LMFDB - Embedded newform 325.2.x.c.93.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.3
Character	$\chi$	$=$	325.93
Dual form			325.2.x.c.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52518 + 0.880562i) q^{2} +(-0.845033 + 3.15371i) q^{3} +(0.550780 - 0.953979i) q^{4} +(-1.48821 - 5.55407i) q^{6} +(0.694909 - 1.20362i) q^{7} -1.58226i q^{8} +(-6.63370 - 3.82997i) q^{9} +(0.949498 - 3.54358i) q^{11} +(2.54314 + 2.54314i) q^{12} +(-1.51879 - 3.27006i) q^{13} +2.44764i q^{14} +(2.49484 + 4.32119i) q^{16} +(-3.92917 + 1.05282i) q^{17} +13.4901 q^{18} +(-2.25062 + 0.603051i) q^{19} +(3.20863 + 3.20863i) q^{21} +(1.67219 + 6.24068i) q^{22} +(-5.51848 - 1.47867i) q^{23} +(4.99000 + 1.33707i) q^{24} +(5.19592 + 3.65003i) q^{26} +(10.7583 - 10.7583i) q^{27} +(-0.765484 - 1.32586i) q^{28} +(-2.47021 + 1.42618i) q^{29} +(0.220086 - 0.220086i) q^{31} +(-4.86960 - 2.81146i) q^{32} +(10.3730 + 5.98888i) q^{33} +(5.06561 - 5.06561i) q^{34} +(-7.30742 + 4.21894i) q^{36} +(3.03968 + 5.26488i) q^{37} +(2.90157 - 2.90157i) q^{38} +(11.5962 - 2.02651i) q^{39} +(-10.9769 - 2.94124i) q^{41} +(-7.71914 - 2.06834i) q^{42} +(-1.43468 - 5.35430i) q^{43} +(-2.85753 - 2.85753i) q^{44} +(9.71874 - 2.60413i) q^{46} -5.06887 q^{47} +(-15.7360 + 4.21645i) q^{48} +(2.53420 + 4.38937i) q^{49} -13.2811i q^{51} +(-3.95609 - 0.352188i) q^{52} +(-0.586010 - 0.586010i) q^{53} +(-6.93496 + 25.8816i) q^{54} +(-1.90444 - 1.09953i) q^{56} -7.60737i q^{57} +(2.51168 - 4.35035i) q^{58} +(-0.878129 - 3.27722i) q^{59} +(-3.03437 + 5.25569i) q^{61} +(-0.141871 + 0.529470i) q^{62} +(-9.21963 + 5.32296i) q^{63} -0.0766898 q^{64} -21.0943 q^{66} +(1.14393 - 0.660446i) q^{67} +(-1.15974 + 4.32821i) q^{68} +(9.32660 - 16.1541i) q^{69} +(1.41960 + 5.29800i) q^{71} +(-6.06002 + 10.4963i) q^{72} +2.15999i q^{73} +(-9.27212 - 5.35326i) q^{74} +(-0.664297 + 2.47919i) q^{76} +(-3.60529 - 3.60529i) q^{77} +(-15.9018 + 13.3020i) q^{78} -3.44072i q^{79} +(13.3474 + 23.1184i) q^{81} +(19.3316 - 5.17990i) q^{82} +1.38257 q^{83} +(4.82822 - 1.29372i) q^{84} +(6.90294 + 6.90294i) q^{86} +(-2.41033 - 8.99549i) q^{87} +(-5.60687 - 1.50236i) q^{88} +(-1.09501 - 0.293408i) q^{89} +(-4.99132 - 0.444348i) q^{91} +(-4.45010 + 4.45010i) q^{92} +(0.508107 + 0.880067i) q^{93} +(7.73094 - 4.46346i) q^{94} +(12.9815 - 12.9815i) q^{96} +(13.7196 + 7.92101i) q^{97} +(-7.73023 - 4.46305i) q^{98} +(-19.8705 + 19.8705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) $ 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.52518	+	0.880562i	−1.07846	+	0.622652i	−0.930482	−	0.366338i	$-0.880611\pi$
$2$	−1.52518	+	0.880562i	−1.07846	+	0.622652i	−0.147983	+	0.988990i	$0.547278\pi$
$3$	−0.845033	+	3.15371i	−0.487880	+	1.82079i	0.0788467	+	0.996887i	$0.474876\pi$
$3$	−0.845033	+	3.15371i	−0.487880	+	1.82079i	−0.566727	+	0.823906i	$0.691790\pi$
$4$	0.550780	−	0.953979i	0.275390	−	0.476990i
$5$		0			0
$5$		0			0
$6$	−1.48821	−	5.55407i	−0.607558	−	2.26744i
$7$	0.694909	−	1.20362i	0.262651	−	0.454925i	−0.704295	−	0.709908i	$-0.748737\pi$
$7$	0.694909	−	1.20362i	0.262651	−	0.454925i	0.966945	+	0.254983i	$0.0820699\pi$
$8$		−	1.58226i		−	0.559415i
$9$	−6.63370	−	3.82997i	−2.21123	−	1.27666i
$10$		0			0
$11$	0.949498	−	3.54358i	0.286285	−	1.06843i	−0.661611	−	0.749847i	$-0.730127\pi$
$11$	0.949498	−	3.54358i	0.286285	−	1.06843i	0.947896	−	0.318581i	$-0.103206\pi$
$12$	2.54314	+	2.54314i	0.734142	+	0.734142i
$13$	−1.51879	−	3.27006i	−0.421237	−	0.906951i
$13$	−1.51879	−	3.27006i	−0.421237	−	0.906951i
$14$			2.44764i			0.654160i
$15$		0			0
$16$	2.49484	+	4.32119i	0.623711	+	1.08030i
$17$	−3.92917	+	1.05282i	−0.952963	+	0.255346i	−0.701619	−	0.712552i	$-0.747539\pi$
$17$	−3.92917	+	1.05282i	−0.952963	+	0.255346i	−0.251344	+	0.967898i	$0.580872\pi$
$18$	13.4901			3.17965
$19$	−2.25062	+	0.603051i	−0.516327	+	0.138349i	−0.507567	−	0.861612i	$-0.669455\pi$
$19$	−2.25062	+	0.603051i	−0.516327	+	0.138349i	−0.00875965	+	0.999962i	$0.502788\pi$
$20$		0			0
$21$	3.20863	+	3.20863i	0.700181	+	0.700181i
$22$	1.67219	+	6.24068i	0.356511	+	1.33052i
$23$	−5.51848	−	1.47867i	−1.15068	−	0.308325i	−0.367444	−	0.930045i	$-0.619767\pi$
$23$	−5.51848	−	1.47867i	−1.15068	−	0.308325i	−0.783239	+	0.621721i	$0.786434\pi$
$24$	4.99000	+	1.33707i	1.01858	+	0.272927i
$25$		0			0
$26$	5.19592	+	3.65003i	1.01900	+	0.715830i
$27$	10.7583	−	10.7583i	2.07043	−	2.07043i
$28$	−0.765484	−	1.32586i	−0.144663	−	0.250563i
$29$	−2.47021	+	1.42618i	−0.458707	+	0.264835i	−0.711500	−	0.702686i	$-0.751984\pi$
$29$	−2.47021	+	1.42618i	−0.458707	+	0.264835i	0.252793	+	0.967520i	$0.418651\pi$
$30$		0			0
$31$	0.220086	−	0.220086i	0.0395287	−	0.0395287i	−0.687066	−	0.726595i	$-0.741102\pi$
$31$	0.220086	−	0.220086i	0.0395287	−	0.0395287i	0.726595	+	0.687066i	$0.241102\pi$
$32$	−4.86960	−	2.81146i	−0.860832	−	0.497001i
$33$	10.3730	+	5.98888i	1.80571	+	1.04253i
$34$	5.06561	−	5.06561i	0.868745	−	0.868745i
$35$		0			0
$36$	−7.30742	+	4.21894i	−1.21790	+	0.703157i
$37$	3.03968	+	5.26488i	0.499721	+	0.865542i	1.00000		0.000322437i	$-0.000102635\pi$
$37$	3.03968	+	5.26488i	0.499721	+	0.865542i	−0.500279	+	0.865864i	$0.666769\pi$
$38$	2.90157	−	2.90157i	0.470696	−	0.470696i
$39$	11.5962	−	2.02651i	1.85688	−	0.324502i
$40$		0			0
$41$	−10.9769	−	2.94124i	−1.71430	−	0.459345i	−0.737827	−	0.674990i	$-0.764148\pi$
$41$	−10.9769	−	2.94124i	−1.71430	−	0.459345i	−0.976472	+	0.215645i	$0.930815\pi$
$42$	−7.71914	−	2.06834i	−1.19109	−	0.319151i
$43$	−1.43468	−	5.35430i	−0.218787	−	0.816524i	−0.984799	−	0.173698i	$-0.944428\pi$
$43$	−1.43468	−	5.35430i	−0.218787	−	0.816524i	0.766012	−	0.642826i	$-0.222238\pi$
$44$	−2.85753	−	2.85753i	−0.430789	−	0.430789i
$45$		0			0
$46$	9.71874	−	2.60413i	1.43295	−	0.383958i
$47$	−5.06887			−0.739371			−0.369686	−	0.929157i	$-0.620535\pi$
$47$	−5.06887			−0.739371			−0.369686	+	0.929157i	$0.620535\pi$
$48$	−15.7360	+	4.21645i	−2.27130	+	0.608592i
$49$	2.53420	+	4.38937i	0.362029	+	0.627053i
$50$		0			0
$51$		−	13.2811i		−	1.85973i
$52$	−3.95609	−	0.352188i	−0.548611	−	0.0488397i
$53$	−0.586010	−	0.586010i	−0.0804946	−	0.0804946i	0.665713	−	0.746208i	$-0.268127\pi$
$53$	−0.586010	−	0.586010i	−0.0804946	−	0.0804946i	−0.746208	+	0.665713i	$0.768127\pi$
$54$	−6.93496	+	25.8816i	−0.943728	+	3.52204i
$55$		0			0
$56$	−1.90444	−	1.09953i	−0.254492	−	0.146931i
$57$		−	7.60737i		−	1.00762i
$58$	2.51168	−	4.35035i	0.329799	−	0.571229i
$59$	−0.878129	−	3.27722i	−0.114323	−	0.426658i	0.884913	−	0.465757i	$-0.154218\pi$
$59$	−0.878129	−	3.27722i	−0.114323	−	0.426658i	−0.999235	+	0.0390991i	$0.987551\pi$
$60$		0			0
$61$	−3.03437	+	5.25569i	−0.388512	+	0.672922i	−0.992250	−	0.124261i	$-0.960344\pi$
$61$	−3.03437	+	5.25569i	−0.388512	+	0.672922i	0.603738	+	0.797183i	$0.293677\pi$
$62$	−0.141871	+	0.529470i	−0.0180177	+	0.0672428i
$63$	−9.21963	+	5.32296i	−1.16156	+	0.670630i
$64$	−0.0766898			−0.00958623
$65$		0			0
$66$	−21.0943			−2.59653
$67$	1.14393	−	0.660446i	0.139753	−	0.0806864i	−0.428493	−	0.903545i	$-0.640955\pi$
$67$	1.14393	−	0.660446i	0.139753	−	0.0806864i	0.568246	+	0.822859i	$0.307622\pi$
$68$	−1.15974	+	4.32821i	−0.140639	+	0.524873i
$69$	9.32660	−	16.1541i	1.12279	−	1.94473i
$70$		0			0
$71$	1.41960	+	5.29800i	0.168475	+	0.628758i	0.997571	+	0.0696517i	$0.0221888\pi$
$71$	1.41960	+	5.29800i	0.168475	+	0.628758i	−0.829096	+	0.559106i	$0.811145\pi$
$72$	−6.06002	+	10.4963i	−0.714181	+	1.23700i
$73$			2.15999i			0.252808i	0.991979	+	0.126404i	$0.0403435\pi$
$73$			2.15999i			0.252808i	−0.991979	+	0.126404i	$0.959656\pi$
$74$	−9.27212	−	5.35326i	−1.07786	−	0.622304i
$75$		0			0
$76$	−0.664297	+	2.47919i	−0.0762000	+	0.284382i
$77$	−3.60529	−	3.60529i	−0.410861	−	0.410861i
$78$	−15.9018	+	13.3020i	−1.80053	+	1.50615i
$79$		−	3.44072i		−	0.387111i	−0.981089	−	0.193555i	$-0.937998\pi$
$79$		−	3.44072i		−	0.387111i	0.981089	−	0.193555i	$-0.0620020\pi$
$80$		0			0
$81$	13.3474	+	23.1184i	1.48305	+	2.56871i
