LMFDB - Embedded newform 450.2.l.b.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	450.289
Dual form			450.2.l.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.17229 - 0.530249i) q^{5} -2.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.17229 - 0.530249i) q^{5} -2.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.70582 + 1.44575i) q^{10} +(4.52874 - 3.29032i) q^{11} +(0.282051 - 0.388209i) q^{13} +(2.20582 - 1.60262i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-3.71113 + 1.20582i) q^{17} +(1.27877 + 3.93564i) q^{19} +(-0.166977 + 2.22982i) q^{20} +(5.32385 + 1.72982i) q^{22} +(0.0930960 + 0.128136i) q^{23} +(4.43767 - 2.30371i) q^{25} +0.479853 q^{26} +(2.59310 + 0.842548i) q^{28} +(-2.17229 + 6.68562i) q^{29} +(0.133446 + 0.410706i) q^{31} -1.00000i q^{32} +(-3.15688 - 2.29360i) q^{34} +(-1.44575 - 5.92284i) q^{35} +(-1.56082 + 2.14828i) q^{37} +(-2.43236 + 3.34786i) q^{38} +(-1.90211 + 1.17557i) q^{40} +(-6.86650 - 4.98880i) q^{41} +3.49890i q^{43} +(1.72982 + 5.32385i) q^{44} +(-0.0489435 + 0.150633i) q^{46} +(6.43001 + 2.08924i) q^{47} -0.434034 q^{49} +(4.47214 + 2.23607i) q^{50} +(0.282051 + 0.388209i) q^{52} +(-5.31375 - 1.72654i) q^{53} +(8.09304 - 9.54889i) q^{55} +(0.842548 + 2.59310i) q^{56} +(-6.68562 + 2.17229i) q^{58} +(6.15537 + 4.47214i) q^{59} +(-5.97449 + 4.34072i) q^{61} +(-0.253830 + 0.349367i) q^{62} +(0.809017 - 0.587785i) q^{64} +(0.406848 - 0.992859i) q^{65} +(-1.96589 + 0.638757i) q^{67} -3.90211i q^{68} +(3.94189 - 4.65099i) q^{70} +(2.18146 - 6.71384i) q^{71} +(-7.99885 - 11.0095i) q^{73} -2.65542 q^{74} -4.13818 q^{76} +(-8.97120 - 12.3478i) q^{77} +(-1.95855 + 6.02781i) q^{79} +(-2.06909 - 0.847859i) q^{80} -8.48746i q^{82} +(-11.0330 + 3.58482i) q^{83} +(-7.42226 + 4.58721i) q^{85} +(-2.83067 + 2.05660i) q^{86} +(-3.29032 + 4.52874i) q^{88} +(-1.38197 + 1.00406i) q^{89} +(-1.05847 - 0.769023i) q^{91} +(-0.150633 + 0.0489435i) q^{92} +(2.08924 + 6.43001i) q^{94} +(4.86472 + 7.87129i) q^{95} +(-11.2840 - 3.66640i) q^{97} +(-0.255119 - 0.351141i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) $ 8 * q + 2 * q^4 + 10 * q^5	$ 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.17229	−	0.530249i	0.971477	−	0.237134i
$5$	2.17229	−	0.530249i	0.971477	−	0.237134i
$6$		0			0
$7$		−	2.72654i		−	1.03054i	−0.857029	−	0.515268i	$-0.827692\pi$
$7$		−	2.72654i		−	1.03054i	0.857029	−	0.515268i	$-0.172308\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		0			0
$10$	1.70582	+	1.44575i	0.539427	+	0.457185i
$11$	4.52874	−	3.29032i	1.36547	−	0.992069i	0.367391	−	0.930067i	$-0.380251\pi$
$11$	4.52874	−	3.29032i	1.36547	−	0.992069i	0.998076	−	0.0620027i	$-0.0197487\pi$
$12$		0			0
$13$	0.282051	−	0.388209i	0.0782267	−	0.107670i	−0.768110	−	0.640317i	$-0.778803\pi$
$13$	0.282051	−	0.388209i	0.0782267	−	0.107670i	0.846337	+	0.532648i	$0.178803\pi$
$14$	2.20582	−	1.60262i	0.589530	−	0.428319i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.71113	+	1.20582i	−0.900081	+	0.292454i	−0.722271	−	0.691611i	$-0.756901\pi$
$17$	−3.71113	+	1.20582i	−0.900081	+	0.292454i	−0.177811	+	0.984065i	$0.556901\pi$
$18$		0			0
$19$	1.27877	+	3.93564i	0.293370	+	0.902899i	0.983764	+	0.179466i	$0.0574369\pi$
$19$	1.27877	+	3.93564i	0.293370	+	0.902899i	−0.690395	+	0.723433i	$0.742563\pi$
$20$	−0.166977	+	2.22982i	−0.0373373	+	0.498604i
$21$		0			0
$22$	5.32385	+	1.72982i	1.13505	+	0.368800i
$23$	0.0930960	+	0.128136i	0.0194119	+	0.0267181i	0.818613	−	0.574346i	$-0.194744\pi$
$23$	0.0930960	+	0.128136i	0.0194119	+	0.0267181i	−0.799201	+	0.601064i	$0.794744\pi$
$24$		0			0
$25$	4.43767	−	2.30371i	0.887535	−	0.460741i
$26$	0.479853			0.0941069
$27$		0			0
$28$	2.59310	+	0.842548i	0.490049	+	0.159227i
$29$	−2.17229	+	6.68562i	−0.403384	+	1.24149i	0.518853	+	0.854863i	$0.326359\pi$
$29$	−2.17229	+	6.68562i	−0.403384	+	1.24149i	−0.922237	+	0.386624i	$0.873641\pi$
$30$		0			0
$31$	0.133446	+	0.410706i	0.0239677	+	0.0737650i	0.962325	−	0.271902i	$-0.0876527\pi$
$31$	0.133446	+	0.410706i	0.0239677	+	0.0737650i	−0.938357	+	0.345667i	$0.887653\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−3.15688	−	2.29360i	−0.541400	−	0.393350i
$35$	−1.44575	−	5.92284i	−0.244376	−	1.00114i
$36$		0			0
$37$	−1.56082	+	2.14828i	−0.256597	+	0.353176i	−0.917808	−	0.397024i	$-0.870043\pi$
$37$	−1.56082	+	2.14828i	−0.256597	+	0.353176i	0.661211	+	0.750200i	$0.270043\pi$
$38$	−2.43236	+	3.34786i	−0.394581	+	0.543094i
$39$		0			0
$40$	−1.90211	+	1.17557i	−0.300750	+	0.185874i
$41$	−6.86650	−	4.98880i	−1.07237	−	0.779120i	−0.0960305	−	0.995378i	$-0.530615\pi$
$41$	−6.86650	−	4.98880i	−1.07237	−	0.779120i	−0.976336	+	0.216258i	$0.930615\pi$
$42$		0			0
$43$			3.49890i			0.533578i	0.963755	+	0.266789i	$0.0859627\pi$
$43$			3.49890i			0.533578i	−0.963755	+	0.266789i	$0.914037\pi$
$44$	1.72982	+	5.32385i	0.260781	+	0.802601i
$45$		0			0
$46$	−0.0489435	+	0.150633i	−0.00721632	+	0.0222096i
$47$	6.43001	+	2.08924i	0.937914	+	0.304747i	0.737795	−	0.675025i	$-0.235867\pi$
$47$	6.43001	+	2.08924i	0.937914	+	0.304747i	0.200119	+	0.979772i	$0.435867\pi$
$48$		0			0
$49$	−0.434034			−0.0620049
$50$	4.47214	+	2.23607i	0.632456	+	0.316228i
$51$		0			0
$52$	0.282051	+	0.388209i	0.0391134	+	0.0538349i
$53$	−5.31375	−	1.72654i	−0.729900	−	0.237159i	−0.0795898	−	0.996828i	$-0.525361\pi$
$53$	−5.31375	−	1.72654i	−0.729900	−	0.237159i	−0.650310	+	0.759669i	$0.725361\pi$
$54$		0			0
$55$	8.09304	−	9.54889i	1.09127	−	1.28757i
$56$	0.842548	+	2.59310i	0.112590	+	0.346517i
$57$		0			0
$58$	−6.68562	+	2.17229i	−0.877864	+	0.285235i
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	0.911313	−	0.411714i	$-0.135070\pi$
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	−0.109952	+	0.993937i	$0.535070\pi$
$60$		0			0
$61$	−5.97449	+	4.34072i	−0.764955	+	0.555772i	−0.900426	−	0.435009i	$-0.856745\pi$
$61$	−5.97449	+	4.34072i	−0.764955	+	0.555772i	0.135471	+	0.990781i	$0.456745\pi$
$62$	−0.253830	+	0.349367i	−0.0322365	+	0.0443697i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	0.406848	−	0.992859i	0.0504632	−	0.123149i
$66$		0			0
$67$	−1.96589	+	0.638757i	−0.240172	+	0.0780366i	−0.426630	−	0.904426i	$-0.640299\pi$
$67$	−1.96589	+	0.638757i	−0.240172	+	0.0780366i	0.186458	+	0.982463i	$0.440299\pi$
$68$		−	3.90211i		−	0.473201i
$69$		0			0
$70$	3.94189	−	4.65099i	0.471146	−	0.555899i
$71$	2.18146	−	6.71384i	0.258891	−	0.796786i	−0.734147	−	0.678991i	$-0.762418\pi$
$71$	2.18146	−	6.71384i	0.258891	−	0.796786i	0.993038	−	0.117795i	$-0.0375825\pi$
$72$		0			0
$73$	−7.99885	−	11.0095i	−0.936194	−	1.28856i	−0.957394	−	0.288786i	$-0.906749\pi$
$73$	−7.99885	−	11.0095i	−0.936194	−	1.28856i	0.0211995	−	0.999775i	$-0.493251\pi$
$74$	−2.65542			−0.308687
$75$		0			0
$76$	−4.13818			−0.474682
$77$	−8.97120	−	12.3478i	−1.02236	−	1.40716i
$78$		0			0
$79$	−1.95855	+	6.02781i	−0.220354	+	0.678181i	0.778376	+	0.627799i	$0.216044\pi$
$79$	−1.95855	+	6.02781i	−0.220354	+	0.678181i	−0.998730	+	0.0503824i	$0.983956\pi$
$80$	−2.06909	−	0.847859i	−0.231331	−	0.0947935i
$81$		0			0
$82$		−	8.48746i		−	0.937283i
$83$	−11.0330	+	3.58482i	−1.21102	+	0.393486i	−0.843806	−	0.536649i	$-0.819690\pi$
$83$	−11.0330	+	3.58482i	−1.21102	+	0.393486i	−0.367219	+	0.930135i	$0.619690\pi$
$84$		0			0
$85$	−7.42226	+	4.58721i	−0.805057	+	0.497553i
$86$	−2.83067	+	2.05660i	−0.305239	+	0.221769i
$87$		0			0
$88$	−3.29032	+	4.52874i	−0.350750	+	0.482765i
