} +(9.55210 + 9.55210i) q^{73} -6.68434i q^{74} -0.0988248i q^{76} +(9.91150 + 2.36497i) q^{77} -9.86329i q^{79} +(-0.870061 + 1.66319i) q^{80} +(-4.68886 + 4.68886i) q^{82} +(-1.63570 - 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +2.99355 q^{86} +(-7.10728 + 7.10728i) q^{88} +5.05313 q^{89} +(-7.18757 - 11.6925i) q^{91} +(-0.756656 - 0.756656i) q^{92} +5.93123 q^{94} +(0.0723134 - 0.138232i) q^{95} +(6.85851 - 6.85851i) q^{97} +(-1.66650 - 5.08082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 - 24 * q^8	\( 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more