$82$	19.3316	−	5.17990i	2.13482	−	0.572024i
$83$	1.38257			0.151757			0.0758783	−	0.997117i	$-0.475824\pi$
$83$	1.38257			0.151757			0.0758783	+	0.997117i	$0.475824\pi$
$84$	4.82822	−	1.29372i	0.526802	−	0.141156i
$85$		0			0
$86$	6.90294	+	6.90294i	0.744364	+	0.744364i
$87$	−2.41033	−	8.99549i	−0.258415	−	0.964418i
$88$	−5.60687	−	1.50236i	−0.597695	−	0.160152i
$89$	−1.09501	−	0.293408i	−0.116071	−	0.0311012i	0.200316	−	0.979731i	$-0.435803\pi$
$89$	−1.09501	−	0.293408i	−0.116071	−	0.0311012i	−0.316387	+	0.948630i	$0.602470\pi$
$90$		0			0
$91$	−4.99132	−	0.444348i	−0.523232	−	0.0465804i
$92$	−4.45010	+	4.45010i	−0.463955	+	0.463955i
$93$	0.508107	+	0.880067i	0.0526882	+	0.0912587i
$94$	7.73094	−	4.46346i	0.797385	−	0.460371i
$95$		0			0
$96$	12.9815	−	12.9815i	1.32492	−	1.32492i
$97$	13.7196	+	7.92101i	1.39301	+	0.804256i	0.993648	−	0.112536i	$-0.0358973\pi$
$97$	13.7196	+	7.92101i	1.39301	+	0.804256i	0.399365	+	0.916792i	$0.369231\pi$
$98$	−7.73023	−	4.46305i	−0.780871	−	0.450836i
$99$	−19.8705	+	19.8705i	−1.99706	+	1.99706i
$100$		0			0
$101$	−2.26191	+	1.30591i	−0.225068	+	0.129943i	−0.608295	−	0.793711i	$-0.708146\pi$
$101$	−2.26191	+	1.30591i	−0.225068	+	0.129943i	0.383227	+	0.923654i	$0.374813\pi$
$102$	11.6948	+	20.2560i	1.15796	+	2.00565i
$103$	−0.960893	+	0.960893i	−0.0946796	+	0.0946796i	−0.752860	−	0.658181i	$-0.771326\pi$
$103$	−0.960893	+	0.960893i	−0.0946796	+	0.0946796i	0.658181	+	0.752860i	$0.271326\pi$
$104$	−5.17409	+	2.40313i	−0.507362	+	0.235646i
$105$		0			0
$106$	1.40979	+	0.377751i	0.136931	+	0.0366905i
$107$	−15.0689	−	4.03770i	−1.45677	−	0.390339i	−0.558394	−	0.829576i	$-0.688582\pi$
$107$	−15.0689	−	4.03770i	−1.45677	−	0.390339i	−0.898372	+	0.439236i	$0.855249\pi$
$108$	−4.33773	−	16.1886i	−0.417398	−	1.55775i
$109$	−9.51962	−	9.51962i	−0.911814	−	0.911814i	0.0846007	−	0.996415i	$-0.473039\pi$
$109$	−9.51962	−	9.51962i	−0.911814	−	0.911814i	−0.996415	+	0.0846007i	$0.973039\pi$
$110$		0			0
$111$	−19.1725	+	5.13726i	−1.81978	+	0.487607i
$112$	6.93475			0.655272
$113$	11.0602	−	2.96358i	1.04046	−	0.278790i	0.302154	−	0.953259i	$-0.402294\pi$
$113$	11.0602	−	2.96358i	1.04046	−	0.278790i	0.738303	+	0.674469i	$0.235627\pi$
$114$	6.69877	+	11.6026i	0.627397	+	1.08668i
$115$		0			0
$116$			3.14204i			0.291731i
$117$	−2.44901	+	27.5095i	−0.226411	+	2.54325i
$118$	4.22510	+	4.22510i	0.388952	+	0.388952i
$119$	−1.46322	+	5.46082i	−0.134133	+	0.500593i
$120$		0			0
$121$	−2.12911	−	1.22924i	−0.193555	−	0.111749i
$122$		−	10.6878i		−	0.967630i
$123$	18.5516	−	32.1324i	1.67274	−	2.89728i
$124$	−0.0887386	−	0.331177i	−0.00796896	−	0.0297406i
$125$		0			0
$126$	9.37439	−	16.2369i	0.835137	−	1.44650i
$127$	5.02598	−	18.7572i	0.445983	−	1.66443i	−0.267343	−	0.963601i	$-0.586146\pi$
$127$	5.02598	−	18.7572i	0.445983	−	1.66443i	0.713327	−	0.700832i	$-0.247188\pi$
$128$	9.85617	−	5.69046i	0.871170	−	0.502970i
$129$	18.0983			1.59346
$130$		0			0
$131$	4.21678			0.368422			0.184211	−	0.982887i	$-0.441027\pi$
$131$	4.21678			0.368422			0.184211	+	0.982887i	$0.441027\pi$
$132$	11.4265	−	6.59711i	0.994552	−	0.574205i
$133$	−0.838130	+	3.12794i	−0.0726751	+	0.271227i
$134$	−1.16313	+	2.01460i	−0.100479	+	0.174035i
$135$		0			0
$136$	1.66583	+	6.21698i	0.142844	+	0.533101i
$137$	5.61121	−	9.71890i	0.479398	−	0.830342i	−0.520323	−	0.853970i	$-0.674188\pi$
$137$	5.61121	−	9.71890i	0.479398	−	0.830342i	0.999721	+	0.0236280i	$0.00752173\pi$
$138$			32.8506i			2.79643i
$139$	1.44435	+	0.833895i	0.122508	+	0.0707301i	0.560002	−	0.828491i	$-0.310800\pi$
$139$	1.44435	+	0.833895i	0.122508	+	0.0707301i	−0.437494	+	0.899221i	$0.644134\pi$
$140$		0			0
$141$	4.28336	−	15.9857i	0.360724	−	1.34624i
$142$	−6.83036	−	6.83036i	−0.573191	−	0.573191i
$143$	−13.0298	+	2.27704i	−1.08961	+	0.190415i
$144$		−	38.2207i		−	3.18506i
$145$		0			0
$146$	−1.90201	−	3.29437i	−0.157411	−	0.272644i
$147$	−15.9843	+	4.28297i	−1.31836	+	0.353253i
$148$	6.69679			0.550473
$149$	11.6304	−	3.11636i	0.952802	−	0.255302i	0.251251	−	0.967922i	$-0.419158\pi$
$149$	11.6304	−	3.11636i	0.952802	−	0.255302i	0.701551	+	0.712620i	$0.252491\pi$
$150$		0			0
$151$	−6.13780	−	6.13780i	−0.499487	−	0.499487i	0.411791	−	0.911278i	$-0.364903\pi$
$151$	−6.13780	−	6.13780i	−0.499487	−	0.499487i	−0.911278	+	0.411791i	$0.864903\pi$
$152$	0.954185	+	3.56107i	0.0773946	+	0.288841i
$153$	30.0972	+	8.06451i	2.43321	+	0.651977i
$154$	8.67341	+	2.32403i	0.698923	+	0.187276i
$155$		0			0
$156$	4.45372	−	12.1787i	0.356583	−	0.975078i
$157$	−9.72344	+	9.72344i	−0.776015	+	0.776015i	−0.979151	−	0.203135i	$-0.934887\pi$
$157$	−9.72344	+	9.72344i	−0.776015	+	0.776015i	0.203135	+	0.979151i	$0.434887\pi$
$158$	3.02977	+	5.24771i	0.241035	+	0.417485i
$159$	2.34330	−	1.35290i	0.185836	−	0.107292i
$160$		0			0
$161$	−5.61460	+	5.61460i	−0.442492	+	0.442492i
$162$	−40.7144	−	23.5065i	−3.19883	−	1.84684i
$163$	3.45081	+	1.99232i	0.270288	+	0.156051i	0.629019	−	0.777390i	$-0.283457\pi$
$163$	3.45081	+	1.99232i	0.270288	+	0.156051i	−0.358730	+	0.933441i	$0.616790\pi$
$164$	−8.85173	+	8.85173i	−0.691204	+	0.691204i
$165$		0			0
$166$	−2.10866	+	1.21744i	−0.163664	+	0.0944915i
$167$	−2.72761	−	4.72436i	−0.211069	−	0.365582i	0.740980	−	0.671527i	$-0.234361\pi$
$167$	−2.72761	−	4.72436i	−0.211069	−	0.365582i	−0.952049	+	0.305945i	$0.901028\pi$
$168$	5.07691	−	5.07691i	0.391692	−	0.391692i
$169$	−8.38655	+	9.93307i	−0.645119	+	0.764082i
$170$		0			0
$171$	17.2396	+	4.61933i	1.31834	+	0.353249i
$172$	−5.89809	−	1.58039i	−0.449725	−	0.120503i
$173$	5.25347	+	19.6062i	0.399414	+	1.49063i	0.814131	+	0.580682i	$0.197214\pi$
$173$	5.25347	+	19.6062i	0.399414	+	1.49063i	−0.414717	+	0.909951i	$0.636119\pi$
$174$	11.5973	+	11.5973i	0.879188	+	0.879188i
$175$		0			0
$176$	17.6813	−	4.73770i	1.33278	−	0.357117i
$177$	11.0774			0.832631
$178$	1.92845	−	0.516728i	0.144544	−	0.0387304i
$179$	−0.485197	−	0.840386i	−0.0362654	−	0.0628134i	0.847323	−	0.531078i	$-0.178213\pi$
$179$	−0.485197	−	0.840386i	−0.0362654	−	0.0628134i	−0.883588	+	0.468264i	$0.844879\pi$
$180$		0			0
$181$		−	18.2170i		−	1.35406i	−0.735956	−	0.677029i	$-0.763267\pi$
$181$		−	18.2170i		−	1.35406i	0.735956	−	0.677029i	$-0.236733\pi$
$182$	8.00393	−	3.71746i	0.593291	−	0.275556i
$183$	−14.0107	−	14.0107i	−1.03570	−	1.03570i
$184$	−2.33965	+	8.73170i	−0.172481	+	0.643709i
$185$		0			0
$186$	−1.54991	−	0.894840i	−0.113645	−	0.0656128i
$187$			14.9229i			1.09127i
$188$	−2.79183	+	4.83560i	−0.203615	+	0.352672i
$189$	−5.47282	−	20.4249i	−0.398089	−	1.48569i
$190$		0			0
$191$	−8.18780	+	14.1817i	−0.592449	+	1.02615i	0.401453	+	0.915880i	$0.368505\pi$
$191$	−8.18780	+	14.1817i	−0.592449	+	1.02615i	−0.993901	+	0.110272i	$0.964828\pi$
$192$	0.0648054	−	0.241857i	0.00467693	−	0.0174545i
$193$	−8.91585	+	5.14757i	−0.641777	+	0.370530i	−0.785299	−	0.619117i	$-0.787491\pi$
$193$	−8.91585	+	5.14757i	−0.641777	+	0.370530i	0.143522	+	0.989647i	$0.454157\pi$
$194$	−27.8998			−2.00309
$195$		0			0
$196$	5.58316			0.398797
$197$	−10.7321	+	6.19621i	−0.764633	+	0.441461i	−0.830957	−	0.556337i	$-0.812206\pi$
$197$	−10.7321	+	6.19621i	−0.764633	+	0.441461i	0.0663234	+	0.997798i	$0.478873\pi$
$198$	12.8088	−	47.8032i	0.910284	−	3.39723i
$199$	2.14630	−	3.71750i	0.152147	−	0.263527i	−0.779869	−	0.625942i	$-0.784715\pi$
$199$	2.14630	−	3.71750i	0.152147	−	0.263527i	0.932017	+	0.362416i	$0.118048\pi$
$200$		0			0
$201$	1.11620	+	4.16571i	0.0787305	+	0.293826i
$202$	2.29988	−	3.98350i	0.161819	−	0.280278i
$203$			3.96425i			0.278236i
$204$	−12.6699	−	7.31496i	−0.887070	−	0.512150i
$205$		0			0
$206$	0.619407	−	2.31166i	0.0431561	−	0.161061i
$207$	30.9447	+	30.9447i	2.15081	+	2.15081i
$208$	10.3414	−	14.7213i	0.717048	−	1.02074i
$209$			8.54782i			0.591265i
$210$		0			0
$211$	−13.4327	−	23.2662i	−0.924747	−	1.60171i	−0.791968	−	0.610562i	$-0.790943\pi$
$211$	−13.4327	−	23.2662i	−0.924747	−	1.60171i	−0.132778	−	0.991146i	$-0.542390\pi$