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	−0.658615	−	0.752480i	$-0.728858\pi$
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	0.512127	+	0.858910i	$0.328858\pi$
$90$		0			0
$91$	−1.05847	−	0.769023i	−0.110958	−	0.0806155i
$92$	−0.150633	+	0.0489435i	−0.0157045	+	0.00510271i
$93$		0			0
$94$	2.08924	+	6.43001i	0.215488	+	0.663205i
$95$	4.86472	+	7.87129i	0.499110	+	0.807577i
$96$		0			0
$97$	−11.2840	−	3.66640i	−1.14572	−	0.372267i	−0.326190	−	0.945304i	$-0.605765\pi$
$97$	−11.2840	−	3.66640i	−1.14572	−	0.372267i	−0.819529	+	0.573038i	$0.805765\pi$
$98$	−0.255119	−	0.351141i	−0.0257709	−	0.0354706i
$99$		0			0
$100$	0.819639	+	4.93236i	0.0819639	+	0.493236i
$101$	7.92116			0.788185			0.394093	−	0.919071i	$-0.371059\pi$
$101$	7.92116			0.788185			0.394093	+	0.919071i	$0.371059\pi$
$102$		0			0
$103$	−5.96740	−	1.93893i	−0.587986	−	0.191048i	−0.000110715	−	1.00000i	$-0.500035\pi$
$103$	−5.96740	−	1.93893i	−0.587986	−	0.191048i	−0.587875	+	0.808952i	$0.700035\pi$
$104$	−0.148283	+	0.456367i	−0.0145403	+	0.0447505i
$105$		0			0
$106$	−1.72654	−	5.31375i	−0.167697	−	0.516117i
$107$		−	10.9662i		−	1.06014i	−0.847954	−	0.530069i	$-0.822166\pi$
$107$		−	10.9662i		−	1.06014i	0.847954	−	0.530069i	$-0.177834\pi$
$108$		0			0
$109$	6.32234	+	4.59345i	0.605571	+	0.439973i	0.847852	−	0.530233i	$-0.177896\pi$
$109$	6.32234	+	4.59345i	0.605571	+	0.439973i	−0.242281	+	0.970206i	$0.577896\pi$
$110$	12.4822	+	0.934712i	1.19013	+	0.0891213i
$111$		0			0
$112$	−1.60262	+	2.20582i	−0.151433	+	0.208430i
$113$	−0.811922	+	1.11751i	−0.0763792	+	0.105127i	−0.845497	−	0.533980i	$-0.820696\pi$
$113$	−0.811922	+	1.11751i	−0.0763792	+	0.105127i	0.769118	+	0.639107i	$0.220696\pi$
$114$		0			0
$115$	0.270175	+	0.228984i	0.0251940	+	0.0213528i
$116$	−5.68712	−	4.13194i	−0.528036	−	0.383641i
$117$		0			0
$118$			7.60845i			0.700415i
$119$	3.28772	+	10.1186i	0.301385	+	0.927566i
$120$		0			0
$121$	6.28408	−	19.3404i	0.571280	−	1.75822i
$122$	−7.02343	−	2.28205i	−0.635871	−	0.206607i
$123$		0			0
$124$	−0.431842			−0.0387805
$125$	8.41837	−	7.35738i	0.752962	−	0.658064i
$126$		0			0
$127$	−0.122790	−	0.169006i	−0.0108959	−	0.0149969i	0.803534	−	0.595258i	$-0.202950\pi$
$127$	−0.122790	−	0.169006i	−0.0108959	−	0.0149969i	−0.814430	+	0.580262i	$0.802950\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$		0			0
$130$	1.04238	−	0.254441i	0.0914227	−	0.0223160i
$131$	1.83177	+	5.63760i	0.160042	+	0.492560i	0.998637	−	0.0521964i	$-0.0166222\pi$
$131$	1.83177	+	5.63760i	0.160042	+	0.492560i	−0.838594	+	0.544756i	$0.816622\pi$
$132$		0			0
$133$	10.7307	−	3.48662i	0.930470	−	0.302328i
$134$	−1.67229	−	1.21499i	−0.144464	−	0.104959i
$135$		0			0
$136$	3.15688	−	2.29360i	0.270700	−	0.196675i
$137$	−8.52603	+	11.7351i	−0.728428	+	1.00260i	0.270773	+	0.962643i	$0.412721\pi$
$137$	−8.52603	+	11.7351i	−0.728428	+	1.00260i	−0.999202	+	0.0399523i	$0.987279\pi$
$138$		0			0
$139$	−4.89680	+	3.55774i	−0.415341	+	0.301763i	−0.775761	−	0.631027i	$-0.782634\pi$
$139$	−4.89680	+	3.55774i	−0.415341	+	0.301763i	0.360419	+	0.932790i	$0.382634\pi$
$140$	6.07971	+	0.455271i	0.513829	+	0.0384774i
$141$		0			0
$142$	6.71384	−	2.18146i	0.563413	−	0.183064i
$143$		−	2.68614i		−	0.224626i
$144$		0			0
$145$	−1.17380	+	15.6749i	−0.0974785	+	1.30173i
$146$	4.20524	−	12.9424i	0.348028	−	1.07112i
$147$		0			0
$148$	−1.56082	−	2.14828i	−0.128299	−	0.176588i
$149$	−13.7401			−1.12563			−0.562815	−	0.826583i	$-0.690282\pi$
$149$	−13.7401			−1.12563			−0.562815	+	0.826583i	$0.690282\pi$
$150$		0			0
$151$	8.45089			0.687724			0.343862	−	0.939020i	$-0.388265\pi$
$151$	8.45089			0.687724			0.343862	+	0.939020i	$0.388265\pi$
$152$	−2.43236	−	3.34786i	−0.197291	−	0.271547i
$153$		0			0
$154$	4.71644	−	14.5157i	0.380062	−	1.16971i
$155$	0.507661	+	0.821412i	0.0407763	+	0.0659774i
$156$		0			0
$157$		−	3.17338i		−	0.253263i	−0.991950	−	0.126632i	$-0.959583\pi$
$157$		−	3.17338i		−	0.253263i	0.991950	−	0.126632i	$-0.0404166\pi$
$158$	−6.02781	+	1.95855i	−0.479547	+	0.155814i
$159$		0			0
$160$	−0.530249	−	2.17229i	−0.0419198	−	0.171734i
$161$	0.349367	−	0.253830i	0.0275340	−	0.0200046i
$162$		0			0
$163$	6.50219	−	8.94949i	0.509291	−	0.700978i	−0.474509	−	0.880251i	$-0.657374\pi$
$163$	6.50219	−	8.94949i	0.509291	−	0.700978i	0.983799	+	0.179272i	$0.0573743\pi$
$164$	6.86650	−	4.98880i	0.536183	−	0.389560i
$165$		0			0
$166$	−9.38519	−	6.81874i	−0.728432	−	0.529237i
$167$	−1.55458	+	0.505112i	−0.120297	+	0.0390868i	−0.368547	−	0.929609i	$-0.620145\pi$
$167$	−1.55458	+	0.505112i	−0.120297	+	0.0390868i	0.248250	+	0.968696i	$0.420145\pi$
$168$		0			0
$169$	3.94607	+	12.1447i	0.303544	+	0.934211i
$170$	−8.07383	−	3.30844i	−0.619234	−	0.253746i
$171$		0			0
$172$	−3.32766	−	1.08122i	−0.253731	−	0.0824423i
$173$	9.99228	+	13.7532i	0.759699	+	1.04564i	0.997239	+	0.0742585i	$0.0236590\pi$
$173$	9.99228	+	13.7532i	0.759699	+	1.04564i	−0.237540	+	0.971378i	$0.576341\pi$
$174$		0			0
$175$	−6.28115	−	12.0995i	−0.474811	−	0.914636i
$176$	−5.59783			−0.421952
$177$		0			0
$178$	−1.62460	−	0.527864i	−0.121769	−	0.0395651i
$179$	4.08212	−	12.5635i	0.305112	−	0.939038i	−0.674524	−	0.738253i	$-0.735651\pi$
$179$	4.08212	−	12.5635i	0.305112	−	0.939038i	0.979635	−	0.200784i	$-0.0643491\pi$
$180$		0			0
$181$	8.23420	+	25.3423i	0.612043	+	1.88368i	0.438118	+	0.898917i	$0.355645\pi$
$181$	8.23420	+	25.3423i	0.612043	+	1.88368i	0.173925	+	0.984759i	$0.444355\pi$
$182$		−	1.30834i		−	0.0969806i
$183$		0			0
$184$	−0.128136	−	0.0930960i	−0.00944629	−	0.00686313i
$185$	−2.25142	+	5.49431i	−0.165528	+	0.403950i
$186$		0			0
$187$	−12.8392	+	17.6717i	−0.938896	+	1.29228i
$188$	−3.97397	+	5.46969i	−0.289831	+	0.398918i
$189$		0			0
$190$	−3.50859	+	8.56227i	−0.254540	+	0.621172i
$191$	7.41747	+	5.38911i	0.536709	+	0.389942i	0.822861	−	0.568242i	$-0.192376\pi$
$191$	7.41747	+	5.38911i	0.536709	+	0.389942i	−0.286152	+	0.958184i	$0.592376\pi$
$192$		0			0
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	−3.66640	−	11.2840i	−0.263232	−	0.810146i
$195$		0			0
$196$	0.134124	−	0.412791i	0.00958028	−	0.0294851i
$197$	−12.4969	−	4.06050i	−0.890369	−	0.289298i	−0.172113	−	0.985077i	$-0.555059\pi$
$197$	−12.4969	−	4.06050i	−0.890369	−	0.289298i	−0.718256	+	0.695779i	$0.755059\pi$
$198$		0			0
$199$	−7.35469			−0.521360			−0.260680	−	0.965425i	$-0.583947\pi$
$199$	−7.35469			−0.521360			−0.260680	+	0.965425i	$0.583947\pi$
$200$	−3.50859	+	3.56227i	−0.248095	+	0.251891i
$201$		0			0
$202$	4.65594	+	6.40836i	0.327591	+	0.450890i
$203$	18.2286	+	5.92284i	1.27940	+	0.415702i
$204$		0			0
$205$	−17.5613	−	7.19616i	−1.22654	−	0.502602i
$206$	−1.93893	−	5.96740i	−0.135091	−	0.415769i
$207$		0			0
$208$	−0.456367	+	0.148283i	−0.0316434	+	0.0102816i
$209$	18.7407	+	13.6159i	1.29632	+	0.941835i
$210$		0			0
$211$	16.3872	−	11.9060i	1.12814	−	0.819641i	0.142716	−	0.989764i	$-0.454416\pi$
$211$	16.3872	−	11.9060i	1.12814	−	0.819641i	0.985423	+	0.170123i	$0.0544164\pi$
$212$	3.28408	−	4.52015i	0.225551	−	0.310445i
$213$		0			0
$214$	8.87181	−	6.44575i	0.606464	−	0.440622i
$215$	1.85529	+	7.60063i	0.126530	+	0.518359i
$216$		0			0
$217$	1.11981	−	0.363848i	0.0760175	−	0.0246996i
$218$			7.81485i			0.529288i
$219$		0			0
$220$	6.58064	+	10.6477i	0.443667	+	0.717868i
$221$	−0.578616	+	1.78080i	−0.0389219	+	0.119789i
$222$		0			0
$223$	9.63635	+	13.2633i	0.645298	+	0.888176i	0.998884	−	0.0472256i	$-0.0150380\pi$
