LMFDB - Embedded newform 475.2.j.b.349.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.50712647503417344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 13x^{10} + 119x^{8} - 552x^{6} + 1863x^{4} - 2450x^{2} + 2401 $ x^12 - 13x^10 + 119x^8 - 552x^6 + 1863x^4 - 2450*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.6
Root			$2.17114 - 1.25351i$ of defining polynomial
Character	$\chi$	$=$	475.349
Dual form			475.2.j.b.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17114 - 1.25351i) q^{2} +(1.05818 - 0.610938i) q^{3} +(2.14257 - 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876i q^{7} -5.72889i q^{8} +(-0.753509 + 1.30512i) q^{9} +O(q^{10})$	\(q+(2.17114 - 1.25351i) q^{2} +(1.05818 - 0.610938i) q^{3} +(2.14257 - 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876i q^{7} -5.72889i q^{8} +(-0.753509 + 1.30512i) q^{9} -0.778124 q^{11} -5.23591i q^{12} +(4.33013 + 2.50000i) q^{13} +(0.278124 + 0.481725i) q^{14} +(-2.89608 - 5.01616i) q^{16} +(-6.12912 + 3.53865i) q^{17} +3.77812i q^{18} +(-1.33281 - 4.15013i) q^{19} +(0.135553 + 0.234784i) q^{21} +(-1.68942 + 0.975385i) q^{22} +(-6.99515 - 4.03865i) q^{23} +(-3.50000 - 6.06218i) q^{24} +12.5351 q^{26} +5.50702i q^{27} +(0.823392 + 0.475385i) q^{28} +(0.110938 - 0.192150i) q^{29} +2.50702 q^{31} +(-2.65287 - 1.53163i) q^{32} +(-0.823392 + 0.475385i) q^{33} +(-8.87147 + 15.3658i) q^{34} +(3.22889 + 5.59261i) q^{36} +1.90466i q^{37} +(-8.09596 - 7.33983i) q^{38} +6.10938 q^{39} +(3.61796 + 6.26648i) q^{41} +(0.588608 + 0.339833i) q^{42} +(6.32128 - 3.64959i) q^{43} +(-1.66719 + 2.88765i) q^{44} -20.2500 q^{46} +(-2.41808 - 1.39608i) q^{47} +(-6.12912 - 3.53865i) q^{48} +6.95077 q^{49} +(-4.32379 + 7.48903i) q^{51} +(18.5552 - 10.7129i) q^{52} +(-3.79361 - 2.19024i) q^{53} +(6.90310 + 11.9565i) q^{54} +1.27111 q^{56} +(-3.94583 - 3.57730i) q^{57} -0.556248i q^{58} +(-1.39608 - 2.41808i) q^{59} +(6.29216 - 10.8983i) q^{61} +(5.44309 - 3.14257i) q^{62} +(-0.289574 - 0.167186i) q^{63} +3.90466 q^{64} +(-1.19180 + 2.06426i) q^{66} +(-9.15414 - 5.28514i) q^{67} +30.3273i q^{68} -9.86946 q^{69} +(4.92070 + 8.52289i) q^{71} +(7.47687 + 4.31678i) q^{72} +(-12.1913 + 7.03865i) q^{73} +(2.38750 + 4.13528i) q^{74} +(-18.2570 - 3.94583i) q^{76} -0.172647i q^{77} +(13.2643 - 7.65817i) q^{78} +(0.792161 + 1.37206i) q^{79} +(1.10392 + 1.91204i) q^{81} +(15.7102 + 9.07028i) q^{82} -9.52106i q^{83} +1.16172 q^{84} +(9.14959 - 15.8476i) q^{86} -0.271105i q^{87} +4.45779i q^{88} +(1.57028 - 2.71981i) q^{89} +(-0.554690 + 0.960752i) q^{91} +(-29.9752 + 17.3062i) q^{92} +(2.65287 - 1.53163i) q^{93} -7.00000 q^{94} -3.74293 q^{96} +(5.51004 - 3.18122i) q^{97} +(15.0911 - 8.71286i) q^{98} +(0.586324 - 1.01554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.17114	−	1.25351i	1.53523	−	0.886365i	0.536121	−	0.844141i	$-0.319889\pi$
$2$	2.17114	−	1.25351i	1.53523	−	0.886365i	0.999108	−	0.0422238i	$-0.0134442\pi$
$3$	1.05818	−	0.610938i	0.610938	−	0.352725i	−0.162394	−	0.986726i	$-0.551922\pi$
$3$	1.05818	−	0.610938i	0.610938	−	0.352725i	0.773333	+	0.634001i	$0.218588\pi$
$4$	2.14257	−	3.71104i	1.07129	−	1.85552i
$5$		0			0
$5$		0			0
$6$	1.53163	−	2.65287i	0.625287	−	1.08303i
$7$			0.221876i			0.0838613i	0.999121	+	0.0419307i	$0.0133509\pi$
$7$			0.221876i			0.0838613i	−0.999121	+	0.0419307i	$0.986649\pi$
$8$		−	5.72889i		−	2.02547i
$9$	−0.753509	+	1.30512i	−0.251170	+	0.435039i
$10$		0			0
$11$	−0.778124			−0.234613			−0.117307	−	0.993096i	$-0.537426\pi$
$11$	−0.778124			−0.234613			−0.117307	+	0.993096i	$0.537426\pi$
$12$		−	5.23591i		−	1.51148i
$13$	4.33013	+	2.50000i	1.20096	+	0.693375i	0.960769	−	0.277350i	$-0.0894562\pi$
$13$	4.33013	+	2.50000i	1.20096	+	0.693375i	0.240192	+	0.970725i	$0.422790\pi$
$14$	0.278124	+	0.481725i	0.0743317	+	0.128746i
$15$		0			0
$16$	−2.89608	−	5.01616i	−0.724020	−	1.25404i
$17$	−6.12912	+	3.53865i	−1.48653	+	0.858249i	−0.999882	−	0.0153485i	$-0.995114\pi$
$17$	−6.12912	+	3.53865i	−1.48653	+	0.858249i	−0.486649	+	0.873598i	$0.661781\pi$
$18$			3.77812i			0.890512i
$19$	−1.33281	−	4.15013i	−0.305769	−	0.952106i
$19$	−1.33281	−	4.15013i	−0.305769	−	0.952106i
$20$		0			0
$21$	0.135553	+	0.234784i	0.0295800	+	0.0512341i
$22$	−1.68942	+	0.975385i	−0.360185	+	0.207953i
$23$	−6.99515	−	4.03865i	−1.45859	−	0.842117i	−0.459647	−	0.888101i	$-0.652024\pi$
$23$	−6.99515	−	4.03865i	−1.45859	−	0.842117i	−0.998942	+	0.0459843i	$0.985358\pi$
$24$	−3.50000	−	6.06218i	−0.714435	−	1.23744i
$25$		0			0
$26$	12.5351			2.45833
$27$			5.50702i			1.05983i
$28$	0.823392	+	0.475385i	0.155606	+	0.0898394i
$29$	0.110938	−	0.192150i	0.0206007	−	0.0356814i	−0.855541	−	0.517735i	$-0.826775\pi$
$29$	0.110938	−	0.192150i	0.0206007	−	0.0356814i	0.876142	+	0.482053i	$0.160109\pi$
$30$		0			0
$31$	2.50702			0.450274			0.225137	−	0.974327i	$-0.427717\pi$
$31$	2.50702			0.450274			0.225137	+	0.974327i	$0.427717\pi$
$32$	−2.65287	−	1.53163i	−0.468965	−	0.270757i
$33$	−0.823392	+	0.475385i	−0.143334	+	0.0827540i
$34$	−8.87147	+	15.3658i	−1.52144	+	2.63522i
$35$		0			0
$36$	3.22889	+	5.59261i	0.538149	+	0.932102i
$37$			1.90466i			0.313124i	0.987668	+	0.156562i	$0.0500410\pi$
$37$			1.90466i			0.313124i	−0.987668	+	0.156562i	$0.949959\pi$
$38$	−8.09596	−	7.33983i	−1.31334	−	1.19068i
$39$	6.10938			0.978284
$40$		0			0
$41$	3.61796	+	6.26648i	0.565030	+	0.978661i	0.997047	+	0.0767950i	$0.0244687\pi$
$41$	3.61796	+	6.26648i	0.565030	+	0.978661i	−0.432017	+	0.901865i	$0.642198\pi$
$42$	0.588608	+	0.339833i	0.0908242	+	0.0524374i
$43$	6.32128	−	3.64959i	0.963985	−	0.556557i	0.0665881	−	0.997781i	$-0.478789\pi$
$43$	6.32128	−	3.64959i	0.963985	−	0.556557i	0.897397	+	0.441223i	$0.145455\pi$
$44$	−1.66719	+	2.88765i	−0.251338	+	0.435330i
$45$		0			0
$46$	−20.2500			−2.98569
$47$	−2.41808	−	1.39608i	−0.352714	−	0.203639i	0.313166	−	0.949698i	$-0.398610\pi$
$47$	−2.41808	−	1.39608i	−0.352714	−	0.203639i	−0.665880	+	0.746059i	$0.731944\pi$
$48$	−6.12912	−	3.53865i	−0.884663	−	0.510760i
$49$	6.95077			0.992967
$50$		0			0
$51$	−4.32379	+	7.48903i	−0.605452	+	1.04867i
$52$	18.5552	−	10.7129i	2.57314	−	1.48561i
$53$	−3.79361	−	2.19024i	−0.521093	−	0.300853i	0.216289	−	0.976329i	$-0.430605\pi$
$53$	−3.79361	−	2.19024i	−0.521093	−	0.300853i	−0.737382	+	0.675476i	$0.763938\pi$
$54$	6.90310	+	11.9565i	0.939393	+	1.62708i
$55$		0			0
$56$	1.27111			0.169859
$57$	−3.94583	−	3.57730i	−0.522637	−	0.473825i
$58$		−	0.556248i		−	0.0730389i
$59$	−1.39608	−	2.41808i	−0.181754	−	0.314808i	0.760724	−	0.649076i	$-0.224844\pi$
$59$	−1.39608	−	2.41808i	−0.181754	−	0.314808i	−0.942478	+	0.334268i	$0.891511\pi$
$60$		0			0
$61$	6.29216	−	10.8983i	0.805629	−	1.39539i	−0.110237	−	0.993905i	$-0.535161\pi$
$61$	6.29216	−	10.8983i	0.805629	−	1.39539i	0.915866	−	0.401484i	$-0.131506\pi$
$62$	5.44309	−	3.14257i	0.691274	−	0.399107i
$63$	−0.289574	−	0.167186i	−0.0364829	−	0.0210634i
$64$	3.90466			0.488082
$65$		0			0
$66$	−1.19180	+	2.06426i	−0.146700	+	0.254093i
$67$	−9.15414	−	5.28514i	−1.11836	−	0.645683i	−0.177375	−	0.984143i	$-0.556761\pi$
$67$	−9.15414	−	5.28514i	−1.11836	−	0.645683i	−0.940981	+	0.338460i	$0.890094\pi$
$68$			30.3273i			3.67772i
$69$	−9.86946			−1.18814
$70$		0			0
$71$	4.92070	+	8.52289i	0.583979	+	1.01148i	0.995002	+	0.0998563i	$0.0318383\pi$
$71$	4.92070	+	8.52289i	0.583979	+	1.01148i	−0.411023	+	0.911625i	$0.634828\pi$
$72$	7.47687	+	4.31678i	0.881158	+	0.508737i
$73$	−12.1913	+	7.03865i	−1.42688	+	0.823812i	−0.996874	−	0.0790121i	$-0.974823\pi$
$73$	−12.1913	+	7.03865i	−1.42688	+	0.823812i	−0.430010	+	0.902824i	$0.641490\pi$
$74$	2.38750	+	4.13528i	0.277542	+	0.480716i
$75$		0			0