$212$	−0.881803	+	0.236279i	−0.0605625	+	0.0162277i
$213$	−17.9080			−1.22703
$214$	26.5382	−	7.11089i	1.81412	−	0.486091i
$215$		0			0
$216$	−17.0224	−	17.0224i	−1.15823	−	1.15823i
$217$	−0.111960	−	0.417839i	−0.00760032	−	0.0283648i
$218$	22.9017	+	6.13650i	1.55110	+	0.415616i
$219$	−6.81198	−	1.82526i	−0.460311	−	0.123340i
$220$		0			0
$221$	9.41035	+	11.2496i	0.633009	+	0.756729i
$222$	24.7179	−	24.7179i	1.65895	−	1.65895i
$223$	9.93870	+	17.2143i	0.665545	+	1.15276i	0.979137	+	0.203199i	$0.0651340\pi$
$223$	9.93870	+	17.2143i	0.665545	+	1.15276i	−0.313593	+	0.949558i	$0.601533\pi$
$224$	−6.76785	+	3.90742i	−0.452196	+	0.261076i
$225$		0			0
$226$	−14.2592	+	14.2592i	−0.948507	+	0.948507i
$227$	9.67768	+	5.58741i	0.642330	+	0.370849i	0.785512	−	0.618847i	$-0.212400\pi$
$227$	9.67768	+	5.58741i	0.642330	+	0.370849i	−0.143181	+	0.989696i	$0.545733\pi$
$228$	−7.25728	−	4.18999i	−0.480625	−	0.277489i
$229$	−12.7032	+	12.7032i	−0.839450	+	0.839450i	−0.988786	−	0.149336i	$-0.952286\pi$
$229$	−12.7032	+	12.7032i	−0.839450	+	0.839450i	0.149336	+	0.988786i	$0.452286\pi$
$230$		0			0
$231$	14.4166	−	8.32344i	0.948545	−	0.547642i
$232$	2.25659	+	3.90853i	0.148152	+	0.256608i
$233$	−0.0102716	+	0.0102716i	−0.000672916	+	0.000672916i	−0.707443	−	0.706770i	$-0.750151\pi$
$233$	−0.0102716	+	0.0102716i	−0.000672916	+	0.000672916i	0.706770	+	0.707443i	$0.250151\pi$
$234$	−20.4887	−	44.1134i	−1.33938	−	2.88378i
$235$		0			0
$236$	−3.61006	−	0.967312i	−0.234995	−	0.0629666i
$237$	10.8510	+	2.90752i	0.704849	+	0.188864i
$238$	−2.57692	−	9.61719i	−0.167037	−	0.623390i
$239$	8.78399	+	8.78399i	0.568189	+	0.568189i	0.931621	−	0.363432i	$-0.118395\pi$
$239$	8.78399	+	8.78399i	0.568189	+	0.568189i	−0.363432	+	0.931621i	$0.618395\pi$
$240$		0			0
$241$	21.5510	−	5.77458i	1.38822	−	0.371973i	0.514122	−	0.857717i	$-0.328118\pi$
$241$	21.5510	−	5.77458i	1.38822	−	0.371973i	0.874101	+	0.485743i	$0.161451\pi$
$242$	4.32969			0.278323
$243$	−40.0994	+	10.7446i	−2.57238	+	0.689267i
$244$	3.34254	+	5.78946i	0.213985	+	0.370632i
$245$		0			0
$246$			65.3435i			4.16615i
$247$	5.39022	+	6.44373i	0.342972	+	0.410005i
$248$	−0.348235	−	0.348235i	−0.0221129	−	0.0221129i
$249$	−1.16832	+	4.36021i	−0.0740390	+	0.276317i
$250$		0			0
$251$	1.04874	+	0.605490i	0.0661959	+	0.0382182i	0.532733	−	0.846284i	$-0.321165\pi$
$251$	1.04874	+	0.605490i	0.0661959	+	0.0382182i	−0.466537	+	0.884502i	$0.654498\pi$
$252$			11.7271i			0.738739i
$253$	−10.4796	+	18.1512i	−0.658846	+	1.14115i
$254$	8.85137	+	33.0338i	0.555385	+	2.07272i
$255$		0			0
$256$	−9.94492	+	17.2251i	−0.621558	+	1.07657i
$257$	−3.30128	+	12.3205i	−0.205928	+	0.768535i	0.783236	+	0.621724i	$0.213567\pi$
$257$	−3.30128	+	12.3205i	−0.205928	+	0.768535i	−0.989165	+	0.146811i	$0.953099\pi$
$258$	−27.6031	+	15.9366i	−1.71849	+	0.992172i
$259$	8.44921			0.525008
$260$		0			0
$261$	21.8489			1.35241
$262$	−6.43135	+	3.71314i	−0.397330	+	0.229399i
$263$	3.06032	−	11.4213i	0.188707	−	0.704266i	−0.805099	−	0.593140i	$-0.797888\pi$
$263$	3.06032	−	11.4213i	0.188707	−	0.704266i	0.993806	−	0.111125i	$-0.0354455\pi$
$264$	9.47599	−	16.4129i	0.583207	−	1.01014i
$265$		0			0
$266$	−1.47605	−	5.50870i	−0.0905025	−	0.337760i
$267$	1.85064	−	3.20541i	0.113258	−	0.196168i
$268$		−	1.45504i		−	0.0888809i
$269$	−14.0608	−	8.11799i	−0.857300	−	0.494963i	0.00580692	−	0.999983i	$-0.498152\pi$
$269$	−14.0608	−	8.11799i	−0.857300	−	0.494963i	−0.863107	+	0.505021i	$0.831485\pi$
$270$		0			0
$271$	0.567117	−	2.11651i	0.0344499	−	0.128569i	−0.946559	−	0.322530i	$-0.895467\pi$
$271$	0.567117	−	2.11651i	0.0344499	−	0.128569i	0.981009	+	0.193961i	$0.0621335\pi$
$272$	−14.3521	−	14.3521i	−0.870222	−	0.870222i
$273$	5.61917	−	15.3657i	0.340088	−	0.929972i
$274$			19.7641i			1.19399i
$275$		0			0
$276$	−10.2738	−	17.7948i	−0.618411	−	1.07112i
$277$	−18.0331	+	4.83197i	−1.08351	+	0.290325i	−0.756031	−	0.654535i	$-0.772864\pi$
$277$	−18.0331	+	4.83197i	−1.08351	+	0.290325i	−0.327475	+	0.944860i	$0.606198\pi$
$278$	−2.93719			−0.176161
$279$	−2.30291	+	0.617063i	−0.137872	+	0.0369426i
$280$		0			0
$281$	7.76642	+	7.76642i	0.463306	+	0.463306i	0.899737	−	0.436432i	$-0.143758\pi$
$281$	7.76642	+	7.76642i	0.463306	+	0.463306i	−0.436432	+	0.899737i	$0.643758\pi$
$282$	7.54354	+	28.1529i	0.449211	+	1.67648i
$283$	−9.43309	−	2.52759i	−0.560739	−	0.150250i	−0.0326932	−	0.999465i	$-0.510408\pi$
$283$	−9.43309	−	2.52759i	−0.560739	−	0.150250i	−0.528046	+	0.849216i	$0.677075\pi$
$284$	5.83607	+	1.56377i	0.346307	+	0.0927927i
$285$		0			0
$286$	17.8677	−	14.9464i	1.05654	−	0.883801i
$287$	−11.1681	+	11.1681i	−0.659229	+	0.659229i
$288$	21.5356	+	37.3008i	1.26900	+	2.19797i
$289$	−0.392513	+	0.226617i	−0.0230890	+	0.0133304i
$290$		0			0
$291$	−36.5740	+	36.5740i	−2.14401	+	2.14401i
$292$	2.06059	+	1.18968i	0.120587	+	0.0696208i
$293$	−29.2511	−	16.8881i	−1.70887	−	0.986615i	−0.935968	−	0.352086i	$-0.885473\pi$
$293$	−29.2511	−	16.8881i	−1.70887	−	0.986615i	−0.772899	−	0.634529i	$-0.781194\pi$
$294$	20.6074	−	20.6074i	1.20185	−	1.20185i
$295$		0			0
$296$	8.33044	−	4.80958i	0.484197	−	0.279551i
$297$	−27.9078	−	48.3377i	−1.61937	−	2.80484i
$298$	−14.9943	+	14.9943i	−0.868598	+	0.868598i
$299$	3.54608	+	20.2916i	0.205075	+	1.17349i
$300$		0			0
$301$	−7.44150	−	1.99395i	−0.428921	−	0.114929i
$302$	14.7660	+	3.95652i	0.849685	+	0.227672i
$303$	−2.20708	−	8.23693i	−0.126793	−	0.473199i
$304$	−8.22083	−	8.22083i	−0.471497	−	0.471497i
$305$		0			0
$306$	−53.0049	+	14.2026i	−3.03009	+	0.811909i
$307$	−16.4317			−0.937804			−0.468902	−	0.883250i	$-0.655350\pi$
$307$	−16.4317			−0.937804			−0.468902	+	0.883250i	$0.655350\pi$
$308$	−5.42510	+	1.45365i	−0.309124	+	0.0828295i
$309$	−2.21839	−	3.84236i	−0.126200	−	0.218584i
$310$		0			0
$311$		−	1.31200i		−	0.0743968i	−0.999308	−	0.0371984i	$-0.988157\pi$
$311$		−	1.31200i		−	0.0743968i	0.999308	−	0.0371984i	$-0.0118434\pi$
$312$	−3.20648	−	18.3483i	−0.181531	−	1.03877i
$313$	19.5519	+	19.5519i	1.10514	+	1.10514i	0.993780	+	0.111361i	$0.0355211\pi$
$313$	19.5519	+	19.5519i	1.10514	+	1.10514i	0.111361	+	0.993780i	$0.464479\pi$
$314$	6.26789	−	23.3921i	0.353718	−	1.32009i
$315$		0			0
$316$	−3.28237	−	1.89508i	−0.184648	−	0.106607i
$317$		−	34.9576i		−	1.96342i	−0.190394	−	0.981708i	$-0.560977\pi$
$317$		−	34.9576i		−	1.96342i	0.190394	−	0.981708i	$-0.439023\pi$
$318$	−2.38263	+	4.12684i	−0.133611	+	0.231422i
$319$	2.70831	+	10.1075i	0.151636	+	0.565914i
$320$		0			0
$321$	25.4674	−	44.1109i	1.42145	−	2.46203i
$322$	3.61926	−	13.5073i	0.201694	−	0.752731i
$323$	8.20814	−	4.73897i	0.456713	−	0.263683i
$324$	29.4060			1.63367
$325$		0			0
$326$	−7.01746			−0.388661
$327$	38.0665	−	21.9777i	2.10508	−	1.21537i
$328$	−4.65382	+	17.3683i	−0.256964	+	0.959004i
$329$	−3.52240	+	6.10098i	−0.194196	+	0.336358i
$330$		0			0
$331$	−0.658550	−	2.45774i	−0.0361972	−	0.135090i	0.945463	−	0.325730i	$-0.105610\pi$
$331$	−0.658550	−	2.45774i	−0.0361972	−	0.135090i	−0.981660	+	0.190641i	$0.938943\pi$
$332$	0.761491	−	1.31894i	0.0417923	−	0.0723863i
$333$		−	46.5676i		−	2.55189i
$334$	8.32019	+	4.80366i	0.455260	+	0.262845i
$335$		0			0
$336$	−5.86009	+	21.8702i	−0.319694	+	1.19312i
$337$	−8.33325	−	8.33325i	−0.453941	−	0.453941i	0.442719	−	0.896660i	$-0.354014\pi$
$337$	−8.33325	−	8.33325i	−0.453941	−	0.453941i	−0.896660	+	0.442719i	$0.854014\pi$
$338$	4.04430	−	22.5346i	0.219981	−	1.22572i
$339$			37.3850i			2.03047i
$340$		0			0
$341$	−0.570921	−	0.988864i	−0.0309171	−	0.0535500i
$342$	−30.3610	+	8.13522i	−1.64174	+	0.439902i
$343$	16.7729			0.905651
$344$	−8.47192	+	2.27005i	−0.456776	+	0.122393i
$345$		0			0
$346$	−25.2770	−	25.2770i	−1.35890	−	1.35890i
$347$	2.77743	+	10.3655i	0.149100	+	0.556449i	0.999539	+	0.0303747i	$0.00967005\pi$
$347$	2.77743	+	10.3655i	0.149100	+	0.556449i	−0.850438	+	0.526075i	$0.823663\pi$
$348$	−9.90908	−	2.65513i	−0.531182	−	0.142330i