$223$	9.63635	+	13.2633i	0.645298	+	0.888176i	−0.353586	+	0.935402i	$0.615038\pi$
$224$	−2.72654			−0.182175
$225$		0			0
$226$	−1.38132			−0.0918843
$227$	4.54779	+	6.25950i	0.301847	+	0.415457i	0.932817	−	0.360350i	$-0.117343\pi$
$227$	4.54779	+	6.25950i	0.301847	+	0.415457i	−0.630970	+	0.775808i	$0.717343\pi$
$228$		0			0
$229$	8.20978	−	25.2671i	0.542517	−	1.66970i	−0.184303	−	0.982869i	$-0.559003\pi$
$229$	8.20978	−	25.2671i	0.542517	−	1.66970i	0.726820	−	0.686828i	$-0.240997\pi$
$230$	−0.0264466	+	0.353170i	−0.00174384	+	0.0232873i
$231$		0			0
$232$		−	7.02967i		−	0.461521i
$233$	−8.66895	+	2.81671i	−0.567922	+	0.184529i	−0.578883	−	0.815411i	$-0.696511\pi$
$233$	−8.66895	+	2.81671i	−0.567922	+	0.184529i	0.0109607	+	0.999940i	$0.496511\pi$
$234$		0			0
$235$	15.0757	+	1.12892i	0.983427	+	0.0736426i
$236$	−6.15537	+	4.47214i	−0.400680	+	0.291111i
$237$		0			0
$238$	−6.25361	+	8.60736i	−0.405361	+	0.557932i
$239$	−16.1448	+	11.7299i	−1.04432	+	0.758742i	−0.971124	−	0.238575i	$-0.923320\pi$
$239$	−16.1448	+	11.7299i	−1.04432	+	0.758742i	−0.0731951	+	0.997318i	$0.523320\pi$
$240$		0			0
$241$	9.58361	+	6.96290i	0.617334	+	0.448520i	0.851989	−	0.523559i	$-0.175396\pi$
$241$	9.58361	+	6.96290i	0.617334	+	0.448520i	−0.234655	+	0.972079i	$0.575396\pi$
$242$	19.3404	−	6.28408i	1.24325	−	0.403956i
$243$		0			0
$244$	−2.28205	−	7.02343i	−0.146093	−	0.449629i
$245$	−0.942847	+	0.230146i	−0.0602363	+	0.0147035i
$246$		0			0
$247$	1.88853	+	0.613621i	0.120164	+	0.0390438i
$248$	−0.253830	−	0.349367i	−0.0161182	−	0.0221849i
$249$		0			0
$250$	10.9004	+	2.48604i	0.689404	+	0.157231i
$251$	−0.782668			−0.0494016			−0.0247008	−	0.999695i	$-0.507863\pi$
$251$	−0.782668			−0.0494016			−0.0247008	+	0.999695i	$0.507863\pi$
$252$		0			0
$253$	0.843216	+	0.273977i	0.0530125	+	0.0172248i
$254$	0.0645546	−	0.198678i	0.00405051	−	0.0124662i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	9.43069i		−	0.588270i	−0.955764	−	0.294135i	$-0.904968\pi$
$257$		−	9.43069i		−	0.588270i	0.955764	−	0.294135i	$-0.0950316\pi$
$258$		0			0
$259$	5.85738	+	4.25564i	0.363960	+	0.264433i
$260$	0.818542	+	0.693745i	0.0507638	+	0.0430243i
$261$		0			0
$262$	−3.48423	+	4.79563i	−0.215257	+	0.296275i
$263$	15.9281	−	21.9231i	0.982168	−	1.35184i	0.0465150	−	0.998918i	$-0.485188\pi$
$263$	15.9281	−	21.9231i	0.982168	−	1.35184i	0.935653	−	0.352921i	$-0.114812\pi$
$264$		0			0
$265$	−12.4585	−	0.932938i	−0.765319	−	0.0573099i
$266$	9.12808	+	6.63194i	0.559678	+	0.406630i
$267$		0			0
$268$		−	2.06706i		−	0.126266i
$269$	1.08743	+	3.34676i	0.0663017	+	0.204056i	0.978719	−	0.205206i	$-0.0657864\pi$
$269$	1.08743	+	3.34676i	0.0663017	+	0.204056i	−0.912417	+	0.409262i	$0.865786\pi$
$270$		0			0
$271$	−4.05388	+	12.4765i	−0.246255	+	0.757896i	0.749172	+	0.662376i	$0.230452\pi$
$271$	−4.05388	+	12.4765i	−0.246255	+	0.757896i	−0.995427	+	0.0955208i	$0.969548\pi$
$272$	3.71113	+	1.20582i	0.225020	+	0.0731135i
$273$		0			0
$274$	−14.5054			−0.876301
$275$	12.5171	−	25.0343i	0.754811	−	1.50962i
$276$		0			0
$277$	−1.89992	−	2.61502i	−0.114155	−	0.157121i	0.748116	−	0.663568i	$-0.230959\pi$
$277$	−1.89992	−	2.61502i	−0.114155	−	0.157121i	−0.862271	+	0.506447i	$0.830959\pi$
$278$	−5.75654	−	1.87041i	−0.345254	−	0.112180i
$279$		0			0
$280$	3.20524	+	5.18619i	0.191550	+	0.309934i
$281$	−1.70160	−	5.23700i	−0.101509	−	0.312413i	0.887386	−	0.461027i	$-0.152519\pi$
$281$	−1.70160	−	5.23700i	−0.101509	−	0.312413i	−0.988895	+	0.148614i	$0.952519\pi$
$282$		0			0
$283$	5.92877	−	1.92637i	0.352429	−	0.114511i	−0.127452	−	0.991845i	$-0.540680\pi$
$283$	5.92877	−	1.92637i	0.352429	−	0.114511i	0.479881	+	0.877334i	$0.340680\pi$
$284$	5.71113	+	4.14938i	0.338893	+	0.246220i
$285$		0			0
$286$	2.17313	−	1.57887i	0.128500	−	0.0933606i
$287$	−13.6022	+	18.7218i	−0.802911	+	1.10511i
$288$		0			0
$289$	−1.43480	+	1.04245i	−0.0844002	+	0.0613203i
$290$	−13.3712	+	8.26388i	−0.785186	+	0.485271i
$291$		0			0
$292$	12.9424	−	4.20524i	0.757397	−	0.246093i
$293$			9.64990i			0.563753i	0.959451	+	0.281877i	$0.0909569\pi$
$293$			9.64990i			0.563753i	−0.959451	+	0.281877i	$0.909043\pi$
$294$		0			0
$295$	15.7426	+	6.45089i	0.916568	+	0.375586i
$296$	0.820571	−	2.52546i	0.0476947	−	0.146789i
$297$		0			0
$298$	−8.07621	−	11.1159i	−0.467842	−	0.643930i
$299$	0.0760012			0.00439527
$300$		0			0
$301$	9.53991			0.549871
$302$	4.96731	+	6.83692i	0.285837	+	0.393420i
$303$		0			0
$304$	1.27877	−	3.93564i	0.0733424	−	0.225725i
$305$	−10.6766	+	12.5973i	−0.611343	+	0.721317i
$306$		0			0
$307$		−	7.69507i		−	0.439181i	−0.975592	−	0.219591i	$-0.929528\pi$
$307$		−	7.69507i		−	0.439181i	0.975592	−	0.219591i	$-0.0704721\pi$
$308$	14.5157	−	4.71644i	0.827109	−	0.268744i
$309$		0			0
$310$	−0.366141	+	0.893520i	−0.0207954	+	0.0507485i
$311$	−0.341616	+	0.248198i	−0.0193712	+	0.0140740i	−0.597429	−	0.801922i	$-0.703811\pi$
$311$	−0.341616	+	0.248198i	−0.0193712	+	0.0140740i	0.578058	+	0.815996i	$0.303811\pi$
$312$		0			0
$313$	−13.5765	+	18.6865i	−0.767391	+	1.05622i	0.229172	+	0.973386i	$0.426398\pi$
$313$	−13.5765	+	18.6865i	−0.767391	+	1.05622i	−0.996563	+	0.0828371i	$0.973602\pi$
$314$	2.56732	−	1.86526i	0.144882	−	0.105263i
$315$		0			0
$316$	−5.12756	−	3.72539i	−0.288448	−	0.209570i
$317$	14.6211	−	4.75068i	0.821203	−	0.266825i	0.131868	−	0.991267i	$-0.457903\pi$
$317$	14.6211	−	4.75068i	0.821203	−	0.266825i	0.689335	+	0.724442i	$0.257903\pi$
$318$		0			0
$319$	12.1601	+	37.4249i	0.680835	+	2.09539i
$320$	1.44575	−	1.70582i	0.0808196	−	0.0953582i
$321$		0			0
$322$	0.410706	+	0.133446i	0.0228878	+	0.00743668i
$323$	−9.49135	−	13.0637i	−0.528113	−	0.726885i
$324$		0			0
$325$	0.357328	−	2.37251i	0.0198210	−	0.131603i
$326$	11.0622			0.612677
$327$		0			0
$328$	8.07205	+	2.62277i	0.445704	+	0.144818i
$329$	5.69639	−	17.5317i	0.314052	−	0.966554i
$330$		0			0
$331$	−9.89931	−	30.4669i	−0.544115	−	1.67461i	−0.723084	−	0.690760i	$-0.757276\pi$
$331$	−9.89931	−	30.4669i	−0.544115	−	1.67461i	0.178969	−	0.983855i	$-0.442724\pi$
$332$		−	11.6007i		−	0.636673i
$333$		0			0
$334$	−1.32240	−	0.960781i	−0.0723586	−	0.0525716i
$335$	−3.93179	+	2.42998i	−0.214816	+	0.132764i
$336$		0			0
$337$	6.86942	−	9.45495i	0.374201	−	0.515044i	−0.579835	−	0.814734i	$-0.696883\pi$
$337$	6.86942	−	9.45495i	0.374201	−	0.515044i	0.954037	+	0.299690i	$0.0968831\pi$
$338$	−7.50587	+	10.3309i	−0.408265	+	0.561929i
$339$		0			0
$340$	−2.06909	−	8.47651i	−0.112212	−	0.459704i
$341$	1.95570	+	1.42090i	0.105907	+	0.0769460i
$342$		0			0
$343$		−	17.9024i		−	0.966638i
$344$	−1.08122	−	3.32766i	−0.0582955	−	0.179415i
$345$		0			0
$346$	−5.25325	+	16.1679i	−0.282417	+	0.869189i
$347$	19.7811	+	6.42727i	1.06191	+	0.345034i	0.787330	−	0.616532i	$-0.211463\pi$
$347$	19.7811	+	6.42727i	1.06191	+	0.345034i	0.274575	+	0.961566i	$0.411463\pi$
$348$		0			0
$349$	−26.1233			−1.39835			−0.699173	−	0.714952i	$-0.746448\pi$
$349$	−26.1233			−1.39835			−0.699173	+	0.714952i	$0.746448\pi$
$350$	6.09673	−	12.1935i	0.325884	−	0.651768i
$351$		0			0
$352$	−3.29032	−	4.52874i	−0.175375	−	0.241383i
$353$	−23.1466	−	7.52079i	−1.23197	−	0.400291i	−0.380542	−	0.924764i	$-0.624263\pi$
$353$	−23.1466	−	7.52079i	−1.23197	−	0.400291i	−0.851428	+	0.524472i	$0.824263\pi$
$354$		0			0
$355$	1.17875	−	15.7411i	0.0625616	−	0.835451i
$356$	−0.527864	−	1.62460i	−0.0279767	−	0.0861035i
$357$		0			0