$76$	−18.2570	−	3.94583i	−2.09422	−	0.452617i
$77$		−	0.172647i		−	0.0196750i
$78$	13.2643	−	7.65817i	1.50189	−	0.867117i
$79$	0.792161	+	1.37206i	0.0891251	+	0.154369i	0.907142	−	0.420826i	$-0.138260\pi$
$79$	0.792161	+	1.37206i	0.0891251	+	0.154369i	−0.818016	+	0.575195i	$0.804926\pi$
$80$		0			0
$81$	1.10392	+	1.91204i	0.122658	+	0.212449i
$82$	15.7102	+	9.07028i	1.73490	+	1.00165i
$83$		−	9.52106i		−	1.04507i	−0.852617	−	0.522536i	$-0.824986\pi$
$83$		−	9.52106i		−	1.04507i	0.852617	−	0.522536i	$-0.175014\pi$
$84$	1.16172			0.126755
$85$		0			0
$86$	9.14959	−	15.8476i	0.986626	−	1.70889i
$87$		−	0.271105i		−	0.0290655i
$88$			4.45779i			0.475202i
$89$	1.57028	−	2.71981i	0.166450	−	0.288300i	−0.770719	−	0.637175i	$-0.780103\pi$
$89$	1.57028	−	2.71981i	0.166450	−	0.288300i	0.937169	+	0.348875i	$0.113436\pi$
$90$		0			0
$91$	−0.554690	+	0.960752i	−0.0581474	+	0.100714i
$92$	−29.9752	+	17.3062i	−3.12513	+	1.80430i
$93$	2.65287	−	1.53163i	0.275089	−	0.158823i
$94$	−7.00000			−0.721995
$95$		0			0
$96$	−3.74293			−0.382011
$97$	5.51004	−	3.18122i	0.559460	−	0.323004i	−0.193469	−	0.981106i	$-0.561974\pi$
$97$	5.51004	−	3.18122i	0.559460	−	0.323004i	0.752929	+	0.658102i	$0.228641\pi$
$98$	15.0911	−	8.71286i	1.52443	−	0.880131i
$99$	0.586324	−	1.01554i	0.0589277	−	0.102066i
$100$		0			0
$101$	3.69726	−	6.40385i	0.367891	−	0.637206i	−0.621344	−	0.783538i	$-0.713413\pi$
$101$	3.69726	−	6.40385i	0.367891	−	0.637206i	0.989236	+	0.146331i	$0.0467465\pi$
$102$			21.6797i			2.14661i
$103$			12.2038i			1.20248i	0.799069	+	0.601240i	$0.205326\pi$
$103$			12.2038i			1.20248i	−0.799069	+	0.601240i	$0.794674\pi$
$104$	14.3222	−	24.8068i	1.40441	−	2.43251i
$105$		0			0
$106$	−10.9820			−1.06666
$107$			1.63355i			0.157921i	0.996878	+	0.0789607i	$0.0251602\pi$
$107$			1.63355i			0.157921i	−0.996878	+	0.0789607i	$0.974840\pi$
$108$	20.4368	+	11.7992i	1.96653	+	1.13538i
$109$	−3.80820	−	6.59600i	−0.364759	−	0.631782i	0.623978	−	0.781442i	$-0.285515\pi$
$109$	−3.80820	−	6.59600i	−0.364759	−	0.631782i	−0.988738	+	0.149660i	$0.952182\pi$
$110$		0			0
$111$	1.16363	+	2.01546i	0.110447	+	0.191299i
$112$	1.11297	−	0.642571i	0.105165	−	0.0607173i
$113$			12.4890i			1.17486i	0.809273	+	0.587432i	$0.199861\pi$
$113$			12.4890i			1.17486i	−0.809273	+	0.587432i	$0.800139\pi$
$114$	−13.0511	−	2.82070i	−1.22235	−	0.264183i
$115$		0			0
$116$	−0.475385	−	0.823392i	−0.0441384	−	0.0764500i
$117$	−6.52558	+	3.76755i	−0.603290	+	0.348310i
$118$	−6.06218	−	3.50000i	−0.558069	−	0.322201i
$119$	−0.785142	−	1.35991i	−0.0719739	−	0.124662i
$120$		0			0
$121$	−10.3945			−0.944957
$122$		−	31.5491i		−	2.85632i
$123$	7.65687	+	4.42070i	0.690397	+	0.398601i
$124$	5.37147	−	9.30365i	0.482372	−	0.835493i
$125$		0			0
$126$	−0.838276			−0.0746795
$127$	−11.2948	−	6.52106i	−1.00225	−	0.578650i	−0.0933378	−	0.995635i	$-0.529754\pi$
$127$	−11.2948	−	6.52106i	−1.00225	−	0.578650i	−0.908914	+	0.416984i	$0.863087\pi$
$128$	13.7833	−	7.95779i	1.21828	−	0.703376i
$129$	4.45935	−	7.72382i	0.392624	−	0.680044i
$130$		0			0
$131$	−3.55469	−	6.15690i	−0.310575	−	0.537931i	0.667912	−	0.744240i	$-0.267188\pi$
$131$	−3.55469	−	6.15690i	−0.310575	−	0.537931i	−0.978487	+	0.206309i	$0.933855\pi$
$132$			4.07419i			0.354613i
$133$	0.920816	−	0.295720i	0.0798448	−	0.0256422i
$134$	−26.4999			−2.28924
$135$		0			0
$136$	20.2726	+	35.1131i	1.73836	+	3.01092i
$137$	4.69880	+	2.71286i	0.401446	+	0.231775i	0.687108	−	0.726556i	$-0.258880\pi$
$137$	4.69880	+	2.71286i	0.401446	+	0.231775i	−0.285662	+	0.958331i	$0.592213\pi$
$138$	−21.4280	+	12.3715i	−1.82407	+	1.05313i
$139$	1.78514	−	3.09196i	0.151414	−	0.262256i	−0.780334	−	0.625363i	$-0.784951\pi$
$139$	1.78514	−	3.09196i	0.151414	−	0.262256i	0.931747	+	0.363107i	$0.118284\pi$
$140$		0			0
$141$	−3.41168			−0.287315
$142$	21.3671	+	12.3363i	1.79308	+	1.03524i
$143$	−3.36938	−	1.94531i	−0.281761	−	0.162675i
$144$	8.72889			0.727408
$145$		0			0
$146$	−17.6460	+	30.5638i	−1.46040	+	2.52948i
$147$	7.35514	−	4.24649i	0.606642	−	0.350245i
$148$	7.06826	+	4.08086i	0.581007	+	0.335445i
$149$	−0.468367	−	0.811235i	−0.0383701	−	0.0664590i	0.846203	−	0.532861i	$-0.178883\pi$
$149$	−0.468367	−	0.811235i	−0.0383701	−	0.0664590i	−0.884573	+	0.466402i	$0.845550\pi$
$150$		0			0
$151$	−0.971925			−0.0790942			−0.0395471	−	0.999218i	$-0.512592\pi$
$151$	−0.971925			−0.0790942			−0.0395471	+	0.999218i	$0.512592\pi$
$152$	−23.7757	+	7.63555i	−1.92846	+	0.619325i
$153$		−	10.6656i		−	0.862265i
$154$	−0.216415	−	0.374841i	−0.0174392	−	0.0302056i
$155$		0			0
$156$	13.0898	−	22.6722i	1.04802	−	1.81523i
$157$	−2.35114	+	1.35743i	−0.187641	+	0.108335i	−0.590878	−	0.806761i	$-0.701218\pi$
$157$	−2.35114	+	1.35743i	−0.187641	+	0.108335i	0.403237	+	0.915096i	$0.367885\pi$
$158$	3.43979	+	1.98596i	0.273655	+	0.157995i
$159$	−5.35241			−0.424474
$160$		0			0
$161$	0.896081	−	1.55206i	0.0706210	−	0.122319i
$162$	4.79353	+	2.76755i	0.376615	+	0.217439i
$163$		−	3.20384i		−	0.250944i	−0.992097	−	0.125472i	$-0.959956\pi$
$163$		−	3.20384i		−	0.250944i	0.992097	−	0.125472i	$-0.0400445\pi$
$164$	31.0069			2.42123
$165$		0			0
$166$	−11.9347	−	20.6716i	−0.926315	−	1.60442i
$167$	8.85240	+	5.11094i	0.685020	+	0.395496i	0.801744	−	0.597668i	$-0.203906\pi$
$167$	8.85240	+	5.11094i	0.685020	+	0.395496i	−0.116724	+	0.993164i	$0.537239\pi$
$168$	1.34505	−	0.776567i	0.103773	−	0.0599134i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	6.42070	+	1.38769i	0.491003	+	0.106119i
$172$		−	31.2780i		−	2.38493i
$173$	−2.30850	+	1.33281i	−0.175512	+	0.101332i	−0.585182	−	0.810902i	$-0.698977\pi$
$173$	−2.30850	+	1.33281i	−0.175512	+	0.101332i	0.409670	+	0.912234i	$0.365644\pi$
$174$	−0.339833	−	0.588608i	−0.0257627	−	0.0446222i
$175$		0			0
$176$	2.25351	+	3.90319i	0.169865	+	0.294214i
$177$	−2.95460	−	1.70584i	−0.222081	−	0.128219i
$178$		−	7.87347i		−	0.590141i
$179$	12.9367			0.966937			0.483468	−	0.875362i	$-0.339377\pi$
$179$	12.9367			0.966937			0.483468	+	0.875362i	$0.339377\pi$
$180$		0			0
$181$	9.30620	−	16.1188i	0.691724	−	1.19810i	−0.279548	−	0.960132i	$-0.590185\pi$
$181$	9.30620	−	16.1188i	0.691724	−	1.19810i	0.971273	−	0.237970i	$-0.0764820\pi$
$182$			2.78124i			0.206159i
$183$		−	15.3765i		−	1.13666i
$184$	−23.1370	+	40.0745i	−1.70568	+	2.95433i
$185$		0			0
$186$	3.83983	−	6.65079i	0.281550	−	0.487659i
$187$	4.76922	−	2.75351i	0.348760	−	0.201357i
$188$	−10.3618	+	5.98240i	−0.755714	+	0.436312i
$189$	−1.22188			−0.0888784
$190$		0			0
$191$	−23.0421			−1.66727			−0.833634	−	0.552317i	$-0.813744\pi$
$191$	−23.0421			−1.66727			−0.833634	+	0.552317i	$0.813744\pi$
$192$	4.13181	−	2.38550i	0.298188	−	0.172159i
$193$	−14.7894	+	8.53865i	−1.06456	+	0.614626i	−0.926691	−	0.375824i	$-0.877360\pi$
$193$	−14.7894	+	8.53865i	−1.06456	+	0.614626i	−0.137872	+	0.990450i	$0.544026\pi$
$194$	7.97539	−	13.8138i	0.572599	−	0.991771i
$195$		0			0
$196$	14.8925	−	25.7946i	1.06375	−	1.84247i
$197$			8.82024i			0.628416i	0.949354	+	0.314208i	$0.101739\pi$
$197$			8.82024i			0.628416i	−0.949354	+	0.314208i	$0.898261\pi$
$198$		−	2.93985i		−	0.208926i
$199$	−1.42771	+	2.47287i	−0.101208	+	0.175297i	−0.912183	−	0.409784i	$-0.865604\pi$
$199$	−1.42771	+	2.47287i	−0.101208	+	0.175297i	0.810975	+	0.585081i	$0.198937\pi$
$200$		0			0
$201$	−12.9156			−0.910995
$202$		−	18.5382i		−	1.30434i
$203$	0.0426336	+	0.0246145i	0.00299229	+	0.00172760i
$204$	18.5281	+	32.0916i	1.29722	+	2.24686i
$205$		0			0
$206$	15.2976	+	26.4963i	1.06584	+	1.84608i
$207$	10.5418	−	6.08632i	0.732707	−	0.423029i
$208$		−	28.9608i		−	2.00807i
$209$	1.03709	+	3.22932i	0.0717373	+	0.223377i
$210$		0			0