$349$	−23.0049	−	6.16415i	−1.23143	−	0.329960i	−0.416291	−	0.909231i	$-0.636670\pi$
$349$	−23.0049	−	6.16415i	−1.23143	−	0.329960i	−0.815135	+	0.579272i	$0.803337\pi$
$350$		0			0
$351$	−51.5197	−	18.8406i	−2.74992	−	1.00564i
$352$	−14.5863	+	14.5863i	−0.777453	+	0.777453i
$353$	12.9342	+	22.4026i	0.688416	+	1.19237i	0.972350	+	0.233527i	$0.0750268\pi$
$353$	12.9342	+	22.4026i	0.688416	+	1.19237i	−0.283935	+	0.958844i	$0.591640\pi$
$354$	−16.8951	+	9.75437i	−0.897963	+	0.518439i
$355$		0			0
$356$	−0.883016	+	0.883016i	−0.0467998	+	0.0467998i
$357$	−15.9854	−	9.22915i	−0.846035	−	0.488458i
$358$	1.48003	+	0.854493i	0.0782218	+	0.0451614i
$359$	19.3811	−	19.3811i	1.02289	−	1.02289i	0.0231615	−	0.999732i	$-0.492627\pi$
$359$	19.3811	−	19.3811i	1.02289	−	1.02289i	0.999732	−	0.0231615i	$-0.00737320\pi$
$360$		0			0
$361$	−11.7529	+	6.78553i	−0.618573	+	0.357133i
$362$	16.0412	+	27.7842i	0.843107	+	1.46030i
$363$	5.67583	−	5.67583i	0.297904	−	0.297904i
$364$	−3.17302	+	4.51688i	−0.166311	+	0.236749i
$365$		0			0
$366$	33.7062	+	9.03156i	1.76185	+	0.472087i
$367$	−23.2524	−	6.23046i	−1.21376	−	0.325227i	−0.405527	−	0.914083i	$-0.632912\pi$
$367$	−23.2524	−	6.23046i	−1.21376	−	0.325227i	−0.808238	+	0.588856i	$0.799579\pi$
$368$	−7.37811	−	27.5355i	−0.384611	−	1.43539i
$369$	61.5524	+	61.5524i	3.20429	+	3.20429i
$370$		0			0
$371$	−1.11255	+	0.298108i	−0.0577609	+	0.0154770i
$372$	1.11942			0.0580393
$373$	−22.4401	+	6.01280i	−1.16190	+	0.311331i	−0.787725	−	0.616027i	$-0.788741\pi$
$373$	−22.4401	+	6.01280i	−1.16190	+	0.311331i	−0.374177	+	0.927357i	$0.622075\pi$
$374$	−13.1406	−	22.7602i	−0.679483	−	1.17690i
$375$		0			0
$376$			8.02030i			0.413615i
$377$	8.41542	+	5.91167i	0.433416	+	0.304467i
$378$	26.3324	+	26.3324i	1.35439	+	1.35439i
$379$	7.19748	−	26.8614i	0.369710	−	1.37978i	−0.491212	−	0.871040i	$-0.663446\pi$
$379$	7.19748	−	26.8614i	0.369710	−	1.37978i	0.860922	−	0.508736i	$-0.169887\pi$
$380$		0			0
$381$	54.9076	+	31.7009i	2.81300	+	1.62409i
$382$		−	28.8395i		−	1.47556i
$383$	8.43549	−	14.6107i	0.431034	−	0.746572i	−0.565929	−	0.824454i	$-0.691482\pi$
$383$	8.43549	−	14.6107i	0.431034	−	0.746572i	0.996963	+	0.0778820i	$0.0248157\pi$
$384$	9.61725	+	35.8921i	0.490778	+	1.83161i
$385$		0			0
$386$	9.06551	−	15.7019i	0.461423	−	0.799207i
$387$	−10.9896	+	41.0136i	−0.558631	+	2.08484i
$388$	15.1129	−	8.72547i	0.767244	−	0.442968i
$389$	15.9554			0.808973			0.404487	−	0.914544i	$-0.367450\pi$
$389$	15.9554			0.808973			0.404487	+	0.914544i	$0.367450\pi$
$390$		0			0
$391$	23.2398			1.17529
$392$	6.94514	−	4.00978i	0.350783	−	0.202524i
$393$	−3.56332	+	13.2985i	−0.179746	+	0.670820i
$394$	10.9123	−	18.9006i	0.549753	−	0.952201i
$395$		0			0
$396$	8.01176	+	29.9003i	0.402606	+	1.50255i
$397$	8.30391	−	14.3828i	0.416761	−	0.721852i	−0.578850	−	0.815434i	$-0.696498\pi$
$397$	8.30391	−	14.3828i	0.416761	−	0.721852i	0.995612	+	0.0935822i	$0.0298318\pi$
$398$			7.55981i			0.378939i
$399$	−9.15637	−	5.28643i	−0.458392	−	0.264653i
$400$		0			0
$401$	−4.73738	+	17.6802i	−0.236574	+	0.882905i	0.740859	+	0.671660i	$0.234418\pi$
$401$	−4.73738	+	17.6802i	−0.236574	+	0.882905i	−0.977433	+	0.211245i	$0.932248\pi$
$402$	−5.37057	−	5.37057i	−0.267859	−	0.267859i
$403$	−1.05396	−	0.385430i	−0.0525015	−	0.0191996i
$404$			2.87708i			0.143140i
$405$		0			0
$406$	−3.49077	−	6.04620i	−0.173244	−	0.300068i
$407$	21.5427	−	5.77235i	1.06783	−	0.286125i
$408$	−21.0142			−1.04036
$409$	11.9171	−	3.19317i	0.589261	−	0.157892i	0.0481458	−	0.998840i	$-0.484669\pi$
$409$	11.9171	−	3.19317i	0.589261	−	0.157892i	0.541116	+	0.840948i	$0.318002\pi$
$410$		0			0
$411$	25.9089	+	25.9089i	1.27799	+	1.27799i
$412$	0.387431	+	1.44591i	0.0190874	+	0.0712350i
$413$	−4.55474	−	1.22044i	−0.224124	−	0.0600538i
$414$	−74.4449	−	19.9475i	−3.65877	−	0.980364i
$415$		0			0
$416$	−1.79775	+	20.1939i	−0.0881418	+	0.990087i
$417$	−3.85038	+	3.85038i	−0.188554	+	0.188554i
$418$	−7.52689	−	13.0370i	−0.368152	−	0.637658i
$419$	15.6063	−	9.01028i	0.762416	−	0.440181i	−0.0677464	−	0.997703i	$-0.521581\pi$
$419$	15.6063	−	9.01028i	0.762416	−	0.440181i	0.830163	+	0.557521i	$0.188248\pi$
$420$		0			0
$421$	12.6982	−	12.6982i	0.618871	−	0.618871i	−0.326371	−	0.945242i	$-0.605826\pi$
$421$	12.6982	−	12.6982i	0.618871	−	0.618871i	0.945242	+	0.326371i	$0.105826\pi$
$422$	40.9746	+	23.6567i	1.99461	+	1.15159i
$423$	33.6254	+	19.4136i	1.63492	+	0.943923i
$424$	−0.927222	+	0.927222i	−0.0450299	+	0.0450299i
$425$		0			0
$426$	27.3128	−	15.7691i	1.32331	−	0.764014i
$427$	4.21722	+	7.30445i	0.204086	+	0.353487i
$428$	−12.1515	+	12.1515i	−0.587367	+	0.587367i
$429$	3.82949	−	43.0163i	0.184890	−	2.07685i
$430$		0			0
$431$	−7.07051	−	1.89454i	−0.340574	−	0.0912566i	0.0844781	−	0.996425i	$-0.473078\pi$
$431$	−7.07051	−	1.89454i	−0.340574	−	0.0912566i	−0.425052	+	0.905169i	$0.639744\pi$
$432$	73.3288	+	19.6484i	3.52803	+	0.945334i
$433$	2.29626	+	8.56975i	0.110351	+	0.411836i	0.998897	−	0.0469516i	$-0.0149506\pi$
$433$	2.29626	+	8.56975i	0.110351	+	0.411836i	−0.888546	+	0.458787i	$0.848284\pi$
$434$	0.538692	+	0.538692i	0.0258581	+	0.0258581i
$435$		0			0
$436$	−14.3247	+	3.83830i	−0.686031	+	0.183821i
$437$	13.3117			0.636785
$438$	11.9967	−	3.21452i	0.573226	−	0.153596i
$439$	−11.8892	−	20.5927i	−0.567440	−	0.982835i	−0.996818	−	0.0797100i	$-0.974601\pi$
$439$	−11.8892	−	20.5927i	−0.567440	−	0.982835i	0.429378	−	0.903125i	$-0.358733\pi$
$440$		0			0
$441$		−	38.8237i		−	1.84875i
$442$	−24.2584	−	8.87123i	−1.15386	−	0.421961i
$443$	5.18634	+	5.18634i	0.246410	+	0.246410i	0.819496	−	0.573085i	$-0.194254\pi$
$443$	5.18634	+	5.18634i	0.246410	+	0.246410i	−0.573085	+	0.819496i	$0.694254\pi$
$444$	−5.65901	+	21.1197i	−0.268565	+	1.00230i
$445$		0			0
$446$	−30.3166	−	17.5033i	−1.43553	−	0.828805i
$447$			39.3124i			1.85941i
$448$	−0.0532924	+	0.0923052i	−0.00251783	+	0.00436101i
$449$	−8.47234	−	31.6192i	−0.399834	−	1.49220i	−0.813388	−	0.581722i	$-0.802379\pi$
$449$	−8.47234	−	31.6192i	−0.399834	−	1.49220i	0.413553	−	0.910480i	$-0.364288\pi$
$450$		0			0
$451$	−20.8450	+	36.1047i	−0.981555	+	1.70010i
$452$	3.26456	−	12.1835i	0.153552	−	0.573063i
$453$	24.5434	−	14.1702i	1.15315	−	0.665772i
$454$	−19.6803			−0.923640
$455$		0			0
$456$	−12.0369			−0.563678
$457$	15.6189	−	9.01757i	0.730621	−	0.421824i	−0.0880283	−	0.996118i	$-0.528057\pi$
$457$	15.6189	−	9.01757i	0.730621	−	0.421824i	0.818649	+	0.574294i	$0.194723\pi$
$458$	8.18868	−	30.5606i	0.382632	−	1.42800i
$459$	−30.9445	+	53.5975i	−1.44437	+	2.50172i
$460$		0			0
$461$	0.541259	+	2.02001i	0.0252090	+	0.0940811i	0.977384	−	0.211471i	$-0.0678255\pi$
$461$	0.541259	+	2.02001i	0.0252090	+	0.0940811i	−0.952175	+	0.305553i	$0.901159\pi$
$462$	−14.6586	+	25.3895i	−0.681981	+	1.18123i
$463$		−	36.2345i		−	1.68396i	−0.539509	−	0.841980i	$-0.681390\pi$
$463$		−	36.2345i		−	1.68396i	0.539509	−	0.841980i	$-0.318610\pi$
$464$	−12.3256	−	7.11618i	−0.572201	−	0.330360i
$465$		0			0
$466$	0.00662125	−	0.0247108i	0.000306723	−	0.00114471i
$467$	−28.6381	−	28.6381i	−1.32521	−	1.32521i	−0.909493	−	0.415719i	$-0.863530\pi$
$467$	−28.6381	−	28.6381i	−1.32521	−	1.32521i	−0.415719	−	0.909493i	$-0.636470\pi$
$468$	24.8946	+	17.4880i	1.15075	+	0.808383i
$469$		−	1.83580i		−	0.0847694i
$470$		0			0
$471$	−22.4482	−	38.8815i	−1.03436	−	1.79157i
$472$	−5.18543	+	1.38943i	−0.238679	+	0.0639538i
$473$	−20.3356			−0.935032
$474$	−19.1100	+	5.12050i	−0.877751	+	0.235193i
$475$		0			0
$476$	4.40360	+	4.40360i	0.201839	+	0.201839i
$477$	1.64301	+	6.13181i	0.0752284	+	0.280756i
$478$	−21.1320	−	5.66230i	−0.966555	−	0.258988i
$479$	32.0790	+	8.59555i	1.46573	+	0.392741i	0.901464	−	0.432854i	$-0.142493\pi$
$479$	32.0790	+	8.59555i	1.46573	+	0.392741i	0.564264	+	0.825594i	$0.309160\pi$
$480$		0			0
$481$	12.5998	−	17.9362i	0.574503	−	0.817820i
$482$	−27.7843	+	27.7843i	−1.26554	+	1.26554i
$483$	−12.9623	−	22.4513i	−0.589804	−	1.02157i
$484$	−2.34534	+	1.35408i	−0.106606	+	0.0615492i