$358$	12.5635	−	4.08212i	0.664000	−	0.215747i
$359$	−26.3001	−	19.1081i	−1.38806	−	1.00849i	−0.996075	−	0.0885176i	$-0.971787\pi$
$359$	−26.3001	−	19.1081i	−1.38806	−	1.00849i	−0.391989	−	0.919970i	$-0.628213\pi$
$360$		0			0
$361$	1.51728	−	1.10237i	0.0798567	−	0.0580193i
$362$	−15.6624	+	21.5574i	−0.823197	+	1.13303i
$363$		0			0
$364$	1.05847	−	0.769023i	0.0554788	−	0.0403077i
$365$	−23.2136	−	19.6744i	−1.21505	−	1.02980i
$366$		0			0
$367$	11.4684	−	3.72632i	0.598648	−	0.194512i	0.00601051	−	0.999982i	$-0.498087\pi$
$367$	11.4684	−	3.72632i	0.598648	−	0.194512i	0.592637	+	0.805469i	$0.298087\pi$
$368$		−	0.158384i		−	0.00825636i
$369$		0			0
$370$	−5.76835	+	1.40803i	−0.299882	+	0.0732003i
$371$	−4.70749	+	14.4882i	−0.244401	+	0.752188i
$372$		0			0
$373$	17.6687	+	24.3188i	0.914849	+	1.25918i	0.965483	+	0.260465i	$0.0838757\pi$
$373$	17.6687	+	24.3188i	0.914849	+	1.25918i	−0.0506342	+	0.998717i	$0.516124\pi$
$374$	−21.8434			−1.12949
$375$		0			0
$376$	−6.76091			−0.348668
$377$	1.98272	+	2.72898i	0.102115	+	0.140550i
$378$		0			0
$379$	7.91486	−	24.3594i	0.406559	−	1.25126i	−0.513027	−	0.858373i	$-0.671476\pi$
$379$	7.91486	−	24.3594i	0.406559	−	1.25126i	0.919586	−	0.392888i	$-0.128524\pi$
$380$	−8.98932	+	2.19427i	−0.461142	+	0.112563i
$381$		0			0
$382$			9.16850i			0.469101i
$383$	−2.69678	+	0.876237i	−0.137799	+	0.0447736i	−0.377104	−	0.926171i	$-0.623080\pi$
$383$	−2.69678	+	0.876237i	−0.137799	+	0.0447736i	0.239306	+	0.970944i	$0.423080\pi$
$384$		0			0
$385$	−26.0354	−	22.0660i	−1.32689	−	1.12459i
$386$	−4.85410	+	3.52671i	−0.247067	+	0.179505i
$387$		0			0
$388$	6.97391	−	9.59876i	0.354047	−	0.487303i
$389$	29.3218	−	21.3035i	1.48667	−	1.08013i	0.511346	−	0.859375i	$-0.329147\pi$
$389$	29.3218	−	21.3035i	1.48667	−	1.08013i	0.975329	−	0.220757i	$-0.0708528\pi$
$390$		0			0
$391$	−0.500000	−	0.363271i	−0.0252861	−	0.0183714i
$392$	0.412791	−	0.134124i	0.0208491	−	0.00677428i
$393$		0			0
$394$	−4.06050	−	12.4969i	−0.204565	−	0.629586i
$395$	−1.05831	+	14.1327i	−0.0532491	+	0.711091i
$396$		0			0
$397$	−32.0364	−	10.4093i	−1.60786	−	0.522425i	−0.638826	−	0.769351i	$-0.720580\pi$
$397$	−32.0364	−	10.4093i	−1.60786	−	0.522425i	−0.969034	+	0.246926i	$0.920580\pi$
$398$	−4.32298	−	5.95007i	−0.216691	−	0.298250i
$399$		0			0
$400$	−4.94424	−	0.744661i	−0.247212	−	0.0372331i
$401$	21.2631			1.06183			0.530915	−	0.847425i	$-0.321848\pi$
$401$	21.2631			1.06183			0.530915	+	0.847425i	$0.321848\pi$
$402$		0			0
$403$	0.197079	+	0.0640347i	0.00981718	+	0.00318980i
$404$	−2.44777	+	7.53347i	−0.121781	+	0.374804i
$405$		0			0
$406$	5.92284	+	18.2286i	0.293945	+	0.904671i
$407$			14.8646i			0.736811i
$408$		0			0
$409$	−21.0670	−	15.3061i	−1.04170	−	0.756838i	−0.0710818	−	0.997470i	$-0.522645\pi$
$409$	−21.0670	−	15.3061i	−1.04170	−	0.756838i	−0.970616	+	0.240633i	$0.922645\pi$
$410$	−4.50046	−	18.4372i	−0.222262	−	0.910549i
$411$		0			0
$412$	3.68806	−	5.07617i	0.181698	−	0.250085i
$413$	12.1935	−	16.7829i	0.600001	−	0.825831i
$414$		0			0
$415$	−22.0659	+	13.6375i	−1.08317	+	0.669438i
$416$	−0.388209	−	0.282051i	−0.0190335	−	0.0138287i
$417$		0			0
$418$			23.1648i			1.13303i
$419$	0.888984	+	2.73601i	0.0434297	+	0.133663i	0.970420	−	0.241422i	$-0.0776137\pi$
$419$	0.888984	+	2.73601i	0.0434297	+	0.133663i	−0.926991	+	0.375085i	$0.877614\pi$
$420$		0			0
$421$	−4.77175	+	14.6859i	−0.232561	+	0.715749i	0.764875	+	0.644179i	$0.222801\pi$
$421$	−4.77175	+	14.6859i	−0.232561	+	0.715749i	−0.997436	+	0.0715697i	$0.977199\pi$
$422$	19.2643	+	6.25934i	0.937770	+	0.304700i
$423$		0			0
$424$	5.58721			0.271339
$425$	−13.6909	+	13.9004i	−0.664107	+	0.674268i
$426$		0			0
$427$	11.8352	+	16.2897i	0.572743	+	0.788313i
$428$	10.4294	+	3.38873i	0.504126	+	0.163800i
$429$		0			0
$430$	−5.05853	+	5.96850i	−0.243944	+	0.287827i
$431$	4.92451	+	15.1561i	0.237205	+	0.730043i	0.996821	+	0.0796708i	$0.0253869\pi$
$431$	4.92451	+	15.1561i	0.237205	+	0.730043i	−0.759616	+	0.650372i	$0.774613\pi$
$432$		0			0
$433$	0.188847	−	0.0613602i	0.00907542	−	0.00294878i	−0.304476	−	0.952520i	$-0.598481\pi$
$433$	0.188847	−	0.0613602i	0.00907542	−	0.00294878i	0.313551	+	0.949571i	$0.398481\pi$
$434$	0.952565	+	0.692079i	0.0457246	+	0.0332209i
$435$		0			0
$436$	−6.32234	+	4.59345i	−0.302785	+	0.219986i
$437$	−0.385248	+	0.530249i	−0.0184289	+	0.0253652i
$438$		0			0
$439$	8.20347	−	5.96017i	0.391530	−	0.284463i	−0.374552	−	0.927206i	$-0.622203\pi$
$439$	8.20347	−	5.96017i	0.391530	−	0.284463i	0.766082	+	0.642743i	$0.222203\pi$
$440$	−4.74617	+	11.5824i	−0.226265	+	0.552170i
$441$		0			0
$442$	−1.78080	+	0.578616i	−0.0847039	+	0.0275220i
$443$		−	30.5446i		−	1.45122i	−0.688107	−	0.725609i	$-0.741558\pi$
$443$		−	30.5446i		−	1.45122i	0.688107	−	0.725609i	$-0.258442\pi$
$444$		0			0
$445$	−2.46963	+	2.91389i	−0.117072	+	0.138131i
$446$	−5.06613	+	15.5919i	−0.239888	+	0.738300i
$447$		0			0
$448$	−1.60262	−	2.20582i	−0.0757167	−	0.104215i
$449$	20.0117			0.944412			0.472206	−	0.881488i	$-0.343458\pi$
$449$	20.0117			0.944412			0.472206	+	0.881488i	$0.343458\pi$
$450$		0			0
$451$	−47.5113			−2.23722
$452$	−0.811922	−	1.11751i	−0.0381896	−	0.0525634i
$453$		0			0
$454$	−2.39092	+	7.35848i	−0.112211	+	0.345351i
$455$	−2.70707	−	1.10929i	−0.126910	−	0.0520042i
$456$		0			0
$457$			7.86472i			0.367896i	0.982936	+	0.183948i	$0.0588878\pi$
$457$			7.86472i			0.367896i	−0.982936	+	0.183948i	$0.941112\pi$
$458$	25.2671	−	8.20978i	1.18065	−	0.383618i
$459$		0			0
$460$	−0.301265	+	0.186192i	−0.0140466	+	0.00868125i
$461$	−18.5967	+	13.5113i	−0.866134	+	0.629283i	−0.929547	−	0.368704i	$-0.879801\pi$
$461$	−18.5967	+	13.5113i	−0.866134	+	0.629283i	0.0634130	+	0.997987i	$0.479801\pi$
$462$		0			0
$463$	16.7111	−	23.0008i	0.776629	−	1.06894i	−0.219016	−	0.975721i	$-0.570285\pi$
$463$	16.7111	−	23.0008i	0.776629	−	1.06894i	0.995646	−	0.0932175i	$-0.0297152\pi$
$464$	5.68712	−	4.13194i	0.264018	−	0.191820i
$465$		0			0
$466$	−7.37425	−	5.35771i	−0.341605	−	0.248191i
$467$	−0.993171	+	0.322701i	−0.0459585	+	0.0149328i	−0.331906	−	0.943312i	$-0.607692\pi$
$467$	−0.993171	+	0.322701i	−0.0459585	+	0.0149328i	0.285948	+	0.958245i	$0.407692\pi$
$468$		0			0
$469$	1.74160	+	5.36009i	0.0804196	+	0.247506i
$470$	7.94793	+	12.8600i	0.366611	+	0.593189i
$471$		0			0
$472$	−7.23607	−	2.35114i	−0.333067	−	0.108220i
$473$	11.5125	+	15.8456i	0.529346	+	0.728583i
$474$		0			0
$475$	14.7413	+	14.5192i	0.676378	+	0.666186i
$476$	−10.6393			−0.487650
$477$		0			0
$478$	−18.9793	−	6.16676i	−0.868094	−	0.282061i
$479$	−0.113977	+	0.350785i	−0.00520774	+	0.0160278i	−0.953627	−	0.300992i	$-0.902682\pi$
$479$	−0.113977	+	0.350785i	−0.00520774	+	0.0160278i	0.948419	+	0.317020i	$0.102682\pi$
$480$		0			0
$481$	0.393753	+	1.21185i	0.0179536	+	0.0552555i
$482$			11.8460i			0.539570i
$483$		0			0
$484$	16.4519	+	11.9530i	0.747815	+	0.543319i
$485$	−26.4563	−	1.98114i	−1.20132	−	0.0899590i
$486$		0			0
$487$	−24.0229	+	33.0647i	−1.08858	+	1.49830i	−0.238874	+	0.971051i	$0.576778\pi$
$487$	−24.0229	+	33.0647i	−1.08858	+	1.49830i	−0.849708	+	0.527253i	$0.823222\pi$
$488$	4.34072	−	5.97449i	0.196495	−	0.270452i
$489$		0			0
$490$	−0.740384	−	0.627503i	−0.0334471	−	0.0283477i
$491$	−31.7128	−	23.0407i	−1.43118	−	1.03981i	−0.989796	−	0.142493i	$-0.954488\pi$
$491$	−31.7128	−	23.0407i	−1.43118	−	1.03981i	−0.441382	−	0.897319i	$-0.645512\pi$
$492$		0			0