$211$	6.44375	+	11.1609i	0.443606	+	0.768348i	0.997954	−	0.0639367i	$-0.0203656\pi$
$211$	6.44375	+	11.1609i	0.443606	+	0.768348i	−0.554348	+	0.832285i	$0.687032\pi$
$212$	−16.2562	+	9.38550i	−1.11648	+	0.644599i
$213$	10.4139	+	6.01248i	0.713550	+	0.411968i
$214$	2.04767	+	3.54667i	0.139976	+	0.242445i
$215$		0			0
$216$	31.5491			2.14665
$217$			0.556248i			0.0377606i
$218$	−16.5363	−	9.54723i	−1.11998	−	0.646620i
$219$	−8.60036	+	14.8963i	−0.581159	+	1.00660i
$220$		0			0
$221$	−35.3865			−2.38035
$222$	5.05280	+	2.91724i	0.339122	+	0.195792i
$223$	17.9334	−	10.3539i	1.20091	−	0.693346i	0.240153	−	0.970735i	$-0.422802\pi$
$223$	17.9334	−	10.3539i	1.20091	−	0.693346i	0.960758	+	0.277389i	$0.0894689\pi$
$224$	0.339833	−	0.588608i	0.0227060	−	0.0393280i
$225$		0			0
$226$	15.6551	+	27.1153i	1.04136	+	1.80369i
$227$		−	4.00000i		−	0.265489i	−0.991150	−	0.132745i	$-0.957621\pi$
$227$		−	4.00000i		−	0.265489i	0.991150	−	0.132745i	$-0.0423790\pi$
$228$	−21.7297	+	6.97850i	−1.43909	+	0.462162i
$229$	−3.53910			−0.233870			−0.116935	−	0.993140i	$-0.537307\pi$
$229$	−3.53910			−0.233870			−0.116935	+	0.993140i	$0.537307\pi$
$230$		0			0
$231$	−0.105477	−	0.182691i	−0.00693986	−	0.0120202i
$232$	−1.10081	−	0.635553i	−0.0722717	−	0.0417261i
$233$	−17.1344	+	9.89252i	−1.12251	+	0.648081i	−0.942040	−	0.335500i	$-0.891095\pi$
$233$	−17.1344	+	9.89252i	−1.12251	+	0.648081i	−0.180468	+	0.983581i	$0.557761\pi$
$234$	−9.44531	+	16.3598i	−0.617459	+	1.06947i
$235$		0			0
$236$	−11.9648			−0.778843
$237$	1.67649	+	0.967923i	0.108900	+	0.0628733i
$238$	−3.40931	−	1.96837i	−0.220993	−	0.127590i
$239$	−23.7741			−1.53782			−0.768910	−	0.639357i	$-0.779201\pi$
$239$	−23.7741			−1.53782			−0.768910	+	0.639357i	$0.779201\pi$
$240$		0			0
$241$	2.27111	−	3.93367i	0.146295	−	0.253390i	−0.783561	−	0.621315i	$-0.786599\pi$
$241$	2.27111	−	3.93367i	0.146295	−	0.253390i	0.929855	+	0.367926i	$0.119932\pi$
$242$	−22.5680	+	13.0296i	−1.45072	+	0.837576i
$243$	−11.9714	−	6.91168i	−0.767964	−	0.443384i
$244$	−26.9628	−	46.7010i	−1.72612	−	2.98972i
$245$		0			0
$246$	22.1655			1.41322
$247$	4.60408	−	21.3026i	0.292950	−	1.35545i
$248$		−	14.3624i		−	0.912016i
$249$	−5.81678	−	10.0750i	−0.368623	−	0.638474i
$250$		0			0
$251$	9.75151	−	16.8901i	0.615510	−	1.06609i	−0.374785	−	0.927112i	$-0.622284\pi$
$251$	9.75151	−	16.8901i	0.615510	−	1.06609i	0.990295	−	0.138982i	$-0.0443832\pi$
$252$	−1.24087	+	0.716415i	−0.0781673	+	0.0451299i
$253$	5.44309	+	3.14257i	0.342204	+	0.197572i
$254$	−32.6968			−2.05158
$255$		0			0
$256$	16.0457	−	27.7919i	1.00285	−	1.73699i
$257$	1.52774	+	0.882043i	0.0952980	+	0.0550203i	0.546892	−	0.837203i	$-0.315811\pi$
$257$	1.52774	+	0.882043i	0.0952980	+	0.0550203i	−0.451594	+	0.892224i	$0.649144\pi$
$258$		−	22.3593i		−	1.39203i
$259$	−0.422598			−0.0262590
$260$		0			0
$261$	0.167186	+	0.289574i	0.0103485	+	0.0179242i
$262$	−15.4355	−	8.91168i	−0.953607	−	0.550565i
$263$	−5.60477	+	3.23591i	−0.345605	+	0.199535i	−0.662748	−	0.748843i	$-0.730610\pi$
$263$	−5.60477	+	3.23591i	−0.345605	+	0.199535i	0.317143	+	0.948378i	$0.397276\pi$
$264$	2.72343	+	4.71713i	0.167616	+	0.290319i
$265$		0			0
$266$	1.62853	−	1.79630i	0.0998518	−	0.110138i
$267$		−	3.83739i		−	0.234844i
$268$	−39.2268	+	22.6476i	−2.39616	+	1.38342i
$269$	14.2429	+	24.6695i	0.868407	+	1.50412i	0.863624	+	0.504136i	$0.168189\pi$
$269$	14.2429	+	24.6695i	0.868407	+	1.50412i	0.00478280	+	0.999989i	$0.498478\pi$
$270$		0			0
$271$	0.246491	+	0.426934i	0.0149732	+	0.0259344i	0.873415	−	0.486977i	$-0.161900\pi$
$271$	0.246491	+	0.426934i	0.0149732	+	0.0259344i	−0.858442	+	0.512911i	$0.828567\pi$
$272$	35.5009	+	20.4964i	2.15256	+	1.24278i
$273$			1.35553i			0.0820402i
$274$	13.6024			0.821749
$275$		0			0
$276$	−21.1460	+	36.6260i	−1.27284	+	2.20463i
$277$			8.78905i			0.528083i	0.964511	+	0.264041i	$0.0850555\pi$
$277$			8.78905i			0.528083i	−0.964511	+	0.264041i	$0.914944\pi$
$278$		−	8.95077i		−	0.536832i
$279$	−1.88906	+	3.27195i	−0.113095	+	0.195887i
$280$		0			0
$281$	2.37147	−	4.10750i	0.141470	−	0.245033i	−0.786581	−	0.617488i	$-0.788151\pi$
$281$	2.37147	−	4.10750i	0.141470	−	0.245033i	0.928050	+	0.372455i	$0.121484\pi$
$282$	−7.40723	+	4.27657i	−0.441094	+	0.254666i
$283$	14.6094	−	8.43473i	0.868438	−	0.501393i	0.00160901	−	0.999999i	$-0.499488\pi$
$283$	14.6094	−	8.43473i	0.868438	−	0.501393i	0.866829	+	0.498606i	$0.166155\pi$
$284$	42.1718			2.50243
$285$		0			0
$286$	−9.75385			−0.576758
$287$	−1.39038	+	0.802738i	−0.0820717	+	0.0473841i
$288$	3.99792	−	2.30820i	0.235580	−	0.136012i
$289$	16.5441	−	28.6552i	0.973183	−	1.68560i
$290$		0			0
$291$	3.88706	−	6.73259i	0.227864	−	0.394671i
$292$			60.3233i			3.53015i
$293$			11.6336i			0.679639i	0.940491	+	0.339820i	$0.110366\pi$
$293$			11.6336i			0.679639i	−0.940491	+	0.339820i	$0.889634\pi$
$294$	10.6460	−	18.4395i	0.620889	−	1.07541i
$295$		0			0
$296$	10.9116			0.634223
$297$		−	4.28514i		−	0.248649i
$298$	−2.03378	−	1.17420i	−0.117814	−	0.0680198i
$299$	−20.1933	−	34.9758i	−1.16781	−	2.02270i
$300$		0			0
$301$	0.809757	+	1.40254i	0.0466736	+	0.0808411i
$302$	−2.11019	+	1.21832i	−0.121428	+	0.0701063i
$303$		−	9.03519i		−	0.519058i
$304$	−16.9578	+	18.7047i	−0.972596	+	1.07279i
$305$		0			0
$306$	−13.3695	−	23.1566i	−0.764281	−	1.32377i
$307$	−5.10143	+	2.94531i	−0.291154	+	0.168098i	−0.638462	−	0.769653i	$-0.720429\pi$
$307$	−5.10143	+	2.94531i	−0.291154	+	0.168098i	0.347308	+	0.937751i	$0.387096\pi$
$308$	−0.640701	−	0.369909i	−0.0365073	−	0.0210775i
$309$	7.45579	+	12.9138i	0.424145	+	0.734641i
$310$		0			0
$311$	14.8202			0.840378			0.420189	−	0.907437i	$-0.361964\pi$
$311$	14.8202			0.840378			0.420189	+	0.907437i	$0.361964\pi$
$312$		−	35.0000i		−	1.98148i
$313$	5.10489	+	2.94731i	0.288546	+	0.166592i	0.637286	−	0.770628i	$-0.280057\pi$
$313$	5.10489	+	2.94731i	0.288546	+	0.166592i	−0.348740	+	0.937219i	$0.613390\pi$
$314$	−3.40310	+	5.89434i	−0.192048	+	0.332637i
$315$		0			0
$316$	6.78905			0.381914
$317$	−3.60146	−	2.07930i	−0.202278	−	0.116785i	0.395439	−	0.918492i	$-0.370592\pi$
$317$	−3.60146	−	2.07930i	−0.202278	−	0.116785i	−0.597718	+	0.801707i	$0.703926\pi$
$318$	−11.6208	+	6.70930i	−0.651665	+	0.376239i
$319$	−0.0863236	+	0.149517i	−0.00483319	+	0.00837133i
$320$		0			0
$321$	0.997999	+	1.72858i	0.0557029	+	0.0964802i
$322$		−	4.49298i		−	0.250384i
$323$	22.8549	+	20.7203i	1.27168	+	1.15291i
$324$	9.46090			0.525606
$325$		0			0
$326$	−4.01604	−	6.95598i	−0.222428	−	0.385256i
$327$	−8.05949	−	4.65315i	−0.445691	−	0.257320i
$328$	35.9000	−	20.7269i	1.98225	−	1.14445i
$329$	0.309757	−	0.536515i	0.0170775	−	0.0295790i
$330$		0			0
$331$	10.6797			0.587008			0.293504	−	0.955958i	$-0.405179\pi$
$331$	10.6797			0.587008			0.293504	+	0.955958i	$0.405179\pi$
$332$	−35.3330	−	20.3995i	−1.93915	−	1.11957i
$333$	−2.48580	−	1.43518i	−0.136221	−	0.0786472i
$334$	25.6264			1.40222
$335$		0			0
$336$	0.785142	−	1.35991i	0.0428330	−	0.0741890i
$337$	22.8157	−	13.1726i	1.24285	−	0.717560i	0.273177	−	0.961964i	$-0.411926\pi$
$337$	22.8157	−	13.1726i	1.24285	−	0.717560i	0.969673	+	0.244404i	$0.0785923\pi$
$338$	26.0537	+	15.0421i	1.41713	+	0.818183i
$339$	7.62999	+	13.2155i	0.414404	+	0.717769i
$340$		0			0
$341$	−1.95077			−0.105640
$342$	15.6797	−	5.03554i	0.847862	−	0.272291i
$343$			3.09534i			0.167133i
$344$	−20.9081	−	36.2139i	−1.12729	−	1.95252i
$345$		0			0
$346$	−3.34139	+	5.78746i	−0.179634	+	0.311136i
$347$	14.6215	−	8.44175i	0.784925	−	0.453177i	−0.0532476	−	0.998581i	$-0.516957\pi$
$347$	14.6215	−	8.44175i	0.784925	−	0.453177i	0.838173	+	0.545404i	$0.183624\pi$
$348$	−1.00608	−	0.580862i	−0.0539317	−	0.0311375i