$485$		0			0
$486$	51.6975	−	51.6975i	2.34505	−	2.34505i
$487$	18.1501	+	10.4790i	0.822460	+	0.474847i	0.851264	−	0.524738i	$-0.175837\pi$
$487$	18.1501	+	10.4790i	0.822460	+	0.474847i	−0.0288042	+	0.999585i	$0.509170\pi$
$488$	8.31589	+	4.80118i	0.376443	+	0.217339i
$489$	−9.19925	+	9.19925i	−0.416004	+	0.416004i
$490$		0			0
$491$	20.3975	−	11.7765i	0.920527	−	0.531466i	0.0367236	−	0.999325i	$-0.488308\pi$
$491$	20.3975	−	11.7765i	0.920527	−	0.531466i	0.883803	+	0.467859i	$0.154975\pi$
$492$	−20.4357	−	35.3957i	−0.921314	−	1.59576i
$493$	8.20437	−	8.20437i	0.369506	−	0.369506i
$494$	−13.8952	−	5.08142i	−0.625173	−	0.228624i
$495$		0			0
$496$	1.50012	+	0.401955i	0.0673572	+	0.0180483i
$497$	7.36326	+	1.97298i	0.330287	+	0.0885002i
$498$	−2.05755	−	7.67888i	−0.0922010	−	0.344099i
$499$	−18.2233	−	18.2233i	−0.815789	−	0.815789i	0.169706	−	0.985495i	$-0.445718\pi$
$499$	−18.2233	−	18.2233i	−0.815789	−	0.815789i	−0.985495	+	0.169706i	$0.945718\pi$
$500$		0			0
$501$	17.2042	−	4.60984i	0.768625	−	0.205952i
$502$	−2.13269			−0.0951865
$503$	−9.77054	+	2.61801i	−0.435647	+	0.116731i	−0.469976	−	0.882679i	$-0.655737\pi$
$503$	−9.77054	+	2.61801i	−0.435647	+	0.116731i	0.0343287	+	0.999411i	$0.489071\pi$
$504$	8.42233	+	14.5879i	0.375160	+	0.649797i
$505$		0			0
$506$		−	36.9117i		−	1.64093i
$507$	−24.2391	−	34.8425i	−1.07649	−	1.54741i
$508$	−15.1258	−	15.1258i	−0.671098	−	0.671098i
$509$	0.411564	−	1.53598i	0.0182422	−	0.0680810i	−0.956205	−	0.292699i	$-0.905447\pi$
$509$	0.411564	−	1.53598i	0.0182422	−	0.0680810i	0.974447	+	0.224618i	$0.0721134\pi$
$510$		0			0
$511$	2.59980	+	1.50100i	0.115008	+	0.0664002i
$512$		−	12.2666i		−	0.542114i
$513$	−17.7249	+	30.7005i	−0.782576	+	1.35546i
$514$	−5.81397	−	21.6980i	−0.256443	−	0.957059i
$515$		0			0
$516$	9.96816	−	17.2654i	0.438824	−	0.760065i
$517$	−4.81289	+	17.9619i	−0.211671	+	0.789965i
$518$	−12.8866	+	7.44005i	−0.566203	+	0.326897i
$519$	−66.2716			−2.90900
$520$		0			0
$521$	−27.2541			−1.19402			−0.597012	−	0.802232i	$-0.703646\pi$
$521$	−27.2541			−1.19402			−0.597012	+	0.802232i	$0.703646\pi$
$522$	−33.3234	+	19.2393i	−1.45853	+	0.842081i
$523$	−5.33334	+	19.9043i	−0.233211	+	0.870354i	0.745737	+	0.666241i	$0.232098\pi$
$523$	−5.33334	+	19.9043i	−0.233211	+	0.870354i	−0.978947	+	0.204113i	$0.934569\pi$
$524$	2.32252	−	4.02272i	0.101460	−	0.175733i
$525$		0			0
$526$	5.38960	+	20.1143i	0.234998	+	0.877024i
$527$	−0.633045	+	1.09647i	−0.0275759	+	0.0477628i
$528$			59.7652i			2.60095i
$529$	8.34861	+	4.82007i	0.362983	+	0.209568i
$530$		0			0
$531$	−6.72641	+	25.1033i	−0.291901	+	1.08939i
$532$	2.52237	+	2.52237i	0.109359	+	0.109359i
$533$	7.05353	+	40.3621i	0.305523	+	1.74828i
$534$			6.51843i			0.282080i
$535$		0			0
$536$	−1.04500	−	1.80999i	−0.0451372	−	0.0781799i
$537$	3.06034	−	0.820015i	0.132063	−	0.0353863i
$538$	28.5936			1.23276
$539$	17.9603	−	4.81245i	0.773604	−	0.207287i
$540$		0			0
$541$	−26.3998	−	26.3998i	−1.13502	−	1.13502i	−0.989331	−	0.145684i	$-0.953462\pi$
$541$	−26.3998	−	26.3998i	−1.13502	−	1.13502i	−0.145684	−	0.989331i	$-0.546538\pi$
$542$	0.998764	+	3.72744i	0.0429006	+	0.160107i
$543$	57.4510	+	15.3940i	2.46546	+	0.660618i
$544$	22.0934	+	5.91991i	0.947248	+	0.253814i
$545$		0			0
$546$	4.96018	+	28.3834i	0.212276	+	1.21470i
$547$	−8.78649	+	8.78649i	−0.375683	+	0.375683i	−0.869542	−	0.493859i	$-0.835586\pi$
$547$	−8.78649	+	8.78649i	−0.375683	+	0.375683i	0.493859	+	0.869542i	$0.335586\pi$
$548$	−6.18109	−	10.7060i	−0.264043	−	0.457336i
$549$	40.2582	−	23.2431i	1.71818	−	0.991992i
$550$		0			0
$551$	4.69944	−	4.69944i	0.200203	−	0.200203i
$552$	−25.5601	−	14.7571i	−1.08791	−	0.628106i
$553$	−4.14131	−	2.39098i	−0.176106	−	0.101675i
$554$	23.2489	−	23.2489i	0.987752	−	0.987752i
$555$		0			0
$556$	1.59104	−	0.918586i	0.0674750	−	0.0389567i
$557$	8.16044	+	14.1343i	0.345769	+	0.598889i	0.985493	−	0.169715i	$-0.0542848\pi$
$557$	8.16044	+	14.1343i	0.345769	+	0.598889i	−0.639724	+	0.768604i	$0.720951\pi$
$558$	2.96899	−	2.96899i	0.125687	−	0.125687i
$559$	−15.3299	+	12.8236i	−0.648386	+	0.542379i
$560$		0			0
$561$	−47.0626	−	12.6104i	−1.98698	−	0.532411i
$562$	−18.6840	−	5.00636i	−0.788137	−	0.211181i
$563$	3.02058	+	11.2729i	0.127302	+	0.475098i	0.999911	−	0.0133211i	$-0.00424036\pi$
$563$	3.02058	+	11.2729i	0.127302	+	0.475098i	−0.872609	+	0.488419i	$0.837574\pi$
$564$	−12.8909	−	12.8909i	−0.542803	−	0.542803i
$565$		0			0
$566$	16.6128	−	4.45140i	0.698290	−	0.187106i
$567$	37.1010			1.55809
$568$	8.38284	−	2.24618i	0.351736	−	0.0942475i
$569$	−1.62041	−	2.80663i	−0.0679311	−	0.117660i	0.830059	−	0.557675i	$-0.188306\pi$
$569$	−1.62041	−	2.80663i	−0.0679311	−	0.117660i	−0.897990	+	0.440015i	$0.854973\pi$
$570$		0			0
$571$			35.5421i			1.48739i	0.668520	+	0.743694i	$0.266928\pi$
$571$			35.5421i			1.48739i	−0.668520	+	0.743694i	$0.733072\pi$
$572$	−5.00430	+	13.6843i	−0.209240	+	0.572169i
$573$	−37.8059	−	37.8059i	−1.57936	−	1.57936i
$574$	7.19911	−	26.8674i	0.300485	−	1.12143i
$575$		0			0
$576$	0.508738	+	0.293720i	0.0211974	+	0.0122383i
$577$			16.1725i			0.673272i	0.941635	+	0.336636i	$0.109289\pi$
$577$			16.1725i			0.673272i	−0.941635	+	0.336636i	$0.890711\pi$
$578$	0.399102	−	0.691264i	0.0166004	−	0.0287528i
$579$	−8.69973	−	32.4678i	−0.361549	−	1.34932i
$580$		0			0
$581$	0.960759	−	1.66408i	0.0398590	−	0.0690378i
$582$	23.5762	−	87.9876i	0.977265	−	3.64720i
$583$	−2.63298	+	1.52015i	−0.109047	+	0.0629584i
$584$	3.41768			0.141424
$585$		0			0
$586$	59.4842			2.45727
$587$	13.7794	−	7.95555i	0.568737	−	0.328361i	−0.187908	−	0.982187i	$-0.560171\pi$
$587$	13.7794	−	7.95555i	0.568737	−	0.328361i	0.756645	+	0.653826i	$0.226837\pi$
$588$	−4.71795	+	17.6076i	−0.194565	+	0.726127i
$589$	−0.362606	+	0.628053i	−0.0149409	+	0.0258785i
$590$		0			0
$591$	−10.4720	−	39.0820i	−0.430760	−	1.60762i
$592$	−15.1671	+	26.2701i	−0.623362	+	1.07970i
$593$		−	6.24369i		−	0.256397i	−0.991748	−	0.128199i	$-0.959080\pi$
$593$		−	6.24369i		−	0.256397i	0.991748	−	0.128199i	$-0.0409195\pi$
$594$	85.1288	+	49.1491i	3.49288	+	2.01661i
$595$		0			0
$596$	3.43286	−	12.8116i	0.140616	−	0.524784i
$597$	9.91021	+	9.91021i	0.405598	+	0.405598i
$598$	−23.2764	−	27.8257i	−0.951842	−	1.13788i
$599$			18.0428i			0.737210i	0.929586	+	0.368605i	$0.120165\pi$
$599$			18.0428i			0.737210i	−0.929586	+	0.368605i	$0.879835\pi$
$600$		0			0
$601$	17.1374	+	29.6828i	0.699048	+	1.21079i	0.968797	+	0.247856i	$0.0797259\pi$
$601$	17.1374	+	29.6828i	0.699048	+	1.21079i	−0.269749	+	0.962931i	$0.586941\pi$
$602$	13.1054	−	3.51159i	0.534137	−	0.143122i
$603$	−10.1180			−0.412035
$604$	−9.23591	+	2.47475i	−0.375804	+	0.100696i
$605$		0			0
$606$	10.6193	+	10.6193i	0.431380	+	0.431380i
$607$	−4.91988	−	18.3613i	−0.199692	−	0.745260i	−0.991002	−	0.133846i	$-0.957267\pi$
$607$	−4.91988	−	18.3613i	−0.199692	−	0.745260i	0.791310	−	0.611415i	$-0.209399\pi$
$608$	12.6551	+	3.39091i	0.513230	+	0.137520i
$609$	−12.5021	−	3.34992i	−0.506610	−	0.135746i
$610$		0			0
$611$	7.69856	+	16.5755i	0.311450	+	0.670573i
$612$	24.2703	−	24.2703i	0.981069	−	0.981069i
$613$	−8.98095	−	15.5555i	−0.362737	−	0.628279i	0.625673	−	0.780085i	$-0.284824\pi$
$613$	−8.98095	−	15.5555i	−0.362737	−	0.628279i	−0.988410	+	0.151806i	$0.951491\pi$
$614$	25.0612	−	14.4691i	1.01139	−	0.583925i
$615$		0			0
$616$	−5.70453	+	5.70453i	−0.229842	+	0.229842i
$617$	−16.3673	−	9.44966i	−0.658922	−	0.380429i	0.132944	−	0.991124i	$-0.457557\pi$
$617$	−16.3673	−	9.44966i	−0.658922	−	0.380429i	−0.791866	+	0.610695i	$0.790890\pi$
$618$	6.76687	+	3.90686i	0.272204	+	0.157157i
$619$	−26.9541	+	26.9541i	−1.08338	+	1.08338i	−0.0871850	+	0.996192i	$0.527787\pi$
$619$	−26.9541	+	26.9541i	−1.08338	+	1.08338i	−0.996192	+	0.0871850i	$0.972213\pi$
$620$		0			0
$621$	−75.2773	+	43.4614i	−3.02077	+	1.74405i
$622$	1.15530	+	2.00104i	0.0463233	+	0.0802343i
$623$	−1.11408	+	1.11408i	−0.0446349	+	0.0446349i