$493$		−	27.4306i		−	1.23541i
$494$	0.613621	+	1.88853i	0.0276081	+	0.0849690i
$495$		0			0
$496$	0.133446	−	0.410706i	0.00599192	−	0.0184412i
$497$	−18.3056	−	5.94784i	−0.821117	−	0.266797i
$498$		0			0
$499$	−42.9767			−1.92390			−0.961950	−	0.273226i	$-0.911909\pi$
$499$	−42.9767			−1.92390			−0.961950	+	0.273226i	$0.911909\pi$
$500$	4.39587	+	10.2799i	0.196589	+	0.459731i
$501$		0			0
$502$	−0.460041	−	0.633192i	−0.0205326	−	0.0282607i
$503$	27.8108	+	9.03628i	1.24002	+	0.402908i	0.854335	−	0.519722i	$-0.173964\pi$
$503$	27.8108	+	9.03628i	1.24002	+	0.402908i	0.385687	+	0.922630i	$0.373964\pi$
$504$		0			0
$505$	17.2071	−	4.20019i	0.765704	−	0.186906i
$506$	0.273977	+	0.843216i	0.0121798	+	0.0374855i
$507$		0			0
$508$	0.198678	−	0.0645546i	0.00881493	−	0.00286415i
$509$	−34.9762	−	25.4117i	−1.55029	−	1.12635i	−0.943441	−	0.331541i	$-0.892431\pi$
$509$	−34.9762	−	25.4117i	−1.55029	−	1.12635i	−0.606854	−	0.794813i	$-0.707569\pi$
$510$		0			0
$511$	−30.0178	+	21.8092i	−1.32791	+	0.964782i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$		0			0
$514$	7.62959	−	5.54322i	0.336527	−	0.244501i
$515$	−13.9910	−	1.04770i	−0.616518	−	0.0461672i
$516$		0			0
$517$	35.9941	−	11.6952i	1.58302	−	0.514354i
$518$			7.24013i			0.318113i
$519$		0			0
$520$	−0.0801246	+	1.06999i	−0.00351370	+	0.0469221i
$521$	2.57704	−	7.93132i	0.112902	−	0.347477i	−0.878602	−	0.477556i	$-0.841523\pi$
$521$	2.57704	−	7.93132i	0.112902	−	0.347477i	0.991504	+	0.130078i	$0.0415229\pi$
$522$		0			0
$523$	−22.3741	−	30.7954i	−0.978353	−	1.34659i	−0.937712	−	0.347413i	$-0.887060\pi$
$523$	−22.3741	−	30.7954i	−0.978353	−	1.34659i	−0.0406405	−	0.999174i	$-0.512940\pi$
$524$	−5.92773			−0.258954
$525$		0			0
$526$	27.0985			1.18155
$527$	−0.990475	−	1.36327i	−0.0431457	−	0.0593850i
$528$		0			0
$529$	7.09964	−	21.8504i	0.308680	−	0.950019i
$530$	−6.56816	−	10.6275i	−0.285303	−	0.461629i
$531$		0			0
$532$			11.2829i			0.489177i
$533$	−3.87340	+	1.25854i	−0.167775	+	0.0545136i
$534$		0			0
$535$	−5.81479	−	23.8217i	−0.251395	−	1.02990i
$536$	1.67229	−	1.21499i	0.0722319	−	0.0524795i
$537$		0			0
$538$	−2.06841	+	2.84693i	−0.0891756	+	0.122740i
$539$	−1.96563	+	1.42811i	−0.0846656	+	0.0615131i
$540$		0			0
$541$	16.3032	+	11.8450i	0.700928	+	0.509254i	0.880234	−	0.474539i	$-0.157385\pi$
$541$	16.3032	+	11.8450i	0.700928	+	0.509254i	−0.179306	+	0.983793i	$0.557385\pi$
$542$	−12.4765	+	4.05388i	−0.535914	+	0.174129i
$543$		0			0
$544$	1.20582	+	3.71113i	0.0516991	+	0.159113i
$545$	16.1696	+	6.62589i	0.692631	+	0.283822i
$546$		0			0
$547$	38.4843	+	12.5043i	1.64547	+	0.534646i	0.977752	−	0.209766i	$-0.0672703\pi$
$547$	38.4843	+	12.5043i	1.64547	+	0.534646i	0.667720	+	0.744412i	$0.267270\pi$
$548$	−8.52603	−	11.7351i	−0.364214	−	0.501298i
$549$		0			0
$550$	27.6105	−	4.58820i	1.17732	−	0.195641i
$551$	−29.0901			−1.23928
$552$		0			0
$553$	16.4351	+	5.34008i	0.698890	+	0.227083i
$554$	0.998847	−	3.07414i	0.0424370	−	0.130608i
$555$		0			0
$556$	−1.87041	−	5.75654i	−0.0793231	−	0.244132i
$557$			21.4012i			0.906799i	0.891307	+	0.453400i	$0.149789\pi$
$557$			21.4012i			0.906799i	−0.891307	+	0.453400i	$0.850211\pi$
$558$		0			0
$559$	1.35831	+	0.986868i	0.0574503	+	0.0417401i
$560$	−2.31172	+	5.64146i	−0.0976881	+	0.238395i
$561$		0			0
$562$	3.23664	−	4.45486i	0.136530	−	0.187917i
$563$	4.46834	−	6.15015i	0.188318	−	0.259198i	−0.704410	−	0.709793i	$-0.748788\pi$
$563$	4.46834	−	6.15015i	0.188318	−	0.259198i	0.892728	+	0.450596i	$0.148788\pi$
$564$		0			0
$565$	−1.17117	+	2.85808i	−0.0492714	+	0.120240i
$566$	5.04331	+	3.66418i	0.211986	+	0.154017i
$567$		0			0
$568$			7.05934i			0.296204i
$569$	4.89551	+	15.0668i	0.205231	+	0.631635i	0.999704	+	0.0243357i	$0.00774706\pi$
$569$	4.89551	+	15.0668i	0.205231	+	0.631635i	−0.794473	+	0.607299i	$0.792253\pi$
$570$		0			0
$571$	7.21925	−	22.2186i	0.302116	−	0.929818i	−0.678622	−	0.734488i	$-0.737422\pi$
$571$	7.21925	−	22.2186i	0.302116	−	0.929818i	0.980738	−	0.195330i	$-0.0625777\pi$
$572$	2.55467	+	0.830062i	0.106816	+	0.0347066i
$573$		0			0
$574$	−23.1414			−0.965904
$575$	0.708317	+	0.354158i	0.0295389	+	0.0147694i
$576$		0			0
$577$	−4.74092	−	6.52531i	−0.197367	−	0.271652i	0.698850	−	0.715268i	$-0.253695\pi$
$577$	−4.74092	−	6.52531i	−0.197367	−	0.271652i	−0.896217	+	0.443616i	$0.853695\pi$
$578$	−1.68671	−	0.548046i	−0.0701580	−	0.0227957i
$579$		0			0
$580$	−14.5450	−	5.96017i	−0.603949	−	0.247483i
$581$	9.77418	+	30.0818i	0.405501	+	1.24800i
$582$		0			0
$583$	−29.7455	+	9.66489i	−1.23193	+	0.400279i
$584$	11.0095	+	7.99885i	0.455575	+	0.330995i
$585$		0			0
$586$	−7.80693	+	5.67207i	−0.322501	+	0.234311i
$587$	21.4035	−	29.4594i	0.883418	−	1.21592i	−0.0920445	−	0.995755i	$-0.529340\pi$
$587$	21.4035	−	29.4594i	0.883418	−	1.21592i	0.975462	−	0.220166i	$-0.0706598\pi$
$588$		0			0
$589$	−1.44575	+	1.05040i	−0.0595709	+	0.0432808i
$590$	4.03437	+	16.5278i	0.166092	+	0.680437i
$591$		0			0
$592$	2.52546	−	0.820571i	0.103796	−	0.0337253i
$593$		−	15.2692i		−	0.627029i	−0.949583	−	0.313515i	$-0.898494\pi$
$593$		−	15.2692i		−	0.627029i	0.949583	−	0.313515i	$-0.101506\pi$
$594$		0			0
$595$	12.5072	+	20.2371i	0.512746	+	0.829641i
$596$	4.24591	−	13.0676i	0.173919	−	0.535269i
$597$		0			0
$598$	0.0446724	+	0.0614863i	0.00182679	+	0.00251436i
$599$	−8.19555			−0.334861			−0.167431	−	0.985884i	$-0.553547\pi$
$599$	−8.19555			−0.334861			−0.167431	+	0.985884i	$0.553547\pi$
$600$		0			0
$601$	42.6346			1.73910			0.869551	−	0.493844i	$-0.164408\pi$
$601$	42.6346			1.73910			0.869551	+	0.493844i	$0.164408\pi$
$602$	5.60742	+	7.71795i	0.228541	+	0.314560i
$603$		0			0
$604$	−2.61147	+	8.03728i	−0.106259	+	0.327032i
$605$	3.39560	−	45.3451i	0.138051	−	1.84354i
$606$		0			0
$607$		−	30.2136i		−	1.22633i	−0.789955	−	0.613165i	$-0.789896\pi$
$607$		−	30.2136i		−	1.22633i	0.789955	−	0.613165i	$-0.210104\pi$
$608$	3.93564	−	1.27877i	0.159611	−	0.0518609i
$609$		0			0
$610$	−16.4670	−	1.23311i	−0.666728	−	0.0499270i
$611$	2.62465	−	1.90692i	0.106182	−	0.0771457i
$612$		0			0
$613$	4.40176	−	6.05850i	0.177785	−	0.244701i	−0.710819	−	0.703375i	$-0.751676\pi$
$613$	4.40176	−	6.05850i	0.177785	−	0.244701i	0.888604	+	0.458674i	$0.151676\pi$
$614$	6.22545	−	4.52305i	0.251239	−	0.182536i
$615$		0			0
$616$	12.3478	+	8.97120i	0.497507	+	0.361460i
$617$	37.7116	−	12.2533i	1.51821	−	0.493297i	0.572946	−	0.819593i	$-0.305801\pi$
$617$	37.7116	−	12.2533i	1.51821	−	0.493297i	0.945268	+	0.326296i	$0.105801\pi$
$618$		0			0
$619$	2.81228	+	8.65530i	0.113035	+	0.347886i	0.991532	−	0.129862i	$-0.0414533\pi$
$619$	2.81228	+	8.65530i	0.113035	+	0.347886i	−0.878497	+	0.477748i	$0.841453\pi$
$620$	−0.938085	+	0.228984i	−0.0376744	+	0.00919620i
$621$		0			0
$622$	−0.401593	−	0.130486i	−0.0161024	−	0.00523199i
$623$	2.73760	+	3.76799i	0.109680	+	0.150961i
$624$		0			0
$625$	14.3859	−	20.4462i	0.575435	−	0.817848i
$626$	−23.0978			−0.923173
$627$		0			0
$628$	3.01806	+	0.980628i	0.120434	+	0.0391313i
$629$	3.20196	−	9.85462i	0.127671	−	0.392930i
$630$		0			0
$631$	4.40146	+	13.5463i	0.175219	+	0.539269i	0.999643	−	0.0267031i	$-0.00850086\pi$
$631$	4.40146	+	13.5463i	0.175219	+	0.539269i	−0.824424	+	0.565972i	$0.808501\pi$
$632$		−	6.33801i		−	0.252113i
$633$		0			0
$634$	12.4375	+	9.03634i	0.493954	+	0.358879i
$635$	−0.356351	−	0.302021i	−0.0141413	−	0.0119853i
$636$		0			0
$637$	−0.122420	+	0.168496i	−0.00485044	+	0.00667606i