$349$	−4.61640			−0.247110			−0.123555	−	0.992338i	$-0.539430\pi$
$349$	−4.61640			−0.247110			−0.123555	+	0.992338i	$0.539430\pi$
$350$		0			0
$351$	−13.7675	+	23.8461i	−0.734857	+	1.27281i
$352$	2.06426	+	1.19180i	0.110025	+	0.0635232i
$353$		−	24.9508i		−	1.32800i	−0.747735	−	0.663998i	$-0.768858\pi$
$353$		−	24.9508i		−	1.32800i	0.747735	−	0.663998i	$-0.231142\pi$
$354$	−8.55313			−0.454594
$355$		0			0
$356$	−6.72889	−	11.6548i	−0.356631	−	0.617703i
$357$	−1.66164	−	0.959347i	−0.0879432	−	0.0507740i
$358$	28.0875	−	16.2163i	1.48447	−	0.857059i
$359$	5.90110	+	10.2210i	0.311448	+	0.539444i	0.978676	−	0.205410i	$-0.0658527\pi$
$359$	5.90110	+	10.2210i	0.311448	+	0.539444i	−0.667228	+	0.744854i	$0.732519\pi$
$360$		0			0
$361$	−15.4472	+	11.0627i	−0.813011	+	0.582248i
$362$		−	46.6616i		−	2.45248i
$363$	−10.9992	+	6.35041i	−0.577310	+	0.333310i
$364$	2.37693	+	4.11696i	0.124585	+	0.215787i
$365$		0			0
$366$	−19.2746	−	33.3845i	−1.00750	−	1.74504i
$367$	22.7183	+	13.1164i	1.18588	+	0.684670i	0.957368	−	0.288870i	$-0.0932795\pi$
$367$	22.7183	+	13.1164i	1.18588	+	0.684670i	0.228516	+	0.973540i	$0.426613\pi$
$368$			46.7850i			2.43884i
$369$	−10.9047			−0.567674
$370$		0			0
$371$	0.485963	−	0.841712i	0.0252299	−	0.0436995i
$372$		−	13.1265i		−	0.680579i
$373$			11.9960i			0.621129i	0.950552	+	0.310565i	$0.100518\pi$
$373$			11.9960i			0.621129i	−0.950552	+	0.310565i	$0.899482\pi$
$374$	6.90310	−	11.9565i	0.356951	−	0.618257i
$375$		0			0
$376$	−7.99800	+	13.8529i	−0.412465	+	0.714411i
$377$	0.960752	−	0.554690i	0.0494812	−	0.0285680i
$378$	−2.65287	+	1.53163i	−0.136449	+	0.0787787i
$379$	−0.313217			−0.0160889			−0.00804444	−	0.999968i	$-0.502561\pi$
$379$	−0.313217			−0.0160889			−0.00804444	+	0.999968i	$0.502561\pi$
$380$		0			0
$381$	−15.9358			−0.816418
$382$	−50.0277	+	28.8835i	−2.55964	+	1.47781i
$383$	26.0572	−	15.0441i	1.33146	−	0.768718i	0.345936	−	0.938258i	$-0.387561\pi$
$383$	26.0572	−	15.0441i	1.33146	−	0.768718i	0.985523	+	0.169540i	$0.0542282\pi$
$384$	9.72343	−	16.8415i	0.496197	−	0.859438i
$385$		0			0
$386$	−21.4066	+	37.0772i	−1.08957	+	1.88718i
$387$			11.0000i			0.559161i
$388$		−	27.2640i		−	1.38412i
$389$	−17.8609	+	30.9360i	−0.905583	+	1.56852i	−0.0854503	+	0.996342i	$0.527233\pi$
$389$	−17.8609	+	30.9360i	−0.905583	+	1.56852i	−0.820133	+	0.572173i	$0.806100\pi$
$390$		0			0
$391$	57.1655			2.89099
$392$		−	39.8202i		−	2.01123i
$393$	−7.52297	−	4.34339i	−0.379484	−	0.219095i
$394$	11.0562	+	19.1500i	0.557006	+	0.964762i
$395$		0			0
$396$	−2.51248	−	4.35174i	−0.126257	−	0.218683i
$397$	−8.27326	+	4.77657i	−0.415223	+	0.239729i	−0.693031	−	0.720907i	$-0.743725\pi$
$397$	−8.27326	+	4.77657i	−0.415223	+	0.239729i	0.277809	+	0.960636i	$0.410392\pi$
$398$			7.15861i			0.358829i
$399$	0.793718	−	0.875485i	0.0397356	−	0.0438291i
$400$		0			0
$401$	−15.4418	−	26.7459i	−0.771124	−	1.33563i	−0.936947	−	0.349471i	$-0.886361\pi$
$401$	−15.4418	−	26.7459i	−0.771124	−	1.33563i	0.165823	−	0.986156i	$-0.446972\pi$
$402$	−28.0416	+	16.1898i	−1.39859	+	0.807474i
$403$	10.8557	+	6.26755i	0.540761	+	0.312209i
$404$	−15.8433	−	27.4414i	−0.788233	−	1.36526i
$405$		0			0
$406$	0.123418			0.00612514
$407$		−	1.48206i		−	0.0734629i
$408$	42.9039	+	24.7706i	2.12406	+	1.22633i
$409$	15.7816	−	27.3345i	0.780349	−	1.35160i	−0.151389	−	0.988474i	$-0.548375\pi$
$409$	15.7816	−	27.3345i	0.780349	−	1.35160i	0.931738	−	0.363130i	$-0.118292\pi$
$410$		0			0
$411$	6.62955			0.327012
$412$	45.2890	+	26.1476i	2.23123	+	1.28820i
$413$	0.536515	−	0.309757i	0.0264002	−	0.0152421i
$414$	15.2585	−	26.4285i	0.749916	−	1.29889i
$415$		0			0
$416$	−7.65817	−	13.2643i	−0.375472	−	0.650337i
$417$		−	4.36245i		−	0.213630i
$418$	6.29966	+	5.71130i	0.308126	+	0.279349i
$419$	26.5070			1.29495			0.647476	−	0.762086i	$-0.275824\pi$
$419$	26.5070			1.29495			0.647476	+	0.762086i	$0.275824\pi$
$420$		0			0
$421$	10.1180	+	17.5248i	0.493119	+	0.854107i	0.999969	−	0.00792731i	$-0.00252337\pi$
$421$	10.1180	+	17.5248i	0.493119	+	0.854107i	−0.506850	+	0.862035i	$0.669190\pi$
$422$	27.9806	+	16.1546i	1.36207	+	0.786394i
$423$	3.64410	−	2.10392i	0.177182	−	0.102296i
$424$	−12.5477	+	21.7332i	−0.609369	+	1.05546i
$425$		0			0
$426$	30.1468			1.46062
$427$	2.41808	+	1.39608i	0.117019	+	0.0675611i
$428$	6.06218	+	3.50000i	0.293026	+	0.169179i
$429$	−4.75385			−0.229518
$430$		0			0
$431$	5.73045	−	9.92543i	0.276026	−	0.478091i	−0.694367	−	0.719621i	$-0.744316\pi$
$431$	5.73045	−	9.92543i	0.276026	−	0.478091i	0.970394	+	0.241529i	$0.0776490\pi$
$432$	27.6241	−	15.9488i	1.32906	−	0.767336i
$433$	−22.4706	−	12.9734i	−1.07987	−	0.623461i	−0.149006	−	0.988836i	$-0.547607\pi$
$433$	−22.4706	−	12.9734i	−1.07987	−	0.623461i	−0.930860	+	0.365375i	$0.880941\pi$
$434$	0.697262	+	1.20769i	0.0334696	+	0.0579711i
$435$		0			0
$436$	−32.6374			−1.56305
$437$	−7.43771	+	34.4136i	−0.355794	+	1.64622i
$438$			43.1225i			2.06047i
$439$	12.6562	+	21.9211i	0.604046	+	1.04624i	0.992202	+	0.124644i	$0.0397789\pi$
$439$	12.6562	+	21.9211i	0.604046	+	1.04624i	−0.388156	+	0.921594i	$0.626888\pi$
$440$		0			0
$441$	−5.23747	+	9.07157i	−0.249403	+	0.431979i
$442$	−76.8291	+	44.3573i	−3.65439	+	2.10986i
$443$	−17.3421	−	10.0125i	−0.823949	−	0.475707i	0.0278272	−	0.999613i	$-0.491141\pi$
$443$	−17.3421	−	10.0125i	−0.823949	−	0.475707i	−0.851776	+	0.523905i	$0.824475\pi$
$444$	9.97262			0.473279
$445$		0			0
$446$	25.9573	−	44.9594i	1.22912	−	2.12889i
$447$	−0.991229	−	0.572286i	−0.0468835	−	0.0270682i
$448$			0.866350i			0.0409312i
$449$	−19.7601			−0.932536			−0.466268	−	0.884644i	$-0.654402\pi$
$449$	−19.7601			−0.932536			−0.466268	+	0.884644i	$0.654402\pi$
$450$		0			0
$451$	−2.81522	−	4.87610i	−0.132563	−	0.229607i
$452$	46.3471	+	26.7585i	2.17999	+	1.25862i
$453$	−1.02847	+	0.593786i	−0.0483216	+	0.0278985i
$454$	−5.01404	−	8.68457i	−0.235320	−	0.407587i
$455$		0			0
$456$	−20.4940	+	22.6052i	−0.959719	+	1.05859i
$457$			34.4647i			1.61219i	0.591785	+	0.806096i	$0.298423\pi$
$457$			34.4647i			1.61219i	−0.591785	+	0.806096i	$0.701577\pi$
$458$	−7.68388	+	4.43629i	−0.359044	+	0.207294i
$459$	−19.4874	−	33.7532i	−0.909595	−	1.57546i
$460$		0			0
$461$	3.96637	+	6.86995i	0.184732	+	0.319965i	0.943486	−	0.331412i	$-0.107525\pi$
$461$	3.96637	+	6.86995i	0.184732	+	0.319965i	−0.758754	+	0.651377i	$0.774192\pi$
$462$	−0.458010	−	0.264432i	−0.0213085	−	0.0123025i
$463$			9.25395i			0.430068i	0.976607	+	0.215034i	$0.0689862\pi$
$463$			9.25395i			0.430068i	−0.976607	+	0.215034i	$0.931014\pi$
$464$	−1.28514			−0.0596612
$465$		0			0
$466$	−24.8007	+	42.9561i	−1.14887	+	1.98990i
$467$		−	9.47183i		−	0.438304i	−0.975691	−	0.219152i	$-0.929671\pi$
$467$		−	9.47183i		−	0.438304i	0.975691	−	0.219152i	$-0.0703290\pi$
$468$			32.2889i			1.49256i
$469$	1.17265	−	2.03108i	0.0541478	−	0.0937868i
$470$		0			0
$471$	−1.65861	+	2.87280i	−0.0764247	+	0.132371i
$472$	−13.8529	+	7.99800i	−0.637633	+	0.368138i
$473$	−4.91873	+	2.83983i	−0.226164	+	0.130576i
$474$	4.85320			0.222915
$475$		0			0
$476$	−6.72889			−0.308418
$477$	5.71704	−	3.30074i	0.261765	−	0.151130i
$478$	−51.6170	+	29.8011i	−2.36091	+	1.36307i
$479$	−17.3574	+	30.0639i	−0.793081	+	1.37366i	0.130969	+	0.991386i	$0.458191\pi$
$479$	−17.3574	+	30.0639i	−0.793081	+	1.37366i	−0.924050	+	0.382270i	$0.875142\pi$
$480$		0			0
$481$	−4.76164	+	8.24740i	−0.217112	+	0.376049i
$482$		−	11.3874i		−	0.518682i
$483$		−	2.18980i		−	0.0996393i
$484$	−22.2710	+	38.5745i	−1.01232	+	1.75339i
$485$		0			0
$486$	−34.6554			−1.57200
$487$			28.5070i			1.29178i	0.763432	+	0.645888i	$0.223513\pi$
$487$			28.5070i			1.29178i	−0.763432	+	0.645888i	$0.776487\pi$