$624$	37.6877	+	45.0537i	1.50872	+	1.80359i
$625$		0			0
$626$	−47.0369	−	12.6035i	−1.87997	−	0.503737i
$627$	−26.9573	−	7.22319i	−1.07657	−	0.288466i
$628$	3.92048	+	14.6314i	0.156444	+	0.583858i
$629$	−17.4864	−	17.4864i	−0.697227	−	0.697227i
$630$		0			0
$631$	10.7162	−	2.87140i	0.426606	−	0.114309i	−0.0391265	−	0.999234i	$-0.512458\pi$
$631$	10.7162	−	2.87140i	0.426606	−	0.114309i	0.465733	+	0.884926i	$0.345791\pi$
$632$	−5.44412			−0.216556
$633$	84.7257	−	22.7022i	3.36754	−	0.902331i
$634$	30.7824	+	53.3166i	1.22252	+	2.11747i
$635$		0			0
$636$		−	2.98061i		−	0.118189i
$637$	10.5046	−	14.9535i	0.416206	−	0.592480i
$638$	−13.0310	−	13.0310i	−0.515901	−	0.515901i
$639$	10.8740	−	40.5824i	0.430170	−	1.60541i
$640$		0			0
$641$	19.7159	+	11.3830i	0.778731	+	0.449600i	0.835980	−	0.548760i	$-0.184900\pi$
$641$	19.7159	+	11.3830i	0.778731	+	0.449600i	−0.0572496	+	0.998360i	$0.518233\pi$
$642$			89.7027i			3.54028i
$643$	17.2987	−	29.9622i	0.682195	−	1.18160i	−0.292115	−	0.956383i	$-0.594359\pi$
$643$	17.2987	−	29.9622i	0.682195	−	1.18160i	0.974310	−	0.225212i	$-0.0723076\pi$
$644$	2.26380	+	8.44862i	0.0892063	+	0.332922i
$645$		0			0
$646$	−8.34592	+	14.4556i	−0.328366	+	0.568746i
$647$	−10.1776	+	37.9832i	−0.400122	+	1.49328i	0.412756	+	0.910842i	$0.364566\pi$
$647$	−10.1776	+	37.9832i	−0.400122	+	1.49328i	−0.812878	+	0.582434i	$0.802100\pi$
$648$	36.5794	−	21.1191i	1.43698	−	0.829638i
$649$	−12.4469			−0.488582
$650$		0			0
$651$	1.41235			0.0553544
$652$	3.80127	−	2.19467i	0.148869	−	0.0859497i
$653$	−2.46961	+	9.21671i	−0.0966433	+	0.360678i	−0.997263	−	0.0739293i	$-0.976446\pi$
$653$	−2.46961	+	9.21671i	−0.0966433	+	0.360678i	0.900620	+	0.434607i	$0.143113\pi$
$654$	−38.7054	+	67.0398i	−1.51350	+	2.62146i
$655$		0			0
$656$	−14.6759	−	54.7711i	−0.572997	−	2.13845i
$657$	8.27270	−	14.3287i	0.322749	−	0.559017i
$658$		−	12.4068i		−	0.483667i
$659$	15.6774	+	9.05138i	0.610707	+	0.352592i	0.773242	−	0.634111i	$-0.218634\pi$
$659$	15.6774	+	9.05138i	0.610707	+	0.352592i	−0.162535	+	0.986703i	$0.551967\pi$
$660$		0			0
$661$	4.48311	−	16.7312i	0.174373	−	0.650768i	−0.822285	−	0.569076i	$-0.807301\pi$
$661$	4.48311	−	16.7312i	0.174373	−	0.650768i	0.996658	−	0.0816920i	$-0.0260324\pi$
$662$	3.16860	+	3.16860i	0.123151	+	0.123151i
$663$	−43.4299	+	20.1712i	−1.68668	+	0.783385i
$664$		−	2.18759i		−	0.0848949i
$665$		0			0
$666$	41.0056	+	71.0239i	1.58894	+	2.75212i
$667$	15.7407	−	4.21770i	0.609482	−	0.163310i
$668$	−6.00925			−0.232505
$669$	−62.6875	+	16.7971i	−2.42364	+	0.649412i
$670$		0			0
$671$	15.7428	+	15.7428i	0.607744	+	0.607744i
$672$	−6.60380	−	24.6457i	−0.254747	−	0.950729i
$673$	−10.2742	−	2.75296i	−0.396040	−	0.106119i	0.0553019	−	0.998470i	$-0.482388\pi$
$673$	−10.2742	−	2.75296i	−0.396040	−	0.106119i	−0.451342	+	0.892351i	$0.649055\pi$
$674$	20.0476	+	5.37175i	0.772207	+	0.206912i
$675$		0			0
$676$	4.85679	+	13.4715i	0.186800	+	0.518136i
$677$	−4.88408	+	4.88408i	−0.187710	+	0.187710i	−0.794706	−	0.606995i	$-0.792375\pi$
$677$	−4.88408	+	4.88408i	−0.187710	+	0.187710i	0.606995	+	0.794706i	$0.292375\pi$
$678$	−32.9198	−	57.0188i	−1.26428	−	2.18979i
$679$	19.0677	−	11.0088i	0.731752	−	0.422477i
$680$		0			0
$681$	−25.7990	+	25.7990i	−0.988620	+	0.988620i
$682$	1.74151	+	1.00546i	0.0666860	+	0.0385012i
$683$	−40.5438	−	23.4080i	−1.55137	−	0.895681i	−0.998031	−	0.0627219i	$-0.980022\pi$
$683$	−40.5438	−	23.4080i	−1.55137	−	0.895681i	−0.553334	−	0.832959i	$-0.686645\pi$
$684$	13.9020	−	13.9020i	0.531555	−	0.531555i
$685$		0			0
$686$	−25.5816	+	14.7696i	−0.976712	+	0.563905i
$687$	−29.3275	−	50.7967i	−1.11891	−	1.93802i
$688$	19.5577	−	19.5577i	0.745630	−	0.745630i
$689$	−1.02626	+	2.80631i	−0.0390973	+	0.106912i
$690$		0			0
$691$	30.4266	+	8.15279i	1.15748	+	0.310147i	0.785960	−	0.618277i	$-0.212169\pi$
$691$	30.4266	+	8.15279i	1.15748	+	0.310147i	0.371523	+	0.928424i	$0.378836\pi$
$692$	21.5974	+	5.78701i	0.821011	+	0.219989i
$693$	10.1083	+	37.7246i	0.383982	+	1.43304i
$694$	−13.3635	−	13.3635i	−0.507273	−	0.507273i
$695$		0			0
$696$	−14.2332	+	3.81379i	−0.539510	+	0.144561i
$697$	46.2265			1.75095
$698$	40.5146	−	10.8558i	1.53350	−	0.410900i
$699$	−0.0237138	−	0.0410735i	−0.000896938	−	0.00155354i
$700$		0			0
$701$			5.09953i			0.192607i	0.995352	+	0.0963034i	$0.0307019\pi$
$701$			5.09953i			0.192607i	−0.995352	+	0.0963034i	$0.969298\pi$
$702$	95.1671	−	16.6311i	3.59185	−	0.627699i
$703$	−10.0161	−	10.0161i	−0.377766	−	0.377766i
$704$	−0.0728169	+	0.271756i	−0.00274439	+	0.0102422i
$705$		0			0
$706$	−39.4538	−	22.7787i	−1.48486	−	0.857286i
$707$			3.62996i			0.136519i
$708$	6.10123	−	10.5676i	0.229298	−	0.397156i
$709$	11.1632	+	41.6615i	0.419241	+	1.56463i	0.776186	+	0.630504i	$0.217152\pi$
$709$	11.1632	+	41.6615i	0.419241	+	1.56463i	−0.356945	+	0.934125i	$0.616182\pi$
$710$		0			0
$711$	−13.1778	+	22.8247i	−0.494208	+	0.855993i
$712$	−0.464249	+	1.73260i	−0.0173985	+	0.0649319i
$713$	−1.53998	+	0.889107i	−0.0576726	+	0.0332973i
$714$	32.5074			1.21656
$715$		0			0
$716$	−1.06895			−0.0399485
$717$	−35.1249	+	20.2793i	−1.31176	+	0.757346i
$718$	−12.4933	+	46.6258i	−0.466248	+	1.74006i
$719$	26.2618	−	45.4868i	0.979400	−	1.69637i	0.314824	−	0.949150i	$-0.398054\pi$
$719$	26.2618	−	45.4868i	0.979400	−	1.69637i	0.664576	−	0.747221i	$-0.268612\pi$
$720$		0			0
$721$	0.488814	+	1.82428i	0.0182044	+	0.0679397i
$722$	11.9502	−	20.6983i	0.444739	−	0.770311i
$723$			72.8453i			2.70915i
$724$	−17.3786	−	10.0336i	−0.645872	−	0.372894i
$725$		0			0
$726$	−3.65873	+	13.6546i	−0.135788	+	0.506769i
$727$	3.04083	+	3.04083i	0.112778	+	0.112778i	0.761244	−	0.648466i	$-0.224589\pi$
$727$	3.04083	+	3.04083i	0.112778	+	0.112778i	−0.648466	+	0.761244i	$0.724589\pi$
$728$	−0.703077	+	7.89758i	−0.0260578	+	0.292704i
$729$		−	55.4569i		−	2.05396i
$730$		0			0
$731$	11.2742	+	19.5275i	0.416991	+	0.722250i
$732$	−21.0828	+	5.64912i	−0.779243	+	0.208797i
$733$	25.6949			0.949061			0.474531	−	0.880239i	$-0.342618\pi$
$733$	25.6949			0.949061			0.474531	+	0.880239i	$0.342618\pi$
$734$	40.9504	−	10.9726i	1.51151	−	0.405007i
$735$		0			0
$736$	22.7156	+	22.7156i	0.837307	+	0.837307i
$737$	−1.25419	−	4.68068i	−0.0461985	−	0.172415i
$738$	−148.079	−	39.6777i	−5.45087	−	1.46056i
$739$	−16.5169	−	4.42570i	−0.607586	−	0.162802i	−0.0581076	−	0.998310i	$-0.518507\pi$
$739$	−16.5169	−	4.42570i	−0.607586	−	0.162802i	−0.549478	+	0.835508i	$0.685173\pi$
$740$		0			0
$741$	−24.8766	+	11.5540i	−0.913863	+	0.424447i
$742$	1.43434	−	1.43434i	0.0526563	−	0.0526563i
$743$	9.18480	+	15.9085i	0.336958	+	0.583628i	0.983859	−	0.178946i	$-0.0572688\pi$
$743$	9.18480	+	15.9085i	0.336958	+	0.583628i	−0.646901	+	0.762574i	$0.723935\pi$
$744$	1.39250	−	0.803960i	0.0510515	−	0.0294746i
$745$		0			0
$746$	28.9305	−	28.9305i	1.05922	−	1.05922i
$747$	−9.17154	−	5.29519i	−0.335569	−	0.193741i
$748$	14.2362	+	8.21926i	0.520526	+	0.300526i
$749$	−15.3314	+	15.3314i	−0.560196	+	0.560196i
$750$		0			0
$751$	−28.0217	+	16.1783i	−1.02252	+	0.590355i	−0.914834	−	0.403830i	$-0.867679\pi$
$751$	−28.0217	+	16.1783i	−1.02252	+	0.590355i	−0.107690	+	0.994184i	$0.534346\pi$
$752$	−12.6460	−	21.9036i	−0.461154	−	0.798742i
$753$	−2.79576	+	2.79576i	−0.101883	+	0.101883i
$754$	−18.0406	−	1.60605i	−0.657000	−	0.0584890i
$755$		0			0
$756$	−22.4992	−	6.02865i	−0.818288	−	0.219260i
$757$	0.589155	+	0.157864i	0.0214132	+	0.00573766i	0.269510	−	0.962998i	$-0.413138\pi$
$757$	0.589155	+	0.157864i	0.0214132	+	0.00573766i	−0.248097	+	0.968735i	$0.579805\pi$
$758$	12.6757	+	47.3062i	0.460401	+	1.71824i
$759$	−48.3879	−	48.3879i	−1.75637	−	1.75637i
$760$		0			0
$761$	11.9275	−	3.19596i	0.432371	−	0.115854i	−0.0360677	−	0.999349i	$-0.511483\pi$
$761$	11.9275	−	3.19596i	0.432371	−	0.115854i	0.468439	+	0.883496i	$0.344817\pi$
$762$	−111.659			−4.04496
$763$	−18.0732	+	4.84271i	−0.654295	+	0.175318i
$764$	9.01936	+	15.6220i	0.326309	+	0.565184i
$765$		0			0