$638$	−23.1299	+	31.8356i	−0.915721	+	1.26038i
$639$		0			0
$640$	2.22982	+	0.166977i	0.0881416	+	0.00660036i
$641$	7.51057	+	5.45675i	0.296649	+	0.215528i	0.726147	−	0.687540i	$-0.241309\pi$
$641$	7.51057	+	5.45675i	0.296649	+	0.215528i	−0.429497	+	0.903068i	$0.641309\pi$
$642$		0			0
$643$		−	1.98146i		−	0.0781411i	−0.999236	−	0.0390706i	$-0.987560\pi$
$643$		−	1.98146i		−	0.0781411i	0.999236	−	0.0390706i	$-0.0124397\pi$
$644$	0.133446	+	0.410706i	0.00525853	+	0.0161841i
$645$		0			0
$646$	4.98990	−	15.3573i	0.196325	−	0.604226i
$647$	−2.92153	−	0.949261i	−0.114857	−	0.0373193i	0.251025	−	0.967981i	$-0.419232\pi$
$647$	−2.92153	−	0.949261i	−0.114857	−	0.0373193i	−0.365882	+	0.930661i	$0.619232\pi$
$648$		0			0
$649$	42.5908			1.67184
$650$	2.12943	−	1.10544i	0.0835231	−	0.0433589i
$651$		0			0
$652$	6.50219	+	8.94949i	0.254645	+	0.350489i
$653$	1.03712	+	0.336982i	0.0405858	+	0.0131871i	0.329240	−	0.944246i	$-0.393208\pi$
$653$	1.03712	+	0.336982i	0.0405858	+	0.0131871i	−0.288654	+	0.957434i	$0.593208\pi$
$654$		0			0
$655$	6.96846	+	11.2752i	0.272280	+	0.440559i
$656$	2.62277	+	8.07205i	0.102402	+	0.315161i
$657$		0			0
$658$	17.5317	−	5.69639i	0.683457	−	0.222069i
$659$	1.39899	+	1.01642i	0.0544968	+	0.0395943i	0.614700	−	0.788761i	$-0.289277\pi$
$659$	1.39899	+	1.01642i	0.0544968	+	0.0395943i	−0.560203	+	0.828355i	$0.689277\pi$
$660$		0			0
$661$	−19.3524	+	14.0604i	−0.752723	+	0.546885i	−0.896670	−	0.442700i	$-0.854021\pi$
$661$	−19.3524	+	14.0604i	−0.752723	+	0.546885i	0.143947	+	0.989585i	$0.454021\pi$
$662$	18.8296	−	25.9167i	0.731833	−	1.00728i
$663$		0			0
$664$	9.38519	−	6.81874i	0.364216	−	0.264618i
$665$	21.4614	−	13.2639i	0.832237	−	0.514351i
$666$		0			0
$667$	−1.05890	+	0.344057i	−0.0410007	+	0.0133219i
$668$		−	1.63458i		−	0.0632437i
$669$		0			0
$670$	−4.27694	−	1.75258i	−0.165233	−	0.0677079i
$671$	−12.7745	+	39.3160i	−0.493155	+	1.51778i
$672$		0			0
$673$	16.9348	+	23.3088i	0.652789	+	0.898487i	0.999216	−	0.0395903i	$-0.0126053\pi$
$673$	16.9348	+	23.3088i	0.652789	+	0.898487i	−0.346427	+	0.938077i	$0.612605\pi$
$674$	11.6870			0.450165
$675$		0			0
$676$	−12.7697			−0.491144
$677$	25.4770	+	35.0661i	0.979161	+	1.34770i	0.937280	+	0.348577i	$0.113335\pi$
$677$	25.4770	+	35.0661i	0.979161	+	1.34770i	0.0418814	+	0.999123i	$0.486665\pi$
$678$		0			0
$679$	−9.99660	+	30.7664i	−0.383634	+	1.18070i
$680$	5.64146	−	6.65630i	0.216340	−	0.255257i
$681$		0			0
$682$			2.41738i			0.0925662i
$683$	24.2160	−	7.86826i	0.926600	−	0.301071i	0.193429	−	0.981114i	$-0.438039\pi$
$683$	24.2160	−	7.86826i	0.926600	−	0.301071i	0.733172	+	0.680044i	$0.238039\pi$
$684$		0			0
$685$	−12.2985	+	30.0129i	−0.469901	+	1.14673i
$686$	14.4833	−	10.5228i	0.552976	−	0.401761i
$687$		0			0
$688$	2.05660	−	2.83067i	0.0784073	−	0.107918i
$689$	−2.16901	+	1.57588i	−0.0826325	+	0.0600361i
$690$		0			0
$691$	4.00531	+	2.91003i	0.152369	+	0.110703i	0.661358	−	0.750071i	$-0.269980\pi$
$691$	4.00531	+	2.91003i	0.152369	+	0.110703i	−0.508989	+	0.860773i	$0.669980\pi$
$692$	−16.1679	+	5.25325i	−0.614610	+	0.199699i
$693$		0			0
$694$	6.42727	+	19.7811i	0.243976	+	0.750881i
$695$	−8.75078	+	10.3249i	−0.331936	+	0.391648i
$696$		0			0
$697$	31.4981	+	10.2343i	1.19307	+	0.387653i
$698$	−15.3549	−	21.1342i	−0.581191	−	0.799940i
$699$		0			0
$700$	13.4483	−	2.23478i	0.508298	−	0.0844667i
$701$	17.5718			0.663677			0.331838	−	0.943336i	$-0.392331\pi$
$701$	17.5718			0.663677			0.331838	+	0.943336i	$0.392331\pi$
$702$		0			0
$703$	−10.4508	−	3.39567i	−0.394159	−	0.128070i
$704$	1.72982	−	5.32385i	0.0651952	−	0.200650i
$705$		0			0
$706$	−7.52079	−	23.1466i	−0.283049	−	0.871134i
$707$		−	21.5974i		−	0.812253i
$708$		0			0
$709$	22.8097	+	16.5722i	0.856636	+	0.622382i	0.926968	−	0.375141i	$-0.122406\pi$
$709$	22.8097	+	16.5722i	0.856636	+	0.622382i	−0.0703318	+	0.997524i	$0.522406\pi$
$710$	13.4277	−	8.29876i	0.503932	−	0.311447i
$711$		0			0
$712$	1.00406	−	1.38197i	0.0376286	−	0.0517914i
$713$	−0.0402028	+	0.0553344i	−0.00150561	+	0.00207229i
$714$		0			0
$715$	−1.42432	−	5.83506i	−0.0532665	−	0.218219i
$716$	10.6871	+	7.76465i	0.399397	+	0.290179i
$717$		0			0
$718$		−	32.5087i		−	1.21321i
$719$	5.60333	+	17.2453i	0.208969	+	0.643141i	0.999527	+	0.0307534i	$0.00979067\pi$
$719$	5.60333	+	17.2453i	0.208969	+	0.643141i	−0.790558	+	0.612387i	$0.790209\pi$
$720$		0			0
$721$	−5.28656	+	16.2704i	−0.196882	+	0.605940i
$722$	1.78367	+	0.579548i	0.0663812	+	0.0215686i
$723$		0			0
$724$	−26.6464			−0.990307
$725$	5.76179	+	34.6729i	0.213988	+	1.28772i
$726$		0			0
$727$	26.8609	+	36.9708i	0.996214	+	1.37117i	0.927619	+	0.373527i	$0.121852\pi$
$727$	26.8609	+	36.9708i	0.996214	+	1.37117i	0.0685952	+	0.997645i	$0.478148\pi$
$728$	1.24430	+	0.404299i	0.0461170	+	0.0149843i
$729$		0			0
$730$	2.27230	−	30.3445i	0.0841018	−	1.12310i
$731$	−4.21905	−	12.9849i	−0.156047	−	0.480263i
$732$		0			0
$733$	−12.7450	+	4.14109i	−0.470746	+	0.152954i	−0.534777	−	0.844993i	$-0.679604\pi$
$733$	−12.7450	+	4.14109i	−0.470746	+	0.152954i	0.0640312	+	0.997948i	$0.479604\pi$
$734$	9.75564	+	7.08789i	0.360087	+	0.261619i
$735$		0			0
$736$	0.128136	−	0.0930960i	0.00472314	−	0.00343157i
$737$	−6.80130	+	9.36119i	−0.250529	+	0.344824i
$738$		0			0
$739$	36.3758	−	26.4286i	1.33811	−	0.972191i	0.338595	−	0.940932i	$-0.390048\pi$
$739$	36.3758	−	26.4286i	1.33811	−	0.972191i	0.999511	−	0.0312587i	$-0.00995158\pi$
$740$	−4.52967	−	3.83907i	−0.166514	−	0.141127i
$741$		0			0
$742$	−14.4882	+	4.70749i	−0.531877	+	0.172817i
$743$			19.5304i			0.716502i	0.933625	+	0.358251i	$0.116627\pi$
$743$			19.5304i			0.716502i	−0.933625	+	0.358251i	$0.883373\pi$
$744$		0			0
$745$	−29.8474	+	7.28565i	−1.09352	+	0.266926i
$746$	−9.28897	+	28.5885i	−0.340093	+	1.04670i
$747$		0			0
$748$	−12.8392	−	17.6717i	−0.469448	−	0.646140i
$749$	−29.8997			−1.09251
$750$		0			0
$751$	−19.8988			−0.726117			−0.363058	−	0.931766i	$-0.618267\pi$
$751$	−19.8988			−0.726117			−0.363058	+	0.931766i	$0.618267\pi$
$752$	−3.97397	−	5.46969i	−0.144916	−	0.199459i
$753$		0			0
$754$	−1.04238	+	3.20811i	−0.0379612	+	0.116833i
$755$	18.3578	−	4.48108i	0.668108	−	0.163083i
$756$		0			0
$757$		−	13.8807i		−	0.504502i	−0.967662	−	0.252251i	$-0.918829\pi$
$757$		−	13.8807i		−	0.504502i	0.967662	−	0.252251i	$-0.0811709\pi$
$758$	24.3594	−	7.91486i	0.884775	−	0.287481i
$759$		0			0
$760$	−7.05899	−	5.98276i	−0.256056	−	0.217017i
$761$	−10.4454	+	7.58905i	−0.378646	+	0.275103i	−0.760787	−	0.649001i	$-0.775187\pi$
$761$	−10.4454	+	7.58905i	−0.378646	+	0.275103i	0.382141	+	0.924104i	$0.375187\pi$
$762$		0			0
$763$	12.5242	−	17.2381i	0.453408	−	0.624063i
$764$	−7.41747	+	5.38911i	−0.268355	+	0.194971i
$765$		0			0
$766$	−2.29402	−	1.66670i	−0.0828862	−	0.0602204i
$767$	3.47225	−	1.12820i	0.125376	−	0.0407370i
$768$		0			0
$769$	−1.40694	−	4.33011i	−0.0507355	−	0.156148i	0.922479	−	0.386048i	$-0.126160\pi$
$769$	−1.40694	−	4.33011i	−0.0507355	−	0.156148i	−0.973214	+	0.229900i	$0.926160\pi$
$770$	2.54853	−	34.0332i	0.0918427	−	1.22647i
$771$		0			0
$772$	−5.70634	−	1.85410i	−0.205376	−	0.0667306i
$773$	24.9028	+	34.2757i	0.895691	+	1.23281i	0.971822	+	0.235715i	$0.0757430\pi$
$773$	24.9028	+	34.2757i	0.895691	+	1.23281i	−0.0761318	+	0.997098i	$0.524257\pi$
$774$		0			0
$775$	1.53834	+	1.51516i	0.0552587	+	0.0544261i
$776$	11.8647			0.425919
$777$		0			0
$778$	34.4698	+	11.1999i	1.23580	+	0.401537i