$488$	−62.4355	−	36.0471i	−2.82632	−	1.63178i
$489$	−1.95735	−	3.39022i	−0.0885142	−	0.153311i
$490$		0			0
$491$	15.5949	+	27.0112i	0.703788	+	1.21900i	0.967127	+	0.254293i	$0.0818428\pi$
$491$	15.5949	+	27.0112i	0.703788	+	1.21900i	−0.263339	+	0.964703i	$0.584824\pi$
$492$	32.8108	−	18.9433i	1.47922	−	0.854030i
$493$			1.57028i			0.0707221i
$494$	−16.7070	−	52.0223i	−0.751681	−	2.34059i
$495$		0			0
$496$	−7.26053	−	12.5756i	−0.326007	−	0.564661i
$497$	−1.89103	+	1.09178i	−0.0848242	+	0.0489732i
$498$	−25.2581	−	14.5828i	−1.13184	−	0.653469i
$499$	8.09334	+	14.0181i	0.362308	+	0.627535i	0.988340	−	0.152262i	$-0.0486556\pi$
$499$	8.09334	+	14.0181i	0.362308	+	0.627535i	−0.626032	+	0.779797i	$0.715322\pi$
$500$		0			0
$501$	12.4899			0.558006
$502$		−	48.8944i		−	2.18226i
$503$	−14.9146	−	8.61094i	−0.665008	−	0.383943i	0.129174	−	0.991622i	$-0.458767\pi$
$503$	−14.9146	−	8.61094i	−0.665008	−	0.383943i	−0.794183	+	0.607679i	$0.792101\pi$
$504$	−0.957790	+	1.65894i	−0.0426633	+	0.0738951i
$505$		0			0
$506$	15.7570			0.700483
$507$	12.6981	+	7.33126i	0.563943	+	0.325593i
$508$	−48.3998	+	27.9437i	−2.14740	+	1.23980i
$509$	−18.2956	+	31.6889i	−0.810939	+	1.40459i	0.101268	+	0.994859i	$0.467710\pi$
$509$	−18.2956	+	31.6889i	−0.810939	+	1.40459i	−0.912207	+	0.409729i	$0.865623\pi$
$510$		0			0
$511$	−1.56171	−	2.70496i	−0.0690859	−	0.119660i
$512$		−	48.6224i		−	2.14883i
$513$	22.8549	−	7.33983i	1.00907	−	0.324062i
$514$	4.42260			0.195072
$515$		0			0
$516$	−19.1089	−	33.0976i	−0.841224	−	1.45704i
$517$	1.88157	+	1.08632i	0.0827512	+	0.0477765i
$518$	−0.917520	+	0.529730i	−0.0403135	+	0.0232750i
$519$	−1.62853	+	2.82070i	−0.0714847	+	0.123815i
$520$		0			0
$521$	−3.63667			−0.159325			−0.0796626	−	0.996822i	$-0.525384\pi$
$521$	−3.63667			−0.159325			−0.0796626	+	0.996822i	$0.525384\pi$
$522$	0.725968	+	0.419138i	0.0317748	+	0.0183452i
$523$	30.8507	+	17.8117i	1.34901	+	0.778850i	0.988109	−	0.153756i	$-0.0491369\pi$
$523$	30.8507	+	17.8117i	1.34901	+	0.778850i	0.360898	+	0.932605i	$0.382470\pi$
$524$	−30.4647			−1.33086
$525$		0			0
$526$	−8.11250	+	14.0513i	−0.353722	+	0.612664i
$527$	−15.3658	+	8.87147i	−0.669346	+	0.386447i
$528$	4.76922	+	2.75351i	0.207554	+	0.119831i
$529$	21.1214	+	36.5834i	0.918322	+	1.59058i
$530$		0			0
$531$	4.20784			0.182605
$532$	0.875485	−	4.05079i	0.0379571	−	0.175624i
$533$			36.1796i			1.56711i
$534$	−4.81020	−	8.33151i	−0.208158	−	0.360540i
$535$		0			0
$536$	−30.2780	+	52.4431i	−1.30781	+	2.26520i
$537$	13.6893	−	7.90354i	0.590739	−	0.341063i
$538$	61.8469	+	35.7073i	2.66641	+	1.53945i
$539$	−5.40856			−0.232963
$540$		0			0
$541$	−1.58632	+	2.74759i	−0.0682014	+	0.118128i	−0.898110	−	0.439772i	$-0.855059\pi$
$541$	−1.58632	+	2.74759i	−0.0682014	+	0.118128i	0.829908	+	0.557900i	$0.188393\pi$
$542$	1.07033	+	0.617957i	0.0459747	+	0.0265435i
$543$		−	22.7420i		−	0.975955i
$544$	21.6797			0.929508
$545$		0			0
$546$	1.69916	+	2.94304i	0.0727175	+	0.125950i
$547$	−24.5782	−	14.1902i	−1.05089	−	0.606731i	−0.127991	−	0.991775i	$-0.540853\pi$
$547$	−24.5782	−	14.1902i	−1.05089	−	0.606731i	−0.922898	+	0.385044i	$0.874186\pi$
$548$	20.1350	−	11.6250i	0.860127	−	0.496594i
$549$	9.48240	+	16.4240i	0.404699	+	0.700959i
$550$		0			0
$551$	−0.945310	−	0.204307i	−0.0402715	−	0.00870377i
$552$			56.5411i			2.40655i
$553$	−0.304428	+	0.175762i	−0.0129456	+	0.00747415i
$554$	11.0172	+	19.0823i	0.468074	+	0.810728i
$555$		0			0
$556$	−7.64959	−	13.2495i	−0.324415	−	0.561903i
$557$	1.84510	+	1.06527i	0.0781793	+	0.0451368i	0.538580	−	0.842574i	$-0.318961\pi$
$557$	1.84510	+	1.06527i	0.0781793	+	0.0451368i	−0.460401	+	0.887711i	$0.652294\pi$
$558$			9.47183i			0.400974i
$559$	36.4959			1.54361
$560$		0			0
$561$	3.36445	−	5.82739i	0.142047	−	0.246033i
$562$		−	11.8906i		−	0.501575i
$563$		−	20.2609i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$563$		−	20.2609i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$564$	−7.30976	+	12.6609i	−0.307796	+	0.533119i
$565$		0			0
$566$	21.1460	−	36.6260i	0.888834	−	1.53951i
$567$	−0.424237	+	0.244933i	−0.0178163	+	0.0102862i
$568$	48.8268	−	28.1901i	2.04873	−	1.18283i
$569$	34.7530			1.45692			0.728460	−	0.685088i	$-0.240236\pi$
$569$	34.7530			1.45692			0.728460	+	0.685088i	$0.240236\pi$
$570$		0			0
$571$	32.0702			1.34210			0.671048	−	0.741414i	$-0.265845\pi$
$571$	32.0702			1.34210			0.671048	+	0.741414i	$0.265845\pi$
$572$	−14.4383	+	8.33593i	−0.603694	+	0.348543i
$573$	−24.3826	+	14.0773i	−1.01860	+	0.588088i
$574$	−2.01248	+	3.48572i	−0.0839993	+	0.145491i
$575$		0			0
$576$	−2.94220	+	5.09603i	−0.122591	+	0.212335i
$577$		−	30.2740i		−	1.26032i	−0.776464	−	0.630162i	$-0.782988\pi$
$577$		−	30.2740i		−	1.26032i	0.776464	−	0.630162i	$-0.217012\pi$
$578$		−	82.9528i		−	3.45038i
$579$	−10.4332	+	18.0708i	−0.433588	+	0.750996i
$580$		0			0
$581$	2.11250			0.0876411
$582$		−	19.4899i		−	0.807881i
$583$	2.95190	+	1.70428i	0.122255	+	0.0705841i
$584$	40.3237	+	69.8427i	1.66861	+	2.89011i
$585$		0			0
$586$	14.5828	+	25.2581i	0.602408	+	1.04340i
$587$	−2.16168	+	1.24805i	−0.0892222	+	0.0515125i	−0.543947	−	0.839119i	$-0.683071\pi$
$587$	−2.16168	+	1.24805i	−0.0892222	+	0.0515125i	0.454725	+	0.890632i	$0.349738\pi$
$588$		−	36.3936i		−	1.50085i
$589$	−3.34139	−	10.4045i	−0.137680	−	0.428708i
$590$		0			0
$591$	5.38862	+	9.33336i	0.221658	+	0.383923i
$592$	9.55406	−	5.51604i	0.392669	−	0.226708i
$593$	8.62901	+	4.98196i	0.354351	+	0.204585i	0.666600	−	0.745416i	$-0.267749\pi$
$593$	8.62901	+	4.98196i	0.354351	+	0.204585i	−0.312249	+	0.950000i	$0.601082\pi$
$594$	−5.37147	−	9.30365i	−0.220394	−	0.381733i
$595$		0			0
$596$	−4.01404			−0.164421
$597$			3.48898i			0.142794i
$598$	−87.6849	−	50.6249i	−3.58570	−	2.07021i
$599$	16.0351	−	27.7736i	0.655176	−	1.13480i	−0.326673	−	0.945137i	$-0.605928\pi$
$599$	16.0351	−	27.7736i	0.655176	−	1.13480i	0.981850	−	0.189661i	$-0.0607389\pi$
$600$		0			0
$601$	3.68278			0.150224			0.0751119	−	0.997175i	$-0.476069\pi$
$601$	3.68278			0.150224			0.0751119	+	0.997175i	$0.476069\pi$
$602$	3.51619	+	2.03008i	0.143309	+	0.0827397i
$603$	13.7955	−	7.96481i	0.561794	−	0.324352i
$604$	−2.08242	+	3.60686i	−0.0847324	+	0.146761i
$605$		0			0
$606$	−11.3257	−	19.6167i	−0.460075	−	0.796873i
$607$			20.4850i			0.831460i	0.909488	+	0.415730i	$0.136474\pi$
$607$			20.4850i			0.831460i	−0.909488	+	0.415730i	$0.863526\pi$
$608$	−2.82070	+	13.0511i	−0.114395	+	0.529293i
$609$	0.0601518			0.00243747
$610$		0			0
$611$	−6.98040	−	12.0904i	−0.282397	−	0.489126i
$612$	−39.5806	−	22.8519i	−1.59995	−	0.923732i
$613$	9.27664	−	5.35587i	0.374680	−	0.216322i	−0.300821	−	0.953681i	$-0.597261\pi$
$613$	9.27664	−	5.35587i	0.374680	−	0.216322i	0.675501	+	0.737359i	$0.263927\pi$
$614$	−7.38395	+	12.7894i	−0.297992	+	0.516137i
$615$		0			0
$616$	−0.989077			−0.0398511
$617$	−15.3564	−	8.86600i	−0.618224	−	0.356932i	0.157953	−	0.987447i	$-0.449511\pi$
$617$	−15.3564	−	8.86600i	−0.618224	−	0.356932i	−0.776177	+	0.630515i	$0.782844\pi$
$618$	32.3751	+	18.6918i	1.30232	+	0.751894i
$619$	13.2780			0.533689			0.266844	−	0.963740i	$-0.414019\pi$
$619$	13.2780			0.533689			0.266844	+	0.963740i	$0.414019\pi$
$620$		0			0
$621$	22.2409	−	38.5224i	0.892498	−	1.54585i
$622$	32.1768	−	18.5773i	1.29017	−	0.744882i
$623$	0.603462	+	0.348409i	0.0241772	+	0.0139587i
$624$	−17.6933	−	30.6456i	−0.708297	−	1.22681i
$625$		0			0
$626$	14.7779			0.590645
$627$	3.07034	+	2.78359i	0.122618	+	0.111166i
$628$			11.6336i			0.464229i
$629$	−6.73992	−	11.6739i	−0.268738	−	0.465468i
$630$		0			0
$631$	−2.03208	+	3.51966i	−0.0808957	+	0.140115i	−0.903635	−	0.428304i	$-0.859111\pi$