$766$			29.7119i			1.07353i
$767$	−9.38300	+	7.84894i	−0.338801	+	0.283409i
$768$	−45.9191	−	45.9191i	−1.65696	−	1.65696i
$769$	−12.1625	+	45.3911i	−0.438591	+	1.63684i	0.293733	+	0.955888i	$0.405102\pi$
$769$	−12.1625	+	45.3911i	−0.438591	+	1.63684i	−0.732324	+	0.680956i	$0.761564\pi$
$770$		0			0
$771$	−36.0657	−	20.8225i	−1.29887	−	0.749905i
$772$			11.3407i			0.408161i
$773$	−17.0750	+	29.5748i	−0.614145	+	1.06373i	0.376389	+	0.926462i	$0.377166\pi$
$773$	−17.0750	+	29.5748i	−0.614145	+	1.06373i	−0.990534	+	0.137269i	$0.956168\pi$
$774$	−19.3540	−	72.2301i	−0.695665	−	2.59626i
$775$		0			0
$776$	12.5331	−	21.7080i	0.449913	−	0.779272i
$777$	−7.13986	+	26.6463i	−0.256141	+	0.955931i
$778$	−24.3349	+	14.0498i	−0.872449	+	0.503709i
$779$	26.4784			0.948688
$780$		0			0
$781$	20.1218			0.720014
$782$	−35.4449	+	20.4641i	−1.26751	+	0.731795i
$783$	−11.2320	+	41.9184i	−0.401399	+	1.49804i
$784$	−12.6449	+	21.9016i	−0.451603	+	0.782199i
$785$		0			0
$786$	−6.27545	−	23.4203i	−0.223838	−	0.835374i
$787$	−4.35267	+	7.53904i	−0.155156	+	0.268738i	−0.933116	−	0.359576i	$-0.882921\pi$
$787$	−4.35267	+	7.53904i	−0.155156	+	0.268738i	0.777960	+	0.628314i	$0.216255\pi$
$788$			13.6510i			0.486296i
$789$	33.4332	+	19.3027i	1.19026	+	0.687194i
$790$		0			0
$791$	4.11883	−	15.3717i	0.146449	−	0.546554i
$792$	31.4403	+	31.4403i	1.11718	+	1.11718i
$793$	21.7950	+	1.94028i	0.773962	+	0.0689014i
$794$			29.2484i			1.03799i
$795$		0			0
$796$	−2.36428	−	4.09505i	−0.0837997	−	0.145145i
$797$	28.2754	−	7.57637i	1.00157	−	0.268369i	0.279464	−	0.960156i	$-0.409843\pi$
$797$	28.2754	−	7.57637i	1.00157	−	0.268369i	0.722101	+	0.691787i	$0.243176\pi$
$798$	18.6201			0.659145
$799$	19.9164	−	5.33659i	0.704593	−	0.188795i
$800$		0			0
$801$	6.14025	+	6.14025i	0.216955	+	0.216955i
$802$	−8.34312	−	31.1370i	−0.294606	−	1.09948i
$803$	7.65409	+	2.05091i	0.270107	+	0.0723750i
$804$	4.58878	+	1.22956i	0.161834	+	0.0433632i
$805$		0			0
$806$	1.94687	−	0.340228i	0.0685756	−	0.0119840i
$807$	37.4836	−	37.4836i	1.31948	−	1.31948i
$808$	2.06630	+	3.57894i	0.0726922	+	0.125907i
$809$	−29.2507	+	16.8879i	−1.02840	+	0.593748i	−0.916526	−	0.399975i	$-0.869019\pi$
$809$	−29.2507	+	16.8879i	−1.02840	+	0.593748i	−0.111875	+	0.993722i	$0.535686\pi$
$810$		0			0
$811$	34.8970	−	34.8970i	1.22540	−	1.22540i	0.259712	−	0.965686i	$-0.416372\pi$
$811$	34.8970	−	34.8970i	1.22540	−	1.22540i	0.965686	−	0.259712i	$-0.0836277\pi$
$812$	3.78182	+	2.18343i	0.132716	+	0.0766235i
$813$	6.19561	+	3.57704i	0.217290	+	0.125452i
$814$	−27.7735	+	27.7735i	−0.973462	+	0.973462i
$815$		0			0
$816$	57.3902	−	33.1342i	2.00906	−	1.15993i
$817$	6.45783	+	11.1853i	0.225931	+	0.391324i
$818$	−15.3639	+	15.3639i	−0.537186	+	0.537186i
$819$	31.4091	+	22.0643i	1.09752	+	0.770988i
$820$		0			0
$821$	−20.4287	−	5.47385i	−0.712966	−	0.191039i	−0.115935	−	0.993257i	$-0.536986\pi$
$821$	−20.4287	−	5.47385i	−0.712966	−	0.191039i	−0.597031	+	0.802218i	$0.703653\pi$
$822$	−62.3301	−	16.7013i	−2.17401	−	0.582525i
$823$	−13.3506	−	49.8251i	−0.465373	−	1.73679i	−0.655651	−	0.755064i	$-0.727606\pi$
$823$	−13.3506	−	49.8251i	−0.465373	−	1.73679i	0.190278	−	0.981730i	$-0.439061\pi$
$824$	1.52039	+	1.52039i	0.0529652	+	0.0529652i
$825$		0			0
$826$	8.02146	−	2.14934i	0.279102	−	0.0747852i
$827$	2.11823			0.0736582			0.0368291	−	0.999322i	$-0.488274\pi$
$827$	2.11823			0.0736582			0.0368291	+	0.999322i	$0.488274\pi$
$828$	46.5643	−	12.4769i	1.61822	−	0.433601i
$829$	−6.39435	−	11.0753i	−0.222085	−	0.384662i	0.733356	−	0.679845i	$-0.237953\pi$
$829$	−6.39435	−	11.0753i	−0.222085	−	0.384662i	−0.955441	+	0.295183i	$0.904620\pi$
$830$		0			0
$831$		−	60.9544i		−	2.11448i
$832$	0.116476	+	0.250780i	0.00403807	+	0.00869424i
$833$	−14.5785	−	14.5785i	−0.505115	−	0.505115i
$834$	2.48202	−	9.26302i	0.0859453	−	0.320752i
$835$		0			0
$836$	8.15445	+	4.70797i	0.282027	+	0.162829i
$837$		−	4.73549i		−	0.163683i
$838$	−15.8682	+	27.4846i	−0.548159	+	0.949439i
$839$	8.24394	+	30.7668i	0.284612	+	1.06219i	0.949122	+	0.314908i	$0.101974\pi$
$839$	8.24394	+	30.7668i	0.284612	+	1.06219i	−0.664510	+	0.747280i	$0.731360\pi$
$840$		0			0
$841$	−10.4320	+	18.0688i	−0.359725	+	0.623062i
$842$	−8.18545	+	30.5485i	−0.282089	+	1.05277i
$843$	−31.0559	+	17.9301i	−1.06962	+	0.617546i
$844$	−29.5939			−1.01866
$845$		0			0
$846$	−68.3796			−2.35094
$847$	−2.95907	+	1.70842i	−0.101675	+	0.0587020i
$848$	1.07026	−	3.99426i	0.0367529	−	0.137164i
$849$	15.9425	−	27.6133i	0.547147	−	0.947686i
$850$		0			0
$851$	−8.98940	−	33.5489i	−0.308152	−	1.15004i
$852$	−9.86335	+	17.0838i	−0.337913	+	0.585282i
$853$		−	37.3304i		−	1.27817i	−0.769137	−	0.639083i	$-0.779314\pi$
$853$		−	37.3304i		−	1.27817i	0.769137	−	0.639083i	$-0.220686\pi$
$854$	−12.8640	−	7.42706i	−0.440198	−	0.254149i
$855$		0			0
$856$	−6.38871	+	23.8430i	−0.218362	+	0.814937i
$857$	8.71215	+	8.71215i	0.297601	+	0.297601i	0.840074	−	0.542472i	$-0.182512\pi$
$857$	8.71215	+	8.71215i	0.297601	+	0.297601i	−0.542472	+	0.840074i	$0.682512\pi$
$858$	32.0379	+	68.9796i	1.09375	+	2.35493i
$859$		−	3.04501i		−	0.103895i	−0.998650	−	0.0519473i	$-0.983457\pi$
$859$		−	3.04501i		−	0.103895i	0.998650	−	0.0519473i	$-0.0165428\pi$
$860$		0			0
$861$	−25.7834	−	44.6581i	−0.878695	−	1.52194i
$862$	12.4520	−	3.33652i	0.424118	−	0.113642i
$863$	−23.2413			−0.791142			−0.395571	−	0.918435i	$-0.629453\pi$
$863$	−23.2413			−0.791142			−0.395571	+	0.918435i	$0.629453\pi$
$864$	−82.6350	+	22.1420i	−2.81130	+	0.753285i
$865$		0			0
$866$	−11.0484	−	11.0484i	−0.375440	−	0.375440i
$867$	−0.382998	−	1.42937i	−0.0130073	−	0.0485439i
$868$	−0.460275	−	0.123330i	−0.0156228	−	0.00418611i
$869$	−12.1924	−	3.26696i	−0.413600	−	0.110824i
$870$		0			0
$871$	−3.89708	−	2.73763i	−0.132048	−	0.0927609i
$872$	−15.0626	+	15.0626i	−0.510082	+	0.510082i
$873$	−60.6744	−	105.091i	−2.05352	−	3.55680i
$874$	−20.3027	+	11.7218i	−0.686750	+	0.396495i
$875$		0			0
$876$	−5.49316	+	5.49316i	−0.185597	+	0.185597i
$877$	21.6468	+	12.4978i	0.730961	+	0.422021i	0.818774	−	0.574116i	$-0.194654\pi$
$877$	21.6468	+	12.4978i	0.730961	+	0.422021i	−0.0878124	+	0.996137i	$0.527988\pi$
$878$	36.2663	+	20.9383i	1.22393	+	0.706635i
$879$	77.9783	−	77.9783i	2.63014	−	2.63014i
$880$		0			0
$881$	−26.3994	+	15.2417i	−0.889417	+	0.513505i	−0.873752	−	0.486372i	$-0.838320\pi$
$881$	−26.3994	+	15.2417i	−0.889417	+	0.513505i	−0.0156653	+	0.999877i	$0.504987\pi$
$882$	34.1867	+	59.2131i	1.15113	+	1.99381i
$883$	40.0008	−	40.0008i	1.34613	−	1.34613i	0.456315	−	0.889818i	$-0.349169\pi$
$883$	40.0008	−	40.0008i	1.34613	−	1.34613i	0.889818	−	0.456315i	$-0.150831\pi$
$884$	15.9149	−	2.78123i	0.535276	−	0.0935429i
$885$		0			0
$886$	−12.4770	−	3.34320i	−0.419173	−	0.112317i
$887$	43.7550	+	11.7241i	1.46915	+	0.393657i	0.902639	−	0.430398i	$-0.141627\pi$
$887$	43.7550	+	11.7241i	1.46915	+	0.393657i	0.566509	+	0.824055i	$0.308294\pi$
$888$	8.12851	+	30.3360i	0.272775	+	1.01801i
$889$	−19.0839	−	19.0839i	−0.640053	−	0.640053i
$890$		0			0
$891$	94.5952	−	25.3467i	3.16906	−	0.849147i
$892$	21.8962			0.733138
$893$	11.4081	−	3.05679i	0.381757	−	0.102291i
$894$	−34.6170	−	59.9584i	−1.15777	−	2.00531i
$895$		0			0
$896$		−	15.8174i		−	0.528422i
$897$	−66.9901	−	5.96375i	−2.23674	−	0.199124i
$898$	40.7645	+	40.7645i	1.36033	+	1.36033i
$899$	−0.229778	+	0.857542i	−0.00766351	+	0.0286006i
$900$		0			0
$901$	2.91949	+	1.68557i	0.0972623	+	0.0561544i
$902$		−	73.4214i		−	2.44467i
$903$	12.5766	−	21.7834i	0.418524	−	0.724905i
$904$	−4.68916	−	17.5002i	−0.155959	−	0.582047i
$905$		0			0
$906$	−24.9554	+	43.2241i	−0.829089	+	1.43602i
$907$	13.1976	−	49.2541i	0.438219	−	1.63545i	−0.295026	−	0.955489i	$-0.595328\pi$
$907$	13.1976	−	49.2541i	0.438219	−	1.63545i	0.733245	−	0.679965i	$-0.238005\pi$
$908$	10.6605	−	6.15487i	0.353783	−	0.204257i
$909$	20.0064			0.663571
$910$		0			0
$911$	−42.2460			−1.39967			−0.699836	−	0.714304i	$-0.746743\pi$