$779$	10.8535	−	33.4036i	0.388867	−	1.19681i
$780$		0			0
$781$	−12.2114	−	37.5829i	−0.436959	−	1.34482i
$782$		−	0.618034i		−	0.0221009i
$783$		0			0
$784$	0.351141	+	0.255119i	0.0125408	+	0.00911139i
$785$	−1.68268	−	6.89349i	−0.0600574	−	0.246039i
$786$		0			0
$787$	2.67949	−	3.68800i	0.0955135	−	0.131463i	−0.758586	−	0.651573i	$-0.774109\pi$
$787$	2.67949	−	3.68800i	0.0955135	−	0.131463i	0.854099	+	0.520110i	$0.174109\pi$
$788$	7.72353	−	10.6305i	0.275139	−	0.378697i
$789$		0			0
$790$	−12.0556	+	7.45078i	−0.428920	+	0.265087i
$791$	3.04695	+	2.21374i	0.108337	+	0.0787115i
$792$		0			0
$793$			3.54365i			0.125839i
$794$	−10.4093	−	32.0364i	−0.369411	−	1.13693i
$795$		0			0
$796$	2.27272	−	6.99472i	0.0805546	−	0.247921i
$797$	0.410580	+	0.133406i	0.0145435	+	0.00472547i	0.316280	−	0.948666i	$-0.397566\pi$
$797$	0.410580	+	0.133406i	0.0145435	+	0.00472547i	−0.301736	+	0.953391i	$0.597566\pi$
$798$		0			0
$799$	−26.3819			−0.933323
$800$	−2.30371	−	4.43767i	−0.0814483	−	0.156895i
$801$		0			0
$802$	12.4981	+	17.2022i	0.441325	+	0.607432i
$803$	−72.4494	−	23.5402i	−2.55668	−	0.830717i
$804$		0			0
$805$	0.624334	−	0.736644i	0.0220049	−	0.0259633i
$806$	0.0640347	+	0.197079i	0.00225553	+	0.00694180i
$807$		0			0
$808$	−7.53347	+	2.44777i	−0.265027	+	0.0861124i
$809$	−11.8013	−	8.57415i	−0.414912	−	0.301451i	0.360676	−	0.932691i	$-0.382546\pi$
$809$	−11.8013	−	8.57415i	−0.414912	−	0.301451i	−0.775587	+	0.631240i	$0.782546\pi$
$810$		0			0
$811$	−10.3783	+	7.54028i	−0.364432	+	0.264775i	−0.754898	−	0.655842i	$-0.772314\pi$
$811$	−10.3783	+	7.54028i	−0.364432	+	0.264775i	0.390467	+	0.920617i	$0.372314\pi$
$812$	−11.2659	+	15.5062i	−0.395356	+	0.544160i
$813$		0			0
$814$	−12.0257	+	8.73720i	−0.421501	+	0.306239i
$815$	9.37917	−	22.8887i	0.328538	−	0.801754i
$816$		0			0
$817$	−13.7704	+	4.47429i	−0.481767	+	0.156535i
$818$		−	26.0403i		−	0.910478i
$819$		0			0
$820$	12.2707	−	14.4781i	0.428512	−	0.505596i
$821$	12.0441	−	37.0678i	0.420340	−	1.29367i	−0.487046	−	0.873377i	$-0.661925\pi$
$821$	12.0441	−	37.0678i	0.420340	−	1.29367i	0.907386	−	0.420298i	$-0.138075\pi$
$822$		0			0
$823$	15.9469	+	21.9490i	0.555873	+	0.765093i	0.990794	−	0.135375i	$-0.0432240\pi$
$823$	15.9469	+	21.9490i	0.555873	+	0.765093i	−0.434922	+	0.900468i	$0.643224\pi$
$824$	6.27450			0.218582
$825$		0			0
$826$	20.7448			0.721803
$827$	20.7380	+	28.5435i	0.721133	+	0.992554i	0.999485	+	0.0320749i	$0.0102115\pi$
$827$	20.7380	+	28.5435i	0.721133	+	0.992554i	−0.278353	+	0.960479i	$0.589788\pi$
$828$		0			0
$829$	16.9216	−	52.0792i	0.587710	−	1.80879i	−0.000393222	−	1.00000i	$-0.500125\pi$
$829$	16.9216	−	52.0792i	0.587710	−	1.80879i	0.588103	−	0.808786i	$-0.299875\pi$
$830$	−24.0030	−	9.83578i	−0.833155	−	0.341405i
$831$		0			0
$832$		−	0.479853i		−	0.0166359i
$833$	1.61076	−	0.523367i	0.0558094	−	0.0181336i
$834$		0			0
$835$	−3.10915	+	1.92156i	−0.107597	+	0.0664984i
$836$	−18.7407	+	13.6159i	−0.648162	+	0.470917i
$837$		0			0
$838$	−1.69095	+	2.32739i	−0.0584128	+	0.0803984i
$839$	−29.5611	+	21.4774i	−1.02056	+	0.741481i	−0.966398	−	0.257051i	$-0.917249\pi$
$839$	−29.5611	+	21.4774i	−1.02056	+	0.741481i	−0.0541634	+	0.998532i	$0.517249\pi$
$840$		0			0
$841$	−16.5171	−	12.0004i	−0.569556	−	0.413807i
$842$	−14.6859	+	4.77175i	−0.506111	+	0.164445i
$843$		0			0
$844$	6.25934	+	19.2643i	0.215455	+	0.663103i
$845$	15.0117	+	24.2895i	0.516419	+	0.835584i
$846$		0			0
$847$	−52.7324	−	17.1338i	−1.81191	−	0.588725i
$848$	3.28408	+	4.52015i	0.112776	+	0.155222i
$849$		0			0
$850$	−19.2930	−	2.90575i	−0.661743	−	0.0996665i
$851$	−0.420578			−0.0144172
$852$		0			0
$853$	−23.8224	−	7.74038i	−0.815665	−	0.265026i	−0.128670	−	0.991688i	$-0.541071\pi$
$853$	−23.8224	−	7.74038i	−0.815665	−	0.265026i	−0.686995	+	0.726662i	$0.741071\pi$
$854$	−6.22211	+	19.1497i	−0.212916	+	0.655289i
$855$		0			0
$856$	3.38873	+	10.4294i	0.115824	+	0.356471i
$857$		−	26.2947i		−	0.898211i	−0.893479	−	0.449105i	$-0.851743\pi$
$857$		−	26.2947i		−	0.898211i	0.893479	−	0.449105i	$-0.148257\pi$
$858$		0			0
$859$	−6.35565	−	4.61765i	−0.216852	−	0.157552i	0.474057	−	0.880494i	$-0.342789\pi$
$859$	−6.35565	−	4.61765i	−0.216852	−	0.157552i	−0.690908	+	0.722942i	$0.742789\pi$
$860$	−7.80194	−	0.584238i	−0.266044	−	0.0199224i
$861$		0			0
$862$	−9.36697	+	12.8925i	−0.319040	+	0.439121i
$863$	−30.9896	+	42.6535i	−1.05490	+	1.45194i	−0.170414	+	0.985373i	$0.554510\pi$
$863$	−30.9896	+	42.6535i	−1.05490	+	1.45194i	−0.884484	+	0.466570i	$0.845490\pi$
$864$		0			0
$865$	28.9987	+	24.5775i	0.985987	+	0.835661i
$866$	0.160643	+	0.116714i	0.00545887	+	0.00396610i
$867$		0			0
$868$			1.17744i			0.0399648i
$869$	10.9637	+	33.7426i	0.371916	+	1.14464i
$870$		0			0
$871$	−0.306510	+	0.943339i	−0.0103857	+	0.0319638i
$872$	−7.43236	−	2.41492i	−0.251692	−	0.0817795i
$873$		0			0
$874$	−0.655423			−0.0221700
$875$	−20.0602	−	22.9530i	−0.678159	−	0.775954i
$876$		0			0
$877$	9.95090	+	13.6962i	0.336018	+	0.462489i	0.943273	−	0.332018i	$-0.107729\pi$
$877$	9.95090	+	13.6962i	0.336018	+	0.462489i	−0.607255	+	0.794507i	$0.707729\pi$
$878$	9.64376	+	3.13345i	0.325461	+	0.105749i
$879$		0			0
$880$	−12.1601	+	2.96824i	−0.409917	+	0.100059i
$881$	−8.11141	−	24.9644i	−0.273280	−	0.841071i	−0.989669	−	0.143369i	$-0.954206\pi$
$881$	−8.11141	−	24.9644i	−0.273280	−	0.841071i	0.716389	−	0.697701i	$-0.245794\pi$
$882$		0			0
$883$	−2.00274	+	0.650730i	−0.0673976	+	0.0218988i	−0.342522	−	0.939510i	$-0.611281\pi$
$883$	−2.00274	+	0.650730i	−0.0673976	+	0.0218988i	0.275124	+	0.961409i	$0.411281\pi$
$884$	−1.51484	−	1.10059i	−0.0509495	−	0.0370169i
$885$		0			0
$886$	24.7111	−	17.9537i	0.830186	−	0.603165i
$887$	−27.2260	+	37.4733i	−0.914158	+	1.25823i	0.0515686	+	0.998669i	$0.483578\pi$
$887$	−27.2260	+	37.4733i	−0.914158	+	1.25823i	−0.965727	+	0.259561i	$0.916422\pi$
$888$		0			0
$889$	−0.460802	+	0.334792i	−0.0154548	+	0.0112286i
$890$	−3.80900	−	0.285232i	−0.127678	−	0.00956098i
$891$		0			0
$892$	−15.5919	+	5.06613i	−0.522057	+	0.169627i
$893$			27.9779i			0.936244i
$894$		0			0
$895$	2.20577	−	29.4560i	0.0737309	−	0.984606i
$896$	0.842548	−	2.59310i	0.0281476	−	0.0866293i
$897$		0			0
$898$	11.7626	+	16.1898i	0.392523	+	0.540262i
$899$	−3.03571			−0.101247
$900$		0			0
$901$	21.8019			0.726327
$902$	−27.9265	−	38.4375i	−0.929850	−	1.27983i
$903$		0			0
$904$	0.426852	−	1.31372i	0.0141969	−	0.0436936i
$905$	31.3248	+	50.6845i	1.04127	+	1.68481i
$906$		0			0
$907$		−	19.1755i		−	0.636711i	−0.947971	−	0.318355i	$-0.896869\pi$
$907$		−	19.1755i		−	0.636711i	0.947971	−	0.318355i	$-0.103131\pi$
$908$	−7.35848	+	2.39092i	−0.244200	+	0.0793453i
$909$		0			0
$910$	−0.693745	−	2.84209i	−0.0229974	−	0.0942144i
$911$	16.6977	−	12.1316i	0.553219	−	0.401937i	−0.275752	−	0.961229i	$-0.588927\pi$
$911$	16.6977	−	12.1316i	0.553219	−	0.401937i	0.828971	+	0.559292i	$0.188927\pi$
$912$		0			0
$913$	−38.1702	+	52.5367i	−1.26325	+	1.73871i
$914$	−6.36269	+	4.62277i	−0.210459	+	0.152908i
$915$		0			0
$916$	21.4935	+	15.6159i	0.710165	+	0.515965i
$917$	15.3712	−	4.99440i	0.507601	−	0.164929i
$918$		0			0
$919$	−1.93426	−	5.95303i	−0.0638053	−	0.196372i	0.914072	−	0.405552i	$-0.132921\pi$
$919$	−1.93426	−	5.95303i	−0.0638053	−	0.196372i	−0.977877	+	0.209180i	$0.932921\pi$
$920$	−0.327712	−	0.134288i	−0.0108043	−	0.00442733i
$921$		0			0
$922$	−21.8617	−	7.10330i	−0.719977	−	0.233935i