$631$	−2.03208	+	3.51966i	−0.0808957	+	0.140115i	0.822739	+	0.568419i	$0.192445\pi$
$632$	7.86041	−	4.53821i	0.312670	−	0.180520i
$633$	13.6372	+	7.87347i	0.542032	+	0.312942i
$634$	−10.4257			−0.414058
$635$		0			0
$636$	−11.4679	+	19.8630i	−0.454733	+	0.787620i
$637$	30.0977	+	17.3769i	1.19252	+	0.688499i
$638$			0.432830i			0.0171359i
$639$	−14.8312			−0.586712
$640$		0			0
$641$	−2.49254	−	4.31720i	−0.0984493	−	0.170519i	0.812594	−	0.582831i	$-0.198055\pi$
$641$	−2.49254	−	4.31720i	−0.0984493	−	0.170519i	−0.911043	+	0.412311i	$0.864722\pi$
$642$	4.33359	+	2.50200i	0.171033	+	0.0987461i
$643$	−5.08927	+	2.93829i	−0.200701	+	0.115875i	−0.596983	−	0.802254i	$-0.703634\pi$
$643$	−5.08927	+	2.93829i	−0.200701	+	0.115875i	0.396281	+	0.918129i	$0.370300\pi$
$644$	−3.83983	−	6.65079i	−0.151311	−	0.262078i
$645$		0			0
$646$	75.5943	+	16.3380i	2.97422	+	0.642809i
$647$		−	16.9757i		−	0.667385i	−0.942682	−	0.333692i	$-0.891705\pi$
$647$		−	16.9757i		−	0.667385i	0.942682	−	0.333692i	$-0.108295\pi$
$648$	10.9539	−	6.32424i	0.430310	−	0.248440i
$649$	1.08632	+	1.88157i	0.0426419	+	0.0738580i
$650$		0			0
$651$	0.339833	+	0.588608i	0.0133191	+	0.0230694i
$652$	−11.8896	−	6.86445i	−0.465632	−	0.268833i
$653$			24.6797i			0.965790i	0.875678	+	0.482895i	$0.160415\pi$
$653$			24.6797i			0.965790i	−0.875678	+	0.482895i	$0.839585\pi$
$654$	−23.3311			−0.912317
$655$		0			0
$656$	20.9558	−	36.2965i	0.818186	−	1.41714i
$657$		−	21.2148i		−	0.827667i
$658$		−	1.55313i		−	0.0605474i
$659$	0.943308	−	1.63386i	0.0367461	−	0.0636461i	−0.847067	−	0.531485i	$-0.821634\pi$
$659$	0.943308	−	1.63386i	0.0367461	−	0.0636461i	0.883814	+	0.467839i	$0.154967\pi$
$660$		0			0
$661$	−22.3749	+	38.7545i	−0.870284	+	1.50738i	−0.00858048	+	0.999963i	$0.502731\pi$
$661$	−22.3749	+	38.7545i	−0.870284	+	1.50738i	−0.861703	+	0.507413i	$0.830602\pi$
$662$	23.1871	−	13.3871i	0.901191	−	0.520303i
$663$	−37.4452	+	21.6190i	−1.45425	+	0.839611i
$664$	−54.5451			−2.11676
$665$		0			0
$666$	−7.19603			−0.278840
$667$	−1.55206	+	0.896081i	−0.0600959	+	0.0346964i
$668$	37.9338	−	21.9011i	1.46770	−	0.847379i
$669$	12.6511	−	21.9124i	0.489122	−	0.847183i
$670$		0			0
$671$	−4.89608	+	8.48026i	−0.189011	+	0.327377i
$672$		−	0.830467i		−	0.0320360i
$673$			25.4046i			0.979274i	0.871926	+	0.489637i	$0.162871\pi$
$673$			25.4046i			0.979274i	−0.871926	+	0.489637i	$0.837129\pi$
$674$	33.0241	−	57.1994i	1.27204	−	2.20324i
$675$		0			0
$676$	51.4217			1.97776
$677$			3.86946i			0.148716i	0.997232	+	0.0743578i	$0.0236907\pi$
$677$			3.86946i			0.148716i	−0.997232	+	0.0743578i	$0.976309\pi$
$678$	33.1316	+	19.1285i	1.27241	+	0.734627i
$679$	0.705838	+	1.22255i	0.0270876	+	0.0469170i
$680$		0			0
$681$	−2.44375	−	4.23270i	−0.0936448	−	0.162198i
$682$	−4.23540	+	2.44531i	−0.162182	+	0.0936357i
$683$		−	48.5171i		−	1.85645i	−0.372015	−	0.928227i	$-0.621333\pi$
$683$		−	48.5171i		−	1.85645i	0.372015	−	0.928227i	$-0.378667\pi$
$684$	18.9066	−	20.8543i	0.722910	−	0.797382i
$685$		0			0
$686$	3.88004	+	6.72043i	0.148141	+	0.256587i
$687$	−3.74499	+	2.16217i	−0.142880	+	0.0824919i
$688$	−36.6138	−	21.1390i	−1.39589	−	0.805917i
$689$	−10.9512	−	18.9681i	−0.417208	−	0.722626i
$690$		0			0
$691$	−47.6374			−1.81221			−0.906105	−	0.423052i	$-0.860959\pi$
$691$	−47.6374			−1.81221			−0.906105	+	0.423052i	$0.860959\pi$
$692$			11.4226i			0.434222i
$693$	0.225325	+	0.130091i	0.00855937	+	0.00494176i
$694$	21.1636	−	36.6565i	0.803360	−	1.39146i
$695$		0			0
$696$	−1.55313			−0.0588714
$697$	−44.3498	−	25.6054i	−1.67987	−	0.969873i
$698$	−10.0229	+	5.78670i	−0.379371	+	0.219030i
$699$	−12.0874	+	20.9361i	−0.457189	+	0.791874i
$700$		0			0
$701$	−14.2766	−	24.7277i	−0.539218	−	0.933954i	−0.998946	−	0.0458939i	$-0.985386\pi$
$701$	−14.2766	−	24.7277i	−0.539218	−	0.933954i	0.459728	−	0.888060i	$-0.347947\pi$
$702$			69.0310i			2.60541i
$703$	7.90458	−	2.53855i	0.298127	−	0.0957434i
$704$	−3.03831			−0.114510
$705$		0			0
$706$	−31.2760	−	54.1717i	−1.17709	−	2.03878i
$707$	1.42086	+	0.820334i	0.0534370	+	0.0308518i
$708$	−12.6609	+	7.30976i	−0.475825	+	0.274717i
$709$	9.74137	−	16.8726i	0.365845	−	0.633662i	−0.623066	−	0.782169i	$-0.714113\pi$
$709$	9.74137	−	16.8726i	0.365845	−	0.633662i	0.988911	+	0.148507i	$0.0474467\pi$
$710$		0			0
$711$	−2.38760			−0.0895421
$712$	−15.5815	−	8.99600i	−0.583942	−	0.337139i
$713$	−17.5370	−	10.1250i	−0.656765	−	0.379183i
$714$	−4.81020			−0.180017
$715$		0			0
$716$	27.7179	−	48.0088i	1.03587	−	1.79417i
$717$	−25.1572	+	14.5245i	−0.939513	+	0.542428i
$718$	25.6242	+	14.7942i	0.956288	+	0.552113i
$719$	2.05313	+	3.55613i	0.0765689	+	0.132621i	0.901767	−	0.432221i	$-0.142270\pi$
$719$	2.05313	+	3.55613i	0.0765689	+	0.132621i	−0.825199	+	0.564843i	$0.808937\pi$
$720$		0			0
$721$	−2.70774			−0.100842
$722$	−19.6709	+	43.3819i	−0.732074	+	1.61451i
$723$		−	5.55002i		−	0.206407i
$724$	−39.8784	−	69.0714i	−1.48207	−	2.56702i
$725$		0			0
$726$	−15.9206	+	27.5753i	−0.590869	+	1.02341i
$727$	10.7488	−	6.20584i	0.398652	−	0.230162i	−0.287250	−	0.957856i	$-0.592741\pi$
$727$	10.7488	−	6.20584i	0.398652	−	0.230162i	0.685902	+	0.727694i	$0.259408\pi$
$728$	5.50405	+	3.17776i	0.203994	+	0.117776i
$729$	−23.5139			−0.870887
$730$		0			0
$731$	−25.8293	+	44.7376i	−0.955330	+	1.65468i
$732$	−57.0628	−	32.9452i	−2.10910	−	1.21769i
$733$		−	16.3985i		−	0.605693i	−0.953039	−	0.302847i	$-0.902063\pi$
$733$		−	16.3985i		−	0.605693i	0.953039	−	0.302847i	$-0.0979370\pi$
$734$	65.7661			2.42747
$735$		0			0
$736$	12.3715	+	21.4280i	0.456018	+	0.789847i
$737$	7.12305	+	4.11250i	0.262381	+	0.151486i
$738$	−23.6756	+	13.6691i	−0.871509	+	0.503166i
$739$	−23.1018	−	40.0135i	−0.849814	−	1.47192i	−0.881374	−	0.472419i	$-0.843381\pi$
$739$	−23.1018	−	40.0135i	−0.849814	−	1.47192i	0.0315597	−	0.999502i	$-0.489953\pi$
$740$		0			0
$741$	−8.14267	−	25.3547i	−0.299128	−	0.931430i
$742$		−	2.43664i		−	0.0894517i
$743$	−21.4888	+	12.4066i	−0.788347	+	0.455153i	−0.839380	−	0.543544i	$-0.817082\pi$
$743$	−21.4888	+	12.4066i	−0.788347	+	0.455153i	0.0510331	+	0.998697i	$0.483749\pi$
$744$	−8.77457	−	15.1980i	−0.321691	−	0.557185i
$745$		0			0
$746$	15.0371	+	26.0450i	0.550547	+	0.953576i
$747$	12.4261	+	7.17420i	0.454647	+	0.262490i
$748$		−	23.5984i		−	0.862841i
$749$	−0.362446			−0.0132435
$750$		0			0
$751$	5.26955	−	9.12712i	0.192289	−	0.333054i	−0.753720	−	0.657196i	$-0.771742\pi$
$751$	5.26955	−	9.12712i	0.192289	−	0.333054i	0.946008	+	0.324142i	$0.105076\pi$
$752$			16.1726i			0.589756i
$753$		−	23.8303i		−	0.868423i
$754$	1.39062	−	2.40862i	0.0506434	−	0.0877169i
$755$		0			0
$756$	−2.61796	+	4.53443i	−0.0952142	+	0.164916i
$757$	5.36652	−	3.09836i	0.195049	−	0.112612i	−0.399295	−	0.916823i	$-0.630745\pi$
$757$	5.36652	−	3.09836i	0.195049	−	0.112612i	0.594344	+	0.804211i	$0.297412\pi$
$758$	−0.680039	+	0.392621i	−0.0247001	+	0.0142606i
$759$	7.67967			0.278754
$760$		0			0
$761$	35.6084			1.29080			0.645402	−	0.763843i	$-0.276690\pi$
$761$	35.6084			1.29080			0.645402	+	0.763843i	$0.276690\pi$
$762$	−34.5990	+	19.9757i	−1.25339	+	0.723644i
$763$	1.46349	−	0.844949i	0.0529820	−	0.0305892i
$764$	−49.3694	+	85.5103i	−1.78612	+	3.09365i
$765$		0			0
$766$	37.7159	−	65.3258i	1.36273	−	2.36032i
$767$		−	13.9608i		−	0.504095i
$768$		−	39.2116i		−	1.41493i
$769$	−0.0777477	+	0.134663i	−0.00280365	+	0.00485607i	−0.867424	−	0.497570i	$-0.834226\pi$
$769$	−0.0777477	+	0.134663i	−0.00280365	+	0.00485607i	0.864620	+	0.502426i	$0.167559\pi$
$770$		0			0
$771$	2.15550			0.0776283
$772$			73.1787i			2.63376i
$773$	4.40653	+	2.54411i	0.158492	+	0.0915054i	0.577148	−	0.816639i	$-0.304165\pi$