$911$	−42.2460			−1.39967			−0.699836	+	0.714304i	$0.746743\pi$
$912$	32.8729	−	18.9792i	1.08853	−	0.628464i
$913$	1.31275	−	4.89924i	0.0434456	−	0.162141i
$914$	−15.8811	+	27.5068i	−0.525299	+	0.909845i
$915$		0			0
$916$	5.12191	+	19.1152i	0.169233	+	0.631585i
$917$	2.93028	−	5.07539i	0.0967663	−	0.167604i
$918$		−	108.994i		−	3.59735i
$919$	51.0057	+	29.4481i	1.68252	+	0.971405i	0.959976	+	0.280082i	$0.0903615\pi$
$919$	51.0057	+	29.4481i	1.68252	+	0.971405i	0.722546	+	0.691323i	$0.242972\pi$
$920$		0			0
$921$	13.8853	−	51.8206i	0.457536	−	1.70755i
$922$	−2.60426	−	2.60426i	−0.0857667	−	0.0857667i
$923$	15.1687	−	12.6887i	0.499284	−	0.417654i
$924$		−	18.3376i		−	0.603261i
$925$		0			0
$926$	31.9067	+	55.2641i	1.04852	+	1.81609i
$927$	10.0545	−	2.69409i	0.330232	−	0.0884854i
$928$	16.0386			0.526493
$929$	−13.3277	+	3.57114i	−0.437267	+	0.117165i	−0.470736	−	0.882274i	$-0.656011\pi$
$929$	−13.3277	+	3.57114i	−0.437267	+	0.117165i	0.0334683	+	0.999440i	$0.489345\pi$
$930$		0			0
$931$	−8.35053	−	8.35053i	−0.273678	−	0.273678i
$932$	0.00414150	+	0.0154563i	0.000135659	+	0.000506288i
$933$	4.13767	+	1.10869i	0.135461	+	0.0362967i
$934$	68.8958	+	18.4606i	2.25434	+	0.604048i
$935$		0			0
$936$	43.5273	+	3.87499i	1.42273	+	0.126658i
$937$	8.81699	−	8.81699i	0.288038	−	0.288038i	−0.548266	−	0.836304i	$-0.684712\pi$
$937$	8.81699	−	8.81699i	0.288038	−	0.288038i	0.836304	+	0.548266i	$0.184712\pi$
$938$	1.61654	+	2.79992i	0.0527818	+	0.0914207i
$939$	−78.1831	+	45.1390i	−2.55141	+	1.47306i
$940$		0			0
$941$	−22.1697	+	22.1697i	−0.722711	+	0.722711i	−0.969157	−	0.246446i	$-0.920737\pi$
$941$	−22.1697	+	22.1697i	−0.722711	+	0.722711i	0.246446	+	0.969157i	$0.420737\pi$
$942$	68.4752	+	39.5342i	2.23104	+	1.28809i
$943$	56.2265	+	32.4624i	1.83099	+	1.05712i
$944$	11.9707	−	11.9707i	0.389614	−	0.389614i
$945$		0			0
$946$	31.0154	−	17.9068i	1.00840	−	0.582199i
$947$	5.23299	+	9.06381i	0.170049	+	0.294534i	0.938437	−	0.345451i	$-0.112274\pi$
$947$	5.23299	+	9.06381i	0.170049	+	0.294534i	−0.768388	+	0.639985i	$0.778941\pi$
$948$	8.75023	−	8.75023i	0.284194	−	0.284194i
$949$	7.06329	−	3.28057i	0.229284	−	0.106492i
$950$		0			0
$951$	110.246	+	29.5403i	3.57497	+	0.957911i
$952$	8.64046	+	2.31521i	0.280039	+	0.0750362i
$953$	2.94307	+	10.9837i	0.0953353	+	0.355796i	0.997070	−	0.0764935i	$-0.0243724\pi$
$953$	2.94307	+	10.9837i	0.0953353	+	0.355796i	−0.901735	+	0.432290i	$0.857706\pi$
$954$	−7.90533	−	7.90533i	−0.255945	−	0.255945i
$955$		0			0
$956$	13.2178	−	3.54169i	0.427494	−	0.114547i
$957$	−34.1648			−1.10439
$958$	−56.4952	+	15.1378i	−1.82528	+	0.489081i
$959$	−7.79856	−	13.5075i	−0.251828	−	0.436180i
$960$		0			0
$961$			30.9031i			0.996875i
$962$	−3.42306	+	38.4508i	−0.110364	+	1.23970i
$963$	84.4983	+	84.4983i	2.72292	+	2.72292i
$964$	6.36105	−	23.7398i	0.204876	−	0.764606i
$965$		0			0
$966$	39.5396	+	22.8282i	1.27216	+	0.734485i
$967$		−	21.5436i		−	0.692795i	−0.938088	−	0.346398i	$-0.887405\pi$
$967$		−	21.5436i		−	0.692795i	0.938088	−	0.346398i	$-0.112595\pi$
$968$	−1.94498	+	3.36881i	−0.0625141	+	0.108278i
$969$	8.00917	+	29.8906i	0.257292	+	0.960226i
$970$		0			0
$971$	11.5450	−	19.9965i	0.370497	−	0.641719i	−0.619145	−	0.785276i	$-0.712521\pi$
$971$	11.5450	−	19.9965i	0.370497	−	0.641719i	0.989642	+	0.143557i	$0.0458541\pi$
$972$	−11.8358	+	44.1720i	−0.379635	+	1.41682i
$973$	2.00738	−	1.15896i	0.0643537	−	0.0371546i
$974$	−36.9095			−1.18266
$975$		0			0
$976$	−30.2811			−0.969275
$977$	5.83384	−	3.36817i	0.186641	−	0.107757i	−0.403768	−	0.914861i	$-0.632300\pi$
$977$	5.83384	−	3.36817i	0.186641	−	0.107757i	0.590409	+	0.807104i	$0.298966\pi$
$978$	5.92999	−	22.1310i	0.189620	−	0.707672i
$979$	−2.07943	+	3.60167i	−0.0664587	+	0.115110i
$980$		0			0
$981$	26.6905	+	99.6102i	0.852161	+	3.18031i
$982$	−20.7399	+	35.9226i	−0.661837	+	1.14633i
$983$		−	12.0774i		−	0.385209i	−0.981276	−	0.192604i	$-0.938307\pi$
$983$		−	12.0774i		−	0.385209i	0.981276	−	0.192604i	$-0.0616934\pi$
$984$	−50.8419	−	29.3536i	−1.62078	−	0.935758i
$985$		0			0
$986$	−5.28867	+	19.7376i	−0.168426	+	0.628573i
$987$	−16.2642	−	16.2642i	−0.517694	−	0.517694i
$988$	9.11602	−	1.59308i	0.290019	−	0.0506827i
$989$			31.6691i			1.00702i
$990$		0			0
$991$	5.00080	+	8.66164i	0.158856	+	0.275146i	0.934456	−	0.356078i	$-0.115886\pi$
$991$	5.00080	+	8.66164i	0.158856	+	0.275146i	−0.775601	+	0.631224i	$0.782553\pi$
$992$	−1.69050	+	0.452967i	−0.0536733	+	0.0143817i
$993$	8.30749			0.263630
$994$	−12.9676	+	3.47466i	−0.411308	+	0.110210i
$995$		0			0
$996$	3.51607	+	3.51607i	0.111411	+	0.111411i
$997$	−3.81848	−	14.2508i	−0.120932	−	0.451326i	0.878730	−	0.477320i	$-0.158392\pi$
$997$	−3.81848	−	14.2508i	−0.120932	−	0.451326i	−0.999662	+	0.0259937i	$0.991725\pi$
$998$	43.8406	+	11.7471i	1.38775	+	0.371847i
$999$	89.3428	+	23.9393i	2.82668	+	0.757407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.c.93.3	yes	40
5.2	odd	4		325.2.s.c.132.3	✓	40
5.3	odd	4		325.2.s.c.132.8	yes	40
5.4	even	2	inner	325.2.x.c.93.8	yes	40
13.7	odd	12		325.2.s.c.293.3	yes	40
65.7	even	12	inner	325.2.x.c.7.3	yes	40
65.33	even	12	inner	325.2.x.c.7.8	yes	40
65.59	odd	12		325.2.s.c.293.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.132.3	✓	40	5.2	odd	4
325.2.s.c.132.8	yes	40	5.3	odd	4
325.2.s.c.293.3	yes	40	13.7	odd	12
325.2.s.c.293.8	yes	40	65.59	odd	12
325.2.x.c.7.3	yes	40	65.7	even	12	inner
325.2.x.c.7.8	yes	40	65.33	even	12	inner
325.2.x.c.93.3	yes	40	1.1	even	1	trivial
325.2.x.c.93.8	yes	40	5.4	even	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52518 + 0.880562i) q^{2} +(-0.845033 + 3.15371i) q^{3} +(0.550780 - 0.953979i) q^{4} +(-1.48821 - 5.55407i) q^{6} +(0.694909 - 1.20362i) q^{7} -1.58226i q^{8} +(-6.63370 - 3.82997i) q^{9} +(0.949498 - 3.54358i) q^{11} +(2.54314 + 2.54314i) q^{12} +(-1.51879 - 3.27006i) q^{13} +2.44764i q^{14} +(2.49484 + 4.32119i) q^{16} +(-3.92917 + 1.05282i) q^{17} +13.4901 q^{18} +(-2.25062 + 0.603051i) q^{19} +(3.20863 + 3.20863i) q^{21} +(1.67219 + 6.24068i) q^{22} +(-5.51848 - 1.47867i) q^{23} +(4.99000 + 1.33707i) q^{24} +(5.19592 + 3.65003i) q^{26} +(10.7583 - 10.7583i) q^{27} +(-0.765484 - 1.32586i) q^{28} +(-2.47021 + 1.42618i) q^{29} +(0.220086 - 0.220086i) q^{31} +(-4.86960 - 2.81146i) q^{32} +(10.3730 + 5.98888i) q^{33} +(5.06561 - 5.06561i) q^{34} +(-7.30742 + 4.21894i) q^{36} +(3.03968 + 5.26488i) q^{37} +(2.90157 - 2.90157i) q^{38} +(11.5962 - 2.02651i) q^{39} +(-10.9769 - 2.94124i) q^{41} +(-7.71914 - 2.06834i) q^{42} +(-1.43468 - 5.35430i) q^{43} +(-2.85753 - 2.85753i) q^{44} +(9.71874 - 2.60413i) q^{46} -5.06887 q^{47} +(-15.7360 + 4.21645i) q^{48} +(2.53420 + 4.38937i) q^{49} -13.2811i q^{51} +(-3.95609 - 0.352188i) q^{52} +(-0.586010 - 0.586010i) q^{53} +(-6.93496 + 25.8816i) q^{54} +(-1.90444 - 1.09953i) q^{56} -7.60737i q^{57} +(2.51168 - 4.35035i) q^{58} +(-0.878129 - 3.27722i) q^{59} +(-3.03437 + 5.25569i) q^{61} +(-0.141871 + 0.529470i) q^{62} +(-9.21963 + 5.32296i) q^{63} -0.0766898 q^{64} -21.0943 q^{66} +(1.14393 - 0.660446i) q^{67} +(-1.15974 + 4.32821i) q^{68} +(9.32660 - 16.1541i) q^{69} +(1.41960 + 5.29800i) q^{71} +(-6.06002 + 10.4963i) q^{72} +2.15999i q^{73} +(-9.27212 - 5.35326i) q^{74} +(-0.664297 + 2.47919i) q^{76} +(-3.60529 - 3.60529i) q^{77} +(-15.9018 + 13.3020i) q^{78} -3.44072i q^{79} +(13.3474 + 23.1184i) q^{81} +(19.3316 - 5.17990i) q^{82} +1.38257 q^{83} +(4.82822 - 1.29372i) q^{84} +(6.90294 + 6.90294i) q^{86} +(-2.41033 - 8.99549i) q^{87} +(-5.60687 - 1.50236i) q^{88} +(-1.09501 - 0.293408i) q^{89} +(-4.99132 - 0.444348i) q^{91} +(-4.45010 + 4.45010i) q^{92} +(0.508107 + 0.880067i) q^{93} +(7.73094 - 4.46346i) q^{94} +(12.9815 - 12.9815i) q^{96} +(13.7196 + 7.92101i) q^{97} +(-7.73023 - 4.46305i) q^{98} +(-19.8705 + 19.8705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) \) 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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