$923$	−1.99109	−	2.74050i	−0.0655376	−	0.0902047i
$924$		0			0
$925$	−1.97739	+	13.1290i	−0.0650162	+	0.431680i
$926$	28.4306			0.934287
$927$		0			0
$928$	6.68562	+	2.17229i	0.219466	+	0.0713089i
$929$	8.21228	−	25.2748i	0.269436	−	0.829240i	−0.721202	−	0.692725i	$-0.756410\pi$
$929$	8.21228	−	25.2748i	0.269436	−	0.829240i	0.990638	−	0.136515i	$-0.0435900\pi$
$930$		0			0
$931$	−0.555029	−	1.70820i	−0.0181903	−	0.0559841i
$932$		−	9.11507i		−	0.298574i
$933$		0			0
$934$	−0.844841	−	0.613813i	−0.0276441	−	0.0200846i
$935$	−18.5201	+	45.1959i	−0.605672	+	1.47806i
$936$		0			0
$937$	−4.74434	+	6.53002i	−0.154991	+	0.213326i	−0.879450	−	0.475991i	$-0.842089\pi$
$937$	−4.74434	+	6.53002i	−0.154991	+	0.213326i	0.724459	+	0.689317i	$0.242089\pi$
$938$	−3.31272	+	4.55957i	−0.108164	+	0.148875i
$939$		0			0
$940$	−5.73230	+	13.9889i	−0.186967	+	0.456269i
$941$	−9.25050	−	6.72088i	−0.301558	−	0.219095i	0.426708	−	0.904390i	$-0.359673\pi$
$941$	−9.25050	−	6.72088i	−0.301558	−	0.219095i	−0.728266	+	0.685295i	$0.759673\pi$
$942$		0			0
$943$		−	1.34428i		−	0.0437758i
$944$	−2.35114	−	7.23607i	−0.0765231	−	0.235514i
$945$		0			0
$946$	−6.05249	+	18.6277i	−0.196783	+	0.605637i
$947$	−3.41457	−	1.10946i	−0.110959	−	0.0360527i	0.253011	−	0.967463i	$-0.418579\pi$
$947$	−3.41457	−	1.10946i	−0.110959	−	0.0360527i	−0.363970	+	0.931411i	$0.618579\pi$
$948$		0			0
$949$	−6.53006			−0.211975
$950$	−3.08154	+	20.4601i	−0.0999784	+	0.663815i
$951$		0			0
$952$	−6.25361	−	8.60736i	−0.202681	−	0.278966i
$953$	37.7205	+	12.2561i	1.22189	+	0.397015i	0.847768	−	0.530367i	$-0.177946\pi$
$953$	37.7205	+	12.2561i	1.22189	+	0.397015i	0.374117	+	0.927381i	$0.377946\pi$
$954$		0			0
$955$	18.9704	+	7.77359i	0.613869	+	0.251547i
$956$	−6.16676	−	18.9793i	−0.199447	−	0.613835i
$957$		0			0
$958$	−0.350785	+	0.113977i	−0.0113333	+	0.00368243i
$959$	31.9962	+	23.2466i	1.03321	+	0.750672i
$960$		0			0
$961$	24.9287	−	18.1117i	0.804150	−	0.584249i
$962$	−0.748964	+	1.03086i	−0.0241476	+	0.0332363i
$963$		0			0
$964$	−9.58361	+	6.96290i	−0.308667	+	0.224260i
$965$	3.18149	+	13.0337i	0.102416	+	0.419571i
$966$		0			0
$967$	−7.72673	+	2.51057i	−0.248475	+	0.0807343i	−0.430606	−	0.902540i	$-0.641700\pi$
$967$	−7.72673	+	2.51057i	−0.248475	+	0.0807343i	0.182132	+	0.983274i	$0.441700\pi$
$968$			20.3357i			0.653614i
$969$		0			0
$970$	−13.9478	−	22.5680i	−0.447837	−	0.724616i
$971$	8.61796	−	26.5234i	0.276564	−	0.851175i	−0.712238	−	0.701938i	$-0.752318\pi$
$971$	8.61796	−	26.5234i	0.276564	−	0.851175i	0.988801	−	0.149237i	$-0.0476818\pi$
$972$		0			0
$973$	9.70032	+	13.3513i	0.310978	+	0.428024i
$974$	−40.8702			−1.30957
$975$		0			0
$976$	7.38487			0.236384
$977$	−25.1902	−	34.6713i	−0.805905	−	1.10923i	−0.991942	−	0.126690i	$-0.959565\pi$
$977$	−25.1902	−	34.6713i	−0.805905	−	1.10923i	0.186038	−	0.982543i	$-0.440435\pi$
$978$		0			0
$979$	−2.95489	+	9.09423i	−0.0944388	+	0.290653i
$980$	0.0724739	−	0.967820i	0.00231509	−	0.0309159i
$981$		0			0
$982$		−	39.1992i		−	1.25090i
$983$	−31.2682	+	10.1596i	−0.997300	+	0.324042i	−0.761786	−	0.647829i	$-0.775677\pi$
$983$	−31.2682	+	10.1596i	−0.997300	+	0.324042i	−0.235514	+	0.971871i	$0.575677\pi$
$984$		0			0
$985$	−29.3000	−	2.19409i	−0.933576	−	0.0699096i
$986$	22.1918	−	16.1233i	0.706731	−	0.513470i
$987$		0			0
$988$	−1.16718	+	1.60648i	−0.0371328	+	0.0511089i
$989$	−0.448335	+	0.325734i	−0.0142562	+	0.0103577i
$990$		0			0
$991$	−17.8090	−	12.9390i	−0.565720	−	0.411020i	0.267828	−	0.963467i	$-0.413694\pi$
$991$	−17.8090	−	12.9390i	−0.565720	−	0.411020i	−0.833548	+	0.552447i	$0.813694\pi$
$992$	0.410706	−	0.133446i	0.0130399	−	0.00423693i
$993$		0			0
$994$	−5.94784	−	18.3056i	−0.188654	−	0.580617i
$995$	−15.9765	+	3.89981i	−0.506489	+	0.123632i
$996$		0			0
$997$	−30.0965	−	9.77894i	−0.953165	−	0.309702i	−0.209164	−	0.977881i	$-0.567074\pi$
$997$	−30.0965	−	9.77894i	−0.953165	−	0.309702i	−0.744001	+	0.668179i	$0.767074\pi$
$998$	−25.2611	−	34.7689i	−0.799625	−	1.10059i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.b.289.2		8
3.2	odd	2		50.2.e.a.39.1	yes	8
12.11	even	2		400.2.y.a.289.1		8
15.2	even	4		250.2.d.c.51.2		8
15.8	even	4		250.2.d.b.51.1		8
15.14	odd	2		250.2.e.a.199.2		8
25.9	even	10	inner	450.2.l.b.109.2		8
75.29	odd	10		1250.2.b.c.1249.2		8
75.38	even	20		250.2.d.b.201.1		8
75.41	odd	10		250.2.e.a.49.2		8
75.47	even	20		1250.2.a.h.1.3		4
75.53	even	20		1250.2.a.i.1.2		4
75.59	odd	10		50.2.e.a.9.1	✓	8
75.62	even	20		250.2.d.c.201.2		8
75.71	odd	10		1250.2.b.c.1249.7		8
300.47	odd	20		10000.2.a.o.1.2		4
300.59	even	10		400.2.y.a.209.1		8
300.203	odd	20		10000.2.a.bb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.9.1	✓	8	75.59	odd	10
50.2.e.a.39.1	yes	8	3.2	odd	2
250.2.d.b.51.1		8	15.8	even	4
250.2.d.b.201.1		8	75.38	even	20
250.2.d.c.51.2		8	15.2	even	4
250.2.d.c.201.2		8	75.62	even	20
250.2.e.a.49.2		8	75.41	odd	10
250.2.e.a.199.2		8	15.14	odd	2
400.2.y.a.209.1		8	300.59	even	10
400.2.y.a.289.1		8	12.11	even	2
450.2.l.b.109.2		8	25.9	even	10	inner
450.2.l.b.289.2		8	1.1	even	1	trivial
1250.2.a.h.1.3		4	75.47	even	20
1250.2.a.i.1.2		4	75.53	even	20
1250.2.b.c.1249.2		8	75.29	odd	10
1250.2.b.c.1249.7		8	75.71	odd	10
10000.2.a.o.1.2		4	300.47	odd	20
10000.2.a.bb.1.3		4	300.203	odd	20

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.17229 - 0.530249i) q^{5} -2.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.17229 - 0.530249i) q^{5} -2.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.70582 + 1.44575i) q^{10} +(4.52874 - 3.29032i) q^{11} +(0.282051 - 0.388209i) q^{13} +(2.20582 - 1.60262i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-3.71113 + 1.20582i) q^{17} +(1.27877 + 3.93564i) q^{19} +(-0.166977 + 2.22982i) q^{20} +(5.32385 + 1.72982i) q^{22} +(0.0930960 + 0.128136i) q^{23} +(4.43767 - 2.30371i) q^{25} +0.479853 q^{26} +(2.59310 + 0.842548i) q^{28} +(-2.17229 + 6.68562i) q^{29} +(0.133446 + 0.410706i) q^{31} -1.00000i q^{32} +(-3.15688 - 2.29360i) q^{34} +(-1.44575 - 5.92284i) q^{35} +(-1.56082 + 2.14828i) q^{37} +(-2.43236 + 3.34786i) q^{38} +(-1.90211 + 1.17557i) q^{40} +(-6.86650 - 4.98880i) q^{41} +3.49890i q^{43} +(1.72982 + 5.32385i) q^{44} +(-0.0489435 + 0.150633i) q^{46} +(6.43001 + 2.08924i) q^{47} -0.434034 q^{49} +(4.47214 + 2.23607i) q^{50} +(0.282051 + 0.388209i) q^{52} +(-5.31375 - 1.72654i) q^{53} +(8.09304 - 9.54889i) q^{55} +(0.842548 + 2.59310i) q^{56} +(-6.68562 + 2.17229i) q^{58} +(6.15537 + 4.47214i) q^{59} +(-5.97449 + 4.34072i) q^{61} +(-0.253830 + 0.349367i) q^{62} +(0.809017 - 0.587785i) q^{64} +(0.406848 - 0.992859i) q^{65} +(-1.96589 + 0.638757i) q^{67} -3.90211i q^{68} +(3.94189 - 4.65099i) q^{70} +(2.18146 - 6.71384i) q^{71} +(-7.99885 - 11.0095i) q^{73} -2.65542 q^{74} -4.13818 q^{76} +(-8.97120 - 12.3478i) q^{77} +(-1.95855 + 6.02781i) q^{79} +(-2.06909 - 0.847859i) q^{80} -8.48746i q^{82} +(-11.0330 + 3.58482i) q^{83} +(-7.42226 + 4.58721i) q^{85} +(-2.83067 + 2.05660i) q^{86} +(-3.29032 + 4.52874i) q^{88} +(-1.38197 + 1.00406i) q^{89} +(-1.05847 - 0.769023i) q^{91} +(-0.150633 + 0.0489435i) q^{92} +(2.08924 + 6.43001i) q^{94} +(4.86472 + 7.87129i) q^{95} +(-11.2840 - 3.66640i) q^{97} +(-0.255119 - 0.351141i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) \) 8 * q + 2 * q^4 + 10 * q^5	\( 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

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