$773$	4.40653	+	2.54411i	0.158492	+	0.0915054i	−0.418656	+	0.908145i	$0.637499\pi$
$774$	13.7886	+	23.8826i	0.495621	+	0.858441i
$775$		0			0
$776$	−18.2249	−	31.5664i	−0.654236	−	1.13317i
$777$	−0.447183	+	0.258181i	−0.0160426	+	0.00926220i
$778$			89.5552i			3.21071i
$779$	21.1847	−	23.3671i	0.759020	−	0.837212i
$780$		0			0
$781$	−3.82891	−	6.63187i	−0.137009	−	0.237307i
$782$	124.114	−	71.6575i	4.43832	−	2.56247i
$783$	1.05818	+	0.610938i	0.0378161	+	0.0218331i
$784$	−20.1300	−	34.8662i	−0.718928	−	1.24522i
$785$		0			0
$786$	−21.7779			−0.776793
$787$			22.5070i			0.802289i	0.916015	+	0.401144i	$0.131387\pi$
$787$			22.5070i			0.802289i	−0.916015	+	0.401144i	$0.868613\pi$
$788$	32.7323	+	18.8980i	1.16604	+	0.673213i
$789$	−3.95389	+	6.84833i	−0.140762	+	0.243807i
$790$		0			0
$791$	−2.77101			−0.0985257
$792$	−5.81793	−	3.35899i	−0.206731	−	0.119356i
$793$	54.4917	−	31.4608i	1.93506	−	1.11721i
$794$	−11.9749	+	20.7412i	−0.424975	+	0.736078i
$795$		0			0
$796$	6.11796	+	10.5966i	0.216845	+	0.375587i
$797$		−	29.2219i		−	1.03509i	−0.855655	−	0.517546i	$-0.826846\pi$
$797$		−	29.2219i		−	1.03509i	0.855655	−	0.517546i	$-0.173154\pi$
$798$	0.625847	−	2.89574i	0.0221547	−	0.102508i
$799$	19.7610			0.699093
$800$		0			0
$801$	2.36645	+	4.09881i	0.0836144	+	0.144824i
$802$	−67.0525	−	38.7128i	−2.36770	−	1.36699i
$803$	9.48634	−	5.47694i	0.334766	−	0.193277i
$804$	−27.6725	+	47.9303i	−0.975936	+	1.69037i
$805$		0			0
$806$	31.4257			1.10692
$807$	30.1431	+	17.4031i	1.06109	+	0.612618i
$808$	−36.6870	−	21.1812i	−1.29064	−	0.745153i
$809$	−25.8664			−0.909412			−0.454706	−	0.890641i	$-0.650256\pi$
$809$	−25.8664			−0.909412			−0.454706	+	0.890641i	$0.650256\pi$
$810$		0			0
$811$	9.84841	−	17.0579i	0.345824	−	0.598985i	−0.639679	−	0.768642i	$-0.720933\pi$
$811$	9.84841	−	17.0579i	0.345824	−	0.598985i	0.985503	+	0.169657i	$0.0542660\pi$
$812$	0.182691	−	0.105477i	0.00641120	−	0.00370151i
$813$	0.521661	+	0.301181i	0.0182954	+	0.0105629i
$814$	−1.85777	−	3.21776i	−0.0651150	−	0.112782i
$815$		0			0
$816$	50.0882			1.75344
$817$	−23.5714	−	21.3699i	−0.824658	−	0.747638i
$818$		−	79.1295i		−	2.76670i
$819$	−0.835929	−	1.44787i	−0.0292097	−	0.0505927i
$820$		0			0
$821$	−2.04021	+	3.53375i	−0.0712038	+	0.123329i	−0.899429	−	0.437067i	$-0.856017\pi$
$821$	−2.04021	+	3.53375i	−0.0712038	+	0.123329i	0.828225	+	0.560395i	$0.189351\pi$
$822$	14.3937	−	8.31020i	0.502038	−	0.289852i
$823$	−9.18538	−	5.30318i	−0.320182	−	0.184857i	0.331292	−	0.943528i	$-0.392516\pi$
$823$	−9.18538	−	5.30318i	−0.320182	−	0.184857i	−0.651474	+	0.758671i	$0.725849\pi$
$824$	69.9145			2.43559
$825$		0			0
$826$	0.776567	−	1.34505i	0.0270202	−	0.0468004i
$827$	13.3407	+	7.70228i	0.463903	+	0.267834i	0.713684	−	0.700468i	$-0.247025\pi$
$827$	13.3407	+	7.70228i	0.463903	+	0.267834i	−0.249781	+	0.968302i	$0.580359\pi$
$828$		−	52.1615i		−	1.81274i
$829$	−21.2350			−0.737523			−0.368761	−	0.929524i	$-0.620218\pi$
$829$	−21.2350			−0.737523			−0.368761	+	0.929524i	$0.620218\pi$
$830$		0			0
$831$	5.36956	+	9.30036i	0.186268	+	0.322626i
$832$	16.9077	+	9.76164i	0.586168	+	0.338424i
$833$	−42.6021	+	24.5964i	−1.47608	+	0.852213i
$834$	−5.46837	−	9.47149i	−0.189354	−	0.327971i
$835$		0			0
$836$	14.2062	+	3.07034i	0.491331	+	0.106190i
$837$			13.8062i			0.477212i
$838$	57.5505	−	33.2268i	1.98805	−	1.14780i
$839$	−3.04567	−	5.27526i	−0.105148	−	0.182122i	0.808651	−	0.588289i	$-0.200198\pi$
$839$	−3.04567	−	5.27526i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$840$		0			0
$841$	14.4754	+	25.0721i	0.499151	+	0.864555i
$842$	43.9350	+	25.3659i	1.51410	+	0.874167i
$843$		−	5.79528i		−	0.199600i
$844$	55.2248			1.90092
$845$		0			0
$846$	5.27457	−	9.13582i	0.181343	−	0.314096i
$847$		−	2.30630i		−	0.0792453i
$848$			25.3725i			0.871295i
$849$	10.3062	−	17.8509i	0.353708	−	0.612640i
$850$		0			0
$851$	7.69224	−	13.3234i	0.263687	−	0.456719i
$852$	44.6251	−	25.7643i	1.52883	−	0.882672i
$853$	−30.2804	+	17.4824i	−1.03678	+	0.598586i	−0.918920	−	0.394444i	$-0.870937\pi$
$853$	−30.2804	+	17.4824i	−1.03678	+	0.598586i	−0.117862	+	0.993030i	$0.537604\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	9.35844			0.319865
$857$	−3.59530	+	2.07575i	−0.122813	+	0.0709061i	−0.560148	−	0.828393i	$-0.689256\pi$
$857$	−3.59530	+	2.07575i	−0.122813	+	0.0709061i	0.437335	+	0.899299i	$0.355922\pi$
$858$	−10.3213	+	5.95900i	−0.352363	+	0.203437i
$859$	14.1245	−	24.4644i	0.481923	−	0.834715i	−0.517862	−	0.855464i	$-0.673272\pi$
$859$	14.1245	−	24.4644i	0.481923	−	0.834715i	0.999785	+	0.0207495i	$0.00660523\pi$
$860$		0			0
$861$	−0.980847	+	1.69888i	−0.0334272	+	0.0578976i
$862$		−	28.7327i		−	0.978640i
$863$			51.8272i			1.76422i	0.471046	+	0.882108i	$0.343876\pi$
$863$			51.8272i			1.76422i	−0.471046	+	0.882108i	$0.656124\pi$
$864$	8.43473	−	14.6094i	0.286955	−	0.497021i
$865$		0			0
$866$	−65.0490			−2.21046
$867$		−	40.4297i		−	1.37307i
$868$	2.06426	+	1.19180i	0.0700655	+	0.0404523i
$869$	−0.616399	−	1.06764i	−0.0209099	−	0.0362170i
$870$		0			0
$871$	−26.4257	−	45.7707i	−0.895401	−	1.55088i
$872$	−37.7878	+	21.8168i	−1.27966	+	0.738809i
$873$			9.58832i			0.324516i
$874$	26.9894	+	84.0400i	0.912931	+	2.84270i
$875$		0			0
$876$	36.8538	+	63.8326i	1.24517	+	2.15670i
$877$	40.8763	−	23.5999i	1.38029	−	0.796913i	0.388099	−	0.921618i	$-0.373132\pi$
$877$	40.8763	−	23.5999i	1.38029	−	0.796913i	0.992194	+	0.124705i	$0.0397985\pi$
$878$	54.9567	+	31.7292i	1.85470	+	1.07081i
$879$	7.10738	+	12.3103i	0.239726	+	0.415218i
$880$		0			0
$881$	−33.8935			−1.14190			−0.570951	−	0.820984i	$-0.693425\pi$
$881$	−33.8935			−1.14190			−0.570951	+	0.820984i	$0.693425\pi$
$882$			26.2609i			0.884250i
$883$	−18.2439	−	10.5331i	−0.613954	−	0.354467i	0.160557	−	0.987027i	$-0.448671\pi$
$883$	−18.2439	−	10.5331i	−0.613954	−	0.354467i	−0.774512	+	0.632560i	$0.782004\pi$
$884$	−75.8181	+	131.321i	−2.55004	+	4.41680i
$885$		0			0
$886$	−50.2029			−1.68660
$887$	6.24816	+	3.60738i	0.209793	+	0.121124i	0.601215	−	0.799087i	$-0.294683\pi$
$887$	6.24816	+	3.60738i	0.209793	+	0.121124i	−0.391422	+	0.920211i	$0.628017\pi$
$888$	11.5464	−	6.66630i	0.387471	−	0.223706i
$889$	1.44687	−	2.50605i	0.0485264	−	0.0840501i
$890$		0			0
$891$	−0.858986	−	1.48781i	−0.0287771	−	0.0498434i
$892$		−	88.7356i		−	2.97109i
$893$	−2.57107	+	11.8961i	−0.0860374	+	0.398087i
$894$	−2.86946			−0.0959693
$895$		0			0
$896$	1.76564	+	3.05818i	0.0589860	+	0.102167i
$897$	−42.7360	−	24.6737i	−1.42691	−	0.823830i
$898$	−42.9019	+	24.7694i	−1.43166	+	0.826567i
$899$	0.278124	−	0.481725i	0.00927595	−	0.0160664i
$900$		0			0
$901$	31.0020			1.03283
$902$	−12.2245	−	7.05780i	−0.407031	−	0.234999i
$903$	1.71373	+	0.989423i	0.0570294	+	0.0329259i
$904$	71.5480			2.37965
$905$		0			0
$906$	−1.48863	+	2.57839i	−0.0494565	+	0.0856612i
$907$	−1.01208	+	0.584322i	−0.0336054	+	0.0194021i	−0.516709	−	0.856161i	$-0.672843\pi$
$907$	−1.01208	+	0.584322i	−0.0336054	+	0.0194021i	0.483103	+	0.875563i	$0.339510\pi$
$908$	−14.8442	−	8.57028i	−0.492621	−	0.284415i
$909$	5.57184	+	9.65071i	0.184806	+	0.320094i
$910$		0			0
$911$	−12.3313			−0.408553			−0.204276	−	0.978913i	$-0.565484\pi$
$911$	−12.3313			−0.408553			−0.204276	+	0.978913i	$0.565484\pi$
$912$	−6.51689	+	30.1530i	−0.215796	+	0.998467i
$913$			7.40856i			0.245188i
$914$	43.2018	+	74.8278i	1.42899	+	2.47508i
$915$		0			0
$916$	−7.58276	+	13.1337i	−0.250542	+	0.433951i
$917$	1.36607	−	0.788701i	0.0451116	−	0.0260452i
$918$	−84.6199	−	48.8553i	−2.79287	−	1.61247i
$919$	−52.8895			−1.74466			−0.872332	−	0.488913i	$-0.837393\pi$
$919$	−52.8895			−1.74466			−0.872332	+	0.488913i	$0.837393\pi$
$920$		0			0
$921$	−3.59880	+	6.23331i	−0.118585	+	0.205395i
$922$	17.2231	+	9.94375i	0.567212	+	0.327480i
$923$			49.2070i			1.61967i
$924$	−0.903965			−0.0297383
$925$		0			0
$926$	11.5999	+	20.0916i	0.381197	+	0.660252i
$927$	−15.9274	−	9.19570i	−0.523125	−	0.302027i
$928$	−0.588608	+	0.339833i	−0.0193220	+	0.0111556i
$929$	0.695704	+	1.20500i	0.0228253	+	0.0395346i	0.877212	−	0.480102i	$-0.159401\pi$
$929$	0.695704	+	1.20500i	0.0228253	+	0.0395346i	−0.854387	+	0.519637i	$0.826067\pi$
$930$		0			0
$931$	−9.26409	−	28.8466i	−0.303618	−	0.945410i
$932$			84.7817i			2.77712i
$933$	15.6824	−	9.05425i	0.513419	−	0.296423i
$934$	−11.8730	−	20.5647i	−0.388497	−	0.672897i
$935$		0			0
$936$	21.5839	+	37.3844i	0.705491	+	1.22195i
$937$	−28.8987	−	16.6847i	−0.944080	−	0.545065i	−0.0528430	−	0.998603i	$-0.516828\pi$
$937$	−28.8987	−	16.6847i	−0.944080	−	0.545065i	−0.891237	+	0.453538i	$0.850162\pi$
$938$		−	5.87970i		−	0.191979i
$939$	7.20250			0.235045
$940$		0			0
$941$	−17.6616	+	30.5908i	−0.575753	+	0.997233i	0.420207	+	0.907428i	$0.361958\pi$
$941$	−17.6616	+	30.5908i	−0.575753	+	0.997233i	−0.995959	+	0.0898043i	$0.971376\pi$
$942$			8.31633i			0.270961i
$943$		−	58.4467i		−	1.90329i
$944$	−8.08632	+	14.0059i	−0.263187	+	0.455854i
$945$		0			0
$946$	−7.11951	+	12.3314i	−0.231475	+	0.400927i
$947$	−11.4810	+	6.62853i	−0.373081	+	0.215398i	−0.674804	−	0.737997i	$-0.735772\pi$
$947$	−11.4810	+	6.62853i	−0.373081	+	0.215398i	0.301723	+	0.953396i	$0.402438\pi$
$948$	7.18400	−	4.14769i	0.233326	−	0.134711i
$949$	−70.3865			−2.28484
$950$		0			0
$951$	−5.08131			−0.164773
$952$	−7.79076	+	4.49800i	−0.252500	+	0.145781i
$953$	15.8225	−	9.13511i	0.512540	−	0.295915i	−0.221337	−	0.975197i	$-0.571042\pi$
$953$	15.8225	−	9.13511i	0.512540	−	0.295915i	0.733877	+	0.679282i	$0.237709\pi$
$954$	8.27501	−	14.3327i	0.267913	−	0.464039i
$955$		0			0
$956$	−50.9377	+	88.2268i	−1.64744	+	2.85346i
$957$			0.210953i			0.00681916i
$958$			87.0308i			2.81184i
$959$	−0.601918	+	1.04255i	−0.0194369	+	0.0336658i
$960$		0			0
$961$	−24.7149			−0.797253
$962$			23.8750i			0.769762i
$963$	−2.13197	−	1.23090i	−0.0687019	−	0.0396651i
$964$	−9.73201	−	16.8563i	−0.313447	−	0.542906i
$965$		0			0
$966$	−2.74493	−	4.75436i	−0.0883168	−	0.152969i
$967$	39.0686	−	22.5562i	1.25636	−	0.725360i	0.283995	−	0.958826i	$-0.408340\pi$
$967$	39.0686	−	22.5562i	1.25636	−	0.725360i	0.972365	+	0.233466i	$0.0750066\pi$
$968$			59.5491i			1.91398i
$969$	36.8433	+	7.96283i	1.18358	+	0.255803i
$970$		0			0
$971$	−7.80118	−	13.5120i	−0.250352	−	0.433622i	0.713271	−	0.700888i	$-0.247213\pi$
$971$	−7.80118	−	13.5120i	−0.250352	−	0.433622i	−0.963623	+	0.267266i	$0.913880\pi$
$972$	−51.2990	+	29.6175i	−1.64542	+	0.949982i
$973$	0.686032	+	0.396081i	0.0219932	+	0.0126978i
$974$	35.7338	+	61.8928i	1.14499	+	1.98317i
$975$		0			0
$976$	−72.8904			−2.33317
$977$		−	26.2319i		−	0.839233i	−0.907701	−	0.419617i	$-0.862165\pi$
$977$		−	26.2319i		−	0.839233i	0.907701	−	0.419617i	$-0.137835\pi$
$978$	−8.49935	−	4.90710i	−0.271779	−	0.156912i
$979$	−1.22188	+	2.11635i	−0.0390513	+	0.0676389i
$980$		0			0
$981$	11.4781			0.366466
$982$	67.7175	+	39.0967i	2.16095	+	1.24763i
$983$	−29.7404	+	17.1706i	−0.948572	+	0.547659i	−0.892637	−	0.450776i	$-0.851147\pi$
$983$	−29.7404	+	17.1706i	−0.948572	+	0.547659i	−0.0559353	+	0.998434i	$0.517814\pi$
$984$	25.3257	−	43.8654i	0.807354	−	1.39838i
$985$		0			0
$986$	1.96837	+	3.40931i	0.0626856	+	0.108575i
$987$		−	0.756969i		−	0.0240946i
$988$	−69.1904	−	62.7284i	−2.20124	−	1.99565i
$989$	−58.9577			−1.87475
$990$		0			0
$991$	−1.65159	−	2.86064i	−0.0524645	−	0.0908712i	0.838600	−	0.544747i	$-0.183374\pi$
$991$	−1.65159	−	2.86064i	−0.0524645	−	0.0908712i	−0.891065	+	0.453876i	$0.850041\pi$
$992$	−6.65079	−	3.83983i	−0.211163	−	0.121915i
$993$	11.3010	−	6.52461i	0.358625	−	0.207052i
$994$	−2.73713	+	4.74084i	−0.0868163	+	0.150370i
$995$		0			0
$996$	−49.8514			−1.57960
$997$	8.50727	+	4.91168i	0.269428	+	0.155554i	0.628628	−	0.777706i	$-0.283617\pi$
$997$	8.50727	+	4.91168i	0.269428	+	0.155554i	−0.359200	+	0.933261i	$0.616950\pi$
$998$	35.1436	+	20.2902i	1.11245	+	0.642274i
$999$	−10.4890			−0.331857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.b.349.6		12
5.2	odd	4		95.2.e.b.26.3	yes	6
5.3	odd	4		475.2.e.d.26.1		6
5.4	even	2	inner	475.2.j.b.349.1		12
15.2	even	4		855.2.k.g.406.1		6
19.11	even	3	inner	475.2.j.b.49.1		12
20.7	even	4		1520.2.q.j.881.2		6
95.7	odd	12		1805.2.a.h.1.1		3
95.12	even	12		1805.2.a.g.1.3		3
95.49	even	6	inner	475.2.j.b.49.6		12
95.68	odd	12		475.2.e.d.201.1		6
95.83	odd	12		9025.2.a.z.1.3		3
95.87	odd	12		95.2.e.b.11.3	✓	6
95.88	even	12		9025.2.a.ba.1.1		3
285.182	even	12		855.2.k.g.676.1		6
380.87	even	12		1520.2.q.j.961.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.3	✓	6	95.87	odd	12
95.2.e.b.26.3	yes	6	5.2	odd	4
475.2.e.d.26.1		6	5.3	odd	4
475.2.e.d.201.1		6	95.68	odd	12
475.2.j.b.49.1		12	19.11	even	3	inner
475.2.j.b.49.6		12	95.49	even	6	inner
475.2.j.b.349.1		12	5.4	even	2	inner
475.2.j.b.349.6		12	1.1	even	1	trivial
855.2.k.g.406.1		6	15.2	even	4
855.2.k.g.676.1		6	285.182	even	12
1520.2.q.j.881.2		6	20.7	even	4
1520.2.q.j.961.2		6	380.87	even	12
1805.2.a.g.1.3		3	95.12	even	12
1805.2.a.h.1.1		3	95.7	odd	12
9025.2.a.z.1.3		3	95.83	odd	12
9025.2.a.ba.1.1		3	95.88	even	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.17114 - 1.25351i) q^{2} +(1.05818 - 0.610938i) q^{3} +(2.14257 - 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876i q^{7} -5.72889i q^{8} +(-0.753509 + 1.30512i) q^{9} +O(q^{10})\)	\(q+(2.17114 - 1.25351i) q^{2} +(1.05818 - 0.610938i) q^{3} +(2.14257 - 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876i q^{7} -5.72889i q^{8} +(-0.753509 + 1.30512i) q^{9} -0.778124 q^{11} -5.23591i q^{12} +(4.33013 + 2.50000i) q^{13} +(0.278124 + 0.481725i) q^{14} +(-2.89608 - 5.01616i) q^{16} +(-6.12912 + 3.53865i) q^{17} +3.77812i q^{18} +(-1.33281 - 4.15013i) q^{19} +(0.135553 + 0.234784i) q^{21} +(-1.68942 + 0.975385i) q^{22} +(-6.99515 - 4.03865i) q^{23} +(-3.50000 - 6.06218i) q^{24} +12.5351 q^{26} +5.50702i q^{27} +(0.823392 + 0.475385i) q^{28} +(0.110938 - 0.192150i) q^{29} +2.50702 q^{31} +(-2.65287 - 1.53163i) q^{32} +(-0.823392 + 0.475385i) q^{33} +(-8.87147 + 15.3658i) q^{34} +(3.22889 + 5.59261i) q^{36} +1.90466i q^{37} +(-8.09596 - 7.33983i) q^{38} +6.10938 q^{39} +(3.61796 + 6.26648i) q^{41} +(0.588608 + 0.339833i) q^{42} +(6.32128 - 3.64959i) q^{43} +(-1.66719 + 2.88765i) q^{44} -20.2500 q^{46} +(-2.41808 - 1.39608i) q^{47} +(-6.12912 - 3.53865i) q^{48} +6.95077 q^{49} +(-4.32379 + 7.48903i) q^{51} +(18.5552 - 10.7129i) q^{52} +(-3.79361 - 2.19024i) q^{53} +(6.90310 + 11.9565i) q^{54} +1.27111 q^{56} +(-3.94583 - 3.57730i) q^{57} -0.556248i q^{58} +(-1.39608 - 2.41808i) q^{59} +(6.29216 - 10.8983i) q^{61} +(5.44309 - 3.14257i) q^{62} +(-0.289574 - 0.167186i) q^{63} +3.90466 q^{64} +(-1.19180 + 2.06426i) q^{66} +(-9.15414 - 5.28514i) q^{67} +30.3273i q^{68} -9.86946 q^{69} +(4.92070 + 8.52289i) q^{71} +(7.47687 + 4.31678i) q^{72} +(-12.1913 + 7.03865i) q^{73} +(2.38750 + 4.13528i) q^{74} +(-18.2570 - 3.94583i) q^{76} -0.172647i q^{77} +(13.2643 - 7.65817i) q^{78} +(0.792161 + 1.37206i) q^{79} +(1.10392 + 1.91204i) q^{81} +(15.7102 + 9.07028i) q^{82} -9.52106i q^{83} +1.16172 q^{84} +(9.14959 - 15.8476i) q^{86} -0.271105i q^{87} +4.45779i q^{88} +(1.57028 - 2.71981i) q^{89} +(-0.554690 + 0.960752i) q^{91} +(-29.9752 + 17.3062i) q^{92} +(2.65287 - 1.53163i) q^{93} -7.00000 q^{94} -3.74293 q^{96} +(5.51004 - 3.18122i) q^{97} +(15.0911 - 8.71286i) q^{98} +(0.586324 - 1.01554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more